PERSPECTIVES
ON PSYCHOLOGISM EDITED BY
MARK A. NOTTURNO
E.]. BRILL LEIDEN • NEW YORK • K0BENHAVN • KOLN 1989
PSYCHOLOGISM J.N. MOHANTY The word 'psychologism' has been used, in the brief history of just about a century, pejoratively, and not descriptively. Like many such words 'capitalism' in socialist countries and 'socialist' in western democracies labeling a philosopher's idea as involving psychologism has been taken as tantamount to saying why it should be rejected. Brentano, in exasperation, complains that 'psychologism' is "a recently fashionable term, at the sound of· which many an ingenuous philosopher, like many orthodox Catholics at 'Modernism', makes the sign of the cross, as though the devil himself lurked in the word. I If this is the case, then let us not be swayed by the pejorative connotation the word has acquired and let us make an effort to understand and save the phenomenon on which psychologistic doctrines are based without falling prey to some of their ruinous excesses. There is also something odd about the complaint of psychologism. The very same people who sought to demolish psychologism have themselves been accused of it. Thus Kant is the first to have sought to avoid psychologism (ind~ the introduction of this word by J.E. Erdmann2 was to highlight the contrast with 'criticism') and yet, not long after Erdmann, Windelband insisted that Kant's criticism was in fact dependent on his psychological theories.3 As is well-known, Husserl the critic par excellence of psychologism, suffered the same fate. Not even Frege escaped this fate: his insistence on the assertion sign has been read as introducing psychologistic elements into logic- not to speak of Philip Kitcher's recent attempt to find a psychological account of knowledge in Frege.4 Less known perhaps is Carnap's case: he attacked psychologism,S and is then attacked by Popper as being psychologistic.6 What, in view of this cross fIre, is the prospect that we can ever be free from psychologistic elements in our thinking? But what after all is psychologism? And why should it be so easily taken for granted that psychologism does indeed need to be gotten rid of] I will not pretend to add more clarification to a theme to which Frege and Husserl devoted so much of their energy. But no less a thinker than Frege seems to have been confused. In his review of Husserl's Philosophie der Arithmetik, Frege accused the psychologistic logician of reducing everything to subjective ideas.7 Now, note that reducing everything to subjective ideas amounts to what is known as subjective idealism, and that is not eo ipso psychologism. The following may suffice to show that psychologism does not necessarily amount to fI
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subjective idealism. A psychologistic philosopher may believe, consistently, that there are indeed mind-independent, objective realities. He may even further hold that we do have knowledge of this objective reality. What he must hold is that such knowledge is made possible not only through the structure of the reality that is known but also through the structure of the mind that knows. In so far as knowledge is made possible by the structure of the mind, we cannot sufficiently explicate the foundations of knowledge save by explicating the way the human mind works. It is not, then, surprising that Kant, whose theory of knowledge, as transcendental philosophy, wanted to set itself off from all psychologism, remained nonetheless under the constant threat of psychologism. For the line that divides the transcendental foundation from a psychologistic foundation is so thin that its transgression may go unnoticed. Psychologism, then, is not an ontological thesis. It is an epistemological thesis, which traces back all epistemological questions to some aspects of psychology. It need not have to hold, however, that everything is nothing but mental representations. Once we have thus separated the ontological question, we can certainly go on to ask: what is it that the psychologistic thinker holds which makes his position both interesting and disturbing? There is a trivial assertion to the effect that knowing is a mental experience, that all knowledge whatsoever is merely a mental performance and accomplishment- from which it appears to follow that only a science of mind - psychology, to be sure - can provide the foundational expectations of knowledge. (One may likewise argue that since all knowledge is expressed in language, a study of language should also have that foundational status! I do not intend to make this last remark only as an aside. My ulterior motive is to emphasize that when these two trivialities supplement each other, a more interesting thesis is likely to emerge. But more of this later.) But the psychologistic consequence is taken to follow from a trivial assertion because of a certain equivocation in the use of the word 'psychological'. 'Psychological' may mean the mental as such, or it may mean the mental as thematized in the science of psychology, or it may apply - as when one speaks of psychological laws - to the propositions stating laws or lawlike connections within the psychological discourse. To claim then that because all knowledge is a mental performance or accomplishment, the foundations of knowledge must be explicated in psychological tenns may mean either: (1) that all knowledge must ultimately rest upon the mental as such, Le., as lived experience; or (2) that all knowledge must ultimately be analyzable into those components, such as ideas or presentations which empiricist psychology took mental life to consist in; or, finally, (3) that we must look at the laws of mental life for the source of the laws of our more developed logical and epistemic performances. Dilthey's psychologism was of the frrst sort, Mill's of the third sort; whereas the psychologism Frege and Husserl were criticizing was either or both of the second and third sorts. There is obviously a reason
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why the second and the third sorts are put together: the sorts of psychological laws one takes into account depend upon the sorts of elements into which mental life is decomposed and whose law-like connections the psychology under consideration is formulating. Of the Diltheyan sort of foundationalism, I will only say this much: while it may be true that any act of knowing or thinking must be a lived experience on the part of the knower or the thinker, that lived experience, by itself, has no explanatory value in so far as the knowledge or the thought - whether the specific performances or the generic - is concerned. The inner lived experience is, if that theory be true, only a necessary accompaniment of, for example, an act of judging, but it does not give us any insight into the structure of judgment or into the conditions of its possibility. Such a psychologism is harmless, it gives necessary but not sufficient conditions of our cognitive concepts. If we did not have this inner lived experience of what we are doing (judging, etc.), we might not have had the appropriate concepts (of judging, e.g.), but simple inner experience does not by itself enable us to have the right concepts. Thus when Lipps says "nur das Erleben kann der Quell sein, aus welchem der Logiker schopft," the point is just a hannless triviality, if true.8 Let us now consider the second sense of 'psychological'. The mental as thematized in empirical, introspectionist, associationist psychology becomes a private, discrete, event concerned with other such events by the laws of association. It is in this sense that Frege and Husserl found psychologism unacceptable for obvious reasons. How can the necessary truths of logic, they asked, be founded upon the more or less probable, empirical generalizations of such psychologies? But while they were right in calling into question psychologism in this sense, it is not obvious that the only remaining option is an epistemological theory for which thinking is a grasping of thoughts and knowing a grasping of whatever is known. I shall make myself clearer. The issue is not that of Platonism, which is an ontological question: are there abstract entities? The issue is epistemological: are the fundamental principles of knowledge, or of thought, grounded, in some sense, in the nature of human mind? I agree with the Frege-Husserl critique that psychology - in the sense of the British empiricists, associationist psychology - cannot play this foundational role. It is no use to return to the immediacy of Diltheyan lived experience (or, the Brentanian inner perception)., The opponent of psychologism would want to strip the mental of all contents. If the mental is reduced to the mere 'grasping', the bare act with no content, if all alleged content is expelled out into the world and the mental left to be the bare Sartrean nothingnesspsychologism cannot even fmd a foothold from which to get off the ground. Psychologism knew only one sort of content within the mental: this is what Locke, Berkeley, and Hume, the British empiricists, called sensations, impressions, or ideas (Frege called them Vorstellungen). These contents and the laws that weld them together are not the sorts of things that could provide the basis for higher order cognitive achievements. Rightly, therefore,
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the anti-psychologists rejected any such attempt, but many of them left the psychologistic concept of the mental precisely as it was. This is where the crux of the matter lies. What, in fact, the anti-psychologistic thinkers did is a poor compromise. The received picture of mental life as consisting of incurably private particulars was not iL~lf challenged. That picture was left unchanged; however, it has no role to play in thinking and other cognitive achievements. Let us call these latter the 'noetic acts'. The noetic acts were construed as bare grasping, bare recognition- having no contents of their own and no structure. What is grasped, asserted, recognized falls on the other side of our acts, in fact belongs to the world- a real or unreal entity, a concrete physical object or an abstract entity such as a number, for example. Being bare acts with no content or structure of their own, little can be said or done about them. This compromise left the logician to do his work, and the empirical psychologist his. They are assigned different domains, neatly marked off from each oth~r; but it provided, in my view, a poor philosophy of mind and a poor philosophy of logic. My goal is to bring them closer, to ground philosophy of logic and epistemology in a philosophy of mind- without having to court the ruinous consequences of psychologism. This goal can be sought to be achieved in a number of ways, as follows: 1. Make the rules that mental operations follow important, but the acts and operations themselves dispensable. The rules would have a logical structure, the acts with their subjectivity and privacy would be irrelevant for foundational purposes. This move is easily derivable from the Kantian. This is in fact what the Marburg neoKantians, notably Cassirer did. 2. The preceding move has also a strange similarity with the cognitivist reading of Husserl that Hubert Dreyfus gives. If the Husserlian noema is a set of rules and determines what the object must have to be by way of conforming to these rules, we get rid of the subjectivistic consequences of psychologism, and are able to make a rapproacJunent with a different sort of psychology, namely, with a 'computational theory of mind'. 3. Keep the mental act, but give it a structure. This can be done by assigning a content (not an object) to an act, and by making sure that the content is not a subjective, private particular but rather a structure that numerically different acts, performed by different individuals, may share in common, and so somewhat universal-like. This is done by Husserl in his thesis about the act as having meaning, a Sinn, or noesis-noerna correlation. 4. Finally, raise a psychological conception of the mental to a transcendental level- a strategy adopted by transcendental philosophers from Kant to Husserl. There are certainly other possibilities, and I have not tried to be exhaustive. For my present purpose, I shall argue that a good philosophy of mind needs to combine the above four principles - the truths in each of them, that is to say - and, given the resulting, enriched picture of mental life, the fundamental insight of an enlightened psychologism can be
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preserved and reconciled with the undoubtedly valid point of the anti-psychological thinkers. First, some brief comments on each of the four: (1) Cassirer insisted that the essential content of the Kantian philosophy is not the relation of the world to the ego, but rather its relation to "the legality (Gesetzlichkeit) and the logical structure of experience. "9 His argument rests on the consideration that the concrete ego, the '1', is the subject as much of true knowledge as of error. But since the Kantian philosophy is concerned with the conditions of the possibility of truth, we have to be satisfied with a theoretically normative autonomy of the logical principles which need no further philosophical grounding. Now, the principles of the Kantian Grundgesetze which underlie physics, are, for one thing, reached by a process of 'transcendental argument' starting from the fact of Newtonian physics and its concepts of space, time, etc. If you start with a different physical theory, you would reach a set of Grundgesetze different from the Kantian. Thus the validity of the set of principles chosen as foundational is relative to the already taken-for-granted validity of a theory. So far so good. But there is a different level of questioning: namely, how are these principles themselves constituted? By what sort of mental operation? As meaning-structures, how are they possible? Recall the Humean question regarding the principle of causality! (Correlatively, how do we understand such principles? Through what sort of mental operationssuch as counting, imagining, phantasizing possibilities, etc.?) (2) If mental life, in its cognitive operations, consists in entertaining Fregean Sinne, and if a Sinn consists in a set of rules prescribed for whatever is to be the referent, one may - as Dreyfus suggests - appropriate a Frege-Husserl theory into a computational theory of mind. According to Dreyfus, Husserl thought of the noemata or Sinne as meaningful complex formal structures, since even without the digital computer to supply a model for his intuitions, he thought of the noema as a "strict rule for possible synthesis. "10 And if a computational theory is a mathematical theory about how the mind operates, to ground knowledge on such a theory, even if psychologistic, would hardly generate the consequences which Frege and Husserl drew from psychologism. But there is a deceptive gain: we are to explain, how logical thinking and cognition are possible. We answer by inserting these abilities into the most basic stratum of mind. The mind is like a computing machine. Our conceptual gain is very little. The psychological theory that is used, itself presupposes formal logic and mathematics, and so cannot provide for their foundation- not to speak of the narrowly syntactical idea of computation that the theory has to work with. This last point incidentally shows the untenability of Dreyfus' interpretation of the Husserlian noerna; for Husserl the rules are also semantic as well as syntactical. (3) The third way out appeals to the thesis of intentionality- not the simple Brentano thesis that an act is directed towards an object, but the enriched Brentano-Husserl thesis to the effect that every act has its correlative Sinn, so that we have always a concrete meaningful act- a Sinn
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structure. Every act is performed by some one, at a point of time or enduring through a temporal stretch, has a certain act-quality (Le., is either a believing, doubting, imagining, remembering, judging, etc.), and has a content (or Sinn) which is the structure shareable by other acts perfonned by other individuals. Given such a conception of mental or noetic acts, there can be a perfectly good eidetic psychology which would discover universally valid laws by which acts of a certain quality and having certain structure and temporal location would intentionally imply acts of some other sorts. Besides, one can simply abstract the Sinne from their imbeddedness in acts, and relate them to other Sinne by familiar logical relations. Such an eidetic psychology - as Brentano well saw - can provide foundations for logic and cognition is a certain sense- without entailing psychologism in a perjorative sense. One way of doing this is as follows: Even if we leave out of consideration, as irrelevant, the historical factual nature of research or any reference to the psychological/biographical antecedents, there still remains another sort of psychical locution which is involved in an essential manner in theoretical inquiry. One may say, for example: "Supposing A, is it an open question whether B holds good or not? Is B a valid consequence or supposition?" Or: "If one is certain that A, one cannot have any more doubt that B." Or: "We do not know if B, but from the already developed theory we have 'reasons' to believe that most probably B:' These locutions concern the context of justification, and eventually refer to certain sorts of relations between appropriate mental acts having specified contents. 11 Long before Brentano, the Indian logicians developed a theory of inference as a theory of eidetic, rule-governed, psychology of inferential cognition. Take the following time-worn instance. One sees smoke on a distant mountain. This leads one to remember the rule (previously learnt) 'Wherever there is smoke, there is fIfe', which one recollects as having been instantiated in cases such as the familiar stove in the kitchen. It is now recognized that this column of smoke is a mark of fife in accordance with the rule just remembered. At this point, if there is no hindrance, the person would infer: 'There is a fife on the mountain'. What we have in this rough account is a sequence of psychological events: a perception, a remembrance, a recognition, leading finally to an inferential cognition. These events belong to one and the same person, and are individuated both by ownership and temporal position. How can any such temporal sequence yield a logical rule? We can do that by: (i) replacing the particular cognizer by a variable and universal quantifier over it; (ii) retaining the appropriate relations of succession, but doing away with the actual temporal positions; (iii) identifying the cognitions involved by their contents and relative temporal positions; and (iv) requiring that all
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cognitions figuring in the rule must have one and the same knower. Then we get a rule such as the following: For any knower 5, if 5 has a perceptual cognition Fx, and then remembers the rule 'Wherever F, there G', as instantiated in the uncontroversial case 0, and then perceives in x the same F as before but this time as figuring in the remembered rule, then 5 will have an inferential cognition of the form 'Ox' provided there is no relevant hindrance. 12
This is a rough account of how such an eidetic psychology of cognition would proceed. (4) Now as to the last Le., the transcendental turn. I shall try to present its nature in several steps. First, let us bear in mind the fact that we do not have a concept of the mental that is not an interpretation of it in the light of a theory: this is true as much of the view that it is an inner, cognitive, computational structure as of the view that the mental is the bodily of a certain sort. When the mental is taken for granted as being the psychological, one is interpreting it with a familiar psychological theory. One and the same mental act may be conceived as a private particular, as a psychological experience occurring within the interiority of an ego, or under any other description. It is not beside the point that Frege regarded psychologism - as Hans Sluga has shown - as an ally of naturalism. 13 The next step would consist in suspending these, or any such, interpretive frameworks. Now that we recognize that what passed for an ontologically self-evident thesis is in fact an interpretation, let us set them aside and salvage what is an indispensable phenomenal constraint which these interpretations had, in any case, to reckon with. These are, to my mind, the intentionality of the mental life: its directedness towards the world, its having a content or a structure, which is but the way the world is presented to it; its Sinn which is but the world's 'mode of presentation'. Couldn't the act's Sinn be a causal consequence of the world's acting upon the mind? If this were so, the 'transcendental' move would be stopped. But such a naturalism is not any longer open, now that we have set it aside as another of those interpretive frameworks. It is important, for my purpose, to emphasize that that was not an arbitrary decision. A naturalistic psychology simply cannot deliver the goods. The point has been well fonnulated by Fodor: 1.. a naturalistic psychology requires law-like relations between an organism and an object in its environment when one is thinking about the other, but for this one needs a description of the object such that the causal connection obtains in virtue of its satisfying that description. But such a description is not available until all the other sciences are complete. So let us begin with whatever description of the object the thinker has in mind- the Sinn or the noema. There is no access to the object per se save by means of such a Sinn. Once, then, the naturalistic framework: is 'put under brackets', one can still go on to talk the mentalistic language, but no longer in the sense of
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psychological theories. The mental acts are now taken precisely as they are experienced/performed, with their Sinn-structure, and as thus referring to their objects. One then begins to see that the act with its Sinn and the object as so described, Le., under such and such description, are but necessary correlates. Keeping this move in mind, we can take a look at such mentalistic assertions as these: Cantor: "Unter einer 'Mannigfaltigkeit' oder 'Menge' verstehe ich niimlich allgemein jedes Viele, welches sich als Eines denken lasst... "IS Or even Hilbert: "Die Grundidee meiner Beweistheorie ist nichts anderes als die Tiitigkeit unseres Verstandes zu beschreiben, ein Protokoll aber die Regeln auj'zunehmen, noch denen unser Denken tatsiichlich verjiihrt... "16 Or Brouwer: "This neo-intuitionism considers the intuition of two-oneness (the fundamental phenonmenon of the human intellect) as the basal intuition of mathematics which creates not only the numbers one and two, but also all finite ordinal numbers..."17 Or, following Brouwer, Heyting: "Mathematical objects are by their very nature dependent on human thought Their existence is guaranteed only insofar as they can be determined by thought"18 We find in these a mentalistic locution that intends to be 'transcendental', rather than psychologistic. Or, perhaps, like the Kantian locution of synthesis, it belongs to 'transcendental psychology', an Ersatz psychology, and so involves a sort of 'psychologism' that does not rob our cognitive accomplishments of their objectivity and intersubjectivity. What, iIi effect, I am proposing is briefly: what psychologism and anti-psychologism have in common is a certain conception of psychological discourse. It is an interpretation of the mental as a merely private particular which makes psychologism and so also its opponent's stance possible in the fIrst place. What we need to do is recognize this as an interpretation. A genuine overcoming of psychologism requires, not a rejection of this, or of any other, interpretive framework, but, fust of all, a recognition that an interpretive framework should not be construed as an ontology. The framework or frameworks need to be subjected to the famed epocM, and their origin - historical and genetic - sought for. The positive view that has guided this lecture, not defended within it, is that the logical and the mental cannot be radically sundered completely from each other- that our thoughts and theories are products of our acts of thinking, that in the long run all meaningfulness must lie in our being able to perform such operations. To delineate then the constitution of the logical, we need to look at the noetic operations that go into it. Such a constructivism, if psychologistic, should rather be called a sort of transcendental psychologism. The radical anti-psychologistic thinker is wrong in reifying thoughts into things, the psychologistic thinker erred in reducing thoughts into subjective ideas. Each saw one side of the truth: the noetic act and the objective Sinn are but two sides of a structure, separable only by abstraction.
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Why is it that in spite of these precautions 'psychologism' is a trap into which one always tends to fall? By 'refuting' psychologism - as by refuting 'relativism' - one cannot altogether escape it. It is only by seeing through it, by following it as far as possible, by appropriating the truth in it, that we can hope to overcome it But the line that separates the eidetic from the particular, the transcendental from the empirical, is so thin, that 'the illusion of psychologism' will persist. Aren't such things as concepts, propositions, thoughts, and theories produced by the mind, in the mind and not out in the world. All depends upon how one construes 'production', 'being in', and ' minds'. I have suggested some constructions, but nothing guarantees that a transcendental philosopher will not fall into the trap. Basically, as Seebohm has recently insisted, it is due to the paradox of subjectivity which is both in the world and of the world or, as Foucault has put it, "an empirico-transcendental doublet" There are not two different sets of mental acts: one empirical, the other transcendental. One and the same act is both, depending upon how one looks at it, and what function one assigns to it
10 ENDNOTES 1. Franz Brentano, Psychologie von Empirischen Standpunkt (Leipzig: Duncker & Humblot, 1874), Vol. 2, p. 179 (my translation). 2. See: J.E. Erdmann, Grundriss der Geschichle der Philosophie, Vols. I and IT, (Berlin: W. Hertz, 1870); Vol. I, p. 636. Cf., Carl Stumpf, "Psychologie und Erkenntnistheorie," ABHANDLUNGEN DER AKADEMIE DER WISSENSCHAFfEN, Band XIX, II Abteihmg, p. 468. 3. Cf., IbilL, p. 468, fn. 1. 4. See: Philip Kitcher, "Frege's Epistemology," PIllLOSOPlllCAL REVIEW, LXXXXVIll, (1979), PP. 235-262. 5. See: Rudolf Camap, Logical Foundations of Probability, 2nd 00. (Chicago: University, 1971), pp. 39-47. 6. See: Karl Popper, The Logic of Scientifze Discovery (New York: Basic Books, 1959), p. 95. 7. See: Gottlob Frege, "Rezension von E. Husser!, Philosophie der Arithmetik," ZEITSCHRIFf FOR PIDLOSOPIDE UNO PIDLOSOPffiSCHE KRITIK, 103, (1894), pp. 313-332. 8. Theodor Lipps, "Zur 'Psychologie' Wld 'Philosophie'," in Psychologisclu! Untersuchungen, Band II, Heft 1, (Leipzig: Verlag von W. Engelmann, 1912), pp. 1-29, esp. 11. 9. Ernst Cassirer, Dos Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, Band 2, 2nd ed. (Berlin: Bruno Casirer, 1922), p. 662. 10. Dreyfus quotes this from Hussed on p. 11 of his "Introduction" to: Hubert L. Dreyfus, 00., Husserl, Intentionality and Cognitive Science (Cambridge: MIT,
1984). 11. See: Edmund Husserl, Einleitung in die Logik und Erkenntnistheorie, 00., U. Melle, Husserliana, Band XXIV (The Hague: M. Nijhoff, 1984), chapter 4, esp. 25. 12. For more on this, see: IN. Mohanty, "Psychologism in Indian Logical Theory," in B.K. Matilal and J.L. Shaw, oos., Analytic Philosophy in Comparative Perspective (Dordrecht: Reidel, 1985), pp. 203-211. 13. See: Hans Sluga, Goulob Frege (London: Routledge and Kegan Paul, 1980). 14. Cf., e.g., Jerry Fodor, "Methodological Solipsism considered as a Research Strategy in Cognitive Psychology," reprinted in Dreyfus, 00., Husserl, Intentionality
and Cognitive Science. 15. Georg Cantor, Grundlagen emer allgemeinen Mannigfaltigkeitslehre, (Leipzig:
B.G. Teubner, 1883), p. 204. 16. David Hilbert, Die Grundlagen der Mathematik (Leipzig: B.G. Teubner, 1928), excerpt in o. Becker, 00., Grundlagen der Mathematik in geschichtlicher Entwicklung (Freiburg/Munchen: Verlag Karl Alber, 1954), p. 383. 17. L.E.I Brouwer, ''Intuitionism and Formalism," in Paul Benacerraf and Hilary Putnam, oos., Philosophy of Mathematics, Selected Readings, 2nd 00. (Cambridge: Cambridge University, 1983), esp. p. 80. 18. A. Heyting, ''The Intuitionist FOWldations of Mathematics," in Benacerraf and Putnam, eds., Philosophy of Mathematics, esp. p. 53.
THE MORE DANGEROUS DISEASE: TRANSCENDENTAL PSYCHOLOGISM, ANTHROPOLOGISM AND HISTORISM mOMAS M. SEEBOHM I. Introduction Hussed's arguments against psychologism l in the "Prolegomena" tell us that psychologism is simply a kind of relativism and that relativism can be refuted because it is self-contradictory. It has been said that the argument is spurious because the argument against relativism is spurious. 2 Indeed, the argument was later restated by Husser! himsele According to psychologism, empirical psychology as a science is the final arbitrator in all questions concerning validity claims of knowledge. Husser! argued that psychologism implies relativism. Relativism denies that scientific knowledge has universal objective validity. Hence psychologism denies the objective validity of its own judgments concerning validity claims of knowledge. Furthermore, already in the "Prolegomena" Husser! had pointed out that there is one type of relativism which cannot be refuted, viz., the individual relativism which claims the relativity of validity claims not for the species but for each individual.4 In connection with Husserl's later critique of Dilthey and world-view philosophy, another type of relativism entered in, namely, historism. 5 Husserl did not offer arguments against historism. He only emphasized the devastating consequences. It is obvious that consequentialist arguments cannot be directed against historism. Like individual relativism, historism is not committed to a belief in the objective validity of scientific knowledge. In general, it can be said that consequentialist arguments have some plausibility only with respect to a specific type of psychologism and not with respect to what Husser! later called 'anthropologism'. In the later writings Husser! considered the transcendental phenomenological reduction as the only remedy against psychologism in the broader sense. Historism is the main topic of this paper and is taken up in sections two and three. In the first section it is necessary, however, to discuss the different types of psychologism and/or anthropologism mentioned by Husserl in order to determine historism's systematic place among them.
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ll. Different Types of Psychologism The main topic of the Prolegomena is naturalistic psychologism, i.e., the psychologism which is developed in a psychology understood as a natural science. Since psychologism so understood reduces psychic phenomena to physical phenomena, Husserl calls this type of psychologism 'naturalism'. The relativism connected with it is the 'relativism of the species' which is also called 'anthropologism'. The term 'naturalism' also indicates that this psychologism is a counterpart to historism. The "Prolegomena" mentions other types of psychologism, fIrst of all transcendental psychologism. 6 With this tenn Husserl refers to Kant's attempted justification of the objective validity of principles a priori through the assumption of a transcendental subject. The frrst edition of the Logical Investigations characterized phenomenology as 'descriptive psychology'. The psychologists of the time frequently claimed that descriptive psychology is the main tool of epistemology.' Already in 1903 Husserl rejected this view. 8 He claimed though this was not made clear enough in the rust edition - that the descriptions in the Logical Investigations do not refer to empirical persons and psychic facts. Rather, as phenomenological they refer to the a priori essential structures of the experience in which logical objects are given. A description of inner experience and structures of intentionality is thus not a naturalistic psychology, although it can still be understood as an empirical discipline. Twenty years later Husserl wrote that the Logical Investigations, though not an empirical descriptive psychology, still represents a subtle psychologism. Indeed, any attempt to justify validity claims by means of a turn to the subject without explicitly perfonning the transcendental phenomenological reduction represents a transcendental psychologism of some sort.10 If in investigations of the structures of experience on1y the eidetic reduction were performed, then the investigation would not be phenomenology proper but rather eidetic psychology. Since in this case there would be no transcendental phenomenological reduction, the being of the subject would still be a being in the world. Thus eidetic psychology is later characterized as 'transcendental psychologism' or 'anthropologism'.11 It ought to be kept in mind that in comparison with the "Prolegomena" there is a significant shift in the meaning of these terms. When Husserl uses 'transcendental psychologism' against Kant in his later writings, he does not point to a mistake in the theory of the a priori, but to the constructions Kant had to use because he did not know the reduction. 12 'Anthropologism' no longer means that 'relativism of the (biological) species' which is the result of naturalistic psychologism. It is rather a term applied universally to all positions in which the subject, because of the missing reduction, is in the last instance understood as a being in the world, even when - as in the case of Kant - it is a world behind the world of experience, Le., a metaphysical world. Thus, transcendental psychologism has now to be
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distinguished as a more universal and subtle mistake than logical psychologism. What is called 'transcendental psychologism' in the Logical Investigations is thus later characterized as a type of 'logical psychologism' is by no means the same as the transcendental psychologism mentioned in the Formal and Transcendental Logic. 13 In his critical remarks about Heidegger, Husserl tells us that though Heidegger offers an intentional psychology, he rejects the reduction and therefore does not have a real understanding of the constitution of the object and reality. His philosophy, like the philosophy of his forerunners Dilthey and Scheler, is thus an anthropologism connected to an objectivism and naturalism. From these comments it is obvious that the tenn 'naturalism' no longer refers to the natural sciences in any sense. Rather, in its most general sense it signifies the thesis that the existence of the world is not bracketed because the reduction is not perfonned. 14 The relation between descriptive and eidetic psychology, including their tendency toward either transcendental psychologism or transcendental phenomenology is by no means a negative relation of mutual exclusion. On the contrary, Husserl in his later writings asserts again and again that all the contents of eidetic psychology's descriptions are also without restriction valid in transcendental phenomenology. The only difference is the attitude with which these contents are considered. In eidetic psychology they are still considered with the mundane attitude. In transcendental phenomenology they are considered with the transcendental attitude, which is the result of the reduction. Furthermore, in addition to the Cartesian path there is a path to the transcendental phenomenological reduction via psychology. All that is necessary is a thorough critical phenomenological reflection on the presuppositions of the descriptions of eidetic psychology itself, i.e., an intentional analysis of the cognitive activities of eidetic psychology itself. The paragraphs which immediately precede the explication of this interplay of psychology and transcendental phenomenology in the Crisis 1s offer the formula which in part elucidates the principle of this explication. It is the formula of the paradox of subjectivity: On the one hand, the world and all its contents are given as the correlate of the consciousness which conceives them. On the other hand, we can think of the being of consciousness only as a being in the world The second part of the paradox explains why anthropologism is a necessary part of the self-apprehension of subjectivity. The 'where' of its being can be apprehended only in the world. This, in turn, explains why such a self-apprehension is necessarily infested with relativism. To be in the world is to be in one specific context in the world. Whatever is in the world in a context is in its being determined by this context But under this presupposition it must be admitted that the way in which consciousness has the world as its correlate is detennined by the specific context, and, therefore, is different in different contexts. The additional puzzle is that the way in which this determination is thought depends upon the basic structme of the world-view and the different ways in which determinations can be thought in different world-views.
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The paradox of subjectivity is helpful in some respects but leads to some other difficulties in the theory of the reduction. Given the paradox, the reduction can be understood as an arbitrary decision in favor of the frrst part of the paradox. It is not obvious that in the reduction a full account of the paradox can be given, and thus it is not obvious that the overcoming of relativism is more than a decision to deny the motives for accepting relativistic positions. 16 This question will not be discussed or answered in this paper, but an answer would presuppose the thorough analysis of the different types of anthropologism that is the topic of this paper. It follows from what has been said that historism is a kind of anthropologism or transcendental psychologism. As such, it is the counterpart of naturalistic psychologism or naturalism in the sense of Husserl's early writings. Some hints for a further analysis can be gained from Husserl's judgments about Dilthey. The judgment is negative and critical in connection with the early critique of historism. 17 It is positive in later writings. Dilthey's descriptive psychology is there praised as a forerunner of a phenomenological psychology.18 Husserl' s theory of the constitution of the cultural world seems to be heavily influenced by Dilthey's.19 Most interesting for the present purpose, however, is that Husserl in manuscripts20 sketched out the idea of a path to the transcendental phenomenological reduction via the human sciences. According to Husserl the human sciences in their research employ a specific epocM. If this epocM is radicalized, it leads into the phenomenological epocM and with it into the reduction. A universal human science under a radicalized epoc he has as its correlate the contents of all cultures, past and present, and is, hence, coextensive with transcendental phenomenology. A universal human science in Dilthey's sense is necessarily a universal historical human science. The conception of history which emerged in the nineteenth century in the historical school and which culminated in Dilthey belongs to a universal human science. It is, however, this conception of history out of which historism was developed. There is, hence a parallel: the universal human science is related to historism on the one hand and to transcendental phenomenology on the other in the same way that descriptive eidetic psychology is related either to transcendental psychology or tnmscendental phenomenology. Both are instances of the paradox of subjectivity. The world in which consciousness has its being is in the frrst case the 'historical world' of the universal human science, and the contexts are the historical contexts of different cultures and epochs. An analysis of historism presupposes, therefore, a study of the genesis of the historical world which is the correlate of historical research in the late nineteenth and early twentieth centuries. Not very much can be gained from Husserl in this respect In connection with studies on the origin of geometry, he made some possibly helpful remarks about the significance of writing for all higher activities of the intellect,21 but he never reflected on either the specific methods of the human sciences and history, their correlate, viz., the historical world, or the genesis of both. This task would
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be parallel to Husserl's analysis of the genesis of science out of the
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prescientific realm and by no means - as the following considerations will show - included in or dependent on the genesis of science. Following Dilthey22 one can assume that the genesis of the conception of history of the universal human science is closely connected to, and to a very high degree identical with, the development of hermeneutics qua methodology of the interpretation of texts. It presupposes the historical-philological method. Hermeneutics as a methodology and art has its own genesis. The second section of this paper will point out that this genesis is guided by a certain necessity. The analysis of historism is given the paradox of subjectivity - itself a necessarily generated mcxle of self-apprehension of consciousness. Two remarks about the mode of presentation are in place. Husserl presented his description of the genesis of science in the Crisis in the form of a narrative. Section II of this paper uses the same procedure for the explication of the genesis of what will be called 'hermeneutical consciousness'. The task of narrative is, however, to reveal a necessity of the development. Two characteristics of this 'necessity' can be mentioned. (1) It should become obvious that a certain level N of the development can be reached only if the preceding levels are given in the order in which they occurred. (2) Given a certain level, and if a reflection which is guided by a certain interest in the unity of the literary tradition takes place, only a limited - perhaps only one - possibility is left. Whether it actually takes place or not is, however, a contingency. Those who are uncomfortable with the assumption of a material a priori may claim that it cannot have the character of an absolute objective validity because such a 'feeling of necessity' is at best a result of the situation of those who reflect upon the development. Indeed, one conclusion of this paper will be that no 'refutation' of such historistic assumptions is possible. Secondly, readers will be frustrated because the paper talks about rules and methods without explicating them. I have given such explications elsewhere. 23 What the paper analyzes are reflections about a methodological practice that had hitherto been taken for granted. The main question is how such reflections changed the principles and not what kind of rules could be derived for practice from the principles.
ITI. The Genesis of the Historical World View The expression 'type of hermeneutical consciousness' will refer for the purposes of this essay to the specific structure of the understanding of the Ipast, the tradition, and its significance, a structure of understanding which is Ilcharacteristic of a type of consciousness. The term 'hermeneutical' has a 'Imethodological meaning in the old conception of henneneutics, but in this \essay the term will have broader use. Its use will also, however, be
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narrower than the more recent meaning in philosophy according to which consciousness, Dasein, is throughout hermeneutical. Given the definition which has been chosen here, it can be said that historism is a very complex type of hermeneutical consciousness which has itself a 'history' in which less complex types of hermeneutical consciousness can be found. The analysis of this genesis is the task of this section. The mediation of the past into the present via traces, i.e., fixed life-expressions, is a necessary component of hermeneutical consciousness in general. Fixed life expressions are tools, buildings, objects used in cultsbut also memorized and habitualized patterns of actions, including all kinds of speech acts. 24 If written discourse is not among the ensemble of fixed life-expressions, the hermeneutical consciousness and the culture connected with it is often characterized as the culture of the 'savage mind'- a term which should be used without all the pejorative connotations which it sometimes has had. It is, however, doubtful, whether the past can have for such a hermeneutical consciousness the meaning of a realm with identifiable objects.~ The following analysis will restrict itself, therefore, to the types of hermeneutical consciousness which relate to the past first of all via written discourse. This restriction does not imply: (a) that the historical world-view itself is restricted to this domain; or (b) that the paradox of subjectivity can be fully understood without referring to structures which belong in the most archaic forms of hermeneutical consciousness. Expositions of the term 'hermeneutics' begin very often with an interpretation of the use of 'hermeneuein' in Plato's lon.7f, However, in the classical Attic period there was no 'art of interpretation', and even when it was developed in the Hellenistic period. ' hermeneia' was not a technical term connected with it A more appropriate anticipation of this art is rather to be found in the various hints in Plato's Epinomis. Those who with the aid of divination practice the ' hermeneutike techne' to interpret the poets, the laws and signs and oracles are there called the ' exegetai'.XI Methodical rules for such interpreting were not known at Plato's time. Even a grammar was still missing and with it the rules of 'grammatical exegesis', which presuppose the art of grammar. By contrast. the later employment of this term indicates that what was at stake was already the interpretation of written discourse. However, the art of grammar was not only the art of writing correctly and of analysing a text according to given grammatical rules. It also included all rules and methodical viewpoints for the exegesis of texts. The mastering and practicing of the art of grammar led to philology. Philology meant for the Hellenistic age - as well as for the later humanistic tradition - universal erudition, i.e., the results of the practice of the art of grammar. It included all wisdom which the tradition had to offer: divine revelation, poetry, philosophy, the sciences etc. 28 Since the art of grammar also included the art of criticism in all fields, philology was also able to answer the question 'what is truth' in all fields. Finally, the true philologists also had to be a masters in the field of rhetoric, and the true rhetorician had to be a perfect philologist According to Quintilian and
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others, rhetoric is only by implication the art of delivering effective speeches. Essentially it is the art of applying the knowledge supplied by philological education to newly given concrete situations. In this sense it is also the art of the invention of new knowledge. 29 Three main characteristics of this philological-rhetorical type of hermeneutical consciousness must be emphasized for the purposes of this investigation. (1) The literary tradition represents for it a harmonious unity of a system of truths, values, duties and beauty, an ideal of humanity - the same which later guided the humanists of the Renaissance - which is of significance for any present time and which provides the framework for the education of future generations. (2) Interpretation, explication, and application are for this type of hermeneutical consciousness an inseparable unity. (3) It has a conception of history which is quite different from the one which provides the medium of modern historism.30 In the early periods of classical antiquity, 'historia' meant the investigation of facts of all kinds, and later it was a term also for a literary genre, namely, the one in which reports about the results of such investigations were given. There was in the art of grammar a level which corresponded precisely to this meaning of 'historia', namely the 'explanation of facts and words' in the so-called historical exegesis. In the nineteenth century it was still recognized as a relevant activity of the henneneutical method.31 Later on, 'facts' were often understood primarily as deeds. The Romans coined the well-known expression 'res gestae', things done. The word 'factum' corresponds in Latin to this narrower interpretation of 'fact'. Seen from the rhetorical point of view mentioned above, such reports about res gestae were used as examples of deeds and acts, which could be applied to present situations. It has been shown that this concept of 'historia' still dominated the early Christian literature. 32 Christianity introduced some changes in hermeneutical consciousness (which will be discussed immediately), but it cannot - as is usually thought - be credited with invention of an idea which was later of great significance for the development of hermeneutical consciousness, namely, the idea of universal history. The genesis of this idea has other roots. Roman historians collected histories about the deeds of the Romans in chronological order. But Rome turned out to be much more than one polis among others. Its fate became the fate of the known world. It was Vergil who created the idea of a development which had a goal-directed history leading to the Roman empire as an empire of peace. This idea had an impact on the work of Christian chronologists and historians much later (circa 500 A.D.) and only after a serious change within the hermeneutical consciousness had taken place in the New Testament. The criticism of the Hellenistic philosophers who said that philology is only a collection of facts and as such has no access to truth and universality was a repetition of Aristotle's description of 'historia' .33 It was repeated again and again but had no real impact on the development of hermeneutical consciousness. The critique of the skeptics 'against the
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grammarians', however, was an expression of a change. They pointed out that 'the art of grammar is circular in all of its rules- an early preview of the hermeneutical circle. Of even greater significance was their downgrading of the tradition as a whole into a source 'diaphonies', contmdictions. The skeptical method showed that the tradition was no longer the general source of wisdom and truth but rather throughout contradictory.34 The skepticism of this type has nothing in common with the skepticism of historism. The fonner type of skepticism is ahistorical, and its attitude is the counterpart of the attitude of the philologist It was, fwthermore, not only a philosophical position but also an expression of an experience of henneneutical consciousness. One had not to be a skeptic in order to know that there were contmdictions in the tradition. The most significant diaphony was the contradiction of the conception of reason and virtue developed in philosophy since the classical Attic period with both the myths of the poets/prophets and archaic lawgiving. In order to save the unity of the tradition, the Stoics developed the method which was later called 'higher' hermeneutics, i.e., allegorical interpretation. The myths were said to have not only a literal meaning, but also a higher meaning in which the truths of reason are revealed in the fonn of an allegory. The Stoics also invented a theory of culture which explained why those who created the myth had to tell the truth in allegories.3' A modification of the new technique of interpretation and its justification was later adopted by Jewish Hellenistic philosophers for the interpretation of the Old Testament36 The problem of diaphonies created in a literary tradition swfaced also in the New Testament. In Luke 24:27 we read that Jesus interpreted (dihermeneusen) Moses and the Prophets in the light of his own deeds and teachings. This principle of the typological interpretation became a general principle of the interpretation of the Old Testament. The present, later period of a tradition is the archetype which contains more truth (sensus plenior) than the earlier period, or ektype. The ektype can be fully understood only in the light of the archetype. The hermeneutical consciousness of the early Christian church was in every respect 'critical'. It was no longer possible to gloss over the diaphonies that emerged between its own and other traditions. The rabbinic tmdition of interpreting the Old Testament had frrst to be 'cut off as a false tradition. In the next step the gnosis, i.e., the attempt to harmonize the Hellenistic tradition with the Christian tradition via allegorical interpretation, had to be 'cut off' as false from the tradition of the true patristic literature. In general, other literary traditions including the schools of the philosophers along with theological teachings not accepted by church- were considered as sactae, heresies cut off from the true catholic tradition.37 The demand of the church that 'the worldly power prosecute what was cut off from its tradition is an immediate consequence of the type of hermeneutical consciousness represented by the early church. It is a type which is not
the
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restricted to the Christian tradition. With modifications it can be found elsewhere, e.g., in the development of Islam. Even a type of hermeneutical consciousness which tries to save its unity by continually cutting off false traditions creates in itself diaphonies- if only because the excluded ideas reenter the tradition in disguise. The problem of the diaphonies occurs now in: (1) the repeated attempts to prove the concordance of the tradition with itself against the apparent sic et non, Le., the systematically collected contradictions; and (2) the revival of higher hermeneutics and allegorical interpretation, though the church condemned all attempts to use such techniques to harmonize the New Testament with elements of the Hellenistic tradition and admitted only the typological interpretation of which it had to apply the methods of higher interpretation to its own tradition. The tension between the literal meaning of the Scriptures and the dogmatic teachings, moral teachings, and institutional structure of the church was obvious. Allegorical interpretation of the New Testament was necessary for the justification of the dogmas. Other types of higher interpretation - the moral and the anogogical - were added. 38 Together with this new type of hermeneutical consciousness a new concept of history developed Its basic structure is given with Augustin's distinction between the sacred history and the history of the gentiles. 39 In the Byznatine monk chronicles- bu't also in the self-understanding of the Holy Roman Empire the sacred history has its 'worldly' aspect in its connection with Rome.40 The sacred history is in its structure not a historical development in the modem sense. It is - to use Heidegger's term - an ekstatic history in which anything has significance not 'in itself but rather with respect to the crucial events of the Creation, the Fall, the Incarnation of the Word, and the coming of the Kingdom of God. Though it is 'universal', it has nothing in common with the nineteenth century historians' idea of a 'universal history'. The history of the gentiles also exhibits no development or any significance for itself. The old conception of history dominates it. Each story told serves as an example of either God's punishment of evil deeds or reward for virtuous deeds, and this is the only reason for remembering such stories. The modem conception of history depends upon a radical turn in hermeneutical consciousness, but this turn was prepared by certain intellectual developments during the Middle Ages. Thomas Aquinas had already recommended restricting higher hermeneutics to the cases in which 'the Scriptures themselves, at the level of their liteml sense, ask for such interpretations.41 Likewise the Franciscans, who dominated the movement of the devotio moderna, favoured the literal sense.42 Nevertheless, it must be recognized that Luther's principle scriptura sancta est sui ipsius interpres initiated a revolution in hermeneutical consciousness. If the Scriptures can be understood out of themselves, then such an understanding can be used as the basis of a critique of the tradition of the interpretation of the Scriptures. Since this tradition had - as a unity of interpretation and application continuously developed new contents which cannot be found in the
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Scriptures, the critique was a cntlque of the tradition in principle. The tradition itself was the result of an ongoing distinction between the true and the many false traditions. The new principle turns this distinction against the 'true' tradition itself to the extent to which it is possible to declare that this tradition is 'false' .43 The situation created by this turn was not stable. An interpretation of the Scriptures which turned against the old tradition of interpretation necessarily created its own tradition. The Reformation soon had its own 'fathers'. The underlying principle of the new type of hermeneutic consciousness implies, however, the possibility that it can be turned against this new tradition. Seen from a formal point of view, this procedure can be iterated indefinitely and was in fact iterated by the steadily increasing number of Protestant sects. Thus a situation was created which could be used for the development of a counterargument. The Council of Trent decided that no understanding of the Scriptures without the mediation of tradition is possible. The Council argued that, to begin with, a tradition of translation is necessary. Hence the question had to arise: which tradition is the true tradition? The Council claimed that an answer could not be found in an interpretation of the Scriptures, but rather had to be found in the nature of the tradition. The answer was: the tradition which can prove that it is connected without interruption to the Scriptures is the one which is true and which alone can deliver a true interpretation of the Scriptures" The task of the Protestant theologians was to prove against this formal argument that it is indeed possible to find criteria and methodical rules which allow us to understand the Scriptures without, and if necessary, against the tradition. The principle they developed was the fIrst canon of hermeneutics. This canon says that the text can be understood as it was understood by the contemporary addressee. The claim that a text has to be understood according to the original intention of the author is another and, if properly understood, by no means 'psychological' - fonnulation of this canon. The methodologically pure formulation would be: the text has to be understood out of its own context and not out of the context of the interpreter. The Latin fonnulation is sensus non est inferrendus sed efferendus.44 With respect to the Scriptures, the understanding of the contemporary addressee could be reconstructed with the aid of the art of grammar and its resulting philosophy. The practice of this art had survived as a subculture during the Middle Ages and surfaced again in the humanism of the Renaissance. 4s The Renaissance as well involved a hermeneutical consciousness which declared a tradition of interpretation to be false and recommended an immediate return to the sources. However, because the texts in question were not texts which grounded the basic system of truths, values, and noons, the Renaissance - in comparison with the Reformation was in itself of only secondary significance.
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The alliance of the Reformation with the Renaissance had serious consequences. It is certainly true that the Protestant theologians and humanists did not separate interpretation, explication, and application.46 It is also true that humanists and some - though not all! - Protestant theologians propagated an ideal of erudition and education in which a harmonious unity of the literary traditions of Christianity and classical antiquity was presupposed. But it is also true that the further development showed with logical necessity that such assumptions were not compatible with a rigorous application of the fast canon. Although Protestant Theologians employed the art of grammar, they did not - like the Hellenistic and humanistic philologists - regard its result, wisdom or philologia, as the truth. Rather, they regarded a specific text, the New Testament, as the source of truth, and they used the art of grammar as well as philologia as the instrument to understand it out of its own context. A few other texts within this context could be considered as sources of truth as well, but some - especially those which occurred within the pagan and rabbinic traditions - had to be considered as false. Consequently, the texts emerging in these latter traditions had to lack any application. Thus for these texts the unity of interpretation and explication with application was dissolved. The method of understanding a text out of its own context is, as such, neutral with respect to the question of application. But it does demand a lot of work. Indeed, the method can stretch indefmitely through the universe of texts and contexts and the meanings they reveal. The interest of the interpreter determines the selection of groups of texts to be subjected to methodical interpretation. This interest and the texts selected can be deliberately changed. In the last instance, this interest of the interpreter is determined out of his/her context. But that does not undermine the methodical attitude as such. Furthermore, it should not be forgotten that the interest can be a pure professional interest, and fmally that it can be mere curiosity about what strange things people believed and thought to be true. The rigorous application of the method showed the diaphonies in the literary tradition in all their harshness. That the ' spirit of the Greeks' and the 'spirit of Christianity' are irreconcilable was later the experience of Hegel, HOlderlin, and their contemporaries. Indeed, a new level of the hermeneutical consciousness' experience of the thoroughly contradictory character of the literary tradition is the presupposition of Hegel's attempt to think the whole of the development of mind or spirit as a movement through contradictions.47 However, for the newly developed methodology in henneneutics, the attempt was soon itself a text which has to be understood out of its context48 The philologist and, as will be shown in the next section, the histo~ practiced what Husser} later called a universal epocM in which the question of truth, value judgments and application were bracketed. What was and is at stake from the professional point of view is the reconstruction of the original meaning of a text in its context This reconstruction has to
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eliminate the non-understanding and misunderstanding which arises in any interpretive tradition that does not employ such an epoche. The professional attitude is - in this sense which is defmed by the first canon - 'objective' and 'contemplative'.49 It registers the truth claims made in texts, but it does not, as such, share them. It understands and withholds any judgment about agreement or disagreement. The given account of the genesis of this type of hermeneutical consciousness entails the rejection of some currently fashionable opinions about the nature of the philological-historical method developed by the hermeneuticists of the nineteenth century. It is claimed that the ideal of objectivity in interpretation depends upon the Cartesian idea of scientific method as a method of discovering truth, and it is then objected that this idea does not fit the real task of interpretation. The Cartesian idea of method is indeed a verificationist idea, but for the methodologists of the nineteenth century the method was not a method of discovering truth, but a method of avoiding error.so The hermeneuticists of the nineteenth century obviously had an idea of method which would today be called 'falsificationist'. Furthermore, they knew the limits of the professional methodological attitude. They were well aware that with respect to works of genius - what we today call 'eminent texts' - the question of truth cannot be separated from the task of interpreting them.~l It is sometimes also asserted that the philological-historical method and its claim for objectivity borrows something form the principles determining the methods of the natuml sciences. However, on the basis of the narrative given above, it can be said that, on the contrary, the idea that the truth of the Scriptures can be understood outside of and against the tradition provided a major justification of the attempts to gain a similar access to nature. This does not mean that the methods in the natural and human sciences have no common roots,S2 but these roots go much fwilier back. It also does not mean that a certain alliance between historism and naturalism is impossible- such an alliance will be considered in the next section. But the opinion that scientism or naturalism is a genetic presupposition of the modern conception of history and historism cannot be maintained. Finally, it is frequently claimed that the Enlightenment's prejudice against prejudice is responsible for the development of the hermeneutical method of the nineteenth century. However, it was the above delineated turn of the hermeneutical consciousness at the time of the Reformation which made the Enlightenment's prejudice against prejudice and tradition possible- and with it the development of the hermeneutical method.
IV. The Modern Conception of History and Historism The philological-historical method has as its primary objects the texts and their meanings. The meaning of a text is to be understood out of its own
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context This implies that every text is in some sense determined by its context It is possible to have a fairly precise concept of what a context is. There is a quasi-temporal order in the process of determination of any context A text is determined by the texts to which it refers explicitly or implicitly, and in the realm of its efficient history it determines the texts which refer to it. Thus contexts are webs and dimensions of developments. Already from this point of view, in which only the interpretation of meaning of texts is the concern, it can be said that the method is intrinsically historical. The historical connectednessS3 of texts is not restricted to historical textual connectedness. (I mention in passing that the use of language is another connectedness which has as well its historical dimension. 54) The most relevant historical dimension is, of course, given in texts with reports about events happening in their present context or in the context of their past. But even texts which do not report events at all always report one event: their being written by one or more known or unknown authors. Thus texts themselves are fixed life-expressions which belong to a second order context of events and deeds, a context which is reported by some texts. It is this specific second order context in which the author occurs. Though it is possible to neglect the author at the level of historical textual connectedness, he cannot be banished from this second order level of the historical effective connectedness to which some texts refer and to which all texts belong. History written under the modem conception of history has the character of a construct produced on the basis of a complex web of fixed life-expressions and knowledge of the natural environment in which they have been produced. Historical writings are explicationsss of a certain epoch or development in a culture at a temporal and/or geographical distance from the explicating historian.56 There are two ways of constructing such writings. One way involves an immediate application in the explication. It presupposes the assumption of the wholeness of the historical development, which in some sense culminates in the present or in a historical period that will supposedly follow the present. Hence, each period receives its significance from the outside. Dozens of such secularized universal histories of salvation or damnation have been created since the beginning of the nineteenth century.57 They are themselves an object for a reflective hermeneutical consciousness. Since they constitute conflicting traditions of interpreting history as a whole, the history of the modern literary tradition repeats the Hellenistic pattern in which an increase of diaphonies leads natumlly to skepticism. The other approach rejects from the outset such 'metaphysical' interpretations of history.sa It is grounded in an application of the first canon to historical epochs. Every culture has to be understood out of itseJ.F9 and has its significance primarily for itself, and not for us as mediated through a world historical process in which it has a certain function. Therefore, the attitude of the historian is objective, contemplative, and tolerant with respect
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to foreign systems of values and truth claims. But that means that the historian also has a relativistic point of view. Each value system and system of truth claims is regarded as having validity only with respect to its historical context Historical positivism and historical relativism thus belong together and are both constitutive for historism. The level of the historical connectedness of deeds and events is presented to the present not only through texts but also through fixed life expressions of other kinds such as buildings, tools, cult objects, works of art, etc. These 'silent' traces or witnesses are the object of archeological hermeneutics. Such traces are primarily those which can be understood as being connected with 'inscription' that are the products of intentional acts of authors. But such traces are always connected with traces from the unintentional animalic life of the authors and with traces of the natural environment to which this life as animalic life belongs. Efficient history is a web of events in an environment. In this web these events are related as causes and effects, which are analyzed in historical explanations. The difficult question of the logical structure of historical explanations cannot be discussed here.60 It must suffice to note that they are similar to the explanations which we give in the realm of the life-world and are strongly analogous to the explanations given by courts of justice. (fhe original meaning of 'causa' was 'guilt'.) Furthermore, actions can here be explained by referring to 'motives' which can be understood, and the understanding implies here the understanding of values and nonns as well. However, the fIrst canon requires that such an understanding be exercised from the historist's point of view. Only the norms and values which belong to the context of an action are valid viewpoints for explanations. An explanation is falsified if it can be shown that it uses viewpoints foreign to the context Because historical explication is not restricted to the hermeneutical interpretation of meaning, historism can be combined with naturalism. One possible mode of combining historism and naturalism is to graft scientific explanations onto historical explanations in the same way in which they can be grafted upon explanations in our life-world. Historians have always exploited this possibility not only to explain actions, but also to secure data concerning traces. History reaches down to the level of cultures of the 'savage mind' which have not left traces in written discourse. (Indeed, in our and other literary traditions there are histories and even traditions of cultural contacts with such cultures.) The task of understanding such cultures out of their own context is most difficult The impact of scientifically secured traces and explanations of such cultures increases with the temporal distance. The investigations finally lead back to a grey zone in which there are fewer and fewer fIXed life-expressions or traces which can be distinguished as in some sense 'human' from those traces left by animalic life. The hermeneutical consciousness which is generated by this combination of historism and naturalism views the past of humanity and its significance for the present and future. However, with the growing temporal
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distance it is less and less chamcteristic for the 'human condition' in geneml. Science has thus moved mankind out of the center of the universe. Historism combined with naturalism teaches: (8) that mankind is 8 very brief episode in the history of nature; (b) that the character of mankind shows 8 high degree of plasticity; and, as 8 conclusion (c) that this character will develop in the future - if it survives at all - into something which is quite different from what it is now. However, there is 8 puzzle connected with this type of hermeneutical consciousness, 8 puzzle which does not invalidate this consciousness but rather indicates bow it stands under the paradox of subjectivity. Science, seen from the viewpoint of history, has had its own history and its own historical epochs with diaphonical bUth claims. Moreover, especially in the light of the historico-naturalistic type of hermeneutical consciousness, it is not reasonable to expect that in two thousand years, science - if there is something like that at all - will be in principle similar to our science. We cannot even expect that our science will be regarded as something better than myth. Thus, the attempts in the second half of the twentieth century to develop 8 theory of science on the basis of the history of science have had a consequence which surprised its developers, namely, that the claim for the validity of scientific methods, 'paradigms', came to be regarded as historically relative.'· However, the practitioners of 8 paradigm in any historical epoch cannot know this paradigm as historically relative unless they adopt 8 hermeneutical consciousness which has the first canon of hermeneutics as its guiding principle. The puzzle is that the historist contradicts himself: he claims on the one hand that all truth claims have validity only in their contexts, but also on the other hand that historical investigations of such truth claims and their contexts have some objective validity, i.e., that the fust canon and all methodical moves following from it create some type of unrestricted, context-free, objective validity. Gadamer has exploited this puzzle to cast serious doubts on the possibility of historical objectivity.'2 He claims that the modern conception of philology and history somehow implies that the interpreter has attained a standpoint 'outside of history' and can reflect at a neutral level of pure contemplation. However, in order to refute the possibility of any such standpoint, Gadamer attacks the fust canon in the form of the principle of the 'original intention of the author' and the 'understanding of the contemporary addressee' .'3 In its place he offers the thesis that the validity claims for an interpretation depend on the tradition in which the interpretation is made. He claims that every interpretation of the past is itself valid only for the tradition in which it is given. From these claims it follows that there can be no difference between correct and incorrect interpretations in geneml. Interpretations are always only different.64 Gadamer's thesis that no interpretation can sepamte itself from its tradition has a prima facie family resemblance to the position of the Council of Trent The difference, however, is that the Council of Trent gave a criterion of the we tradition. Gadamer gives no such criterion. Thus, his
26
THOMAS M. SEEBOHM
abandonment of the first canon only leads to a radicalized historism for which historical relativism is itself a position that has only historical validity. However, no practitioner of such a radicalized historism can even have historically objective knowledge of historical relativism as historically relative unless he or she adopts a hermeneutical consciousness based on the ftrSt canon. Furthermore, if such a practitioner of radicalized historism simply decides not to attempt to obtain historically objective knowledge of historical relativism as historically relative, then this decision must itself be considered as a disguised renewed longing for ahistoricaJ objective knowledge. The ftrSt canon is thus the presupposition not only of historism's objectivism, but also of its relativism. As explicated above, without the ftrSt canon there is only the mutual exclusive relationship of traditions to be false- with the well known political consequences included. The attempt to overcome historism's objectivism through the rejection of the ftrSt canon eliminates the possibility of both relativism and the tolerance of other traditions. Conversely, the retention of this tolerance presupposes the retention not only of historism's relativism, but also of its objectivism, i.e., it presupposes a hermeneutical consciousness which adopts the fast canon. Just as Gadamer's attempt to exploit this puzzle to cast doubt on historical objectivity is self-defeating, so any utilization of this puzzle which attempts to 'refute' the fast canon, and so historical relativism, on behalf of an ahistorical objectivism must also fail. To repeat: such an ahistorical objectivism had as its product intolerant traditions. The price for the tolerance that the fast canon brings is a historical, and so historically relative, objectivism. What has been said should by no means be understood as a refutation of radicalized historism or effective-historical consciousness." As long as it does not deny historical objectivism it cannot be refuted. But the relation of the two intertwined levels of historism is itself in need of an explication. This explication can be given with the aid of the paradox of subjectivity. Indeed in this specific instance of the paradox the 'world' is the 'historical world', the world of history, the world given through an open multiplicitly of past and possible future consciousness which is under the universal epocM of the human sciences as Husserl characterized it, but such a consciousness is the hermeneutical consciousness of the first level of historism. As such, it is nothing but the choice of the ftrSt part of the paradox of subjectivity and therefore has the close affmity to the transcendental-phenomenological reduction which Husserl ascribed to it. The historism of the second level - the radicalized historism of historicity and effective-historical consciousness - is only a reduction of the historist's view to the second part of the paradox. It asserts that the historist's point of view can be given only as a part of the historical world itself and is, therefore, determined by its own context and its own tradition. The task of this paper has been to explicate how historism is itself a specific and most radical instance of the paradox of subjectivity. Only a few hints about the consequences of this explication can be given. The fast
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consequence is pragmatic. Since the paradox of subjectivity belongs to the structure of the self-apprehension of consciousness, all research which is in some sense concerned about subjectivity and consciousness is self-referential and hence infested with the paradox. It is pointless to exploit this paradox to develop so-called 'refutations' of naturalism, psychologism, and historism. What has been characterized as 'the historico-naturalistic approach' has collected most of the knowledge that has resulted from mankind's experience of itself and its environment- though this knowledge is by no means ordered in any kind of 'system' which modem philosophers from Descartes to Hegel wanted. This approach is also open in the highest degree to new experiences. Any putatively competing henneneutical consciousness most likely already belongs to a stage of the history of this approach. To go back to earlier stages would involve both a scientific and moral regression. The second consequence concerns the possibility of a prima philosophia, a frrst philosophy. Some may be tempted to try to overcome this paradox through a return to or renewal of 'dialectical interpretation' . Intensive studies of this potion have convinced me that its only outcome is an ordering of phenomena on the basis of logical presuppositions which are given the present state of the art - unsatisfactory in every respect. Rather, it is the late writings of Husser! which clearly determine what phenomenological research has to investigate in order to achieve a better understanding of the self-giveness of consciousness, namely, passive synthesis and especially the problems of temporality and intersubjectivity in order to formulate a new transcendental aesthetic.
28 ENDNOTES James H. Wilkinson gave highly valuable advice concerning the presentation of the structure and style on the material in this essay. 1. See: Edmund Husserl, "Prolegomena to Pure Logic," in Logical Investigations (Halle: M. Niemeyer, 1900), Vol. L 34-38. In order to refer to all English or Gennan edition of Hussed's writings I cite - wherever this is possible the paragraph number. I also give references to the volwnes of Husserliana. For the "Prolegomena" this reference is Husserliana, XVllI, 1975. If it is necessary to refer to pages, the reference will be given to an English translation. 2. See: Dagfinn F011esdal, Husserl und Frege (Oslo: I Kommisjon hos Aschehoug, 1958), pp. 36 ff. Cf., IN. Mohanty, Husserl and Frege (Bloomington: Indiana University, 1982), pp. 20 ff. 3. Cf., EdmlDld Husserl, "Philosophy as a Rigorous Science," in Q. Lauer, 00., Phenomenology and the Crisis of Philosophy (New York: Harper & Row, 1965), especially pp. 92-105. 4. See: Hussed, "Prolegomena," 35. 5. See: HusserI, "Philosophy as a Rigorous Science," p. 129. Lauer and others often translate 'Historismus' as 'historicism'. I follow Karl Popper, The Poverty of Historicism (London: Routlege & Kegan Paul, 1960) in distinguishing between historicism and historism. Popper understands by historicism a theory - like those of Hegel and Marx - which gives an account of universal history as a whole. From the historist's 'positivistic' point of view - as well as from Popper's - historicism would be rejected as bad metaphysics. Cf., note 59 below. 6. See: HusserI, "Prolegomena," 28, n. 38, 58. The German word is 'Transzendentalpsychologismus' . 7. Cr., H. Spiegelberg, The Phenomenological Movement (The Hague: Martinus Nijhoff, 1960), Vol. I, especially p. 57 (about Stumpf). 8. See: Edmund HusserI, "Preface to the Prolegomena," in Edmund HusserI, Logical Investigations, Vol. I, ed. IN. Findlay (London: Routledge & Kegan Paul, 1970), p. 47. 9. See: EdmlBld Husserl, Formal and Transcendental Logic. Husserliana XVII, 56,99. 10. For an account with more references, see: Thomas M. Seebohm, Die Bedingungen der Moglichkeit der TranszendenJalphilosophie (Bonn: Bouvier, 1962), pp. 156-159. 11. Husserl's notes about Heidegger are published in: Alwin Diemer, Edmund Husserl. Versuch einer systematischen Darstellung seiner Phanomenologie (Meisenheim: Hain, 1956), pp. 29-30. 12. Cr., Seebohm.., Bedingungen, sec. 6-8 for references. 13. See: Husserl, Formal and Transcendental Logic, 56,99. 14. See: Diemer, Edmund Husserl, pp. 29-30. 15. See: Husserl, Phenomenology and the Crisis of Philosophy, 53, 55. 16. For a criticism of this kin~ cf., Gerhard Funke, "Practical Reason in Kant and Husser!," in T.M. Seebohm and J.1. Kockelmans, eds., Kant and Phenomenology (Washington: Center for Advanced Research in Phenomenology and University Press of America, 1984), pp. 1-29. 17. See: Husserl, "Philosophy as a Rigorous Science," 122 ff. 18. See: Edmund HusserI, Phiinom£nologische Psychologie. Husserliana. IX (The Hague: Martinus Nijhoff, 1968), "Introduction," 1,2, Beilage IJI.
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19. See: Edmund Husser!, ldi!en II, Husserliana, W (The Hague: Martinus ·Nijhoff, 1952), Dritter Abschnitt, "Die Konstitution dec geistigen Welt" 20. See: Ibid., Beilage IV, 311-315; Beilage xn, 11-12. See also: Edmund Husserl, Erne Philosophie, Vol~ II, HusserliaM, VII (The Hague: Martinus Nijhoff, 1959), Beilage XXVI, 458; and EdmlDld Husserl, Phiinomenologische Psychologie, Beilage V, 376-379. 21. See: Jacques Derrida, Edmu.nd Husserl's Origin of Geometry: An Introduction, trans. J.P. Leavey (New York: Nicolas Hays, 1977). 22. Cf., Thomas M. Seebohm, ''Boeckh and Dilthey," in 1. N. Mohanty, ed, Phenomenology and tlu! Human Sciences (The Hague: Martinus Nijhoff, 1979). Cf., Wilhelm Dilthey, Selected Writings, ed. H.P. Rickman (Cambridge: Cambridge University, 1976), especially pp. 247-263, ''The Development of Hermeneutics." 23. See: Thomas M. Seebohm, Zw Kritilc di!r hermeneutischen Vernunft (Bonn: Bouvier, 1972). Cf., also the essay mentioned in the prior footnote. 24. Cf., Dilthey, Selected Writings, especially pp. 247-263.
25. See: Thomas M. Seebohm, "The Significance of Written Discourse for Henneneutics," in 1.1. Pilotta, eel., Interpersonal Communication (Washington: The Center for Advanced Research in Phenomenology and U.P. of America, 1982), pp. 141-160. 26. Plato, Ion, 534c. 21. Plato, Epinomis, 957c. 28. Cf., Gradmann, "Grammatik," in August Friedrich von Pauly and Georg Wissowa, eds., Realencyclopijdie der Idassischen Altertwnswissenschoften Vol. VII (Stuttgart: Druckenmuller, 1912). Material for the following considerations is also taken from: Heimich Kuch, PhiloioglU. Untersuchlmgen eines Wortes von seinen ersten Anfdngen in der Tradition bis ZIU ersten iberlieferten lexikalischen Festlegung (Berlin: Akademie-Verlag, 1965. 29. See: Quintilian, The Institutio Oratoria of Quintilian, Vol. I, ed. H.E. Butler (London: Loeb, 1960), chapter 1 of book 2; and Ibid., Vol. IV, chapter 1 of book
12.
30. GA. Press, The Development of 1M Idea of History in Antiquity, (Kingston: McGill-Queen's University, 1982). Its discussion of 'mstoria' is the counterpart to the discussion of 'philologia' in the above cited book of Kuch. 31. August Boec~ Enzyklopiidie IU&d Methodenlehre der Philogischen Wissenschoften, ed. Bratuscheck (Leipzig: B.G. Teubner, 1877), pp. 93 ff.; translated in abridged form by 101m Paul Pritchard as On Interpretation and Criticism (Norman: University of Oklahoma, 1968), pp. 76 ff. Cf., also Thomas Bitt, Hermeneutik IU&d Kritik, Handbuch der Klassischen Altertwnswissenschoften, ed. I. MUller (MuncheD, C.H. Beck), Vol. I., Abtlg. 3. 32. Press, TIu! Development of the Idea of History in Antiquity, pp. 123-124 in the conclusion. 33. Kuch, Philologus, pp. 75, 100 ff. 34. See: Sextus Empiricus, Against the Professors, 00. R.G. Bury (London: Loeb, 1949), Vol. IV. See also: Sextus Empiricus, Outlines of Pyrrhonism (London: Loeb, 1955), Vol. I, especially chs. 4-6. 35. Cf., Karl Reinhard, Poseidonios (M1lnchen: C.H. Beck, 1921); and Leo Strauss, PhUosophie und Gesetz (Berlin: Schocken, 1935), pp. 87 ff., esp. p. 118. The second level myth tells us that in the beginning all people were good and followed the will of God. Later with the increased number of men evil spread out, and finally only very few just people were left. To these God gave the art of writing and they wrote down what is good and true. But they could not address the
30
THOMAS M. SEEBOHM
unjust and uneducated rabble directly. They had to tell the truth in the disguise of myths in order to be understood. 36. Eusebius of Caesarea, Praeparatio Evangelica, Lib. XIII, caput 11, 12, Migne PO XXI, pp. 1095 ff. reports that Aristobul created the new version of the myth according to which the time of Noah and his children was the time of old when all people were just The last just men were the prophets, and the Greeks learned all their wisdom from the prophets or from the Egyptians, who in tum learned it from the prophets. This tradition was still alive in the eighteenth century. Cf., Johann Jakob Brucker, Historia Critica philisophiae a mundi incunabilis ad nostram ~tam dedu£ta, Vol. I (Leipzig: Breitkipf), pp. 1741-44. 37. For a formal defInition of 'hairesis', cf., Johannes Darnascenus, Dialectica, Migne PO vI. 94, 657. It is already the leading principle of Eusebius of Caesarea, Historia Ecclesiae, Migne PO XX. 38. The new crisis announces itself as early as Abelard's four rules for the treatment of contradictions, the sic et non in the tradition. Cf., M. Grabmann, Geschicte der Scholastischen Methode (Freiburg im Breisgaie: Herdersche Verlagshandlung, 1911), Vol. II, pp. 200 ff. The main source for the new types of higher interpretation is Thomas Aquinas, Summa Theologiae, Pars I, Quaestio I, Art. 10. Cf., E. v. Dobschtitz, Vom vierfochen Schriftsinn. Geschichte einer Theorie, Beitrage ZlU Kirchengeschichte (Leipzig, 1921), pp. 1-13. 39. See: Press, The Develop11U!nt of the Idea of History in Antiquity, Section V, pp. 89-119 for more material on this topic. 40. It is the conception of the 'Holy Roman Empire' first developed in the Byzantine chronicles written by monks after Justini~ e.g., by Georgios Hannatolos. 41. See: Thomas Aquinas, Summa Theologiae, Pars I, Quaestio 1, Art 10. 42. See, for instance: Nikolaus de Lyra, Biblia sacra cum glossa ordinaria ... et Postilia Lirani Franciscani. Opera et studio Theologorum Duacensium, T. IV, Antverpriae apud Joannem Meurium, Anno M DC XXXIV. 43. For the following passage, cf., Dilthey, Selected Writings. 44. About the sources, cf., Emilio Betti, Allgemeine Auslegungslehre als Methodik der Geisteswissenschaften (fUbingen: Mohr, 1967), (abridged German version of the Italian original Teoria genoale della Interpretazione (Milano: Giuffre, 1955). For a discussion of the justifications of the validity of this canon, cf., the material mentioned in notes 25, 23 above. 45. Cf., E.R. Curtius, Ewopiiische Literalur und Lateinisches Mittelalter, 3rd ed. (Munich: Bern, 1962), pp. 47 ff. about Martianus Capella. More material is given in: Kuch, Philologus, pp. 128 ff. 46. Cf., Hans-Georg Gadamer, Truth and Method (New York: Seabury, 1975), p. 162 about Chladenius. 47. Hegel's Phenomenology of the Mind must be understood as a significant document of a stage in the development of hermeneutical consciousness in the sense in which this term has been introduced in this essay. 48. See: Dilthey, Selected Writings, pp. 229, 253. Cf., Gadarner, Truth and Method, pp. 144, 173-187 about the 'dialectic' between Hegel and the so-called 'historical school' in Germany. 49. See: Gadarner, Truth and Met~ p. 187. 50. Cf., Boeckh, Enzyklopiidie IUId Methodlehre der Philogischen Wissenschaften, pp. 52 ff., 43 ff. (Pritchard 35 ff.) 51. See: Boeckh, Enzyldopiidie IUId Methodenlehre tIer Philogischen Wissenschaften, p. 241. Cf., Seebohm, "Boeckh and Dilthey," p. 24 about page 157 of the English translation by Pritchard
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52. The common root is medieval Averroism which: (1) is the consequence of a cultural contact; (2) represented an Aristotelian naturalism; and fmally (3) developed the theory of a double truth- the truth of faith which depends on will and the scientific truth which depends on reason. This Latin version does not correspond to the original Arabic and Jewish tradition in which 'faith' was for the rabble and 'science' for the few wise men. Cf., note 35 above about the roots of this version. 53. The concept stems from Dilthey; see, for example: Diithy, Selected Writings,
p.229. 54. About the 'lower levels' of hermeneutics, cf., Seebohm, "Boeckh and Dilthey," pp. 91-92, 97-98. 55. Recent literature restricts itself in many cases to the discussion of interpretation and application. Traditional methodical hermeneutics and its sources reveal a more complex pattern in which 'explication' plays a significant role, cf., Ibid., p. 90. 56. Cf., Dilthey, Selected Writings, p. 230. 57. Hegel as well as Marx - and nowadays Heidegger as well as Derrida - give us accounts of history as a whole and its meaning. 58. Positivistic historism's use of the word 'metaphysical' is taken over from Kant's concept of special metaphysics and means an acco\Dlt of history as a whole, i.e., what was called 'historicism' by Popper, cf., note 5 above. In this sense, Derrida is 'metaphysical'. 59. See: Gadamer, Truth and Met~ p. 178 about Ranke. 60. See: Thomas M. Seebohm, "Historische Kausalerklirung," in Gunter Posch, ed, Kausalitiit, Neue Texte (Stuttgart: Reclam, 1981), pp. 260-288. 61. Thomas S. Kuhn, The Structure of Scientific Revolution (Chicago: Chicago University, 1962) faced the problem of relativism in the theory of science after his attempt to ground theory of science in historical research! 62. Namely: Gadamer, Truth and Method. 63. See: Ibid., pp. 336, 356. 64. See: Ibid., p. 264. 65. See: Ibid., p. 305.
ENTAILMENTS FROM 'NATURALISM = PHENOMENOLOGY' JOSEPH MARGOLIS
I. Introduction We intend, here, to support a heterodox thesis and, by extension from it, a whole series of further heterodoxies. The thesis maintains that 'naturalism = phenomenology', and the argument in its favor claims that it is well-nigh ineluctable. What follows from it is quite remarkable, so its defense should be examined with some care. The relationship between naturalism and phenomenology has, of course, been memorably mapped by Edmund Husserl in a way completely opposed to the equation given, mapped also with a sense of genuine foreboding that would have regarded its defense as little more than the mad courting of conceptual disaster. Nevertheless, the equation is defensible- and strategically important; and, it may be claimed, the entire movement of contemporary Western philosophy is effectively committed (reasonably committed) to its support, including the work of a good number of phenomenologists. If it were read in a suitably comprehensive way - as addressing the entire nmge of first-order knowledge: roughly, knowledge of the real world that includes physical nature and human minds and human culture; or, possibly, what is true, where what is 'true' may not (on a theory) accord with what is merely 'real', may, instead, address another 'world' entirely (the 'worlds' of logic or geometry or arithmetic or the 'meal' world Husserl dabbled in 1) - then a very large number of powerful theorems may be shown to follow directly from our equation. At the risk of excessive compression, then, we may effect an important economy.. The argument to be considered goes more or less as follows. If naturalism = phenomenology, then (1) ontological and epistemological questions cannot be disjoined, (2) frrst- and second-order cognitive aptitudes cannot be disjoined, and (3) all forms of cognitive privilege foundationalism or logocentrism - must be abandoned;2 and if (1), (2), and (3) hold, then (4) knowledge of reality and truth cannot be disjoined.
'NATURALISM
=PHENOMENOLOGY'
33
ll. First-order and Second-order Powers If we admit that the real world is cognizable as it is independent of human inquiry, or if we admit that human agents are capable of knowing what is true of that world or of a world altogether independent of their minds and of the real or natural world itself, or if we admit that human agents are capable of knowledge of the real structures and properties of a world they themselves constitute, that is nevertheless not merely an artifact of some particular inquiry or flight of imagination - these alternatives being hardly equivalent to one another - then there are only a limited number of conceptual strategies by which to ensure, in part or whole, that human agents can achieve the knowledge they would thus pursue. That is, there are only a limited number of strategies if the ones required are supposed to be cognitively sufficient in first-order terms. Call any such strategy privileged, in the sense that a second-order assurance of such frrst-order knowledge is taken (somehow) to be entailed in or abstractable from a given ftrst-order cognitive competence. When the source of assurance lies in a reflexively detectable feature of fIrSt-order experience or cogniscent reports or the like, the legitimating argument may be said to be foundationalist; and when it does not depend on such a feature but can be counted on nevertheless, the legitimating argument may be said to be logocentric. 3 The logocentric may, then, be said to include the foundationalist commitment and more. Foundationalist and logocentric arguments may be as arbitrary as you please, but in principle they suppose that our fIrSt-order inquiries somehow provide a basis for our second-order assurance; they suppose that, distributively, fIrSt-order claims of determinate sorts either ensure knowledge directly or provide the best, or at least a viable and privileged, source of or constraint on the body of knowledge. W.V. Quine, for example, in the very process of repudiating the pertinence of intentional complications with regard to the prospects of any rigorous empirical science,4 clearly proceeds in a logocentric (but not in a foundationalist) way- in a way, in fact, that has dominated most of Anglo-American theorizing about knowledge and science for nearly forty years. It would certainly not suit Quine to acknowledge only that his own regimented brand of extensionalism was entitled to an epistemological inning. Quine clearly intends to discharge intentionality as utterly irrelevant epistemologically: "If we are limning the true and ultimate structure of reality," he says - and he means what he says - "the canonical scheme for us is the austere scheme that knows no quotation but direct quotation and no propositional attitudes but only the physical constitution and behavior of organisms."' It is possible that Quine is registering here an altogether undefended prejudice. But it is difficult to believe that reading in the face of his sustained interest in the puzzles of knowledge and science, his persistent efforts over an entire career to entrench his extensionalism, and the ve adhered to his apparent seriousness with which his man allow
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instruction. For the moment, our interest does not concern such maneuvers and countermaneuvers. It rests rather with the plain fact that the requisite fast-order competence is taken to be a natural capacity of the members of human communities: to form, codify, discipline, enlarge, confmn, even improve those relatively systematic collections of claims that they are pleased to treat as the core of the various sciences. Our concern, we may say, is almost nosological. The would-be legitimation of fust-order knowledge (or of somces of knowledge) is, trivially, a second-order matter. ·When the required assurance is taken to instantiate a specifically cognitive aptitude of its own, legitimation is (as remarked) either foundationalist or logocentric. When it is not - that is, when the legitimation of frrst-order cognitive competence is itself denied any special competence (when it is denied cognitive 'privilege', when it neither applies distributively nor relies on fast-order evidence when applied holistically) - it functions (we may say) in the pragmatist manner. It is conceivable (but indefensible) to favor [rrst-order cognitive competence and to deny the pertinence or eligibility of second-order legitimation. For such a maneuver either installs, logocentrically again, some fIrst-order aptitude (and so violates the pretended repudiation of second-order arguments) or it abandons every rntional concern regarding the compared relevance and power of competing would-be resources. This second policy (segregating frrst- and second-order inquiries) has also come to be called pragmatism- largely through the recent efforts of Richard Rorty. Pragmatism in this second sense calls for an end to traditional philosophy, on the grounds that any legitimating inquiry cannot fail to be logocentric. Pragmatism in the frrst sense - in denying privilege but pursuing matters of legitimation - cannot but tend in the direction of holism, internalism, historicism, relativism, and an emphasis on the role of praxis. (We need not return to the details of that story.') What concerns us rather is that both logocentric and pragmatist forms of legitimation are construed naturalistically, that is, as involving no cognitive powers other than those entailed or embedded or exercised in, or assignable to, the native capacities of human investigators. (They involve no cognitively greater titans or gods, no revelations.) Needless to say, the first-order powers admitted as cognitively apt on pragmatist grounds are apt only in the sense of salience, not of privilegethat is, only in the sense of what, provisionally, perspectivally, reflexively, in a way internal to the very achievement to be accounted for, appear to be the most promising candidates (for the time being) for the explananda required. They are subject to revision or replacement for all sorts of reasons having to do with how salience itself may be altered over the range of historically shifting experience and within the equilibrative, diachronically deployed pressures of trying to match our picture of the real world and our picture of our cognizing powers apt for producing that picture. The importance of admitting salience is just that it precludes privilege and acknowledges the profound transience and contingent stability of what, in
'NATURALISM
=PHENOMENOLOGY'
35
terms of the implicit consensus of actual societies pursuing inquiries of high discipline, appears to them to be their science and cognitive power. In short, the validity of our second-order legitimations is an artifact of the relative stability of our informal saliences, which are themselves, quite frankly, affected by our own ongoing efforts at science and legitimation. So doubts regarding the force of legitimation cannot escape applying with equal relevance to the ftrSt-order standing of our scientific accomplishments. By the same token, endorsing the latter as at least sufficiently reliable and promising so that we may press on with our fIrst-order work is tantamount to endorsing the legitimacy of legitimation. In a word, legitimation need not (and does not here) presuppose privilege or risk its constitutive and regulative function in abandoning privilege. Once we see matters in this light, it proves surprisingly easy to demonstrate that there is no principled division or disjunction of an epistemically pertinent sort between what may be legitimated as naturalism and as phenomenology. This goes entirely contrary, of course, to the main theme of Husserl's master project, which, in a very real sense, could be said to be focused on ensuring the most profound disjunction possible between naturalism and phenomenology. To press the 'correction' against Husserl is to side with a good many who have been perceptibly influenced by Husserl's own attempt to correct naturalism's pretensions of privilege. It is to side, to a considerable extent, with the programmatic intentions of Heidegger, Merleau-Ponty, Sartre, Derrida, and (stretching things some) Gadamer- insofar as those theorists mean to pursue phenomenological corrections of a naive naturalism; but it is also to insist on the obvious convergence (not necessarily intended) between their (quite varied) programs and such others (also eschewing logocentric advantage to one degree or another) that have evolved, for example, from American pragmatist sources (from Peirce and Dewey and James and Quine), from Continental Hegelian and Marxist and Frankfurt Critical sources, and, of course, from Nietzsche and his most recent adherents (Derrida and Foucault, in particular). For the essential criticism made of Husserl - by this time, almost banal though it is assuredly still effective is simply that, in correcting the pretension of privilege among the naturalists, Husserl failed to admit (indeed, resisted to a preposterous extent) the plain fact that the validity of that correction could not but extend to the further (cognate) pretensions of phenomenology as well. Husserl apparently 'did not understand' what he was doing in demonstrating that the naturalists did not understand the limitations of their own undertaking.7 This is surely the neatly focused message of Merleau-Ponty's 'adjustment' of Husserl's theme. (We may allow it to stand proxy for the convergent intent of the rather different figures just mentioned.) The perceiving mind [says Merleau-Ponty] is an incarnated mind I have tried, first of all, to re-establish the roots of the mind in its body and in its world, going against doctrines which treat perception as a simple result of the action of
36
JOSEPH MARGOLIS external things on OlD' body as well as against those which insist on the autonomy of consciousness [that is against empiricism and rationalism as forms of naturalism or objectivism]. These philosophies commonly forget - in favor of a pure exteriority or of a pure interiority - the insertion of the mind in corporality, the ambiguous relation which we entertain with our body and, correlatively, with p:rceived things.'
It is a message reinforced in the opening lines of Phenomenology of
Perception: What is phenomenology? ... Phenomenology is the study of essences; and according to it, all problems amount to rmding defmitions of essences: the essence of perception, or the essence of consciousness, for example. But phenomenology is also a philosophy which puts essences back into existence, and does not expect to arrive at an understand.ing of man and the world from any starting point other than that of their 'facticity'. It is a transcendental philosophy which places in abeyance the assertions arising out of the natural attitude, the better to understand them; but it is also a philosophy for which the world is always 'already there' before reflection begins- as an inalienable presence; and all its efforts are concentrated upon re-achieving a direct and primitive contact with the world, and endowing that contact with a philosophical status.'
Merleau-Ponty's intended corrective exhibits the necessary tact and subtlety of functioning as a corrective within the pale of Husserl's own deeply admired endeavor. It may be instructive, therefore - for a reason which will gradually become clear - to juxtapose without elaborate preparation a rather famous if somewhat primitive (but characteristic) remark of John Dewey's (already refined, in 1938, from earlier speculations going back before the tum of the century) that clearly converge (innocently) with the deeper intent of Merleau-Ponty's pronouncement but without having to work through the unfortunate disjunction Husserl imposed on his followers. It shows at a stroke the obvious, the marvelously simple, sense (within the American pragmatist movement) in which naturalism could be said to be 'phenomenologically' constrained (natively) without ever having to pass through an official correction. In context, the passage in question was intended by Dewey to concede the preformational and incarnate biological and social world within which human inquiry cannot but proceed, the horizonal and contingent nature of its every effo~ the place it affords withal for a viable logic and science, and (perhaps most important) the respect in which standard (otherwise logocentric) oppositions between cognizing subject and cognized world are already treated by Dewey as no more than abstractly posited within what (mythically) precedes such oppositions. The linkage with Heidegger's myth of Sein and Dasein is plain enough; it supplies the reason for linking Dewey and Merleau-Ponty as well. tO The remark itself is drawn from Dewey's Logic:
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Inquiry is the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole. 11
Dewey's essential point - one must bear in mind how early relative to phenomenology it was made - is that "the unsettled or indetenninate situation might have been called a problematic situation [and that, existentially, it is] precognitive."12 The full import of these remarks remains still to be drawn out: they may actually be a little surprising. But for the moment it is perhaps enough to exhibit the unintended convergence between a 'phenomenologized' naturalism and a 'natumlized' phenomenology. For, by the partly mythic, partly naturalized device of the 'problematic situation', Dewey genuinely intends to risk the fixity of every would-be structure of an 'independent' world (including whatever, of would-be inquiring agents, is similarly 'independent' of or prior to their explicit inquiry); and, in doing that, he has surely avoided and completely bypassed the unnecessary traffic of the whole of official phenomenology. Clearly, Merleau-Ponty means to offset the idealist and solipsistic possibilities that, though never intended by Husserl, invariably beckon from some point deep within Husserl's theory. Nevertheless, it is Merleau-Ponty himself, who, 'adjusting' Husserl, still insists - ambiguously - that "the world is always 'already there' before reflection begins-- as an inalienable presence": so that all the efforts of philosophy "are concentrated upon re-achieving a direct and primitive contact with the world, and endowing that contact with a philosophical [that is, with an epistemically pertinent] status." Merleau-Ponty may have meant this in the "pragmatist" sense (or in a sense very much like it- holistically and mythically). That certainly would not be an unfair reading of a related, late manuscript entry: ttWe will not admit a preconstituted world, a logic, except for having seen them arise from our experience of brute being, which is as it were the umbilical cord of our knowledge and the source of meaning for US."13 SO construed, the passage represents Merleau-Ponty's thoroughly un-privileged (mythic) speculation about the conceptual connection between the 'presence' of an unnamed and unnameable brute world - 'there' prior to our objectifying inquiries - and the valid work of those same inquiries, also (ambiguously now, as the activity of 'mobile bodies') precognitively 'located' in that same brute world But the question still nags, whether and to what extent the 'lived body', the 'embodied subject', the original percipient source of science, is, as the very center of consciousness (not in the idealist's manner) also and for 'that reason the 'source' of the cognizable world that surrounds it "The whole universe of science," Merleau-Ponty remarks, "is built upon the world as directly experienced, and if we want to subject science itself to rigorous scrutiny and arrive at a precise assessment of its meaning and scope, we must begin by reawakening the basic experience of the world of which science is the second-order expression." "I am [he adds] the absolute
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source, my existence does not stem from my antecedents, from my physical and social environmenl..[it is through that original] consciousness, through which from the outset a world forms itself round me and begins to exist for me. To return to things themselves is to return to that world which precedes knowledge, of which knowledge always speaks, and in relation to which every scientific schematization is an abstract and derivative language.... tt14 Here, it is difficult to avoid the conclusion that, in an impossibly gymnastic way, the 'second-order' pronouncements of science are somehow to be reconciled (in a cognitively pertinent way) with the precognitive but (seemingly) distributed encounters of 'primary' perception. Otherwise, why say that science 'speaks' of the things of the 'world which precedes knowledge', and why mention the semiotized 'relation' holding between the two? It is true that Merteau-Ponty insists that "our relation to the [originally perceived] world is not that of a thinker to an object of thought, tt and yet he explicitly says (and means) that the analysis of primary perception is essential to psychology (possibly to all the sciences, though, here, he hedges - inconsistently - under questioning).1' There is reason to believe that Merleau-Ponty did not resolve this difficulty- could not (and, in a way, did not want to). FOf, in insisting on the continuity of science and philosophy and on the continuity of science and primary perception, he characterizes science as a second-order coding and systematization of whatever is given (albeit precognitively) in primary perception; and that makes no sense unless what is thus given (in a 'fust-order' respect) bears in a cognitively pertinent (recoverable) way on our science. It is partly for this reason that he assigns intentionality to the 'lived body' functioning below the level of explicit consciousness. He opposes innatism, but already in the primary biology of the human organism Merleau-Ponty finds a need for a somewhat equivocal vocabulary that is not yet fully 'mental' (or behavioral in the mentally informed sense) but that still requires a mode of perception and experience that may serve to fix the 'frrst-order' intentional life that discursive consciousness and science 'refer' to in their 'second-order' way. So he says, at the very close of The Structure of Behavior, "The natural 'thing', the organism, the behavior of others and my own behavior exist only by their meaning; but this meaning which springs forth in them is not yet a Kantian object; the intentional life which constitutes them is not yet a representation; and the 'comprehension' which gives access to them is not yet an intellection. "16 This may serve to clarify the essential equivocation (not inadvertence) of one of Merleau-Ponty's characteristic pronouncements: "Our own body is in the world as the heart is in the organism: it keeps the visible spectacle constantly alive, it breathes life into it and sustains it inwardly, and with it forms a system. "17 Nevertheless, the existentialized phenomenology is meant to support an opposition to every form of cognitive privilege-- what we have unceremoniously associated with Dewey's seemingly thinner theme. The irony is that it is Dewey's pronouncement that is the clearer of the two and that helps us to extricate Merleau-Ponty from his own dilemma: here,
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naturalism hurries to the rescue of phenomenology. The intentionality of the lived body need not be compromised; it must, however, either be raised to a mythic pronouncement (like Heidegger's or Foucault's) or else it must descend to the pronouncements of a tempered naturalism 'critically' informed by that myth (as in Dewey's solution). But in favoring the better alternative, we must not devalue or defuse Merleau-Ponty's equivocation. On the one hand, he asserts that "my existence does not stem from my anteeendents, from my physical and social environment" and, on the other, that "Our own body is in the world as the heart is in the organism"; on the one hand, he affirms our presence in a "world which precedes knowledge" and, on the other, speaking of his notorious glass cube, that it is "by conceiving my body itself as a mobile object [in that world] that I am able to to interpret perceptual appearance and construct the cube as it truly is."IB Viewed in the manner favored, phenomenology is a naturalism shorn of its own logocentric pretensions and attentive (especially) to the preformative conditions under which all inquiry proceeds; and, similarly viewed, naturalism is simply phenomenologized. The intended reconciliation is meant to be comprehensive: there is nothing left that, in principle (though not, of course, in determinate detail), needs to be added in order to ensure the viability of the frrst- and second-order epistemic concerns with which we began. Deconstruction, therefore, is merely the ultimately attenuated instruction of any such reconciliation: that is, the instruction that every particular such reconciliation is. subject to the future supplement of a now-unfathomable future such adjustment; that the conceptual relation between the one and the other is and must remain opaque yet effective; that there is no sense at all to pretending to be able to project mtional sunnises of continuity, progress, verisimilitude, or totalizing based on cognitive sources external to the contingent work of just such surmises; and that every such surmise is, if internal to such work, fatally 'infected' by an absence of privilege. In effect, these considerations mark the almost unnoticed common error of such varied projects as those of Peirce, Quine, Chisholm, Popper, Gadamer, Habennas, Apel- and Husser!.1'
III. Constraints on Phenomenology Now, then, what are the benefits of all this? Husserl had resisted the simple conclusion that naturalism = phenomenology, for the double reason that he (rightly) saw that naturalism could claim no cognitive privilege and that he (wrongly) supposed that phenomenology could. There are really three essential strategies on which Hussed and Merleau-Ponty diverge in this regard (taking Merleau-Ponty as proxy for all the reconciling maneuvers intended by our partial list of favorable movements and figures provided just above). These are centered on: (1) cognitive 'voices' or sources; (2)
\intentiOnal or propositional content; and (3) dependencY__Ol'_~()Il~_gency
on.
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preformational processes. A glance at the passages cited from Merleau-Ponty confrrms that, for Merleau-Ponty, it is the same incarnated and 'enworlded' mind that pursues natumlized perceptual truths and processes them phenomenologically; and that that dual enterprise is 'factically' encumbered by the same Lebenswelt within which humans live and exercise these abilities. Merleau-Ponty, therefore, opposes any principled or privileged disjunction of cognitive voices between the naturalist and the phenomenologist (1), although, as we have seen, he introduces a further, uneasy complication. He also opposes any pretense that phenomenological inquiry can escape the constructive role of the existential preconditions of 'primary' or 'lived perception' (3).20 Furthennore, once his stand on (1) and (3) is declared, it becomes clear that any further distinction regarding the special content of this or that inquiry can neither override the constraints just admitted regarding (1) and (3) nor escape whatever strictures are there imposed. Hence, for Merleau-Ponty, any distinction regarding (2) - even the phenomenological pursuit of essences - will be entirely neutral as regards the disjunction between naturalism and phenomenology. (To be sure, naturalism in Dewey's sense cannot be characterized as even interested in Merleau-Ponty's revision of the Husserlian pursuit of essences, the skillful work of eidetic variations. But the point of linking Dewey and Merleau-Ponty is not to erase such differences but to provide a fair sense in which the special work of the one could be quite easily fitted to the conceptual orientation of the other. In any case, the point of distinction (2) is just that it raises no epistemological issue of its own that would affect our fmdings regarding (1) and (3).) Husserl implicitly opposes all three of Merleau-Ponty's stands and for the same reason. This may be seen, without actually explicating Husserl's entire theory, by juxtaposing two brief remarks of his on the role of the Lebenswelt. First, Husserl says, "Things, objects (always understood purely in the sense of the life-world), are 'given' as being valid for us in each case (in some mode or other of ontic certainty) but in principle only in such a way that we are conscious of them as things or objects within the world-horizon. Each one is something, 'something of the world of which we are constantly conscious as a horizon."21 But then, secondly, he says: Now, how can the pregivenness of the life-world become a universal subject of investigation in its own right? Clearly, only through' a total change of the natural attitude, such that we no longer live, as heretofore, as human beings within natural existence, constantly effecting the validity of the pregiven world; rather, we must constantly deny ourselves this. Only in this way can we arrive at the transformed and novel subject of investigation, "pregivenness of the world as such": the world purely and exclusively as - and in respect of how - it has meaning and ontic validity, and continually attains these in new forms, in our conscious life. Only thus can we study what the world is as the ground-validity for natural life, with all its projects and undertakings, an~ correlatively, what natural life and its subjectivity ultimately are, i.e., pmely as the subjectivity which functions here in affecting validity. The life which effects world-validity in
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natural world-life does not permit of being studied from the attitude of natmal world-life. What is required, th~ is a total transfonnation of [cognitive] attitude, a completely unique, universal epoche.22
Segregating the cognitive voices of naturalism and phenomenology (1) and declaring the one but not the other subject to the preformative influence of the Lebenswelt (3), Husserl moves effortlessly to affirm that the pertinent cognitive pronouncements of particular (naturalistic and phenomenological) sciences are of profoundly different epistemic sorts (2). Husserl's position, then~ depends entirely on his insistence on the cognitive privilege of transcendental phenomenology. He agrees (in effect) with Merleau-Ponty that the epistemic fortunes of (2) depend entirely on the resolution of the matters sorted under (1) and (3); but, for that very reason, Husserl and Merleau-Ponty part company. This bears directly, of course, on Husserl's fundamental criticism of Galileo's geometry and on his own attempt to ground geometry in some transcendentally apodictic, 'primary' or "original meaning-giving achievement which, as idealization practiced on the original ground of all theoretical and practical life - the immediately intuited world (and here especially the empirically intuited world of bodies) - resulted in the geometrical ideal constructions. tt23 It may be, as Merleau-Ponty enthusiastically affmns, that Husserl was seeking "a way between psychology and philosophy- a mode of thinking... which would be neither eternal and without root in the present nor a mere event destined to be replaced by another event tomorrow, and consequently deprived of any intrinsic value." But the characterization is more apt autobiographically. Hence, the following manifesto, possibly one of the most explicit Merleau-Ponty ever offered, points to the essential division between the two: One may say indeed that psychological knowledge is reflection [Merleau-Ponty had just announced that 'Reflection is historicity'] but that it is at the same time an experience. According to the phenomenologist (Hussed), it is a 'material a priori'. Psychological reflection is a 'constatation' (a finding). Its task is to discover the meaning of behavior through an effective contact with my own behavior and that of others. Phenomenological psychology is therefore a search for the essence, or meaning, but not apart from the facts. Finally this essence is accessible only in and through the individual situation in which it appears. When pushed to the limit, eidetic psychology becomes analytic-existential. 2A
So seen, the 'primacy' of perception is meant to account (holistically) for the (mythic) origination of a phenomenologized naturalism within the space of an existential, precognitive presence in the world, and to permit and enable an (internalist) recovery of whatever, reflectively, can appear as the (existentially) thus-encumbered essences or meanings within the flux of experience. Ultimately, therefore, Merleau-Ponty refuses Husserl's "total change of the natural attitude."
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What, however, is an unexpected bonus resulting from this otherwise curious review of the convergence and opposition of naturalism and phenomenology is the illumination (and resolution) of Husserl's famous diatribe against psychologism. Given (1)-(3) and the divergence between Husserl and Merleau-Ponty (and the mild promise of Dewey's seemingly thinner naturalism), the puzzle of psychologism cannot but prove shallower (in one sense) than Husserl supposed and incapable (in another) of a resolution favorable to his own extreme philosophical program (or to Frege's). Furthermore, even that profound issue proves, quite transparently, to be only one among a large family of expanding questions that the reconciliation of naturalism and phenomenology entails. These matters should prove instructive. Before turning to them, we need to remind ourselves that, in Husserl, one fmds all the principal forms of cognitive privilege, both foundationalist and logocentric. These include Husserl's reliance on: (a) the apodictic (self-disclosure yielding unconditional cognitive certainty); (b) the originary (assurance regarding the ultimate source on which correspondence, essences, the epistemic link between the possible and the actual and between the necessary and the contingent depend); and (c) the totalized (achievement of the conceptual closure within which every considered possibility is related to the inclusive system of all such possibilities). Ultimately, for Husserl, these three are only different aspects of one and the same transcendental source of epistemic assurance.2S It makes no difference that Husserl concedes (in a sense) the provisional, step-by-step, 'infinite' exercise of what is required by his own notion of transcendental phenomenology. No such concession ever blunted, for Husserl, the full accessibility and necessity of the transcendental leap itself: Instead of this universal abstention in individual steps [in effect, the naturalized approximation of the epoche Husserl requires], a completely different sort of universal epoche if possible [he insists], namely, one which puts out of action, with one blow, the total performance running through the whole of natural world-life and through the whole network (whether concealed or open) of validities- precisely that total performance which, as the coherent 'natural attitude', makes up 'simple' 'straightforward' on-going life.... An attitude is arrived at which is above the pregivenness of the validity of the world, above the infmite complex whereby, in concealment, the world's validities are always founded on other validities, above the whole manifold but synthetically unified flow in which the world has and forever attains its content of meaning and its ontic validity.26
Through the 'liberation' thus effected, one can and does (that is, "the philosopher [now] situated above his own natural being and above the natural world"27 can and does) discover "the universal, absolutely self-enclosed and absolutely self-sufficient correlation between the world itself and world-consciousness. "28 It is only this extraordinary great gasp of Husserl's that makes one uncertain of just how much (later)
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phenomenologists are willing to admit regarding the convergence between naturalism and phenomenology. Also, to retreat from Husserl's extreme position (to suggest even that Husserl himself relented) is to make utter nonsense of his own anti-psychologism. If we assume the force of our original equation, such a strategy would completely subvert the entire purpose of the transcendental function of Russerl's phenomenology. That is why, to risk a sly conjecture, the good-humored simplicity of Dewey's pragmatism (itself a de-privileged, de-Iogocentric, precipitate of Hegelianized 'phenomenology') is enjoying such an inning at the present moment (The recovery of William James was rightly bound to follow.~ We are not here concerned with the vagaries of why Husserl - or, in his own way, Merleau-Ponty - obscures the convergence indicated. The important thing is to draw out its lesson. This surely includes at least the following: (i) that naturalism un-phenomenologized cannot fail to be logocentric; (ii) that phenomenology un-naturalized has no epistemic relevance whatsoever, and where it supposes it does it cannot fail to be foundationalist; and (iii) that, given (i) and (ii) - in effect, the symbiosis of frrst- and second-order knowledge - all science, the fruits of all acknowledged inquiry, cannot fail to be psychologized (psychologistic). Admittedly, these are rather cryptic fmdings, but they have a surprising force. For one thing, (i) signifies that any frrst-order inquiry that posits an epistemically pertinent relationship between cognizing subject and cognized object or world, that is itself not construed holistically in the pragmatist manner as a precognitive artifact of the structuring power of the Lebenswelt within which we come to occupy such a cognizing role, posits to that extent an initial or privileged transparency or correspondence or similarly favorable preharmony in virtue of which such frrst-order work succeeds as it does. This is, in fact, just the critical theme that Merleau-Ponty and Dewey explicitly enunciate and unwittingly share: in Merleau-Ponty, the 'relation' between 'primary' and 'reflective' experience; in Dewey, that between affmning the 'problematic situation' and rejecting the 'spectator' theory of perception and knowledge.30 It shows not only: (i-a) that any adequate epistemology must take the form of a realist/idealist symbiosis, but also (I-b) that that symbiosis must be phenomenologically encumbered. Kant ultimately fails to escape the logocentric predicament, though he does take the fIrst step; he fails to question the conceptual preconditions for the transcendental arguments he sought to refme over an entire lifetime. It is an irony that Husserl takes the second step but converts it at once into a new Cartesianism; Husserl simply places the Transcendental Ego beyond the life-worldly encumbmnces of the natural, the empirical ego. What (ii) signifies, then is that phenomenology has no other function but to experiment, within the life-worldly constraints of naturalistic science, with the conceptual variability of whatever saliently appear as the encumbering limitations, distortions, prejudices, interests, habits and the like that (precognitively) affect the cognized horizons, invariances, regularities, universalities, necessities, essences, laws, rules, theories, principles,
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categories, concepts, and systems of concepts with which we organize the body of our particular disciplines. (The point may be usefully intruded, here, that Bertrand Russell's demonstration of the fatal paradox of Frege's original logicist account of arithmetic - the rightful mate and source of Husserl's anti-psychologism - decisively demonstrates that, even in the world of numbers [Frege's 'third realm'], one cannot count of the required measure of self-evidence both Frege and Husserl needed for their respective versions of anti-psychologism.'l) It takes but a step, therefore, to see that, once the reciprocity of (i) and (ii) is acknowledged, there is no principled second-order difference to be made out in legitimating the 'critical' first-order functioning of Hegelian, Marxist, Husserlian, Frankfurt Critical, Nietzschean, Wittgensteinian, and pragmatist accounts of the preformative constitution of the subject/object relation: there are only those fIrst-order differences and their (now) de-privileged second-order mates. (Those differences, are, of course, well worth considering.) The reciprocity of (i) and (ii) also signifies that there is no science or serious inquiry except as it is the work of a community of actual inquiring agents (selves) who address their cognizing powers to this or that sector of the world. To paraphrase Kant, naturalism without phenomenology is blind, and phenomenology without naturalism is empty. The reflexive analysis of the prefonnative conditions constituting any inquiry (as the inquiry it is) need be no more blind or empty than the inquiry it purports to examine: indeed, it is that inquiry, seen through the reciprocity of (i) and (ii). (On the argument here advanced, anything less or more pretends to a form of privilege.) What needs to be remembered are: (ii-a) that cognizing subjects (selves) are preformed by their environing world but in ways we can only guess at - reflexively, distributively, always 'prejudicially' (in Gadamer's sense'2J within the holist space of what we take our world to be; (ii-b) that what we take our world to be is, reciprocally, an artifact of what we take ourselves to be as the cognitively apt creatures that we are; and (ii-c) that both of these sorts of conjecture are assignable only to cognizing subjects, who regard themselves as addressing an objective world accessible to their native powers. Since, however, our frrst- and second-order reflections are symbiotically linked - are intentional in that sense - and since, given (i) and (ii), self and world are similarly symbiotized, we may reasonable draw out another element of the dawning lesson: (iv) that science and the legitimation of science cannot be conceptually disjoined. What we regard as the fruitful prospects and determinate promise of our first-order science are, ineluctably, the causal consequence and more of our second-order reflections on the nature of self and world." There you have the precise point of worrying the deep equivocation of Merleau-Ponty's insistence on the 'primacy' of perception and the 'relation' between science and the 'brute' world. There you have, also, the clue to the essential pathos of Imre Lakatos's doomed effort to form, in fIrst-order terms, a linear measure of the inherent promise of scientific research
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programs scrupulously compared across and within any interval of historical work.'" Kuhn's and Feyerabend's discontinuities and incommensurabilities the one meant mildly enough, the other more radically - completely subvert Lakatos's dream, merely by invoking (in their respectively thin ways) the phenomenological (or critical) theme. It may then prove a further economy to add, as a consequence of these last remarks, another strand of the intended lesson drawn from the convergence of naturalism and phenomenology: (v) that (cognizing) self and (cognized) world are never more than historicized referents - possibly discontinously, even incommensurably, certainly relativistically, posited referents - that cannot but be symbiotically linked. That is, what the nature of self and world is and what the cognitive relationship between them is are artifacts of salient truth-claims that, on a theory powered by the very ability to make such claims, supposes every such conjecture to be prefonnatively constituted under diachronically shifting conditions about which we must also conjecture only from the vantage of the other. In a plain sense, therefore, critique is no more than the first-order inquiry (or its second-order legitimation) into the historically prefonnative conditions of any putatively objective, distributed truth-claims engaging cognizing subjects and cognized world- itself similarly affected. Accordingly, psychologism is the second-order theory (or its narrow rust-order application to logic, arithmetic, geometry, transcendental phenomenology) that the legitimation of all such claims must forego any and all forms of foundationalism and logocentrism. It is easy to see that, however unlikely it may seem, critique and psychologism effectively require the same commitment: simply that naturalism = phenomenology (in the sense supplied). Reviewed in terms of these distinctions, deconstruction is nothing but a negative idiom - almost a via negativa - by which (i)-(v) are affmned or at least favorably featured. It is perhaps the most attenuated version possible of a purely (necessarily) mythologized instruction regarding the preformational contingencies affecting the emergence of cognizing subject and cognized world In what may well be one of Jacques Derrida's most felicitous formulations, the 'critical', interventionist function of deconstruction is unmistakable acknowledged: "The incision of deconstruction," he says, "which is not a voluntary decision or an absolute beginning, does not take place just anywhere, or in an absolute elsewhere. An incision, precisely, it can be made only according to lines of force and forces of rupture that are localizable in the discourse to be deconstructed."3S It effectively explains Derrida's resistance to any straightforward Marxist historicism (in his Positions), where historicism (in the French context) is taken by Derrida to conceal some logocentric privilege. But, in doing that, it also demonstrates that deconstruction is the mythologized unity of all fonns of discourse tempered in accord with (i)-(ii). In this sense, deconstruction catches up the hisroricizing theme common to Hegel, Marx, Nietzsche, Husserl, Heidegger, Merleau-Ponty, Lukacs, Gadamer, Habermas, Derrida, Foucault (and Dewey). But the theme itself (in the hands of just
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these theorists) takes a naturalistic form (either logocentrically or not), a phenomenological or critical form (again, either logocentrically or not), and (on occasion) a deconstructive form (one that is purely mythological or ultimately converges with that of the others). Nietzsche's 'will to power' is, undoubtedly, the purest version of an exclusively deconstructive theme. Denida's 'differance' is merely an extraordinarily abstract adjustment of Nietzsche's theme fitted to (and intended to combat) recent preoccupations with structuralism, (Husserlian) phenomenology, Marxism, and historicismall of which are clearly prone to logocentric excess. Foucault's 'power/knowledge' is also a formula derived from Nietzsche but deliberately employed (with consummate skill) naturalistically, phenomenologically (that is, critically), and deconstructively at one and the same time.36 (It is, in fact, just this complexity that has baffled Foucault's commentators and encouraged the simpler but altogether inadequate picture of the straightforward social critic and activist. 37 Furthennore, it cannot (and certainly should not) be denied that Marx's notion of praxis plays a similar double role (critical and deconstruetive) that, within the often opposed phenomenological tradition, is best exemplified by Heidegger's tale of Sein and Dasein (and Derrida's differance)- though, of course, with an entirely different message on its critical side. The double role involves the mythological genesis of symbiotized subjects and objects - cogniscent, subcognitivety mobile (in Merteau-Ponty's sense), technologically active (in Heidegger's) pmxically effective (in Marx's) - and the critically oriented, distributive review and assessment of frrst-order life and work and inquiry informed by the particular second-order legitimating themes Marx happens to favor. Understandably, such a second-order choice will be installed, rhetorically, in the very idiom of the deconstructive mythology preferred, if indeed a deconstructive theme is actually prepared. Clearly, it would not be easy to demonstrate that Marx does work deconstructively, but it is certainly not an unreasonable suggestion. In fact, in a particularly important passage in The German Ideology, in which he specifically criticizes Ludwig Feuerbach's conception of praxis, Marx observes: He does not see how the sensuous world arolDld him is not a thing given direct from all eternity, remaining ever the same, but the product of industry and of the state of society; and, indeed, in the sense that it is an historical product, the result of the activity of a whole succession of generations, each standing on the shoulders of the preceding one, developing its industry and its intercourse, modifying its social system according to the changed needs. Even the objects of the simplest 'sensuous certainty' are only given him through social development, industry, and commercial intercourse.3I
This is certainly a passage that reminds one of the treatment of related themes in the thin naturalism of Thomas Kuhn, the anti-naturalistic phenomenology of Husser!, and the Nietzsehean genealogies of Foucault. It
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may well be that, without acknowledging the 'deconstructive' side of Marx's account of praxis, we risk failing to offset the familiar charge of incoherence so often leveled against him. That charge, tantamount to that of the sociology of knowledge, cannot stand once the subject/object relationship is treated in the historicized and praxicalized way Marx does,,39 Once one concedes incommensurabilities at the conceptual or cognitive level, and once one construes these as historically and praxically generat~ then the usual dilelnma invoked - either incoherence (assuming the privilege of a cognitively fixed stance) or vicious regress (the self-referential stigma of construing knowledge as ideology) - cannot fail to dissolve. The sociological thesis need not, of course, be restricted to the Marxist idiom: it could be deconstructive although Marxist; and it could, as with Foucault, be Nietzschean as well. But we must break off abruptly here, if we are ever to collect compendiously all the issues broached.
IV. The Ineluctability of Psychologism In drawing out the lesson of the convergence of naturalism and phenomenology, we mentioned but did not actually pursue a constituent item of our earlier tally- namely (iii) that science cannot but be psychologized (psychologistic). The meaning of the key term is a source of considerable quarrel. It could, for example, merely mean what it usually means in the naturalistic tradition, as in Quine's Millian conception of logic. On that view, logic, the study of the 'laws of thought', is a sub-study of the psychology of thinking. On Husserl's and Brentano's view, a grasp of the laws or of the necessary, self-evident constraints of logic may well require reflexive attention to the processes of thought in which they are embedded; but the laws are not merely the contingent regularities, or idealizations drawn from the regularities, of those processes. They are not psychologistic in that sense, though they need not, for that reason alone, entail the irrelevance of psychological process: what is reflexively presented (to consciousness, say) may well be (initially) psychological, but what is self-evident or apodictic in what is thus presented may (on an argument) depend on other grounds (psychologically embedded) that may be brought to bear. This is, in fact, Roderick Chisholm's view, partially based on a reading of Brentano's view;40 it could also have accommodated Husserl's view (contrary to Chisholm's intent) if we were (as we are not) prepared favorably to segregate what we had sorted in an earlier tally as (1) and (3), the difference between distinct cognitive sources or 'voices' (in Hussert's account, the empirical ego and the Transcendental Ego) and the affmnation and denial, respectively, of one or the other's being preformatively encumbered by the Lebenswelt. On Chisholm's reading of Brentano - and in his own name - a "person's self-presenting properties...are such that he can be absolutely certain that they are all had by one and the same thing-
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JOSEPH MARGOLIS
namely, himself. "41 On Chisholm's (and Brentano's) view, phenomena or appearances - the 'elements of consciousness' - are intentional: "a phenomenon or appearance is an appearance to something or to some one"; hence, "there is something else to which [a phenomenon, even the phenomenon of being that to which a phenomenon appears] appears only as a phenomenon, and....this something else exists in itself and is apprehended as such."42 The apodictic, therefore, on Brentano's and Husserl's (mature) views, is drawn (on both accounts) from psychological phenomena, is not equivalently or identically construed by them, and is viewed on neither account as psychologistic. As Chisholm summarizes the matter elsewhere, the psychologistic "conception of the truths of logic, if it were tenable [which he holds it is not], would reduce 'reason' as a source of knowledge, to our 'inner consciousness'- Le., reduce [what he earlier identified as] (4) to (3)," namely: 3) 'Inner consciousness', or the apprehension of our own states of mind- for example, our awareness of our own sensations, of our beliefs and desires, of how we feel, of what we are undertaking to do; 4) Reason, as the source of our a priori knowledge of necessity- our knowledge, for example, of some of the truths of logic or mathematics.43
Chisholm's (and of course Brentano's) view would be construed psychologistically by Husser/. It is not so construed by Chisholm himself, apparently because the distinction between his (3) and (4) entails a distinction between any phenomenal content presented to a cognizing self and that self, and because the certitude assigned to the awareness of what is thus presented depends on the selfs reflexive awareness and not on (the mere awareness of) the psychological content of what is presented. On an interesting reading of Frege's anti-psychologism, Mark Notturno holds that all forms of psychologism that Frege opposed (Notturno actually manages to fonnulate four distinct fonns) are committed to the thesis that "truth is... dependent upon the judging subject. "« On Fregean grounds, then, truth is mind-independent: "A third realm [a realm of things other than spatio-temporal physical entities and other than mental ideas] must be recognized. ... The thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the fIrst time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets. "4S Husserl would not be satisfied with Frege's fonnulation - though of course Frege's criticism of Hussert's Philosophy of Arithmetic decisively influenced his own version of anti-psychologism - simply because Frege did not pursue (whereas Husserl required, for his transcendental phenomenology) a disjunctive distinction (as we have already seen) between the empirical ego and the Transcencental Ego. So Hussert's criticism of Chisholm (and Brentano) would have depended on Chisholm's c~~~~!1& _~~ _J~9- _"Yllile __
'NATURALISM = PHENOMENOLOGY'
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preserving apodicticity. The attack on psychologism is, then, neither an attack on the mere ineliminability of psychological sources of the materials on which a priori, apodictic truths are alleged to depend nor a mere affrrmation of the a priori or apodictic as such. This is often not appreciated. Furthennore, as Chisholm goes on to say, to grasp the absolute certainty of a person's self-presenting properties "is the closest [one] comes - and can come - to apprehending himself directly. But this awareness that there is something having the properties in question is what constitutes our basis, at any time, for all the other things that we may be said to know at that time."46 Unfortunately, if the phenomenological or critical theme of preformation is admitted, and if the very nature of the cognizing self is subject, in praxical and historicist terms, to diachronically changing preformational forces, then Chisholm's (and Brentano's) line of argument in effect, Descartes's - cannot fail to be inadequate for any body of science sustained beyond the specious present; and in the specious present, it would be pointless to affirm or deny the claim. The conceptual necessity of assigning the mere 'possession' of conscious states to a cogniscent self (Strawson's rejection of 'no ownership'47) is altogether independent of the apodictic standing of anything therein distributively presented. So there is a fair sense in which Chisholm's recovery of the apodictic is itself subject to the contingencies of the Lebenswelt and, for that reason, is ultimately psychologistic. The quick conclusion suggests itself at once: Frege's 'third realm' is an entirely arbitrary posit, insufficiently motivated philosophically, question-begging; and Husserl's transcendental source of apodicticity is itself simply subject, contrary to his own argument, to the prefonnative forces of the Lebenswelt. If so, then there is no escape from psychologism. More than that, one cannot fail to see that the vindication of psychologism is essentially the same as the vindication of the sociology-of-knowledge thesis. Both depend on a clear grasp of the force of historicist and praxicalist concessions within the tenns of our original equation. The naturalistic, therefore psychologistic, view is explicitly favored, confessedly under Quine's direct influence, by Gilbert Harman. Psychologism, on Harman's view, maintains that "the valid principles of inference are those principles in accordance with which the mind works,ft that is, the principles involved in "the working of the mind when nothing goes wrong: how it works ideally:'48 Harman's notion is that induction is the psychological process of ftinference to the best explanatory statement" yielding, in real-life terms, what may be called 'knowledge of the world'. On that view, there is no 'inductive logic': "Deductive logic is the only logic there is." Induction is inference - mental processing - directed (according to Harman's solution of the problem of induction) "to the best total explanatory account" "Deductive arguments," he adds, "are not inferences but are explanatory conclusions that can increase the coherence of one's view": "There are neither inductive arguments nor deductive inferences. There are only deductive arguments and inductive inferences."49
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For Harman, therefore, "reasoning is a mental process," "mental states and processes are functionally defmed," reasoning itself is modeled by programs of inference the function of which lies "in giving us knowledge," and deductive arguments assign "an abstract structure consisting of certain propositions as premises, others as conclusions, perhaps others as intermediate steps" by which the successful functioning of actual processes of reasoning can be explained- the mapping of the reasoning process can be fitted to what appear to be the ideal formal conditions of success.'O Both because deduction is explanatory of induction and because there are no independent sources of apodicticity that Harman would or could acknowledge, the theory is thoroughly psychologistic. It is worth noting how extremely casual and straightforward is Hannan's reference to 'knowledge of the world', to how the mind works 'ideally' to achieve knowledge, to how deductive logic serves as a theory of the structure of inferential processes yielding in real-life circumstances 'the best total explanatory account' of the supposed events of the world. From Husserl's view, psychologism confuses and conflates the processes of the thinking of empirical egos or natural minds and the 'processing' of certain a priori 'pure ideal truths' (such as 2+2=4 or the law of non-contradiction) "in whose meanings not the least is said about the spatio-temporal, factual world"- whose truth holds "irrespective of whether there is a world or not ,,51 Quine, of course, had rendered the notions of logical necessity and apodicticity inherently problematic for naturalists: by rejecting, in the 'Two Dogmas' paper, any principled analytic-synthetic distinction. Hannan effectively follows him in this, for he abandons the explicit use of the expression 'logical necessity' and insists, without further explanation, on treating 'truth-conditional structures' in a way relativized to given natural languages- but so as not to preclude different such languages from exhibiting the same such structures. Harman nowhere discusses the conditions WIder which such structures are suitably 'idealized'. He merely claims universal scope for a suitable theory: "If all obvious implications could not be accounted for by means of a fmite list of axioms, smoething would be wrong with the theory of logical form. "52 Michael Dummett hints at an additional way of characterizing psychologism, but he does not carry the analysis out sufficiently. The Frege of "Der Gedanke," he says, "launches a renewed assault on psychologism, i.e. the intrusion of appeal to mental processes in the analysis of sense. tt He adds: "in doing so, [Frege] produces his most WIcharacteristic piece of writing: for, in the process, he for once essays a criticism of the idealist thesis that we are aware only of our own ideas, and hence have no ground for believing in the existence of a world external to us. US) The point at stake seems to be just that the domain of sense [Sinn] is not (whatever it is) the same as the domain of sensory experience, of psychological processes, or even of the 'outer' world of normal experience and empirical science. But, as we have already seen, that distinction (our consideration (2» would affect absolutely nothing regarding the apodictic assurances with
'NATURALISM = PHENOMENOLOGY'
51
which Sinn could be examined. Dummett has nothing really to say about that; and, in fact, his own (self-styled) anti-realist insistence on decidability undermines, if it can be construed as relevant at all, any Fregean or Husserlian sources of assunmce.54 Unless we actually link this theme - the specification of the intentional content or 'objects' of logic or arithmetic, what logic or arithmetic is 'a!x>ut' - with some further, nunified theory of the cognizable nature of the world or reality within which such 'objects' may be found, the very question of psychologism simply does not arise at all. In an odd sense, then, on Dummett's line of argument, in spite of what Harman openly declares, Harman does not actually opt for a psychologistic account of logic- in the narrow sense in which he confines logic to certain formal structures that thinking may instantiate in the mental processes of inference. It is only when he subsumes (as, of course, he does) this paired distinction under his more general naturalism that he rightly claims to be advocating psychologism. By a curious reversal, then, Frege remains a psychologist manqUe (for all one knows), in the sense that (like Dummett after him) Frege neglects to explain what the nature of the privileged cognitive competence of man is by which the truths of the 'third realm' may be assuredly grasped." The short conclusion stares us in the face: that either psychologism is quite trivially avoided (by making 100 much of our consideration (2); or it is altogether unavoidable, once the equivalence of natunilism and phenomenology is conceded, once we concede the reciprocity of (i) and (ii) of the tally of the previous section. Item (v) of that same tally now leads us to a further consolidation. For, the point of (v) is just that what is posited as the symbiotized subject and object of cognitive inquiry is an artifact of the historically preformative conditions that we posit in some present interval of just such inquiry. But that, as we saw, is exactly what Marx intended, in explicating (against Feuerbach) his own notion of praxis. Exactly the same lesson could be drawn from what, on its 'critical' side, Heidegger and Foucault intend by the use of their respective myths of Sein and Dasein and ,power!knowledge' . Surprising as it may seem, therefore, the issues of critique and psychologism are essentially the same. By 'critique' or 'critical' philosophy - adhering to (i) and (ii) - one merely means the legitimation of fIrst-order accounts of the preformational conditions under which any well-defmed frrst-order science or inquiry (physics, mathematics, sociology, medicine, law) is said to be so constituted. Phenomenology, then, is simply a particular kind of genemlized second-order theory of such preformational forces- as are, also, Hegelian, Marxist, pragmatist, Nietzsehean, Frankfurt Critical and similar undertakings. Here, then, for sheer convenience, also as a memento of the needlessness of an entire philosophical history, also for the sake of a nice irony, we are deliberately collapsing the distinction between 'phenomenology' and 'critique'- that is, as far as their generic second-order function is concerned, though oot, of course, in terms of their actual fIrst-order claims or in terms of their particular (un-privileged)
52
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second-order policies or in terms of the agonistic roles particular champions may have pursued vis-a-vis one another. One might well say that Karl Mannheim's thesis of the sociology of knowledge, extended, generalized, and (thereby considerably) altered from Marx's original critique of ideology is the affmnative analogue, applied in the human sciences, to what (usually without explicit attention to historicist and praxical considerations) is criticized in the anti-psychologist's attack on psychologism. Mannheim speaks of "the characteristics and composition of the total structure of the mind of this epoch or of this group.ttS(i There is no way to make such specifications coherent without either retreating to a privileged access to a fixed and independent reality (the anti-psychologist's view) or to a frank admission of a serially historicized, preformative passage of cognitive orientations within the horizon of which the pluralized, relativized, potentially incommensurable structures "of the mind of this epoch or of this group" could possibly be said to be detected (the praxicalist's and the critiquer's view). That the latter maneuver places in jeopardy the entire question of what we should mean by objectivity goes without saying: it is in a sense just what Mannheim inherits from Max Weber's unresolved obsession with fixing the objectivity of sociology under the joint conditions of the 'interested' status of presently active human agents and the historical conditions forming those same interests. S7 On the argument here advanced, the retreat to privilege has been cut off and the advance toward a recovered objectivity remains problematic. Be that as it may, we surely see the sense in which no other options lie at hand, and we surely see both the irresistibility and the force of afftrrning that naturalism = phenomenology.
53 ENDNOTES 1. See: Edmund Husserl, ''The Task and the Significance of the Logical Investigations," trans. I.N. Mohanty, in Readings on Edmund Husserl's Logical Investigations, ed. IN. Mohanty (The Hague: Martinus Nijhoff, 1977), 11, 198-199. See also: Gottlob Frege, ''The Thought: A Logical Inquiry," trans. A.M. and M. Quinton, in Essays on Frege, ed. E.D. Klemke (Urbana: University of Illinois, 1968). 2. Many of the detailed analyses and arguments on which the support of our equation depends - suitably independently - are provided in: Joseph Margolis, Pragmatism withou.t Foundations: Reconciling Realism and Relativism (Oxford: Basil Blackwell, 1986). 3. The term 'logocentrism' was coined by Derrida, partly at least in criticism of Husser!. We are using it here more generally. The term appears in: Jacques Derrida, Of Grammatology, trans. Gayatri Chakravorti Spivak (Baltimore: The Jolms Hopkins University, 1976)- see, particularly, ''Translator's Preface." See also: Jacques Derrida, "The Supplement of Origin," in Speech and Phenomena and Other Essays on Husserl's Theory of Signs, trans. David B. Allison (Evanston: Northwestern University Press, 1973). 4. W.V. Quine, Word and Object (Cambridge: MIT, 1960), p. 219. 5. Quine, Word and Object, p. 221. 6. See further: Richard Rorty, Philosophy and the Mirror of Nature (Princeton: Princeton University, 1979); and Richard Rorty, Consequences of Pragmatism (Minneapolis: University of Minnesota, 1982). The discussion is aired in Pragmatism without Foundations and constitutes an important point of contrast affecting the present program. 7. Husserl's own intention and his usage of 'naturalism' and 'phenomenology' are conveniently given in: Edmund HusserI, Phenomenology and the Crisis of Philosophy, trans. Quentin Lauer (New York: Harper & Row, 1965). 8. Maurice Merleau-Ponty, "An Unpublished Text by Maurice Merleau-Ponty: A Perspective of His Work," trans. Arleen B. Dallery, in The Primacy of Perception, ed James M. Edie (Evanston: Northwestern University, 1964), pp. 3-4. 9. Maurice Merleau-Ponty, "Preface," Phenomenology of Perception, trans. Colin Smith (London: Routledge and Kegan Paul, 1962), p. vii, italics added. 10. This, indeed, is very close to the point of Rorty's deconstruetive reading of Dewey (and Heidegger). See: Richard Rorty, "Overcoming the Tradition: Dewey and Heidegger," in Consequences of Pragmatism. 11. John Dewey, Logic; The TJu!ory of Inquiry (New York: Henry Holt, 1938), pp. 104-105. The term 'situation' is somewhat clarified on pp. 66-67. In a class on Dewey's logic that I attended at Columbia University, Ernest Nagel made a great deal of (that is, fO\B1d utterly baffling, utterly untenable) the notion that it was the 'objective situation' that was 'indeterminate'. Nagel preferred assigning the intended indetenninacy, bafflement, uncertainty and the like to the inquiring subject But, of course, Dewey was profoundly opposed (avant la lettre) to the 'logocentric' implications of the simple, relatively constant relationship between subject and object. For an early anticipation of the doctrine of the Logic, actually directed against Peirce, see: John Dewey, 'The Superstition of Necessity," in John Dewey, The Early Works. 1882-1898 Vol. 4, 00. 10 Ann Boydston et ale (Carbondale, TIL: Southern Illinois University, 1972); and John Dewey, ''The Reflex Are Concept in Psychology," in Vol. 5 of the same series. See also: R.W. Sleeper, The Necessity of Pragmatism (New Haven: Yale University, 1986); Sandra B. Rosenthal, Speculative Pragmatism (Amherst: University of Massachusetts, 1986); and Joseph Margolis,
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''The Relevance of Dewey's Epistemology," in New Studies in the Philosophy of John Dewey, ed Steven M. Calm (Hanover, N.H.: University Press of New England, 1977). 12. Dewey, Logic, p. 107 (in the context of pp. 105-107). 13. Mawice Merleau-Ponty, "Preobjective Being: The Solipsist World," in The Visible and the Invisible, trans. Alphonso Lingis (Evanston: Northwestern University, 1968), p. 157. 14. Merleau-Ponty, Phenomenology of Perception, pp. viii-ix. Only the expression 'speaks' was italicized in the original. Cf., also, pp. 201-206. 15. Maurice Merleau-Ponty, ''The Primacy of Perception and Its Philosophical Consequences," trans. James M. Edie, in The Primacy of Perception, p. 12. Cf., p. 38, where Merleau-Ponty answers a question posed by a certain M. Cesario 16. Maurice Merleau-Ponty, The Structure of Behavior, trans. Alden L. Fisher (Boston: Beacon Press, 1963), p. 224. Cf., also, pp. 170-176, 184. 17. Merleau-Ponty, Phenomenology of Perception, p. 203, italics added. 18. Merleau-Ponty, Phenomenology of Perception, p. 203. 19. The details are provided in Pragmatism without Foundations. The issue regarding Husserl is developed further in Joseph Margolis, Science without Unity; Reconciling the Human and Natural Sciences (Oxford: Basil Blackwell, 1987), Ch. 2- and here. 20. Merleau-Ponty's distinction between first-order and second-order considerations is captured (in reverse order) by the neat (but difficult) formula: "The knowledge of a truth is substituted for the experience of an immediate reality." Merleau-Ponty, The Structure of Behavior, p. 176. 21. Ednllmd Husserl, The Crisis of European Sciences and Transcendental Phenomenology, trans. David Carr (Evanston: Northwestern University, 1970), p. 143. 22. Ibid., p. 148. 23. Ibid., p. 49. See also: Appendix IV, ''The Origin of Geometry" and pp. 68-69. 24. Maurice Merleau-Ponty, "Phenomenology and the Sciences of Man," trans. John Wild, in The Primacy of Perception, pp. 92, 95. 25. A conveniently brief, sympathetic account of (what amounts to) these elements in Husserl is given in: Timothy 1. Stapleto~ Husserl and Heidegger: The Question of a Phenomenological Beginning (Albany: SUNY, 1983). 26. Husserl, The Crisis of European Sciences and Transcendental Phenomenology, p.150. 27. Ibid., p. 152. 28. Ibid., p. 151. 29. The point is very briefly noted in: Gerald E. Myers, William James; His Life and Thought (New Haven: Yale University, 1986), pp. 490n35. Myers does give a number of leads, however, about the relationship between James' pragmatism and phenomenology proper: see particularly pp. 490n35, 504n30. There is also an intriguing, somewhat impressionistic chapter that specifically associates Dewey and James and Merleau-Ponty in: John J. McDennott, Streams of Experience: Reflections of the History and Philosophy of American CultlUe (Amherst: University of Massachusetts, 1986). The sub-title of that chapter, Ch. 9, is actually "A Phenomenology of Relations in an American Philosophical Vein." 30. The clearest linkage between these two themes, in Dewey, is the following: ''The new realism [Dewey's] fmds...that thinking (including all the operations of discovery and testing as they might be set forth in an inductive logic) is a mere
'NATURALISM = PHENOMENOLOGY'
55
psychological preliminary, utterly irrelevant to any conclusions regarding the nature of objects known. The thesis of the following essays is that thinking is instrumental to a control of the environment, a control effected through acts which would not be undertaken without the prior resolution of a complex sitlUllion into assured elements and an accompanying projection of possibilities- without, that is to say, thinking." John Dewey, Essays in Experimental Logic (New York: Dover, n.d), p. 30, italics added. The formula is clearly as phenomenological as it is naturalistic. In a similar vein, Dewey opposes the assumption "that knowledge has a uniquely privileged position as a mode of access to reality in comparison with other modes of experience." John Dewey, The Quest for Certainty (New York: Minton, Balch, 1929), p. 106. I have consulted, here: Arthur E. Murphy, "Dewey's Epistemology and Metaphysics," in The Philosophy of John Dewey, 2nd 00., ed. Paul Arthur Schilpp (New York: Tudor, 1951). 31. The point is effectively pressed in: Mark Amadeus Notturno, Objectivity, Rationality and the Third Realm: Justifl.Cation and the Grounds of Psychologism; A Study of Frege and Popper (Dordrecht: Martinus Nijhoff, 1985), Ch. 6. 32. See: Hans-Georg Gadamer, Truth and Method, trans. from 2nd ed. Garrett Barden and John Cumming (New York: Seabury, 1975). 33. This is the central issue explored in Science without Unity, Pt One. The argument here sketched amounts to a reductio of Rorty's' thesis in Philosophy and the Mirror of Nature. 34. See : Imre Lakatos, "Falsification and the Methodology of Scientific Research Programs," in Imre Lakatos, Philosophical Papers, Vol. 1, ed. John Worrall and Gregory Currie (Cambridge: Cambridge University, 1978). 35. Jacques Derrida, Positions, trans. Alan Bass (Chicago: University of Chicago, 1981), p. 82. I have italicized the final phrase. 36. See: Michel Foucault, ''Truth and Power," in Power/Knowledge: Selected Interviews and Other Writings 1972-1977, 00. Colin Gordon, trans. Colin Gordon et ala (New York: Pantheon, 1980). See also: Michel Foucault, "Nietzsche, Genealogy, History," in Language, Counter-Memory, Practice; Selected Essays and Interviews, ed. Donald F. Bouchard, trans. Donald F. Bouchard and Sherry Simon (Ithaca: Cornell University, 1977). The most single impressive example of Foucault's applicaJion of his (deconstructive) theme at the level of frrst-order naturalistic and phenomenological (critical) history may be found in: Michel Foucault, Discipline and Punish; the Birth of the Prison, trans. Alan Sheriden (New York: Vintage, 1977). But see also: Michel Foucault, The History of Sexuality, Vol. 1, trans. Robert Hurley (New York: Random House, 1978). 37. See, for example: Mark Poster, Foucault, Marxism and History; Mode of Production versus Mode of Information (Cambridge: Polity, 1984). 38. Karl Marx, The German Ideology, in Karl Marx: Selected Writings, 00. David McLellan (Oxford: Oxford University, 1977), p. 174. Nicholas Lobkowicz notes the passage but makes very little of it; see: Nicholas Lobkowicz, Theory and Practice; History of a Concept from Aristotle to Marx (Notre Dame: University of Notre Dame, 1967), Ch. 25. Michel Henry is much clearer about the import of the passage. As Henry remarks: "As long as Marx remained Feuerbachian and understood reality as sensuous reality, sensuous representations had the meaning of reaching this reality in itself; images, dreams, religion were its 'mere representations'. But when reality is defmed by praxis, the ontological meaning of original representaJion, of the representation which presents being as an object and which in this presentation gives it as it is in itself, is lost.... The representaJion which reveals itself to be unequal to its ontological claims, which, as it gives us external
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being, cannot give us being but is only a mere representation of it, this representation is ' consciousness' ." This Henry takes to be "the key concept to the whole Marxian interpretation of ideology." See: Michel Henry, Marx; A Philosophy of Human Reality, trans. Kathleen McLaughlin (Bloomington: Indiana University, 1983), p. 161, also, further, the whole of Cbs. 4-5. For an explicit comparison of Marx's efforts and deconstruction, see: Michael Ryan, Marxism and Deconstruction (Baltimore: Johns Hopkins University, 1982), Cbs. 2-3. It is interesting to compare here, on Heidegger: Reiner SchUrmann, Heidegger on Being and Acting: From Principles to Anarchy, trans. Christine-Marie Gros and the author (Bloomington: Indiana University, 1987). The 'soft' convergence between Marx's view and the views, already examined, of Merleau-Ponty and Dewey is clear enough. 39. For a recent, somewhat bland, sketch of the issue, see: Anthony Giddens, Central Problems in Social Theory; Action, Structure and Contradiction in Social Analysis (Berkeley: University of California, 1979), Ch. 5. See also: Karl Mannheim, Ideology and Utopia (New York: Harcourt, Brace and World, 1936); and Karl Mannheim, Essays on the Sociology of Knowledge (London: Routledge and Kegan Paul, 1952). 40. Roderick M. Chisholm, "Brentano's Descriptive Psychology," in The Philosophy of Brenlano, 00. Linda L. McAlister (Atlantic Highlands, N.J.: Humanities, 1976). 41. Roderick M. Chisholm, The First Person; An Essay on Reference and Intentionality (Minneapolis: University of Minnesota, 1981), p. 89. This needs to be read in the context of Chisholm's discussion of the whole of Ch. 7. See also: Franz Brentano, "On the Unity of Consciousness," in Psychology from an Empirical Standpoint, 00. Oskar Kraus; English ed. Linda L. McAlister, trans. Antos C. Rancurello et ale (New York: Humanities, (1973), especially p. 160 (cited by Chisholm). 42. Chisholm, "Brentano's Descriptive Psychology," p. 98. 43. Roderick M. Chisholm, The Foundations of Knowing (Minneapolis: University of Minnesota.. 1982), pp. 114, 119; cf., also, p. 155. 44. Nottwno, Objectivity, Rationality, and The Third Realm, p. 56. Cf. the rest of
Ch.3. 45. Frege, ''The Thought: A Logical Inquiry," pp. 523-524. 46. Chisholm, The First Person, p. 89. 47. See: P.F. StrawsOD, Individuals (London: Methuen, 1959). Cf. Margolis, Science withowl Unity, Ch. 3. 48. Gilbert Harman, Thought (Princeton: Princeton University, 1973), pp. 18-19. Cf., "Preface," p. viii. 49. Ibid., pp. 20-21, 162, 168, 172, italics added. The theme is quite Millan in spirit See: John Stuart Mill, Logic, 00. JM. Robson (Toronto: University of Toronto, 1973). 50. Harm~ Thought, pp. 43-44, 46-47m 48, 164; cf. Ch. 5, sec. 2. 51. Husser!, ''The Task and Significance of the Logical Investigations," pp. 198-199. 52. Harm~ Thought, p. 76, in the context of Ch. 5. 53. Michael Dummett, Frege: Philosophy of Language (New York: Harper and Row, 1973), p. 659. 54. See: Michael Dummett, Truth and Other Enigmas (Cambridge: Harvard University, 1978). 55. See: Dummett, Frege: Philosophy of Language, pp. 155-159; Hans Sluga, Gottlob Frege (London: Routledge and Kegan Paul, 1980); N~~~~_l!'Y~~tivJry~
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Rationality and the Third Realm; I.N. Mohanty, Hu,sserl and Frege (Bloomington: Indiana University, 1982), p. 43 and Ch. 2; and the charge made in Isaac Levi, The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance (Cambridge: MIT, 1980), Ch. 18: ''The Curse of Frege." Levi, it may be no~ treats Frege's curse as the imposition of a disjunctive choice between psychologism and anti-psychologism and claims to have beglDl to offer a third "alternative to suffering from its tyranny" (p. 428). But it is not clear that there can be a genuine alternative, and it is certainly not clear how Levi wishes us to understand his own option as such an alternative. On the contnuy, at least in terms of the distinctions here advanced, it seems to be a form of psychologism itself- that is, an option that could not demonstrate more than a naturalistic form of objectivity. NotturDo presses the objection in a reasonable way, quite apart from his quarrel with Levi regarding Popper's objection to psychologism; see~ Notturno, Objectivity, Rationality, and the Third Realm, pp. 216-217. A recent collection of new essays on Frege confrrms, at least implicitly, Frege's neglect of the epistemological issue. See: Crispin Wright, ed, Frege; Tradition and Influence (Oxford: Basil Blackwell, 1984), particularly the papers by Peter Carruthers, Harold Noonan, Bob Hale, Gregory Currie, and John Skorupski. 56. Mannheim, Ideology and Utopia, p. 56, italics added See also: Marx, The German Ideology, passim. 57. See further: Peter Hamilton, Knowledge and Social Structure,· An Introduction to the Classical Argument in the Sociology of Knowledge (London: Routledge and Kegan Paul, 1974); Gunter W. Remmling, The Sociology of Karl Mannheim (New York: Hwnanities, 1975); and Ted Benton, Philosophical Foundations of the Three Sociologies (London: Routledge and Kegan Paul, 1977). Unfortunately, the issue of the sociology of knowledge has not advanced very far beyond the repetition of the original puzzle.
PSYCHOLOGISM AND THE PRESCRIPTIVE FUNCTION OF LOGIC HERMAN PHILIPSE
I. Introduction Psychologism, as a view on the nature and epistemology of logic, is rejected by most modern philosophers. But the grounds for its dismissal may vary, and the question which grounds are the correct ones is not altogether immaterial. For the answer to this question often betrays the conception of logic one holds oneself. Husserl and Frege are usually praised for having finally refuted the doctrine of psychologism. Sometimes, however, reasons for doing so are attributed to them which they themselves would have thought to be misleading. In this paper I shall discuss an example of such a reason. A common view of the matter is expressed by Herbert Feigl in the following observation: Ever since Frege's and Hussed's devastating critiques of psychologism, philosophers should know better than to attempt to reduce normative to factual categories. It is one thing to describe the actual regularities of thought or language; it is an entirely different sort of thing to state the rules to which thinking or speaking ought to conform. l
Similar quotations can easily be found. So G.Radnitzky writes: Thanks largely to the pioneering work of Frege and Husserl, psychologism in logic and metamathematics is largely a thing of the past: the attempt to reduce the norms of logic to laws of thought is now merely a historical curiosity. 2
According to these authors, it seems, Husserl and Frege considered psychologism as a special case of the naturalistic fallacy, as an attempt to deduce ought from is. Such an interpretation rests on the assumption that they would have conceived logic as an essentially normative or prescriptive discipline. In the following pages it is argued that Husserl explicitly (and Frege implicitly) rejected such a view. Neither Husserl nor Frege conceived of logic as an essentially nonnative discipline. As a consequence they
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would have considered the idea that psychologism is incorrect because it commits the naturalistic fallacy as fundamentally mistaken. The 'fork' they use in combatting psychologism did not consist of the dichotomy between the factual and the normative, but, in the case of Husserl of the distinction between the factual and the ideal or, in Frege, the distinction between the subjective and the objective or between the objectively real and the objectively non-real. To make this historical point is, of course, not to say that Husserl and Frege were right, and I shall briefly discuss to what extent they were.
II. Theoretical Laws and Practical Prescriptions Of course, neither Frege nor Husserl denied the possibility of logical prescriptions or norms. But they both thought that the norms of logic are somehow derived from non-normative laws, the theoretical laws of pure logic. These theoretical laws would express an is rather than an ought. On the basis of such a view, one clearly cannot refute psychologism by saying that it commits the naturalistic fallacy, for one presupposes that it is legitimate to derive logical norms from non-normative propositions, Le. the laws of pure logic. What justifies this idea of the nature of logic? Husserl's Logical Investigations are on this point more revealing than the work of Frege. It is an integral part of this picture of logic that in general normative disciplines stand in need of theoretical foundations, a thesis Husserl tries to justify by his analysis of normative propositions in Chapter Two of the frrst volume of the Logical Investigations, the "Prolegomena zur reinen Logik. tt3 I shall fIrst summarize and discuss this analysis, and argue later that Frege must have held a similar view. Husserl's analysis of nonnative propositions serves several purposes. It not only purports to settle the question, much debated at the end of the nineteenth century, whether logic is a theoretical or a practical discipline,4 it also enables l-Iusserl to defme more precisely what psychologism is. In fact, he conceives both psychologism and his own conception of logic as 'pure' logic as two distinct answers to one and the same question, a question which he thinks of as being neutral in relation to all possible positions in the philosophy of logic. To elucidate the nature of norms, so Husserl seems to presuppose, is to define nonns in terms of something else. The customary observation that nonns express what ought to be the case (a Seinsollen) whereas theoretical laws express what is the case, is not sufficiently precise. A reduction of nonns to commands leaves many occurrences of ought unexplained, for a command presupposes an authority who issues it, and often there is no such authority.s Rather, Husserl attempts to define norms in terms of value judgments. Apparently inspired by syllogistic logic, he enlists four 'forms'
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of normative propositions, accompanied by the value-judgments in terms of which they may be defined: 1) 'An A should be B' = 2) 'An A should not be B' == 3) 'An A may be (is allowed) 4) 'An A need not to be B' =
=
'An A which is not B is a bad A', or 'Only an A which is a B is a good A' 'An A which is a B is a bad A', or 'Only an A which is not B is a good A' ,An A which is B is not, for that reason, a bad A' 'An A which is not B is not, for that reason, a bad A'
Apart from slight modifications to account for the distinction between necessary and sufficient conditions for being good or bad, Husserl is convinced that this list of the 'forms' of normative propositions is exhaustive.' Clearly, the four forms constitute the deontic Square of Opposition. The expressions 'good' and 'bad', as used in the forms of the value-judgments which are, according to Husserl, equivalent to forms of nonnative propositions, have a general meaning. 'Good' in the analysing expression means: what is somehow valuable. But in the substitution-instances of these fonns, 'good' and 'bad' will acquire the particular meaning determined by a certain evaluation (Werthaltung) which is presupposed, so Husserl thinks, by the corresponding form. Accordingly, in some value-judgments 'good' will mean useful, in others agreeable, in others beautiful, etc. From this Husserl infers that each norm presupposes an evaluation, by which specific notions of good and bad are defmed for a certain domain of objects. Such an evaluative definition may be of two kinds. If we define, for example, 'good' as what is a means to pleasure and 'bad' as what causes pain, the objects of the domain can be ordered along a scale, and good and bad are relative or polar opposites. If however, we define 'good' as deductively valid and 'bad' as deductively invalid, good and bad are absolute opposites.' HusserI's definition of normative propositions incorporates the idea that all forms in this way presuppose an evaluation: In relation to a general Wlderlying valuation, and the content of the corresponding pair of value-predicates detennined by it, every proposition is said to be 'normative' that states a necessary, or a sufficient, or a necessary and sufficient condition for having such a predicate.a
Moreover, this idea of an 'underlying valuation' or an evaluative definition enables Husserl to explain what the unity of a nonnative science or discipline consists in. A normative science contains all the noons which presuppose one and the same normative definition. Fundamental to such a
-------------------------------------
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nonnative science, so Husserl says, is the norm which states that the objects of the domain should posses the characteristics of the defmed Good (in the highest degree, if the evaluative defmition leaves room for degrees of goodness). He calls this norm the basic norm (Grundnorm) of the nonnative discipline. The answer to the question what differentiates the nonns belonging to a normative science from each other is" implied by Husserl's definition of normative propositions. Assuming certain evaluative definitions of 'good' and 'bad', we shall want to know what circumstances or properties of objects belonging to the domain of the defmition guarantee, contribute to, or exclude goodness or badness in the defined sense. In short, we shall want to know what are the necessary and sufficient conditions for something's being good. If, for example, one accepts, for a certain domain of objects, the hedonistic definition of 'good' as what is a means to pleasure, the question will be what circumstances or properties are required for a particular thing, event, or action to be a means to pleasure. Accordingly, there will be in relation to each kind of object of the domain a number of norms stating what these circumstances or properties are. Having discovered that salted soup in general tastes better than soup without salt, we shall affIrm the norm 'One should put salt in the soup'. The equivalent valuation reads: 'Only a soup which is salted is a good soup'. By substituting the hedonistic defmiens for 'good', we get: 'Only a soup which is salted is a means to pleasure'. For Husserl, the possibility of these substitutions shows that each norm contains a purely theoretical propositional content, which can be stated without normative or evaluative overtones. We may abstract the theoretical content from each particular norm by fIrst substituting for the norm the value-judgment which is, according to Husserl, equivalent to it, and then substituting the defmiens of the evaluative expression for that expression. Husserl affmns this conclusion of his analysis with complete generality: each normative proposition of the form 'An A should be B' contains a purely theoretical proposition of the form 'Only an A which is B has the properties C, where 'c' represents the descriptive content of the relevant evaluative predicate 'good'.9 This would hold mutatis mutandis for all forms of normative propositions: all noons incorporate a theoretical content, which states that certain conditions are necessary or sufficient for something having the properties C specified in the relevant normative definition. Conversely, every purely theoretical proposition may be transformed into a nonn if we assume an evaluative attitude towards the properties C. The nonn can be deduced from the theoretical proposition to the effect that the presence or absence of certain conditions is necessary or sufficient for something to be C, together with the basic nonn that the objects of the domain should have the properties C. Hussed summarizes his analysis by saying that each normative science has one or more theoretical sciences as its basis.
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IlL Psychologism and Pure Logic This idea of the theoretical basis of nonnative propositions is then used by Husserl to clarify the discussion between the proponents of psychologism and of pure logic, a discussion which, during the last half of the nineteenth century, suffered from great confusion. According to Husserl, a large part of the muddle was due to the fact that champions of pure logic like Drobisch and Bergmann grounded their case mainly on the argument that logic is a nonnative discipline. To this, the psychologistic logicians would reply that they did not deny the nonnative or practical character of logic, but only contended that the practical science of logic is, as it were, a technology based on theoretical psychology. This way of putting the problem suggests that the core of the debate between psychologism and the proponents of pure logic is the issue whether logic is a normative discipline. But both parties affmned this, so that one was tempted to conclude that the dispute is merely verbal. In Chapter One of the "Prolegomena," Husserl discusses the idea of logic as a normative discipline in order to clear the ground for a more correct construction of the dispute. He argues that this conception of logic is so obviously justified that it cannot be at stake in the conflict about psychologism. The central question is rather, so he says at the beginning of Chapter Two, whether the defmition of logic as a normative or practical science captures the essential nature of logic, i.e., whether logic is nothing else than a nonnative discipline, the theoretical basis of which is to be found in other, familiar and established sciences like psychology, or rather a distinct theoretical and non-normative science itself. IO In the remainder of the "Prolegomena," Husserl attacks the fonner and defends the latter view. The theoretical content of the nOnDS for correct deduction belongs not to psychology but to 'pure logic'; its validity is a priori and does not, like the laws of psychology, depend on facts. The issue is not whether logic is a nonnative discipline, but what kind of science provides normative logic with its theoretical basis. And the mistake of psychologism is not that it tries to deduce ought from is, for psychologism might assume, apart from psychology, a basic norm as a premise for the deduction of logical prescriptions. Its mistake is that it conceives this is as a factual is, and thus makes the norms of logic dependent on facts. II We are now in the position to see clearly what is correct and what is misleading in the interpretation of Husserl's position given by Feigl. The way in which Husserl reconstructed the issue of psychologism implies a certain view of psychologism itself. Psychologism does not necessarily identify the description of regularities of thought with stating the rules to which thinking ought to confonn, as Feigl suggests. Rather, it distinguishes the two and then affmns a relation between them, viz. that the former is the theoretical basis of the latter. Nor does psychologism necessarily 'reduce nonnative to factual categories'. If Husserl's account of nonns is correct, we can define normative (or evaluative) categories in non-normative terms.
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But these defmitions have a partial character: they merely express the descriptive content of the defmed expression. As we shall see, Husserl himself was aware of the special nature of his evaluative defmitions. Accordingly, the mistake of psychologism is not that it defines evaluative categories in descriptive terms. Its error rather consists in thinking that the defining expression of the evaluative definition relevant to logic contains factual categories. Although its categories are non-normative, they are not factual. In this sense the mistake of psychologism did consist in the attempt to reduce nonnative to factual categories. 12 Husserl's conception of psychologism and its corollary, the rejection of the argument that psychologism is incorrect because it commits the general error of deducing ought from is, both depend upon his analysis of nonnative propositions. This is equally true for Husserl's conception of pure logic. What champions of pure logic like Kant, Drobisch, Bergmann or Herbart were confusedly aiming at, so Husserl claims, is the view he himself defends in the "Prolegomena" and which he expresses as follows: ...That it is the true sense of our supposed pme logic to be an abstract theoretical discipline providing a basis for a technology just as the previously mentioned disciplines do, its technology being logic in the ordinary, practical sense. 13
Accordingly, psychologism and the conception of pure logic Husserl proposes have an important element in common. They both conceive nonnative logic - or rather logic as a practical discipline (Kunstlehre)14 - as a kind of technology, founded on one or more sciences. For Husserl, the apodictic validity of the norms of logic is to be explained by the idea that the theoretical basis of these norms is to be found in a non-empirical or 'pure' science, which is a priori and has a theoretical unity of its own, irrespective of the unity of normative logic which depends on its underlying nonnative definition. As the comparison of (nonnative) logic with a technology might be seriously misleading, it is important to examine more closely Husserl's analysis of normative propositions. Is it in general correct to say that each nonnative proposition states a necessary, or a sufficient, or a necessary and a sufficient condition for having the characteristics 'c' which are good or bad according to an underlying valuation or evaluative definition? And if this is not true in general, does Husserl's analysis perhaps apply to logical nonns, notwithstanding its incorrectness as a general analysis of normative propositions? Let me fIrst soothe possible qualms concerning Husserl's claim that in a nonnative defmition words like 'good' or 'bad' are defmed by means of defining expressions which do not have any normative or evaluative connotation. The hedonist who defmes 'good' as what is a means to pleasure does not try, as G.E. Moore thought, to define by some kind of real defmition the universal essence of goodness. Rather, the words 'good'
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and 'bad' express a positive or negative evaluation (Werthaltung) in relation to certain possible characteristics of objects of some kind. Such an evaluation is reflected by a normative definition in Husserl's sense. The only general connotation of the word 'good' is that something good is valued positively. But in most contexts, the word 'good' has a definite descriptive meaning as well; there are criteria or standards saying what characteristics some F should have in order to be a good F. And these characteristics are listed in a specific normative definition of the word 'good'. Husserl himself stresses that such a definition is not a definition in the sense of the 'usual logical concept of defmition'.1S What he probably means is that the evaluative connotation of the definiendum 'good' is absent from the defming expression, so that the defmed expression and the defining expression are not altogether equivalent A more serious objection to Husserl's analysis of norms concerns the generality of his reduction of normative propositions to value judgments and of the idea that a normative science is based on a normative definition. Husserl assumes that in general it is possible to state the normative definition underlying a normative discipline without adverting to the specific nonns of that discipline. For the content of these norms is in principle independent of the normative definition; it belongs to a theoretical science, and the reduction of norms to value-judgments would be circular if it were otherwise. But often this is not }X>ssible. If we define, for instance, a 'good Christian' as someone who sincerely tries to practice the Ten Commandments and the rules given in the Sermon on the Mount, then the properties of 'C' , which according to Husserl would constitute the descriptive content of the Christian concept of good, logically certain descriptions of all the nonns of the relevant normative discipline, Le. of Christian morality. In such a case, there is no room for a theoretical science which provides the norms with theoretical contents of the form 'Only an A which is B has the properties C' and the like, for the properties C are defined as the properties which an A has only if it is B. So Husserl is wrong to claim complete generality for his reductive analysis of normative propositions. One might argue that this objection is relevant to the case of logic as well. Husserl nowhere tries to define what is 'good from the logical point of view', but he makes it clear that normative logic essentially consists of the norms for valid deductions. 16 Could one not say that what is good from a logical point of view is to infer correctly, and that to infer correctly is just to follow the norms for valid inference? But such an argument would be confused. For although we certainly infer correctly if we follow the rules of deductive logic, this does not imply that it is impossible to give a definition of deductive validity, that is, a definition of what is good from a logical point of view, without invoking all particular nonns of deductive logic. In general, a deductive argument is said to be valid if, assuming the truth of all the premises, it is conceptualIy or logically impossible that the conclusion is false. And confining ourselves to those arguments the
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(in)validity of which can be brought to light by fonnal analysis, we say that an argument is valid if one of its logical forms has no substitution instances with true premises and a false conclusion, and invalid if its specific logical fonn has at least one substitution instance with true premises and a false conclusion. As these definitions do not contain any particular norm of logic, the objection we are discussing does not invalidate Husserl's analysis of logical norms, although it refutes his general analysis of normative propositions. There are, however, other difficulties in Husserl's analysis of normative propositions as applied to logical norms. In order to detect them it is necessary to carry through the application, a thing Husserl does not try to do. The Grundnorm of deductive logic will be the prescription that 'all deductive arguments should be valid'. Grundnormen (basic norms) in general must be an exception to Husserl's analysis of norms in terms of value-judgments. For if one translates the Grundnorm 'all deductive arguments should be valid' into the value-judgment 'Only a deductive argument which is valid is a good deductive argument', one gets the tautology that 'Only a deductive argument which is valid is a valid deductive argument', because 'good' in relation to deductive argument just means valid. As a consequence, the ' should' in basic norms is irreducible, and the only way to elucidate the basic norm is to substitute the defming expression of the relevant 'good' for it: 'all deductive arguments should be such, that if their premises are all true, it is conceptually impossible that their conclusion is false'. Husserl seems to have perceived that basic norms are an exception to his analysis of norms, for he says: The basic norm is the correlate of the definition of 'good' and 'bad' in the sense in question. It tells us on what basic standard or basic value all normativization must be conduc~ and does not therefore represent a normative proposition in the strict sense. l1
The principal difficulties, however, concern Husserl's assimilation of normative logic to a technology which is based on a theoretical science. Apart from the Grundnorm, all specific norms of logic of, say, the form 'An A should be B' would contain a theoretical proposition of the form 'Only an A which is B is such that if all premises are true, then necessarily the conclusion is true as well'. But how are we supposed to specify the class A? Husserl seems to assume that this is possible without mentioning the properties B or C (C is the 'descriptive' content of 'deductively valid', Le. the property that if all premises are true, then necessarily the conclusion is true). A frrst objection against this assumption would be, that there is, in the case of logic, an internal relation between the concepts A and C. If we specify the class A as the class of deductive arguments, we are already using the property C. One might even say that all the elements of the class A will have the property C. For surely a deductive argument is precisely an argument such that, if its premises are true, then necessarily its conclusion
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is true as well. Consequently, there is no room for a property B which is a necessary condition for A's to be C, and the comparison of logic with a technology turns out to be altogether wrong. This version of the objection, however, is too strong. Although there is certainly an internal relation between the properties A and C, we nevertheless speak of 'invalid deductive arguments', so that it must be possible to specify a class A such that not all A's are C. This will be done by means of the distinction between a claim and its correctness: a deductive argument is an argument whose conclusion is claimed to follow from its premises with necessity. Only if the claim is correct, the argument really has the property C, and now we might try to fmd out under what conditions it is correct, that is, to fmd the properties B. Of course the assimilation of logic to a technology is misleading still. For in the theoretical content of technological rules, the properties A and C are typically not internally related18. A problem concerning the possible candidates for property B is solved by Husserl himself. One might think that a property is a candidate for B only if its presence would be a (necessary or sufficient) condition for any A to be C. But there are no specific requirements which deductive arguments of all kinds have to meet in order to be valid, even though one can sometimes formulate geneml requirements for the validity of a subset of deductive arguments (e.g., having defined syllogisms as arguments with two premises and a conclusion of the S-P form, all of which may be general or particular and affrrmative or negative, we require that a syllogism must contain exactly three terms, that the middle term must be distributed in at least one premiss, that at least one of the premises is affrrmative, etc). Interpreting logic as a theory of science, that is, of deductive theories, Husserl states in section 68 of the "Prolegomena" that a given theory is not required to conform to all 'conditions for formal validity' at the same time. Rather, the laws of logic constitute a 'fund' from which, as Husserl says, a valid theory draws 'the ideal grounds of its essential validity':' And in section 11 he accordingly specifies the form of the rules of the theory of science as follows: "Every (soi-disant) methodical procedure of the form M 1 (or M2...) is a correct one."2C) Quotations of the former kind draw our attention to the main way in which Husserl's comparison of logic with a theoretically backed technology is misleading. Like Frege, Husserl was anxious to rescue the 'objectivity' of logic from the danger of subjectivism and scepticism presented by the psychologistic doctrine. As the psychologistic conception of logic, at least according to Husserl, was the view 'that normative logic is a technology based on theoretical psychology, Husserl saw no other way of explaining the objective validity of logic than by substituting another theoretical science, pure logic, for psychology. Pure logic is conceived very much like psychology, although it is said to be different at crucial points. Its laws are about a domain of objects and are verified by a special kind of perception of these objects (namely, categorical intuition).21 Whereas in psychology the
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geneml law is said to 'explain' a particular fact, the laws of pure logic 'justify' their instances.22 However, pure logic is not a science of facts; its objects are 'ideal', they exist independently of space and time and independently of our knowledge of them. As far as pure logic is concerned with deduction, these objects are ideal meanings, Platonic Essences, and not the mental acts of meaning-intention, which are supposed to be their instances. 23 Although the purely logical laws of deduction are theoretical laws (in contradistinction to nonnative) and are about ideal meanings (propositions, concepts), they are purely conceptual as welL The laws of deduction "have their whole foundation in the 'sense', the 'essence' or the 'content', of the concepts of Truth, Proposition, Object, Property, Relation...etc. "24 And Husserl interprets conceptual laws as laws about concepts, concepts being Platonic Essences, which we can know by 'eidetic intuition'. Thus, Husserl's Platonism is in various ways 'the main foundation of pure logic and of epistemology'.25 There clearly is an intimate connection between Husserl's analysis of nonnative propositions and his conception of logic.. The norms of logic belong to a technology. They have a theoretical content which in itself is not normative. This theoretical content can be expressed in the proposition of pure logic, and the objective validity or truth of these propositions is due to their correspondence with certain objects, the ideal objects of pure logic. Thus, pure logic is like any other theoretical science, except for the nature of its laws: they are necessary, a priori, and not contingent. Within the framework of such a picture, the difference between the laws of logic and the laws of physics or psychology can be accounted for only in one way: by postulating a difference between the respective objects of these sciences. So Husserl affmns that the objects of logic are not facts, like the objects of the empirical sciences. They are ideal objects, existing outside space and time. The fundamental mistake of psychologism was, that it confused judgments as mental acts in time with judgments as ideal entities or propositions, and laws about facts with ideal laws. 26 Such a picture of logic is, however, hardly more satisfactory than psychologism. It is an explanation of 'the obscure by the more obscure. What is the nature of 'ideal objects'? To say that ideal propositions are the 'meanings' of declarative sentences, or the 'ideal species' of certain mental acts does not help us very much.27 And it will not do to persuade the reluctant reader to accept the existence of ideal objects by minimalizing the claim, saying that he should take it at frrst as an indication that propositions of logic and mathematics are valid. 28 If so, the claim is trivial, whereas it was meant to be a non-trivial explanation of the validity of such propositions. Elsewhere, Husserl says that it is out of the question that one may prove the existence of universals without solving the problem how we can know them or how we can become acquainted with them29 But there is no serious attempt to solve this problem in the Logical Investigations,30 and Husserl's endeavor to prove the similarity between perception and categorical intuition, necessary for giving some plausibility to the idea that
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we can 'perceive' supm-sensible entities, is rejected in the second edition.31 Finally, Husserl's later theory of 'eidetic variation' does not support the thesis that we can 'intuit' ideal entities, nor is it a correct description of the procedures by which we test the validity of proposed laws of logic. 32 Husserl's picture of logic, so we might say with the later Wittgenstein, is a product of misleading features of our grammar. Admittedly, we sometimes assert 'that arithmetic is about numbers and the theory of propositional logic is about propositions, that certain formulae are 'true' or 'correct'. But this about is different from the sense in which descriptions are about, and true of, the described object We can always imagine that an object is not as the description says it is, but we cannot imagine that a proposition is not either true or false: it would simply not be a proposition. The traditional law of the excluded middle is rather like an implicit definition of what propositions are. It is not a descriptive truth, but the corollary of a rule for the use of the expression 'proposition', a rule by which we delimit the range of applicability of traditional (two-valued) logic. And a law of logic like '({P~.p)~' (or: 'for all propositions p, q: (~q).p)~') is not true in the sense that it somehow corresponds to a reality which we would have to 'perceive' in order to test the law. Calling a formula like '({P~.p)~' a law of logic means that the formula is a tautology, that whatever propositions we substitute for 'p' and 'q', we get the result 'true' if we carry out the operations indicated by the definitions of the logical constants. These tautologies may be called 'laws of logic' because there is an equivalence between tautologies of a certain form and valid inference-schemata. An inference schema is valid if it has no substitution instances whose premises are true and whose conclusion is false. The definition of the material implication shows that a conditional whose antecedent consists of the conjunction of the premises of a valid schema and whose consequent is its conclusion must be a tautology: the only case in which the conditional is false is the case in which the consequent is false and the antecedent is true, but this case is excluded if the conditional corresponds to a valid inference schema in the way explained. Now inference schemata are certainly not descriptions of some reality, nor are they expressions of general laws about propositions. A correct schema is rather a rule for constructing valid arguments. Consequently, it is a mistake to interpret the laws of logic, which are nothing but reformulations of such schemata, as laws about some independent reality. As I said, there is a sense in which one might say that something 'corresponds to' a law of logic like the Modus Ponens. The law has the fOffil of an implication. It corresponds to an inference-schema because its antecedent consists of the conjunction of the premise-forms of the schema and its consequent is identical with the conclusion-form. This 'correspondence' is clearly not the kind of correspondence that a true description bears to the reality of which it is a description. Now of course the inference-schema itself 'corresponds to' something else as well: It
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corresponds to arguments in ordinary language. The schematic letters 'p' and 'q' correspond in a certain way to statements and the logical constants correspond in quite another way to expressions like 'if...then' and 'not'. To interpret these relations of 'corresponding to' in terms of the correspondence between a description and reality would be equally mistaken. The correspondence between the logical constants and the relevant expressions of common language, for instance, is rather a correspondence between the two sets of rules for the use of these respective signs. This correspondence is governed on the one hand by a requirement of adequacy, which has to guarantee that the logical system may be used in evaluating arguments in common language, and on the other hand by requirements of the system, like truth-functionality and simplicity. The tension between these two kinds of requirement admits of various solutions. One logical system may be further removed from common language than another, but easier to operate. However, although in a sense a formal system is a better instrument for assessing the validity of arguments the closer the rules for the use of its constants correspond to the rules of common language, it would be completely misguided to think that this correspondence is the correspondence of truth, that one system of logic is 'true' or 'nearer to the truth than other systems'. Finally, expressions like 'if...then', 'and', 'or', and 'not' do not ,correspond to' anything. Contrary to what Husserl thought, they are not referring expressions and we do not need a special kind of intuition, categorical intuition, to grasp the aspects of states of affairs to which they presumably refer. These considerations show still another way why the dualistic conception of logic as a normative science and a purely theoretical discipline which provides the former with its theoretical basis, is misleading. This conception presupposes that there is a basic norm telling us to reason correctly, which is completely separated from, and external to, the theoretical content of the nonns of logic. Conversely, the laws of pure logic in themselves would be free from any normative connotation. Now it is of course possible to express the laws of logic without explicitly using normative or evaluative words, e.g. the Modus Ponendo Ponens as '«P~.p)~'. And one might fonnulate a corresponding logical norm, e.g., 'it is permissible to infer from premises of the form 'p~' and 'p' a conclusion of the form 'q". But this does not prove that the technology-conception of logic is correct The validity of the formula of the propositional calculus is in fact nothing but the necessary outcome of a certain way of cOlTlbining schematic letters, brackets and logical constants: it is exhaustively explained by the rules for the use of these signs. These rules correspond in various ways to the rules of use for the expressions of common languages. Rules of language, however, posses an inherent 'normative import': if one wants to use the expression 'if...then', one has to use it correctly. Otherwise, what one says just does not make sense. Here it is artificial to dism.guish between a basic nonn (to use language correctly) and a theoretical content specifying the
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means which we may use in order to confonn to this norm. Moreover, in the process of learning a language we eo ipso learn to reason correctly. For to reason correctly is nothing but to apply the rules of language in an argumentative context, especially the rules for the use of expressions like 'all', 'some', 'if...then', 'and', etc. As the rules for correct reasoning are on par with the rules of language, we do not need a separate and external basic norm which prescribes that we should reason correctly. This norm is inherent in the use of language. So we come to the conclusion that Husserl's application of his analysis of nonnative propositions to logic, his assimilation of logic to a technology, and his contention that there is a purely theoretical logic, whose non-nonnative propositions are 'true' of an ideal world and provide normative logic with its 'theoretical content', is fundamentally misleading.
IV. Husserl and Frege: a coda In one of the first comparative studies on Husserl and Frege, Dagfmn came to the conclusion that Husserl's conception of 'the normative character of logic is different from that of Frege, and that Husser! improved on Frege by his clear distinction between normative and theoretical sciences.33 If what I have argued is correct, Husserl at most 'improved' on Frege in the wrong direction. His 'clear distinction' between normative and pure, theoretical logic was the product of a mistaken application of the distinction between a technology and its theoretical basis in logic. But the historical part of F~llesdal's conclusion is no more correct than its philosophical aspect. In fact, Frege, like Husserl, embraced the conception of logic as a theoretical science, constituting the basis of the norms for valid thinking. F~llesdal's opinion to the contrary rests on a mistaken interpretation of pages XV-XVII of the "Vorwort" to Frege's Grundgesetze der Arithmetik. According to F~llesdal, Frege considered the normative character of logic to be a decisive argument against psychologism;34 and asserted that the laws of logic are essentially prescriptive.35 In fact, Frege states on page XV of the "Vorwort" that the laws of logic should be prescriptions for thinking. But F~llesdal's interpretation misses the point (as well as the letter of the text: Frege says that the laws of logic should be prscriptions!) of this pasage by absttaeting from its argumentative context. Frege is attacking here a specific argument in favour of psychologism, the argument that logic is a part of psychology because the laws of logic are laws of thought (Denkgesetze). Frege's rejoinder is that the argument contains a fallacy of ambiguity. If one takes 'law' in the sense of prescription, it is true that the laws of logic are the 'laws of thought', for they prescribe according to Frege how we should think if we want to attain the truth. But in this sense of 'law', it is not true that the laws of thought belong to psychology. If it were, even the F~llesdal
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laws of physics would belong to psychology, for "each law which says what is the case may be taken as a prescription, viz. to think in accordance with it, and is in this sense a law of thought." The only special claim of the laws of logic to the title of 'laws of thought' is that they are the most general laws, so that they would prescribe how one should think in all domains of thinking. If, however, one takes the word 'law' in the descriptive sense, it is simply false to say that the laws of logic are laws of thought, and the argument in favour of psychologism collapses for this reason.36 One cannot read into this passage any support for the claim that the laws of logic are essentially normative according to Frege. On the contrary, the laws of logic are classified as 'laws which state what is', which, like all such laws, should be taken as prescriptions for our thinking. Frege indicates only one difference between logical and other descriptive laws: the logical laws are the most general laws there are.37 Moreover, the laws of logic are Gesetze des Wahrseins and not psychologische Gesetze des Furwahrhaltens. As a proposition is true or not true independently of our believing it to be true, the laws of being-true are not psychological laws, but "boundry-stones, set in an eternal foundation.... And because they are such, they set the nonns for our thinking, if it wants to attain the truth." The comparison of the laws of logic with the rules of grammar is explicitly rejected.38 F011esdal was of course right that Husserl proposed an elabomte analysis of the distinction between normative and theoretical sciences and the interrelations between them, Whereas Frege was not interested in the issue. But Frege probably would have accepted HusserI's view on this point, so that it might be used to elucidate what Frege meant by his rather lapidary remarks on the
subject.
72 ENDNOTES This is a revised version of a paper read at the University of Oxford during Trinity term 1984. I thank Professor M.A.E Durnmet (New College), Dr. P.M.S. Hacker (St. John's College), and Dr. B. Smith (University of Manchester and Erlangen) for their stimulating comments on an earlier version.
1. Herbert Feigl, "Physicalism, Unity of Science and the Foundation of Psychology," in P.A. Schipp, ed., The Philosophy of Rudolph Carnap (La Salle: Open Court, 1963), p. 250 2. G. Radnitzky, "Popperian Philosophy of Science as an Antidote Against Relativism," in R.S. Cohen et al., eds., Essays in Memory of Imre Lakatos (Dordrecht: Reidel, 1976), p. 505. 3. See: Edmund Husserl, Logische Untersuchungen, Band I, "Prolegomena zur reinen Lokik" (Halle: M. Niemeyer, 19(0). As the considerable differences between the first edition (1900) and the second edition (1913), on which all later editions are based, are irrelevant for the subject of this paper, I will quote from the fifth edition (fllbingen: M. Niemeyer, 1968). For the English reader I add references to the pages of Logical Investigations, trans. IN. Findlay (New York: Humanities Press 1970). 4. 5. 6. 7. 8. 9.
Cf., Hussed, Logical Investigations, Vol. I, sec. 3. See: Ibid., sec. 14. See: Ibid., Vol. L pp. 83-84; Logische Untersuchungen, Band I, p. 43. Cf., Ibid., Vol. I, sec. 14. Ibid., Vol. I, sec. 14, p. 84; Logische Untersuchungen, Band I, p. 44. See: Ibid., Vol. I, sec. 16. 10. See: Ibid., Vol. I, sec. 13; cf., Vol. I, sec. 41. 11. Husserl tries to give a reductio ad absurdum of psychologism by arguing, e.g., that if it were true, factual mistakes in reasoning would falsify logical laws, it would be possible to deny logical laws without contradiction, the laws of logic would be vague and merely probable, psychological research would be relevant to logic, and that, in short, psychologism is a kind of skepticism in the strict sense, Le. a theory which denies or questions certain conditions for the possibility of theories in general. Cf., Ibid., Vol. I, Ch. 4-7 12. So psychologism is incorrect, not because it overlooked the normative character of logic, but because it assumed that a factual science can be the theoretical basis of logical norms. The crucial argument against psychologism is not the normative character of logic, but the 'ideal' character of the theoretical basis of normative logic. Cf., Ibid., Vol. I, sec. 43; Logische Untersuchungen, Band I, pp. 164-165. Cf., Ibid., Vol. II, "Investigation L" sec. 32. 13. Ibid., Vol. I, sec. 13, p. 80; Logische Untersuchungen, Band I, p. 38. 14. Husserl distinguishes between normative disciplines in general and practical disciplines or technologies (Kunstlehren). A practical discipline is a normative discipline the Grundnorm of which states that we should aim at perfonning certain actions in a certain manner. Cf., Ibid., Vol. I, sec. 11, 15. 15. See: Ibid., Vol. I, sec. 14 in [uaem. 16. Pure logic, however, comprises much more than the theoretical basis of the norms for valid deduction. The principle of unity of a theoretical science is essentially independent and different from the principle of unity of a theoretical science. Pure logic, in Husserl's sense, embraces all the 'formal' or 'categorical' sciences. Cf., Ibid., Vol. I, sec. 14, 16, 62-64. 17. Ibid, Vol. I, sec. 14, pp. 85-86; Logische Untersuchlmgen, Band ~_p--"-_~~~-------G
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18. For example, in 'Only a soup which is salted is a means to pleasme', there is no internal relation between the concept of soup and the concept of being a means to pleasme. I asswne, in this objection, that it is impossible to define what arguments are, or, in casu, what deductive arguments are, without using the concept of (deductive) validity. Iri other words, the concept of an argument belongs to pragmatics. An argument essentially embodies a claim to be correct (inductively or deductively); it is not just an ordered set of propositions and statements. 19. See: Ibid., Vol. I, p. 239; Logische Untersuchungen, Band I, p. 246. 20. Ibid., Vol. I, p. 71; Logische UntersucJumgen, Band I, p. 27. 21. Cf., Ibid., Vol. n, ''Investigation VI." 22. Cf., note 19 above. 23. Cf., Ibid., Vol. I, sec. 36, 39, 40, 42, 65; cf., also, Vol. n, "Investigation I," sec. 29. Husser! empahatically warns the reader against the idea that ideal entities are 'more perfect' than factual entities, that 'the ideal' is essentially normative, or that 'ideal species' are somehow the most perfect instances of themselves, a confusion which lies at the root of many objections against Platonism. Cf., Ibid., Vol. II, "Investigation I," sec. 32. For Husser!'s conception of ideal meanings in the Logical Investigations, see especially: Vol. II, ''Investigation 1," Ch. ill, IV. 24. Ibid., Vol. I, p. 144; Logische Untersuchwagen, Band I, p. 122. Cf., Vol. I, sec. 23, 36, 39, 40, 42, 43, 50, 66. 25. See: Ibid., Vol. IT, ''Introduction'' to ''Investigation IT." Cf., however, Edmund Husser! Indeen Zil einer reinen Phii.nomenologie IlfId phiinomenologischen Philosophie I (Halle: M. Niemeyer, 1913), sec. 5. 26. Cf., Ibid., Vol. I, sec. 44-48. 27. Cf., Ibid., Vol. IT, ''Investigation L" ch. 4. In his review of M. Pahigyi, Der Streit der Psychologisten wuJ. Formalisten in tIer modernen Logile, ZEITSCHRIFf FOR PSYCHOLOGIE UNO PHYSIOLOGIE DER SINNESORGANIE, 31 (1903), p. 290, Husserl tells us that the puzzling character of Bolzano's doctrine of Slitze an sich vanished as soon as he realized that Siitze an sich are just what we call the meaning of a statement, and that these meanings are ideal species of certain mental acts. The review is reprinted in volume xxn of the Hwsserliana, ed. and trans. Dallas Willard as "A reply to a Critic of My Refutation of Logical Psychologism," THE PERSONAUST, 53 (1972), pp. 5-13. 28. See: Husserl, Logical Investigations, Vol. II, "Investigation 1," sec. 31, in finem. 29. See: Ibid., Vol. IT, ''Investigation 11," sec. 7, p. 351; Logische Untersuchungen, Band II, pp. 122-123. 30. Cr., Ibid., Vol. IT "Investigation II," sec. 14 and ''Investigation VI," sec. 52. 31. This is the theory of categorical representation of chapter 7 of the ''Investigation VI." It is rejected in the "Vorwort" to the second edition of ''Investigation VI," Ibid., Vol. IT, p. 663; Logische Untersuchungen, Band IT, p. V. 32. As I argued elsewhere. Cf., Hennan Philipse, De FllfIdering van de logica is Husserls 'Logische Untersuchungen' (Leiden, 1983), eh. 1.7. 33. Dagfinn F011esdal, Husserl und Frege. Ein Beitrag ZIlT Beleuchtung der Entsteehung tIer phiinomenologischen Philosophie (Oslo: I Kommisjon hos Aschehoug, 1958), p. 49: "Husserl \D1terscheidet sich aber deutlieh von Frege in seiner Auffassung von dem nonnativen Charakter der Logik. Es scheint als ob er durch seine klare Trennung zwischen theoretischen Wissenschaften \Dld nonnativen Wissenschaften bier weiter gekommen ist a1s Frege." 34. See: Ibid., p. 46.
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35. See: Ibid., p. 45. The passage in F~llesdal to which I am refering read as follows: "B usserl fmdet, im Gege1JSlJlZ Zil Frege, dass tkr normative Charakter der Logik kein enlscheidendes Argument gegen den Psychologismu,s sein kann." Ibid., p. 46, and "In seiner Kritik des Psychologismu,s in ' GTlUIdgesetze der AritJunetik' legt Frege grosses Gewicht QIJ{ den norma/wen ChmakJer der Logik.... Ihre Gesetze sind vorschreibend, und Q44Sschliesslich dies, behauptet Frege (Gg, XV)." Ibid., p. 45. 36. The relevant passage reads as follows: "Dass die logischen Gesetze Richtschnluen fiir das Denken sein sollen ZUI' E"eichlmg der Wahrheit, wird zwar vorweg allgemein zllgegeben; aber es geriith 7UIJ' Zil Leicht in Vergessenhe.it. Der Doppelsinn des Wortes ,Gesetz' ist hier verhiingnisvoll. In dem einen Sinne besagt es, was ist, in tkm andern schreibt es vor, was sein soli. NUl' in diesem Sinne kOnnen die logischen Gesetze Denkgesetze genannt werden, indem sie festsetzen, wie gedacht werden soli. J edes Geselz, das besagt, was ist, kann aufgefasst werden als vorschreibend, es solie Un EinJdange damiJ gedacht werden, UJU.l es ist also in dem Sinne ein Denkgesetz. Das gilt von den geometrischen und physikalischen nicht minder als von den logischen. Diese verdienen den Namen ' Denkgesetze' nur dann mit mehr Recht, wenn damit gesagt sein soil, dass sie die allgemeinsten sind, die ilberall da vorschreiben, wie gedacht werden soli, wo iiberhaupt gedacht wird." Oottlob Frege, Grundgestze der AritJunetik, begriffschriftlich abgeleitet (Jena: Hennann Pohle, 1893), Band I, p. XV). 37. Cf., Gottlob Frege, Die Grundlagen der AritJunetik, eine Logisch-mathematische Untersuchung uber den Begrijf der 7Ahl (Breslau: Wilhelm Koehner, 1884), sec. 14. 38. See: Frege, Grundgesetze, Band I, p. XVI.
FREGE'S ANTI-PSYCHOLOGISM G.P. BAKER and P.M.S. HACKER
I. Introduction One celebrated aspect of Frege's philosophy of logic was his insistence on the need to purge everything psychological from the clarification of the fundamental concepts of logic and from the elucidation of the primitive terms of his logical notation (which he called 'concept-script'). He inveighed against "the irruption of psychology into logic," drawing attention to the extent of the devastation caused by it and diagnosing the germs of this "widespread philosophical disease."1 He proposed to "reject all distinctions that are made from a purely psychological point of view."2 Indeed, he made it one of his fundamental principles "always to separate sharply the psychological from the logical, the subjective from the objective. "3 These pronouncements are the leitmotifs of Frege's antipsychologism. Our task here is to identify the targets of his criticisms, to ,/' clarify the scope and force of his counterarguments and to assess his achievements in this philosophical campaign. The established tradition was to view inference as the primary subjectmatter of logic. Inferences were thought to be sequences of judgments (propositions, thoughts), and judgments to be built up out of concepts or ideas. Hence, treatises on logic standardly began with discussions of concepts, continued with material on the composition of judgments, and culminated in cataloguing laws of thought (and also standard fallacies). The notions of concepts, judgments, and inferences were the basic concepts in the philosophical discussion of logic. The general nature of logic was taken to depend on the nature of these entities. Frege himself was educated in this tradition, and in the broad outline he accepted most of it He made some important improvements. In particular, he held that the soundness of an inference depends only on what is asserted, the thoughts that are put forward as being true. The term 'judgment' (or 'assertion') may be used to designate either what is judged (or asserted) or the act of making a judgment (or assertion). Hence, Frege introduced the term 'judgeblecontent' to make clear that he held logic to concern the objects, not the acts, of judgment. Similarly, he complained that traditional logic had too narrow a notion of concepts. Although judgeable-contents are composed of ideas, concepts are not building-blocks given independently of judgments, but rather concepts must always be precipitated out of judgments. With these two provisos, Frege adhered to the traditional concept of logic. He
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thought a judgeable-content to be a "combination of ideas. ft4 These ideas, or unjudgeable-concepts, were subdivided into objects and things or concepts and functions. s Likewise, he thought that inferences are concatenations of judgments. To infer is "to make a judgment because we are cognizant of other truths as providing justification for it"' In his view, the task of logic is to test in the most reliable manner the validity of chains of reasoning,7 and its goal is to set up the laws of valid inference.8 Frege added the controversial' (and mistaken) idea that "only a thought recognized as true can be made the premise of an inference,ttlO thereby rejecting the idea that indirect proofs involve drawing conclusions from false thoughts. ll Frege's geneml conception of logic is consonant with the traditional view that it is the nonnative science of concepts, judgments, and inferences. Rules of deduction he held to be grounded in truths about concepts and judgments. Frege had a further inclination to side with tradition in philosophy of logic. The laws of thought, or laws of truth, have standardly been taken to be necessary truths, established as absolutely certain, and known a priori. The most elementary laws such as the Law of Identity ('Whatever is, is') or the Law of Non-contradiction ('Nothing both has and lacks a given property') are conceived as self-evident first principles of an a priori science pamllel to Euclidean geometry, and more complicated laws are displayed as the theorems of an axiomatic system developed out of these initial seeds. Frege always subscribed to this conception of logic, and he strove to erect on self-evident axioms a system of propositions of logic which would encompass all forms of inference acknowledged in advanced mathematics. Like most philosophers and mathematicians, Frege was inclined to link this conception of the objectivity of the truths of logic with a Platonist conception of their subject-matter. He was disposed from the outset to view concepts and judgments as abstract entities and to suppose that the propositions of logic are made true by the properties and relations of these denizens of a suprasensible realm. Just as Euclidean geometry is commonly thought to describe relations among mathematical entities (nwnbers, operations, and functions), SO Frege thought of logic as a science about special logical entities, their properties and relations. His conception of what these entities are gradually evolved; he had not 'discovered' the two truth-values or arrived at his later conception of concepts and thoughts when he wrote Begriffsschrift. Nonetheless, his allegiance to a Platonist picture of the subject-matter of logic was the constant companion of his conception of the objectivity of logic. These traditional ideas are part of the framework in which Frege's philosophy of logic evolved. A crucial consequence is that, from his point of view, the burden of proof must always lie on any philosopher who challenges the conventional wisdom. By his lights, to rebut all serious objections is to vindicate the Platonist conception of logic; nothing further can be required. In this respect modem philosophers may be expected to fmd his arguments defective. For the 'postulation of abstract entities' is now viewed as a prima facie intellectual crime, and hence an advocate of any
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fonn of Platonism must discharge the task of proving that no other more economical philosophical explanation is available. Times have changed. So too have the implications of the word 'Platonism'. Indeed, it may promote misunderstanding to classify Frege's conception of logic as a form of Platonism. This gives rise to expectations that his work does not fulfill. That in nun may entail the verdict 'that there is a gulf between his platitudes about concepts or judgments and his claims that concepts and objects are real but non-sensible entities, to be discovered and investigated by the eye of the mind or by the 'logical faculty'. It seems certain that Frege would have seen no gulf here, and the lacuna now detected in his arguments was not one that he was in a position to make good. It would be an interpretative blunder to treat this shortcoming as evidence of foolishness or philosophical ineptitude on Frege's part. But equally, it would be foolish to set it aside as a simple blunder which should be ignored on the grounds of charity. For what Frege did not see to be problematic has decisive importance for understanding his own positions and his criticisms of alternatives. Misconceptions about the framework of his thinking have vitiated most expositions of his anti-psychologism and most assessments of its worth. What Frege considered to be the most serious challenge to his conception of logic came from a form of radical empiricism that flourished in Gennany in the nineteenth century. No doubt this emerged as the antithesis to post-Kantian idealism. It drew inspiration from classical empiricism, but it moved off in a novel direction. It is commonly held to have originated in the writings of Benecke and Fries. They initiated the so-called 'deepening of logic by psychology'12 and appropriated the label 'psychologism' for their ideas. Frege took the definitive expositions of this stream of thought to be E. Husserl's Philosophy of Arithmetic (1893) and B. Erdmann's Logic (1892), and these texts were the primary targets of his tirades against psychological logicians and the incursion of psychology into logic. Qosely allied arguments occur in the writing of Mill and James, and much of the thrust of this radical empiricism persisted in Mach and Schlick. Frege was undoubtedly right to see in this fashionable and influential psychologism the major contempomry threat to the acceptance of his own point of view about logic. The psychological logicians claimed two special insights that called for a new conception of the nature of logic. First, while agreeing that the / subject-matter of logic is concepts, judgments, and inferences, they held that v these entities are all psychological or mental, and hence subjective. Words stand for ideas, all of which are derived from experience by a mental process of abstraction. To understand a word is to have the appropriate idea or image. Understanding an assertion is a matter of combining the ideas associated with its constituent words. A judgment is a combination of ideas (or a complex idea), and an inference is a transition from judgments to another judgment. Since ideas are held to be mental entities, the judgments of which they are the parts must also be mental entities, and so too must
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be the inferences of which judgments are the parts. According to the psychological logicians, the subject-matter of the truths of logic belongs to the domain of the mental and the subjective. The laws of thought are propositions made true by facts about psychological entities. Secondly, the truths of logic were held not merely to be about mental entities, but also to have the status of empirical genemlizations. Psychological logicians claimed that these propositions are not necessary truths, that they rest on inductions based on observations of inner sense or introspection, and hence that they are a posteriori truths. According to this view, the nature of the truths of logic has been misunderstood by most philosophers through the ages. It is alleged to be an illusion of reason to suppose that logic (and mathematics) embodies any genuine non-empirical knowledge. The radical empiricism of the psychological logicians is committed to the thesis that all knowledge is empirical, and it saved the claim that there is knowledge in logic and mathematics by alleging that these so-called a priori sciences actually consist of empirical generalizations. In short, the laws of logic were held to be psychological statements, either natural laws of human thinking or else descriptions of thought-patterns that are, perhaps, variable between cultures or through history. This form of Empiricism or naturalism made a radical break with traditional philosophical thinking about logic. Frege made it his business to challenge the central theses in this cluster of ideas. These are the overt targets of his anti-psychologism. This must be borne in mind when expounding his arguments and assessing their forcefulness. The thinking of the psychological logicians had affinities with classical empiricism in the works of Locke, Berkeley, and Home. But the criticisms of these ideas lay outside the scope of Frege's reflections. 13 Likewise, nineteenth century psychologism had more tenuous affinities with idealism as developed by Kant, Hegel, Schopenhauer, Bradley, etc. But it would be as misguided to look in Frege's writing for refutations of their leading ideas as it would be to characterize idealism as the principle target of Frege's philosophy of logic. I" One is apt to misunderstand his anti-psychologism altogether if one loses sight of its specific target Despite a few asides about the wider implications of his critical comments, the intended scope of his invective against psychological logicians was narrow. His purpose ~as to demolish the pillars of their conception of the nature of logic. In this campaign he did not take it to be necessary to probe the roots of their misconceptions. He thought it sufficient to demonstrate the absurdity of their conclusions and the lack of cogency for their arguments. In particular, Frege argued that psychologism made it unintelligible that there could be an intersubjective science of logic (because of the acknowledged impossibility of sharing ideas). He offered arguments to refute the claim that all ideas are derived by abstraction from experience (focusing for this purpose on number-words and their use in count-statements). And he pointed out that it is a fallacy to infer from the fact that thinking is a mental activity that the objects of thought (propositions or judgments) are mental entities. To establish these points was, in his view, to construct a
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definitive case against psychologism. 15 Nothing more ambitious was required, no deeper exploration of the concepts of inference, thinking, assertion, concepts, concept formation, the normativity of logic, etc. It is an open question how far Frege's purpose-specific remarks about these concepts may make a significant contribution to philosophy of logic and philosophy of mind. He engaged in polemical skirmishes with the psychological logicians in the hope of eliminating an intellectual nuisance, and hence there should be no presumption that his anti-psychologism is a set of eternal verities laying the foundation for philosophical wisdom in the twentieth century.
ll. Frege's Influence and Alleged Achievements Though parochial in intent and origin, Frege's anti-psychologism developed into a protagonist in the drama of modern philosophy of logic. His influence has been immense and his authority often cited in support of campaigns to keep logic uncontaminated by psychological consideration. In part this depends on two factors that have nothing to do with the force of his case. The fIrst is that many of his remarks about purifying logic of everything psychological are colorful and quotable. They are apt to serve as revolutionary slogans and battle cries. The second is that he invented the \/ predicate calculus and thereby solved the riddle of the formalization of inferences involving multiple generality. The prestige of this intellectual achievement rubs off on the philosophical reasoning which accompanies his axiomatization of the truths of logic. Indeed, it is tempting to suppose that Frege's solid achievement in formal logic guarantees the value of his whole philosophy of logic since the foundations of the predicate calculus must be his conception of inferences, judgments (judgeable concepts or thoughts), concepts and concept-formation, the sense/reference distinction, etc. In particular, his rejection of psychologism and his espousal of Platonism in logic are given an imprimatur. There is little wonder in the fact that his anti-psychologism has had more far-reaching influence than he could have foreseen. Though these intrinsic features of his work contributed to the impact of his criticisms of psychologism, extrinsic factors were even more important. Russell and Wittgenstein, the two seminal figures in the development of philosophy of logic in the period 1900-30, both noted and endorsed Frege's anti-psychologism. In his frrst letter to Frege, Russell noted that ttl fmd myself in full accord with you on all main points, especially in your rejection of any psychological element in logic... ."16 For the next decade Russell insisted that propositions must not be taken to be mental entities;' that propositions (or complexes) stand in objective logical relations to one another, and that psychological concepts (e.g., of assertion) must be distinguished from logical ones. Rigorous exclusion of psychology from
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logic was a cornerstone of the Tractatus too. Philosophy of logic has nothing whatever to do with the psychological investigation of thoughtprocesses which entangled many earlier philosophers and blurred the boundary between philosophy and the natural sciences.18 Indeed, Wittgenstein even accused Frege and the authors of Principia Mathematica of having failed to draw the bounds of logic narrowly enough. In particular, he declared that the assertion-sign is logically quite without significance; it merely indicates that these philosophers hold propositions marked with this symbol to be true,19 and that is irrelevant for logic since valid inferences may be made even from false propositions.20 The sole concern of philosophy of logic is to clarify the essential nature of the proposition, the general form of a proposition that can be apprehended once and for all in advance of any experience, and to investigate the forms of elementary propositions, or catalogue simple objects.21 Considerations about the workings of the human mind have no place in these enquiries; the stimulus for this idea and the radical nature of Wittgenstein's anti-psychologism were undoubtedly among his debts to the great works of Frege. Frege's influence on Russell and Wittgenstein multiplied many-fold the historical impact of his criticisms of the intrusion of psychology into logic. For these authors played pivotal roles both in the development of formal logic and in the growth of conventionalism which dominated philosophy of logic for two decades. Principia and the Tractatus were canonical texts among the logicians who built the metalogic of the predicate calculus in the '208 and '30s. The anti-psychologism of these texts coincided with the inclination of such philosopher-mathematicians as Ramsey, GOdel, Church, Tarski, and Carnap to think of themselves as making objective discoveries, and their technical successes reinforced this philosophical point of view. At the same time, the philosophy of logic which the Vienna circle extracted from the Tractatus and brandished as 'conventionalism' seemed to vindicate hard-headed empiricism without recourse to treating the truths of logic and mathematics as laws about mental entities. By holding out the vision of the objectivity of logic without abstract objects, logical empiricism forestalled any resurgence of psychologism among most philosophers who were inclined in temperament towards empiricism.22 These two streams of thought, one formal, the other philosophical, have made it commonplace among philosophers in this century to contrast logic with psychology. Students are indoctrinated with the views that the business of logic is the investigation of the relation of logical consequence among statements; that this depends on having a semantic theory for a language which makes clear what the truth-conditions of any well-formed formula are; and hence that the science of logic belongs to the study of language. From the beginning, undergraduates are taught that validity is a property of ordered sets of sentences or Connulae, not a property of sequences of thoughts or beliefs or of mental processes of reasoning. It is now an uphill battle for a philosopher to argue that psychology or even philosophy of mind has any
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proper place in philosophy of logic. Frege's philosophical heirs have had a total victory in the campaign which he initiated. On the other han~ as the ripples of his anti-psychologism have spread, the perceived content of his initial criticisms has become more and more diffuse and vacuous. Logicians in 1987 are not trying to fend off the thoughts of the particular psychological logicians that Frege attacked. Most of these ideas are neither still in circulation nor regarded as live options. Consequently, slogans borrowed from his writing are now put to uses that he did not intend or even foresee. This evolutionary process is visible from the beginning. Russell too was eager to establish that propositions and relations are not mental entities, but real, objective things which confront us in experience; and he too emphasized the importance of distinguishing the truth of a proposition from its being taken to be true. But the target of his attack was not the naturalist psychologism of early Husserl and Erdmann; it was the very different idealism associated in England with the work of Bradley and Green. Hence, Russell conscripted Frege into an alien crusade \/ against idealism. This was the frrst step down the road of divorcing Frege's anti-psychologism from his supporting philosophical arguments and presenting particular criticisms of specific philosophical reasoning as verites eter1U!lles of great generality, the foundation-stones of sound philosophy of logic. If one then subjects Frege's arguments to careful scrutiny, one fmds that his reasoned case is far too weak to support the sweeping theses listed among his achievements. Should one condemn Frege for this defect? Would it not promote a better under standing to expound the content of his anti-psychologism by reference to his arguments and to examine the assumptions on which his reasoning actually rested? What cannot be disputed is Frege's role as a catalyst in the process of achieving consensus among" philosophers that psychology must be banished from logic. What is in dispute is what his solid achievements were, what were his own decisive contributions to this evolution in philosophy of logic. Even his admirers cannot deny that there are some serious defects in Frege's case. The most obvious one is his employment of the tenns 'psychology' and 'psychological'. Officially these terms connote subjectivity. Frege tended to explain what he claimed to be subjective in terms of mental imagery and the association of ideas. He also held that what is subjective is incommunicable. These notions have odd consequences when combined with his using 'psychological' to label whatever he thought to be irrelevant to logic. The difference in coloring between 'and' and 'but', as well as the difference in word-orqer between 'No fISh are mammals' and 'No mammals are fish' and the difference in modality between 'Possibly every event has a cause' and 'Necessarily every event has a cause' are mistakenly held to belong to psychology and implausibly explained by reference to mental mechanisms.23 At best one can excuse 'these blunders as the by-products of inattention to the details of what is non-logical since Frege's positive identifICation of what is irrelevant to logic was both sound and sharp.24 Overextension of the domain of 'psychology' is matched by misguided
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application of the terms 'logic' and 'logical'. This converse mistake underlies Frege's introduction of the judgment-stroke or the assertion-sign into his concept-script. He held that inferences could only be drawn from propositions asserted to be true.~ Consequently he treated a thought's being asserted as a logical property which had to be symbolized in a logical notation designed to express everything relevant to determining the validity of inferences. Once it is acknowledged that hypotheses or even false judgments have logical consequences, the assertion-sign represents an intrusion of psychology into logic. Frege's assumption that what is subjective is incommunicable is also clearly misguided. He admitted the possibility of expressing judgments about subjective objects (about aches and pains, feelings and emotions, even mental images). Once possessed of the sense/reference distinction he had a ready account of the possibility of objective thoughts about subjective objects, since the senses of every ,/ expression (including designations of mental entities and concept-words ascribing their properties and relations) are held to be objective. 26 Nonetheless, he still affirmed that there is no possibility of communication about what is subjective,27 and he envisaged subjective thoughts that could not be grasped by anyone other than the person expressing them. 2lI Frege here fell into an unresolved muddle. To these sins one might add the fallacy of inferring from the untenability of psychologism about judgments and concepts to the correctness of a Platonistic conception of these logical entities.29 Even if Frege was in no position to discern this error, one has the v right to object that there is manifestly an excluded middle! His case against the psychological logicians and his arguments for his own antithetical conception are by no means fault-free. His alleged achievements, however, are widely held to be substantial, to be decisively established and independent of these demerits, and hence to outweigh the flaws in his anti-psychologism. What were these accomplishments? Different commentators have credited many insights to Frege's account He frrst exposed the conflation of reasons with causes which is integral to psychologism in 10gic.30 He proved that communicability is essential to thoughts, Le., that every thought can be grasped in principle by anybody.31 His claim that the sense of expressions are objective implies the view that what senses speakers attach to words can be ascertained from their behavior,32 hence too that whether different persons understand words in the same way or not can always in principle be discovered.33 Frege perceived that assertoric force (which distinguishes making a judgment from merely expressing a thought) is a logical, not a psychological, feature of utterances; it is essential to a proper understanding of rules of inference, and its representation by the assertion-sign made clear for the ftrst time why in the argument pattern modus ponens (P, and if p, then q, SO q) the conclusion is not already asserted in asserting the conditions for the premise.'" He gave a defmitive criticism of the empiricists' theory of concept acquisition by abstracting from sense-experience.3S He demonstrated that meaning (or understanding an expression) has nothing to do with having
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mental images, pointing out the logical gap between an image and the employment of a word" This argument is held to be Frege's most important contribution to general philosophy, an anticipation of Wittgenstein's private language argument in the Philosophical Investigations.'n Frege's own theory of sense "gave the fIrst plausible account in the history of philosophy of what it is to grasp a thought or to understand a sentence as expressing one";31 thus the positive counterpart of his anti-psychologism was the construction of the fll'St satisfactory theory of understanding a language." Within the compass of his polemics against psychologism there are thought to be the seeds of many of the most important developments of the next hundred years in philosophy of logic and philosophy of language. The grandiose claims made on Frege's behalf envelope his arguments in anachronistic controversies and obscure a clear view of the strengths and weaknesses of his case against the psychological logicians. We shall try to start afresh from a sober statement of his reasoning and work our way gradually towards a proper assessment of his achievements. It will become clear then that many of the insights attributed to him are in fact inconsistent with the main guidelines of his thinking.
HI. Laws of Thought The primary target of Frege's anti-psychologism was the conception of the troths of logic or tile laws of thought which was advocated by Erdmann. The psychological logicians of whom he was the representative held logical laws to be descriptions of patterns of human thinking. Such fundamental principles as the Law of Identity and the Law of Non-contradiction are justified by inductive reasoning from data gathered by introspection or psychological experiments. Philosophers are held to have been mistaken in viewing these laws of thought as necessary truths or self-evident axioms grounding a deductively structured a priori science. They are empirical genenilizations about the workings of the human mind Two different conceptions of these genenilizations were available to radical empiricists. One took them to be the natural laws of mental phenomena; on this view they would be independent of time and culture just as the laws of Newtonian mechanics were thought to hold universally at all times and places. The other view saw them to be historical and anthropological / generalizations; accordingly, nothing could in principle rule out the possibility that laws of thought were subject to evolutionary development or varied in different parts of the world. Insofar as rules for constructing sound arguments and avoiding fallacies were treated by psychological logicians, they were considered to be technical noons grounded in observed empirical regularities. On one view they are analogous to directives about heating rooms which are based on physical laws; the guarantee of the utility of
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modus ponens and the disutility of affmning the consequent must be the psychological impossibility of believing any proposition and its negation simultaneously. Alternatively, rules of deductive inference might be compared with dietary recommendations based on medical knowledge; on this view, observing these principles in thinking would promote the achievement and preservation of mens sana, while violating them would produce cognitive disorder and confusion. This whole conception of logic challenged the traditional consensus about the nature of the propositions of logic, and consequently it also conflicted with the framework of Frege's logical investigations. The notion that the laws of thought are natural laws governing psychological phenomena had many advocates. Sigwart championed this conception, declaring basic logical propositions to be laws of the functioning of human thought which must hold for all thinking beings endowed with the same nature as human beings.40 Boole shared this point of view. He sought a logical symbolism "the laws of whose combinations should be founded upon the laws of the mental processes which they represent,"4! and his aim in The Laws of Thnughl was "to investigate the fundamental laws of those operations of the mind by which reasoning is performed...and upon this foundation to establish the science of Logic."42 By contrast with these later psychological logicians, Erdmann adopted a more radical relativism (later called 'anthropologism' by Husserl). Although the laws of thought govern all human thinking, in his view, human nature might change, and in these conditions the laws of thought would change too. He held that we must concede the possibility of thinking essentially different from our own and the intelligibility of the hypothesis that the laws of thought might undergo evolutionary development: ...logical laws only hold within the limits of our thinking, with out our being able to guarantee that this thinking might not alter in character. For it is possible that such a transformation should occur, whether affecting all or some of these laws, since they are not all analytically derivable from one of them. It is irrelevant that this possibility is unsupported by the deliverances of our self-consciousness regarding om thinking. Though nothing presages its actualization, it remains a possibility. We can only take om thought as it now is, and are not in a position to fetter its future character to its present one.4]
The necessities of thought are thus viewed sub specie humanitatis; they are not unconditional necessities (as most logicians have thought), but rather generalizations conditional upon the actual (and in principle mutable) nature of human thinking. To be sure, we cannot think what nonlogical thought would be like, but this constraint lies within the empirical nature of our minds, not in the nature of the object of thought: ...We cannot help admitting that all the properties whose contradictories we cannot envisage in thought are only necessary if we presuppose the character of om thought, as definitively given in our experience: they are not absolutely
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necessary, or necessary in all possible conditions. On this view our logical principles retain their necessity for our thinking, but this necessity is not seen as absollUe, bill as hypothetil:al. We cannot help assenting to them- such is the nature of our presentation and thinking. They are universally valid, provided our thinking remains the same. They are necessary, since to think means for us to presuppose them, as long, that is, as they express the essence of our thinking."
Frege launched a frontal attack on Erdmann's anthropologism. He objected that this conception subordinated logic to psychology, transforming the science of the laws of thought to the cataloguing of regularities in human thinking. It misrepresented the laws of logic as contingent truths; it depicted them as subjective and potentially variable in content; and it eclipsed their regulative or normative role in the search for truth. At the same time, Frege embarked on a more indirect attack. He tried to trace the roots of these misconceptions to more general confusions about the nature of judgments and concepts, the objectivity of truth, and the process of concept-formation. Much of the strength (and weakness) of his anti-psychologism is apparent only when one follows up those ramifying lines of reasoning. Our initial enterprise will be to expound and evaluate his direct observations about the nature of the laws of logic. There are two main points in Frege's criticisms. The fIrst is the charge that the psychological logicians do not do justice to the normativity of the c..-/ laws of thought His argument now invites misunderstanding. It focuses not on rules of inference (as one might now expect), but rather on the status of the truths of logic such as the Law of Identity and the Dictum de Omni ('Whatever is true of all is true of each'). Psychologism represents these as descriptions of patterns of human thinking, often as psychological laws displaying the nature of the human mind. Frege held this to be inconsistent with the commonplace that logic ranks as a normative science alongside ethics and aesthetics!S The laws of thought must be acknowledged to be _ guiding principles for thought in the attainment of truth; they prescribe or ./ stipulate how one oug1l1 to think if one is to think at all.46 This feature differentiates these basic truths from descriptive generalizations: "The laws in accordance with which we actually draw inferences are not to be identifIed with the laws of valid inferences; otherwise we could never draw a wrong inference."47 Frege accused the psychological logicians of obscuring the fact that logic is concerned with truth just as ethics is with goodness / and aesthetics with beaUty.41 The normativity of logic is not held to be incompatible with representing the science of logic as a system of truths; on the contrary, both ethics and aesthetics, though clearly regulative, were thought to consist of general truths too (e.g., 'Theft is wrong'). What compromises normativity is conceiving of the generalizations of logic as being empirical descriptions, hence as answerable to the nature of something external (the human mind) and consequently liable to experiential refutation. Frege's conception was that this defect could be remedied only by acknowledging the laws of logic to be a priori truths. In this crucial
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respect, he held, they are comparable to moral and aesthetic principles, and this is what he meant to convey in reiterating that logic is a nonnative science. Frege's second main criticism is that the psychological logicians distort ./' the nature of the laws of thought by treating them as contingent on human nature and hence (in Erdmann's version) as potentially variable. Frege held /' that the underlying mistake was a conflation of a proposition's being true with its being taken to be true. Truth, he stressed, is wholly independent of what is believed to be true; no matter how many people take something to be true, no matter what view is destined to be held in the scientific millennium, there is no contradiction in this proposition's being false and in its contradictory's being true.49 Truth cannot be reduced to being taken to be true. That fundamental point, in Frege's view, demolishes the claim that logical laws are contingent, empirical generalizations. The laws of logic are laws of truth, not laws of takings-to-be-true.~ Since truth is an objective property of a thought altogether independent of human thinking and opinion, and since truth is an invariant or immutable property of a thought, the laws of truth must be wholly unrelated to the nature of the human mind and as eternal as truth itself. They must be acknowledged to be necessary truths. The fundamental propositions of logic, the axioms from which all the truths of logic flow, are self-evident truths which are apprehended by the eye of the mind or the faculty of reason, not by inductive arguments based on empirical observations. They are completely general propositions which are known a priori to apply to all judgments and concepts. Frege summarized this view in a famous passage: H being lrue is thus independent of being acknowledged by somebody or other, then the laws of lruth are not psychological laws: they are boundary stones set in an eternal foundation, which our thought can overflow but never displace.'·
These two criticisms dovetailed together in Frege's rejection of the relativism conspicuous in Erdmann's anthropologistic conception of logic. Frege conceded that we might encounter beings who thought in ways flatly contradictory to our own. Such beings would be capable of bringing off judgments contradicting our laws of logic, e.g., judging an object to be different from itself.'2 The psychological descriptions of their patterns of thinking would differ dramatically from the empirical generalizations which describe our thinking. The psychological logician will not merely register these differences and explain them as manifestations of a different mental constitution; he will also conclude that they have one logic, whereas we have another one. Just as ethical relativists deny that there is an Archimedean point from which to evaluate and choose between alternative moral systems, so Erdmann maintained that these beings have laws of thought which are just as legitimate or valid as our own. Frege held this logical relativism to be doubly erroneous. It conflicts with the normativity of logic. Although we can imagine beings who reject the Law of Identity,
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we cannot suppose that these beings are right in so doing. A law of truth is a universal nonn of reasoning which prescribes how judgments are to be made, no matter where, when, or by whom. 55 Once we distinguish between the prescriptive laws of truth and the descriptive generalizations about how and under what conditions thinkers take things to be true, it must be an open question whether thinker's inferences are sound, i.e., whether these laws of taking-to-be-true coincide or not with the laws of truth. The laws of truth, in Frege's view, are the single universal criterion of correctness of inferences. Equally, the laws of truth are in principle timeless and immutable, self-evident truths certified by reason itself. One steps away from logic as soon as one considers human nature and external circumstances as detenninants of judgments; such considerations never bear--on something's being true, but only on our taking it to be true. 54 Like truth itself, the laws of truth are eternal and objective, independent of the nature of the judging subject. Erdmann's relativism in logic conflicts with the unconditional necessity of the laws of logic. Frege epitomized his objection by claiming that, on encountering beings who departed from the Law of Identity, we should say not 'Here we have different logical laws', but rather..-----/ 'Here we have a hitherto unknown type of madness'." The contentions which Frege opposed to Erdmann's theses about logic are undoubtedly correct, though unexciting. The propositions of logic are paradigms of necessary truths; it is nonsense to call them contingent generalizations. It is equally absurd to describe them as empirical statements which are confinned by observations of the functioning of the human mind; one does indeed step outside logic (or outside the bounds of sense) in offering any psychological data as justification for any proposition of logic. Finally, Frege was right to emphasize the normativity of logic; the propositions of logic are obviously relevant to the discrimination of valid and fallacious inference in virtue of somehow setting the standard of what is correct All these points are sound even if their restatement has little value in an era in which naturalist psychologism is not a serious disease among writers on philosophy of logic. Frege's own philosophical explanations of these commonplaces do not, however, advance our understanding of the nature of logic. He did nothing substantial to clarify the normativity of the propositions of logic. He apprehended that it is nonsense to conceive of empirical propositions as v regulative since they are responsible to facts; hence he mimicked the empiricist's strategy of treating ethical propositions as a priori truths and stressed that the source of logic is reason, not experience. But this manoeuvre leaves the regulative roles of logic and moral principles equally obscure. In fact, all that it accomplishes is to secure those propositions against the possibility of empirical disconflfJllation. That nonsense is excluded by classifying them as a priori truths. But Frege thought that the propositions of logic described relations among logical entities (the two truth values True and False, and the first- and second-level functions designated by propositional connectives and quantifiers). Does this not make -../
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these proposlbons answerable to something external? What is held to compromise the nonnativity of the propositions of logic and ethics is the possibility of their being refuted by matters of fact But if the basic truths of logic are grounded in apprehension of relations among abstract entities, the possibility of their being refuted seems to re-emerge. How can one dismiss the possibility that the eyes of the mind might be subject to hallucination or that fresh "logical experience" might compel a revision to the fundamental truths of logic?" As conceived by Frege, a priori propositions seem to be as remote from regulative principles as empirical genenilizations are! His case against Erdmann's relativism seems equally shallow. Dropping from consideration Erdmann's claims about the source of knowledge of logical truths in psychological observations, we are left with the problem of dealing with the philosophical claims that there might be different and incomparable systems of logic (like different systems of morals). Frege evidently held that the laws of truth are unique and detenninate, and he would have denied the possibility of a genuine alternative logic Gust as he opposed the intelligibility of the supposition of non-Euclidean geometries). But did he indicate a procedure for adjudicating between alternative logics (e.g., between 'classical' and Intuitionist logic)? Or outline a method for settling whether his codification of the laws of truth is correct? According to his own conception of logic, these questions are intelligible and hence require answers. A determined relativist could argue that there is a discrepancy between what is truly self-evident and what Frege took to be the fundamental axioms of logic. Frege's claim that the laws of truth are standards of correctness of inferences gives no reason for preferring his own logical principles to every set of competitors, and therefore his opposition to alternative logics, by his own lights, must be judged to be mere dogmatism. These philosophical defects in Frege's position are symptomatic of three misconceptions that lie at the very foundations of his notion of the nature of logic. The fIrst two of them he shared with the psychological logicians whom he attacked. First, it was commonplace to distinguish within the science of logic between necessary truths ('Everything is what it is', 'Whatever is true of each is true of all', etc) and rules of reasoning (both rules for sound reasoning such as the syllogism in Barbara ('All A's are B's; all B's are C's; so all A's are C's') and rules for excluding fallacies (such as affmning the consequent». A similar distinction was drawn in moral philosophy between ethical truths ('Murder is evil') and rules of right conduct ('Thou shalt not murder'). That there are conceptual connections between the two kinds of truths in these cases is indicated by the traditional classification of logic and ethics as normative sciences, and equally by the persistence of disputes whether logic should be mnked as the science or the art of right reasoning. Since logical truths were thought to be substantial, informative propositions which can stand to one another in the relation of entailment, the only available conception of the connection between these and the rules
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of logical inference was that of the relation of a natural law and technical rules of mechanical or biological engineering. Rules of inference are held to stand to the truths of logic just as rules for positioning radiators and excluding draugh~ stand to the physics of heat-generation and transfer, or perhaps as dietary principles stand to generalizations about human metabolism and pathology. In all these cases, particular rules are justified as the most effective means for achieving certain goals, and these goals can be understood and described independently of the rules advocated for attaining them. Erdmann thought these parallels to be exact because he held that logical truths have the status of psychological laws. Frege would have seen only an analogy" since he denied that the truths of logic are empirical. Nonetheless, he conceived of rules of inference as norms which specify the most efficient means to achieve the goal of attaining truth; the goal can be characterized independently of these norms, and the norms themselves are justified by the objective logical relations between judgments which are codified in the propositions of logic of the Basic Laws of Arit1unetic. This conception of logic has two basic defec~. First, it depic~ the concept of bUth as independent of the concept of valid inference. In fact, however, that a judgment can be derived by certain transfonnation-rules from propositions known to be true often serves as a criterion for holding this judgment to be true. Truth is not related to valid inference as health is to diet, but rather as checkmate is to chess. Secondly, Frege's picture of rules of inference obscures just what distinguishes the propositions of logic from all other propositions. By casting these propositions in the same role as laws of physics, it hides from view the fact that they have a completely different function in speech. As Wittgenstein later discerned, they are tautologies, propositions which say nothing all.SI Hence, they cannot serve as grounds justifying technical norms which regulate human thinking; rather, the conceptual connections between tautologies and rules of deductive inference is that to acknowledge that a pattern of propositions exemplifies a rule of inference (e.g., that the scheme 'p, if P then q, so q' is a rule of inference) is to acknowledge that the corresponding conditional expresses a tautology (e.g., that the proposition 'if p and if p then q, then q' or 'p.p~.~.q' is a tautology)." Frege's unquestioned assumption that the laws of logic are (/ significant judgments (propositions with sense) forced upon him the misconception that rules of inference are technical nonns answerable to independent bUths, and this shared misunderstanding underlay his disagreement with Erdmann. Secondly, both Frege and Erdmann thought that the truths of logic must be distinguished from other significant generalizations in terms of their subject-matter. Indeed, both agree that these propositions were statements about concepts, judgments, and inferences; they held that logical laws describe relations among concepts or judgments, thereby fannulating constraints to be respected by any acceptable rules of inference. Disagreement arose from the further clarification of this common ground. Erdmann held concepts and judgments to be mental entities, and the laws
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describing their inter-relations to be genenilizations belonging to empirical psychology. Frege, by contrast, thought concepts and judgments to be imperceptible but real entities in a logical realm, and the laws of truth to be a priori generalizations grounded in deductions from self-evident axioms. The most serious defects in their understanding of logic arose from the point not in dispute between Frege and Erdmann. First, both went disastrously astray in trying to distinguish logical propositions from others in virtue of their content; it is the function or use of the propositions which is diagnostic. Indeed, the propositions of logic, being tautologies, have no content at all. Hence, their function cannot be to say something distinctive (whether about the mind or about the realm of logical entities). The topic neutrality and universal applicability of the propositions of logic are both compromised by the very idea of their having a specific subject-matter. (As Wittgenstein later argued, Frege's view that logical operators designate special logical functions or concepts is incoherent.~ The true function of logical truths is apparent in the reflection that to show that a fonnula is a tautology is to exhibit an internal relation among propositions (e.g., proving that p.p~.--+.q is a tautology is equivalent to showing that q follows from p and p--+q). Secondly, Frege and Erdmann had a corresponding misconception of the role of proofs within an axiomatization of the propositions of logic. They thought that these proofs established the truth of one significant proposition from the previously established truth of other significant propositions. In fact, these proofs demonstrate that a formula is a tautology by deriving it by a sequence of authorized transfonnations from other fonnulas that are tautologies.61 To apprehend this function of derivations within axiomatizations of logical truths is to undennine Frege's case for supposing that the propositions of logic are significant formulae having content or sense. Both Frege and Erdmann lost their grip on the nature of logic before their detailed reasoning even began! Thirdly, although Erdmann (and Husserl) had only a vague and distorted grasp of the connection between the concept of logic and the concept of thinking, Frege went further off course by ignoring this conceptual connection altogether. This is evident in his concession (to Erdmann) that we might encounter beings who think in ways incompatible with our laws of thought: such beings might bring off judgments contradicting the Law of Identity. Frege noted that this would be "a hitherto unknown type of madness." But, as Wittgenstein later objected,62 "he never said what this 'madness' would really be like." What would it be to "bring off a judgment contradicting the Law of Identity"? Frege did not describe what the imaginary beings must do to be judged to think: contra-logically. If they said 'a~', would not we rightly conclude that either they misunderstood ':1-' or meant something other 'than identity by this symbol? Could they think: or even try to think that this book is not identical with itself! Could they express what they think? How, if 'a~' either expresses nothing or fonnulates a different thought? The attempt to describe a case of thinking
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contrary to the Law of Identity cannot so much as get started. It is akin to the attempt to describe what it would be to castle in dmughts or to score a touchdown in bridge. Frege made a mistake in presuming that the concept of thinking can be divorced from the concept of the laws of logic. What we call rules of deductive inference partly defme what we call 'thinking', 'speaking', 'arguing', 'saying the same thing', 'contradicting oneself, etc. Though the laws of logic might be called expressions of our thinking habits Gust as the rules of chess show how we play chess), they are also expressions of our habits of thinking Gust as the rules of chess show what we call 'playing chess')." Frege was wrong to imagine that beings who regularly violated the basic laws of logic in speaking can be said to engage in what we call 'thinking'. The impossibility here is not one that might be circumvented by exercises, by striving every morning to conceive six impossible things before breakfast. It is a grammatical impossibility comparable to playing chess while castling through check, moving rooks diagonally, advancing pawns to the ninth rank, etc. Frege distorted the concept of thinking by divorcing it from the concept of logic. (And thereby he deprived himself of the possibility of arriving at an explanation of the absurdity of imagining alternative logics.) The weaknesses which are apparent in Frege's criticisms of Erdmann's conception of logic lie at the very foundation of his own philosophy of logic. To eradicate them would be to throw his entire clarification of the nature of logic back into the melting pot. Moreover, in discarding the idea that the propositions of logic have content or sense, Frege would have had to abandon his fundamental idea that function/argument analysis is the key to the treatment of propositional connectives and quantifiers.
IV. The Objects of Judgment Despite apparent agreement on taking the subject-matter of logic to be concepts and judgments, the psychological logicians fell into the misconception that the laws of logic are psychological generalizations about human thinking because, in Frege's view,they mistook concepts and judgments for mental entities. Consequently Frege's task of rooting out their errors demanded a clarification of the nature of concepts and judgments and a critical examination of the arguments purporting to show that concepts and judgments are mental objects. His primary concern was to establish a proper understanding of what judgments are since each rule of deductive inference lays down a norm for the derivation of a judgment from other judgments. Like many other logicians, Frege drew a distinction between ~ mental acts of making judgments and the objects of which these acts are directed. As an instance of this kind of act he might cite his judging on 1st January 1879 that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides; in this case what he
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judged, Le., the object of his judgment, would have been the Pythagorean Theorem (i.e., that the square). It is the objects of judgment (canonically he originally called fonnulated in indirect statements) that ./ 'judgeable-contents' and later rechristened 'thoughts' (
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did not sketch a coherent antithesis to be put in opposition to the psychologicians' doctrine about the psychological nature of judgments. The complaint is often voiced that he did not justify his claim that judgments are non-spatial but real abstract objects (compamble to numbers) which exist independently of human thinking and which the mind apprehends in perfonning the acts of thinking and judging. This defect is comparatively superficial. The deep objection is that it is incoherent to treat judgments or thoughm in this manner. It is inconsistent with important aspects of the concept of a judgment (with how we use the terms 'judgmenf and 'thoughC), and it misrepresents other related concepts such as the concept of thinking, of making a judgment, and of asserting something. Frege's criticism is forceful only if attention is narrowed down to the one point that the inference attributed to the psychological logician is fallacious. The weaknesses in his case become more apparent in efforts that he made to buttress his centr3l argument with supplementary objections. He tried to show that the psychological logicians' conception of judgments is not merely unsupported by cogent reasoning, but also inconsistent with commonplaces about the nature of judgments. Like his adversaries, he took judgments to be what truth and falsity are predicated of. Indeed, he explained the concept of a judgment (or thought) by remarking that a thought is "that to which the question 'Is it true?' is in principle applicable."" But, he observed, truth is distinct from being taken to be true. What is true is true independently of whether anyone entertains it, of whether anyone takes it to be true or everyone takes it to be false, or of whether it is affirmed or denied. 61 Moreover, thoughts, if true, are timelessly and eternally true; it makes no sense to state that a particular thought used to be true but is no longer SO.69 Finally, one may convey what one thinks or judges to another, one may communicate thoughts or judgments to others, and this presupposes that it makes sense to say that to people entertain the same thought or make the same judgment Frege argued that acknowledging these platitudes excludes the possibility that the objects of judgment are complex ideas or subjective, psychological entities as the psychological logicians contended. In fact, he elaborated a reductio of their conception of judgments. His reasoning turns on the premise that ideas are subjective, and on an interpretation of the term 'subjective' which he shared with his adversaries. Frege held that the subjectivity of ideas carries three important implications. He did not subject these implications or their alleged interconnections to rigorous philosophical scrutiny. Firs~ ideas need owners; there is no such thing as an idea which is not someone's idea.70 Second, ideas are privately owned or cannot be shared; it makes no sense to claim that another has my ideas (just as another cannot have my pains). Every idea has only one owner; no two men have the same idea' 1 "Another idea is, ex vi termini, another idea."72 Frege understood this thesis not to exclude the possibility that two men have similar or even exactly
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similar ideas. It makes sense to say the other has a mental image exactly like mine (e.g., we both have images correctly described as 'A dark red triangle with a black dot in the lower left corner stands against an even pale blue background....') just as it makes sense to say that another's pain exactly resembles mine (e.g., he has an acute stabbing pain in his left big toe and so do I). What Frege ruled out was the possibility that two people have the very same ideas (mental images, pains, etc). Thus he drew a distinction between numerical and qualitative identity (as in saying that two people own different cars which are exactly alike in being red Volkswagen Passat 1600 GL's), and, like the psychological logicians too, he applied this distinction to ideas, images, pains and other mental entities. He agreed with Erdmann in claiming that two men could have qualitatively identical ideas, but never numerically identical ones. My idea is always different from yours in that my idea is mine while your idea is not mine (but yours). Third, ideas are held to be epistemologically private: only the bearer of an idea knows its nature and characteristics (others can merely make conjectures). In this respect, he argue
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First, the claims that truth is an objective property of judgments (that being true is independent of being taken to be true) and that truth is an immutable or eternal property of thoughts (that a true thought cannot become false) are argued to be inconsistent with taking judgments and thoughts to be existence-dependent on minds. It was true that 2+2=4 even before there were any human beings," and this thought cannot be a fleeting mental item which would pass away with the death of an individual person or the annihilation of mankind. Consequently, thoughts, unlike ideas, must be "independent of our thinking as such. "7' "A thought does not have to be owned by anyone...77 Secondly, if the thought expressed by 2+2=4 or by the Pythagorean Theorem were an idea, it would "belong specially to the person who thinks it";78 it would be impossible for two persons to have the same thought. We would have to distinguish 'my Pythagorean Theorem' from 'his Pythagorean Theorem', since my thought would belong to my consciousness and his to his consciousness.79 If one person asserted that 2+2=4 while another denied this, "there would be no contradiction, because what is asserted by one would be different from what was rejected by the other...[A] contradiction occurs only when it is the very same thought that one person is asserting to be true and another to be false"80 Equally, it would be impossible to communicate any thought to another person, and hence there could be no science of mathematics common to many persons.'l A thought could not "pass out of the private world of one person into that of another. The thought that entered the latter's mind as a result of the communication would be different from the thought in the former's mind"82 The psychological logicians, in Frege's view, fall into absurdity by denying the very possibility of any communication of thoughts and any interpersonal conflict of judgement. Thirdly, the ideas awakened in us by the power of association vary from person to person.83 Consequently, if a thought were related to a sentence in the same kind of way that sensations of taste are related to the chemical composition of foods, then it would be impossible to establish the exact similarity of the thought that different persons attach to the same judgment; but since "the slightest alteration can transfonn a truth into a falsehood,"84 this would have the consequence that it would be impossible to ascertain or resolve any apparently cognitive conflicts. In Frege's view, the psychological logicians put truth beyond the bounds of knowledge, treating judgments as subject to the principle de gustibus non disputanduml 85 This case against 'the conception that judgments are complex ideas is a model of effective dialectic. It exposes internal incoherence in the adversaries' position; agreed concessions are turned against the conclusion to be supported. Nonetheless it has seldom-noted limitations and serious weaknesses which prevent our now taking it to be a paradigm of penetrating philosophical investigation. First, Frege's argument has the form of a reductio of the thesis that every judgment is a complex idea. This conclusion is held to entail that no
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judgment can be shared or communicated (and hence that mutual understanding is impossible), and that implication Frege condemned as absurd. His counterclaim is the negation of this genemlization, namely that some judgments or thoughts can be communicated. This is exactly what he maintained, instancing the Pythagorean Theorem and arithmetical equations as thoughts that can be shared among mathematicians. In his arguments against the psychological logic~s he refrained from advancing the unnecessarily strong thesis that every thought can be shared or communicated. Indeed, in "The Thought," he explicitly envisaged thoughts that are essentially private and limited to the sphere of a single consciousness.86 In criticizing the psychological logicians, Frege did not embrace the thesis that every thought can be communicated, or that there is no such thing as a person having a thought which another cannot understand On the other hand, he did have an inclination towards adopting this radical antithesis, and some of his remarks invite this interpretation. In particular, he regularly argued that the thought expressed by a sentence, Le., its sense, is something objective, hence in contrast to any idea or image that the sentence calls Up.87 This suggests that no thought "belongs specially to the person who thinks it,"· that "the being of a thought may...be taken to lie in the possibility of different thinkers' grasping the thought as one and the same thought, tl89 and even that every thought belongs to a third realm of objective but imperceptible entities. In fact he argued more cautiously that not every thought requires a bearer and ,that a thought such as the Pythagorean Theorem belongs to a third realm.90 Nonetheless there is an unresolved tension in his conception of thoughts. Second, Frege's main weapon against the psychological logicians, the distinction between numerical and qualitative identity of judgments, was something of which his adversaries were forewarned and against which they had forearmed. Defensive preparations had an extensive history in classical empiricism, and they had been brought up to date by Sigwart, Erdmann, etc. Their general sttategy was to argue that commonplaces about truth and communication are only apparently in conflict with identifying judgments with subjective ideas, or equivalently that these commonplaces are only apparently true about judgments. In either case the conflict would be resolved without the need to surrender to the forces mustered by Frege. For example, Erdmann tried to allow for talk of 'objective truth' and 'objective universal certainty', but he did so by explaining these expressions in terms of 'the general agreement of judging subjects'. A defense of identifying judgments with ideas might take the form of arguing that there is no possibility of establishing anything beyond the mere appearance of communication even in mathematics (because of the impossibility of ascertaining numerical identity of ideas) or that qualitative identity of ideas is all that is required for genuine communication and conflict of opinion (because of the impossibility of conveying the exact content of ideas from one person to another).'! In short, Frege might be accused of begging serious questions by assuming that two persons can have numerically the ----------------------------
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same thought and that truth is an eternal, mind-independent property of thoughts. In one sense, this is a fair criticism. Frege did not meet the psychological logicians on this venerable battlefield. He tried to avoid fighting around these prepared positions. On the other hand, this is not clearly a defect in his case against them. The central line of his attack would have been obscured by skirmishes on all these points of scholastic detail. In any case, Frege put his finger on a genuine conceptual confusion in the reasoning of the psychological logicians (namely, the conflation of truth with universal agreement). This makes the apparent weakness rhetorical mther than philosophical. Third, Frege did not root out the various confusions which support the venemble philosophical doctrine that what is subjective or mental cannot be the subject-matter of fully intelligible intersubjective judgments. On the contrary, he himself erected a weak doctrine of the epistemic privacy of the contents of immediate experience, and he supported this with traditional arguments. He directed this conclusion against the claim of the psychological logicians that exact similarity of ideas is all that is required for one person to understand what is asserted by another. Frege's thinking can be expounded so that this target is in sight from the outset. He construed having an idea on the model of perceiving a sensible object; but, in the case of subjective objects, the perception is internal (or introspective). Specifying the content of one's ideas (i.e., what idea one has) is held to be describing the characteristics (or properties) of a subjective object; to say exactly what one thinks is to give a full and complete description of an idea. Consequently, the statement that two persons have exactly similar (Le., qualitatively identical) ideas entails that the characteristics of their (nwnericaJly) distinct ideas match each other exactly. Frege imagined that judgments of similarity must rest au fond on juxtaposition of objects and direct comparison between them. Hence, what is required to establish an exact similarity between two ideas must be ascertaining that they match each other in the same way that two rods can be demonstrated to have the same length by exhibiting their coincidence in length when they are placed side by side. But the fact that two different persons cannot have numerically the same idea rules out the analogous test for qualitative identity of ideas. Frege argued that "an exact comparison is not possible because we cannot have both ideas together in the same consciousness.",2 Although a rod may be moved from one place to another without any change, an idea can not be transported from one mind to another for the purpose of effecting a comparison. Consequently, Frege concluded, it is impossible in principle to attain knowledge that two different persons have exactly similar ideas. The psychological logicians cannot prove that there is qualitative identity of the ideas of any two persons, and hence for all they can demonstrate there may be no successful communication at all. Frege did not push this reasoning to its logical conclusion. On the contrary, he rested with a weak thesis. He suggested that we establish with certainty rough similarities and differences among ideas (and, more generally, among minor experiences); he excluded
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only the possibility of knowledge of any exact correspondence." This moderate skepticism seems intemally unstable; it is not clearly intelligible to speak of knowledge of rough correspondence in any case where knowledge of exact correspondence is in principle impossible. Moreover, although Frege's whole case is straightforward, all of the premises that it rests on seem deeply flawed. Calling ideas 'subjective objects' indicates too great a degree of parallelism between the concept of an idea and the concept of a sensible object; saying what one thinks is altogether unlike looking carefully at an object and describing in detail what one fmds; and the idea that judgments of resemblance must be grounded in juxtaposition of objects involves generalizing one form of comparison as a norm for all forms of comparison. Frege thought that the defects in treating judgments as mental entities could be remedied only by acknowledging that the objects of judgment Gudgeable-contents or thoughts) are abstract objects belonging to a third realm. To have a particular thought (e.g., to entertain the thought that 2+3=5) is comparable to perceiving a physical object (e.g., to seeing the Eiffel Tower). In gmsping this thought "something comes into view whose nature is no longer mental."94 More generally, thoughts "are independent of our thinking and confront each one of us in the same way (objectively).... In this respect they are like physical bodies. "95 The judgeable-content of the equation 2+3=5 "is not the result of an inner process or the product of a mental act which men perform, but something objective...it is something that is exactly the same for all rational beings, for all who are capable of grasping it, just as the sun, say, is something objective. "96 The conception is claimed to inform the metaphors of gmsping a thought, of laying hold of or of seizing it These expressions clarify that "what is grasped, taken hold of, is already there and all we do is take possession of it.",., Thoughts differ from the Eiffel Tower or the sun in being neither perceptible nor located in space and time, but they are nonetheless real and objective, like numbers or the Equator.9I They are essentially timeless, i.e., immune to change in their intrinsic natures. 99 Hence, they are fit bearers of the timeless or eternal properties of truth and falsity. 100 The claim that a thought is something which 'confronts each of us in the same way' expresses the fact that in grasping the thought that 2+3=5 each rational being apprehends the very same object It is the strict parallelism between this act of grasping a thought and that of seeing the Eiffel Tower which secures the numerical identity of what is judged to be true by different persons who think that 2+3=5, and it is only this conception which provides an escape from the philosophical predicament of the psychological logicians, namely that different thinkers have only qualitatively identical thoughts. To the defect diagnosed in Erdmann's psychologism the doctrine of thoughts as abstract objects ('Platonism') is the only conceivable remedy; i.e., if the problem is genuine, then the answer can take no other form. Frege's conception of the objects of judgments may well strike modern philosophers as naive and unsophisticated. One might mock at his
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assumption that the possibility of communication rests on there being thoughts in a third realm which 'confront us all'. It would be easy to make nonsense of his notion that the reality of thoughts presupposes that they have causal powers and thereby have effects on thinkers; 101 he fell into abswdity in trying to explain how "thoughts may indirectly influence the motion of masses.'tl02 Equally one could make fun of his embarrassment about the nature of thinking. Taking the grasping of the law of gravitation to be a mental process, he noted that: ...it is a process which takes place on the very confmes of the mental and which for that reason cannot be completely understood from a psychological standpoint. For in grasping the law something comes into view whose natme is no longer mental in the proper sense, namely the thought; and this process is perhaps the most mysterious of all. t03
In mising these points one would marshall against Frege various age-old objections to Platonism. There are, however, deeper and more far-reaching objections which these familiar philosophical manoeuvres would not encompass. The real defect in Frege's stance is not that he postulates unnecessary entities and countenances superfluous cognitive mysteries. It is that his conception of thought as abstract objects is incoherent, and that this fundamental incoherence spreads like a cancer through the whole of his philosophy of logic. The root of the confusion was the unquestioned assumption that Frege shared with the psychological logicians, namely that it makes sense to distinguish qualitative and numerical identity of thoughts, judgments and ideas. Both parties to the dispute agreed that one can differentiate between two persons' having the very same (identical) thought or idea and their having more or less similar thoughts or ideas, which is the extreme case might be exactly similar. This dispute centered on whether strict identity or only exact similarity is essential to communication, conflict of opinion, and the intersubjectivity of science. Frege argued that numerical identity is required and further that two people cannot have the very same idea (given that ideas are understood to be subjective or mental entities). The core of this argument is an appeal to Leibniz' Law. Suppose that my idea of the Pythagorean Theorem were identical with yours. It would follow that all the properties of my idea must be properties of your idea. But my idea is mine, not yours, and your idea is yours, not mine. Hence, it is self-contradictory to assert that my idea is the very same idea as yours. This would be comparable to asserting that my nose is identical with your nose. 104 This reasoning turns on confusions that Wittgenstein noticed and elaborated as central elements of his argument against the possibility of a private language. U)5 There is only one intelligible use of the expression 'the same' with reference to mental entities such as ideas (mental images) or pains, feelings of elation or depression, and even thoughts. To say that two
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persons have the same image is to say that each has an image which is to be described in the same way (e.g., 'four moons circling around Jupiter in coplanar circular orbits'). Likewise, two persons have the same pain if and only if they have pains of the same quality and intensity in corresponding locations (e.g., both have an acute toothache in the left rearmost molar). It is an abuse of the practice of using 'the same' to maintain that two persons whose images (or pains) are correctly described in the same way have exactly similar but not identical images (or pains). Equivalently, since ideas (or pains) are individuated by reference to persons (their owners), it is nonsense to maintain that specifying the owner of an idea (or pain) is to describe one of its properties. Hence, appeal to Leibniz' Law is out of place. To note the truism that my idea is mine and your idea yours is to provide no reason whatever for denying that my idea is identical with yours. Only a difference in properties justifies concluding that they are not the same. But to claim that being mine is a property of my idea is, absurdly, to convert the owner of an idea into a property of the idea he has. Frege's case against the psychological logicians rests on drawing a distinction between qualitative and numerical identity for complex ideas and therefore it collapses once the distinction is shown to be unintelligible. Indeed, identifying the objects of judgments with complex ideas is compatible with the platitude that different speakers may make the same judgment Once the use of 'the same' is properly understood, the very same argument for claiming that two persons may have the same thought (viz., that each thinks that 2+3=5) also supports the conclusion that they may have the same complex idea (viz., that each has an image of 4 moons circling around Jupiter). Just as Frege's objection rests on a nonsensical presupposition, so too his own positive conception of the objects of judgment is itself nonsensical. The ground of its incoherence is the mirror-image of the ground for the incoherence of his criticism of the psychological logicians. The point of introducing judgeable-contents or thoughts as objects which 'confront us' like the sun or the Eiffel Tower is to explain the possibility of different persons' making the same judgment or entertaining the same thought The conttast between numerical and qualitative identity is familiar from discourse about objects of perception; we say that I now own a car exactly similar to the one I owned last year but not the same one, or that this stamp on the top left corner of the sheet is exactly like the others on the sheet but not identical with the stamp on the bottom right comer. Frege's strategy is to transfer this contrast to thoughts by treating them as non-sensible objects in the third realm. Two mathematicians have the very same thought, not merely exactly similar thoughts, in cogitating about the Pythagorean Theorem. The problem is to make sense of this new joint that Frege has added to discourse about thoughts. What would it be to have not the identical, but merely an exactly similar thought to the one I had yesterday? Or how could Frege explain your having a thought resembling but not the same as the thought that I strive to communicate to you? He
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offered no criterion for distinguishing numerical from qualitative identity of thoughts. He masked the need for making the contrast intelligible by comparing thoughts with the SUD, Mont Blanc, and the Equator rather than with stars, pianos, and chimneys, i.e., with cases where the question 'Is this the same...or only one exactly similar?' are pressing. The most serious objection is not that he left a lacuna here, but that he ruled out the possibility of making a distinction which was necessary for his purposes. For it is by reference to location in space and time that the contrast between 'the very same' and 'exactly similar (but not identical)' is drawn. Yet Frege declared that thoughts (and other abstract objects such as numbers and sets) are essentially non-spatial and timeless. 10fi To surrender these theses would lead to manifest absurdity while to retain them abrogates the conditions necessary for making sense of the claim that different mathematicians apprehend numerically the same thoughts in geometry and arithmetic. Thoughts cannot differ as two stamps of the same design do, but it does not follow from this that the thought that one geometer has on reading the Pythagorean Theorem is numerically identical with the thought that another geometer has. Frege's conception of judgeable.-eonteDts or thoughts as imperceptible but real objects had many corollaries in his thinking. Indeed, it is the cluster point of a galaxy of conceptual confusions. (i) The obverse of the doctrine of the objectivity of thoughts is a picture of thinking which belongs to a framework of Cartesian dualism of mind and matter. Entertaining a thought or thinking about something is held to be a subjective mental activity or process to which the subject himself has privileged access and others have no access at all. Communication about thinking (like discourse about ideas, images, pains, and visual phenomena) is allegedly subject to severe limitation. It is in principle impossible for one person to ascertain whether any person thinks just as he does or whether he has the very same thoughts for the very same reason that Frege held it to be impossible to establish whether owners have exactly similar ideas or images. One might think that he gained little or nothing in substituting the epistemic privacy of thinking for the epistemic privacy of thoughts, and he certainly misrepresented the concept of thinking (and many other concepts) by divorcing this 'inner state' from its outward criteria. (ii) Frege misused the expression 'to entertain a thought' and 'to express a thought'. He held that in considering the proposition that 4 is not a prime number I must entertain the thought that 4 is a prime number. Equally, in using the sentence '4 is not a prime number' to make an assertion, or in asking the question 'Is 4 a prime number?', I am alleged to express the thought that 4 is a prime number. All these claims are nonsensical if measmed against everyday explanations of 'entertaining' or 'expressing' a thought? The concept of thinking is linked to the concept of expressing a thought, and hence misunderstanding about one spillover into evident misconceptions about the other.
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(iii) Frege contrasted making an assertion (or expressing a judgment) with the act of merely expressing a thought (without asserting it). Consequently he fell into the view that making an assertion is the outward manifestation of the performance of a pair of mental acts (entertaining a thought and judging it to be true). He thought that being uttered with the requisite seriousness is what makes the expression of a thought into an assertion, and that the proper mental backing is what must be added to the expression of a thought to transform it into an assertion. (In the judgment-stroke of his concept-script he vainly tried to encapsulate this mental act into a sign POl) In Frege's own view, this ought to carry the implication that I can never know whether another person makes an assertion. It also misrepresents the concept of an assertion by divorcing the act of asserting something from its behavioral criteria: the proper clarification of the distinction between expressing a thought and making an assertion turns on the observable circumstances in which an utterance is made, not on the occurrence of allegedly private mental acts. (iv) Frege's picture of communication in mathematics and science is also subtly but importantly askew. He held that, if I state the Pythagorean Theorem and you understand what I have asserted, then we must now have the same thought. Success in communication is a matter of sharing thoughts. (This idea underlies his introducing thoughts as objects that confront all thinking beings alike.) Likewise, conveying information is often held to be transferring thought from one person to another; Frege would no doubt have disliked this common locution, preferring instead to describe it as bringing about the joint apprehension of thoughts which belong to the public domain. But there is a risk of misunderstanding these claims. If you understand what I asserted in formulating the Pythagorean Theorem, you must be able to explain what I asserted and hence you must be able to express the same thought But it does not follow that you must have this thought (or think that the square of the hypotenuse), just as it does not follow from you knowing what I feel (viz., a toothache) that you must have what I feel (viz., the same pain). Had Frege appreciated this point, he would not have treated 'My idea is mine, your idea is yours' as even a prima facie objection to taking ideas to be what is communicated in scientific and mathematical discourse. (v) Frege mistakenly committed himself to an asymmetry in the grammar of the expressions 'the same thought' and 'the same idea'. On his view, it is an essential truth that my idea cannot be identical with your idea; for my idea is mine, and your idea is yours. On the other hand, no parallel reasoning holds for our thoughts, or at least for objective thoughts in science and mathematics. He hinted at an impropriety in using the expressions 'my thought', 'your thought', 'his thought';I.. but of course, this is both intelligible and sanctioned by ordinary cannons of well-formedness. So his point must be that it adds nothing to characterize what is identified as 'my thought' by calling it 'mine', or at least that to call it 'mine' does not exclude calling it 'yours' and 'his' as well. Consequently, it is
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illegitimate to say 'My thought is mine, not yours, and your thought is yours, not mine', or at least this cannot be called an essential truth about thoughts. This alleged distinction between ideas and thoughts lacks any solid foundation. In fact, the sentence 'My idea is mine (not yours)' (as well as 'My pain is mine') has just as little use in our discourse as Frege claimed for the sentence 'My thought is mine'. (vi) Frege gave a literal and rigorous interpretation to the claim that judgeable-contents or thoughts are objects. These entities have the same logical status as the sun or Mont Blanc; they are objects as opposed to concepts. For this reason, the frrst-Ievel concept of identity is applicable to thoughts stricto sensu; in apprehending the same thought, different speakers confront the same object, just as they do in perceiving Mont Blanc. This is the foundation for Frege's analysis of propositional attitudes as relations between persons and objects (the senses of the sentences which fonnulate indirect statements). More importantly, it is the foundation of his philosophy of logic. For judgeable-contents (later the two truth-values) are the objects which are the values of the functions (concepts) that are the engine of his logical analysis of inference. Hence, these objects are the sine qua non of his conception of propositional connectives and quantifiers as the names of special logical functions. Allocating the objects of judgment (and the True and the False) to the logical category of objects is the rock on which Frege built his logic, and it is this rock which Wittgenstein dynamited in "Notes on Logic" and the Tractatus.
v. Objects ~rege's view, the doctrines of the psychological logicians all grew out of their basic misconception about the nature of judgments. He recognized that their thesis that judgments are subjective ideas had important concomitants, and hence he set about strengthening his counterclaims by criticizing the implications of this root error. This actively expanded into remarks on what judgments are about, on the nature of concepts and on the process of concept-formation. These views had independent importance because they had bearing on misconceptions about the nature of numbers which sowed confusion in philosophy of mathematics and impeded understanding of the fundamental thesis that numbers are imperceptible but real objects in a third realm. This fact no doubt motivated Frege's making more extensive remarks about these supplementary questions than his criticism of the psychological logicians would otherwise have wammted. The notion that judgments are complex ideas suggest that they can always be split up into parts and that these parts must themselves be ideas. A judgment is a combination of ideas. Consequently, in a significant declarative sentence, the significant units into which logical analysis articulates it must each express ideas, and the idea expressed by the whole
In
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sentence must be built up out of the ideas expressed by its significant parts. A judgment is held to be put together out of ready-made ideas. This general schema for the logical analysis of judgments seemed beyond question, even though the articulation of particular judgments into their proper parts might be a subject for dispute. Would it not be absurd to maintain that an idea might have parts which were not themselves ideas? As if a mountain or house could be part of an idea! And would it not be equally absurd to hold that a judgment could fail to be complex? As if an assertion could be made without attaching a predicate to a subject! In Frege's view, the psychological logicians committed themselves to the doctrine that the (logical) subjects and predicates of judgments are uniformly ideas. 109 The psychological logicians gave analyses of judgments based on the venemble patterns of syllogistic logic (and supplemented by notions taken from the contemporary logical algebras elaborated by Boole, Venn, Schroder, etc). They concurred in claiming that the proposition'All men are mortal' expresses the subordination of one concept (man) to another concept (mortality), and hence they were committed to the thesis that concepts are ideas. Indeed, they openly advocated this view. Equally, they took 'Some mammals lay eggs', 'No whales are fish', and 'some birds cannot fly' as expressing relations between pairs of concepts. In all these cases, they acknowledged the forms of judgments hallowed by syllogistic logic, and they accepted that the components of the judgments are ideas. Matters seem less straightforward with singular judgments. What are the parts of the judgment expressed by 'Socrates is mortal'? There had been long-standing disagreement about how to analyze such propositions, and hence the psychological logicians had a choice between two options. According to the frrst, this proposition might be held to express subordination of concepts, and hence to have the same logical form as 'All men are mortal'. On this view, what is distinctive about the name ' Socrates' is that it signifies a concept under which only one object falls; it is an 'individual concept', whereas 'man' signifies a general concept Generalizing this strategy, one could claim that all judgments express relations of concepts. Consequently, the thesis that the parts of judgments are ideas boils down to the claim that concepts are ideas. Frege rejected not only this conclusion (as we shall see), but also the reasoning by which it is here derived. He lodged two main objections (i) The judgment that Socrates is mortal has a different logical form from the judgment that all men are mortal. The frrst expresses the fact that an individual falls under a concept (or that an object has a property), while the second expresses a (second-level) relation between two concepts. 110 Assimilating the two forms has the implication that all judgments express relations between concepts. This blocks recognition of the fact that the simplest form of genemlization involves only one concept (as in 'Everything is extended'), not two (as in 'All men are mortal'), and it equally stands in the way of understanding a correct explanation of universal generalization (viz., the judgment everything has the property is true if and only if every
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object falls undez the concept 11 I Frege's route to the logical analysis of judgments of multiple genenility went through the claim that 'Socrates is mortal' does IIOt express a generalization (or subordination of one concept to another). (ii) Failure to make this distinction is related to correlated with other philosophical confusions. In particular it leads to conflating an individual with the set whose only member is this individual; this followed from treating 'Socrates is mortal' as stating that a singleton set falls within the extension of the concept mortal. It also obliterates the distinction between frrst- and second-level concepts. 112 This is clear enough, in Frege's view, since the judgment that Socrates is mortal states that an object falls under a fIrst-level concept, whereas the judgment that all men are mortal states that the second-level relation of subordination holds between two fIrst-level concepts. The claim that all judgments express relations between concepts annihilates all the main logical distinctions among the forms and components of judgments. 113 Indeed, it ignores the distinction between objects and concepts which is the foundation-stone of Frege's philosophy of logic. lt4 Having proved that this first strategy leads to checkmate, Frege thought that the psychological logicians would have to exploit the only other available option. According to this second strategy, the logical subject of a judgment is what the judgment is said to be about, or what 'the subject-term stands for. Hence, if it is incoherent to claim that the proper name in a singular subject-predicate judgment stands for a concept, and if the subject and predicate are the parts of the judgment, then the implication of the thesis that judgments are complex ideas must be that all singular judgments are about ideas. Hence, the psychological logicians must hold that the only objects about which judgments can be framed are ideas. This conclusion must hold for the judgment that Socrates is mortal, That Mont Blanc is more than 4000 m.high, and that Charlemagne conquered the Saxons. Frege assembled quotations to demonstrate that Erdmann actually affmned this prima facie ridiculous thesis; in view of this evidence, he concluded, "there cannot be any doubt that the object about which an assertion is made, the subject, is according to Herr Erdmann's opinion, supposed to be an idea in the psychological sense of the word."tt5 Frege pointed out that this position is evidently absurd. In uttering the sentence 'Charlemagne conquered the Saxons', I do not mean: .••to assert something about my idea when I speak of Charlemagne; I simply designate a man, independent of me and my ideating, and to assert something about him. We may grant the idealist that the attainment of this intention is not completely sure...; but this can change nothing in the sense. With the sentence 'This blade of grass is green' I assert nothing about my idea; I am not designating any of my ideas with the words 'this blade of grass' ..l repeat: in this sentence there is no talk whatever of my ideas; it is the idealist who foist that sense upon us. II'
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Frege's claim is that Erdmann's 'idealism' misrepresents the thoughts asserted in singular judgments by taking all such judgments to be about ideas. And this objection is held to be independent of the resolution of any epistemological questions, especially the refutation of scepticism about the exterria1 world. Surely, "the things themselves are to be distinguished from the ideas which some person forms of things."1l7 Once again it is important to note that Frege's argument is a reductio ad absurdum of a philosophical generalization and that he conceived the burden of proof to lie with his adversaries. He did not maintain either that no judgment is about an idea (that no expression refers to an idea) or that no object is subjective. On the conttary, he expressly distinguished between subjective and objective objects,118 and he affirmed that everybody "finds it necessary to recognize an inner world distinct from the outer world of sense-impressions, of creations of his imaginations, of sensations, of feelings and moods, a world of inclinations, wishes and decisions. tt119 In particular, he held that the phrase 'the idea of...' is appropriately employed to refer to an idea, and he used it for this purpose in speaking of his idea of the Moon or a painter's idea of Bucephalus. l20 (In Frege's view, Erdmann sowed the seeds of confusion in claiming that 'the Moon' in 'The Moon has a radius of 1()()() miles' refers to an idea, "In the end every thing is drawn into this sphere of psychology; ... even actual objects them selves are treated psychologically, as ideas....Thus everything drifts into idealism and from that point with perfect consistency into solipsism. "121 So the conclusion of Frege's argument is the weak thesis that not all judgments are about ideas. l22 Once it is conceded that "only in a few judgments was the real subject an idea..the ground is pulled from beneath his feet of this whole psychological logic. "123 Frege did not take it to be his business to offer a refutation of Berkeleian idealism. He noted that such a view attempts "to explain how it comes to seem that there is such a thing as what is objective, how we come to assume that the existence of something that is not part of our mind without, however, our thereby having any justification for this assumption. "1:M But he wisely declined to take part in the venerable epistemological and metaphysical embroglio. To the psychological logicians' thesis that all judgments are about ideas Frege juxta}X>sed the claim that singular judgments could be about any objects whatever, irrespective of whether these objects are concrete or not, or whether they are subjective or objective. The sentences 'Jupiter has four moons', '2 is a prime number', and 'My idea of Bucephalus is not very vivid' express judgments about different kinds of objects. Frege's official explanation of this diversity in what judgments may be about turns on his analysis of judgments into functions and arguments. Although every judgment is an abstract object, it can be the value of a function for an argument which is not an imperceptible, objective, non-spatio temporal object. For it is a fundamental feature of the concept of a function that neither its argument nor a function itself is a part of the value of the
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function for this argwnenL This is evident from the simplest case of mathematical functions: it would be absurd to claim that either the number 2 or the fimction x2 is a part of the number 4 on the ground that 4 is the square of 2. Focussing on this point removes any tension from claiming that the planet Jupiter or my idea of Bucephalus can be the argument of a function (concept) whose value is an abstract object Gudgment). One simply abjures the thesis that what a singular judgment is about (an object) is a part of the judgment itself. It seems integral to this project of replacing subject-predicate analysis in logic by function/argument decomposition that part/whole analysis be dropped. Unfortunately Frege found it impossible to make a clean break with this tradition, and the result was a steady trickle of confused theses and fallacious arguments. Originally he called judgeable-contents 'combinations of ideas', 12S and he described objects, concepts, and relations as parts of judgeable-contents. l26 This seems bewildering. How can a concrete object, say Priam's house, be part of an abstract object, viz., the judgment that Priam's house was built of wood? If Frege had drawn no consequences from this discourse about parts and wholes, the obscurity here would have been hannless. But it had the potential to lead his own thinking astray. In particular, it led him to overstate the thesis that he offered as the antithesis to the psychologicians, claim that all judgments are about ideas. He saw that their claim stemmed from the notion that a judgment is a psychological entity, since the subject of a judgment must have the same subjective status as the judgment of which it is a part. l27 The corrective is to acknowledge that "the content of a judgment is something objective, the same for everybody, and as far as it is concerned it is neither here nor there what ideas men have when they grasp it."I28 But adding "What is here being said of the content as a whole applies also to the parts which we can distinguish within it," Frege succumbed to the temptation laid up in part/whole terminology and contradicted his own contention that judgments may be made about subjective objects. Similar, more pernicious confusion persisted after Frege introduced the sense/reference distinction and divided judgeable-contents into truth-values and thoughts. At the level of reference, he analyzed judgments into objects and concepts; every proposition presents a truth-value (the reference of the proposition) as the value of a function (concept) for certain arguments. At frrst, Frege retained talk of parts, stating that the objects and concepts designated by the constituents of a proposition are parts of the truth-value which the whole proposition designates; but he added the caveat that 'part' here must be understood in a special sense. l29 Later he decided that it is confusing to speak of 'parts' in this context. 130 At the level of sense, Frege also decomposed what a sentence expresses (a thought) into function and argument(s); indeed, this decomposition is precisely parallel to the function/argument analysis of the corresponding truth-value, and therefore a fonnula in concept-script serves a double function. 131 Here too Frege retained the tenninology of 'part' and 'whole'. He claimed that the senses
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of the parts of formulae in concept-script are parts of the thought expressed by the whole formula. l32 This led him to draw two conclusions inconsistent with the function/argument analysis of thoughts. First, he argued that Mont Blanc, with all its rocks and snowfields, could not be a part of his thought that Mont Blanc is higher than 4000m, and therefore he concluded that the sense of 'Mont Blanc', which is a part of his thought, must be distinct from the reference of this name. l33 This argument rests on the principle that no concrete object (no mountain) can be part of an abstract object (a thought). This would be a fallacious argument (parallel to concluding that Mont Blanc cannot be part of the True, which is the reference of 'Mont Blanc is higher than 4000m') unless the term 'part' is taken to exclude taking the mountain Mont Blanc to be the argument of a function whose value is a thought. Second, Frege eventually adopted the notion that a thought is composed out of thought-building-blocks (Gedankenbauseine), and he offered this thesis as an explanation of how it is possible to grasp new thoughts. l34 This conception depends on the literal truth of the claim that the parts of a sentence have senses which are parts of the thought expressed by the whole sentence. It is, however, incompatible with the guiding ideas of function/argument analysis of thoughts. Neither a function nor its argument are parts of the value of the function for this argument (save accidentally); and any representation of an object (a thought) as the value of a function for an argument is logically equipollent with any other representation of the same object as the value of another function for other arguments Gust as 4 is no more essentially the value of x2 for the argument 2 than it is the value of x + y for the pair of arguments (3,1». Frege never fully emancipated himself from the influence of the part/whole analysis of judgments which he had diagnosed as the root of the psychological logicians' confused thesis that all judgments must be about ideas. This failure manifests the extreme difficulty of extirpating deep philosophical misconceptions.
VI. Concepts and Concept Formation. According to the psychological logicians, it is an immediate consequence of the thesis that judgments are complex ideas that all concepts are ideas. For concepts are parts of judgments, and therefore the claim that judgments are subjective or psychological entities implies that their proper parts have the same status. Indeed, the predicate of every judgment is held to be a concept, while the subject of some judgments are also concepts (as in the judgment that all men are mortal).13S So every judgment contains at least one concept as a constituent or part, and this must be an idea. Although the term 'idea' ('Vorstellung') and 'concept' ('Begriff) do not have sharply contrasted uses or even consistent implications in the writings of philosophers and psychologists, Frege followed the psychological
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logicians in employing the term 'idea' to signify an inner mental picture. l36 Hence, their thesis that concepts are ideas is equivalent to the claim that what concept-words signify are mental images. In this jargon, the psychological logicians maintained that the content ('Inhalt') of a concept-word, or the sense ('Sinn') of such a word, is always a mental image. In the judgment expressed by 'All men are mortal', both the tenns 'men' and 'mortal' are concept-words which stand for ideas, according to the psychological logicians, and therefore the claim that this proposition expresses a relation between two concepts boils down to the thesis that it states a relation between two mental images. Likewise, the judgment expressed by 'Socrates is mortal' states that the properties of the image associated with the concept-word 'man' are all properties of the image associated with the name 'Socrates' .137 This use of 'idea' as a semi-technical term stresses that what are properly called ideas are essentially mental in nature, and this subjectivity of ideas is understood to carry the implication that "one person's ideas are his and no one else's."13I Frege linked this conception of concepts with two other fundamental theses, both of which were accepted and even espoused by the psychological logicians themselves: ' i) Judgments are held to be put together of a stock of independently grasped, ready-made or pre-existing ideas. l39 This is an immediate consequence of seeing judgments as constructed out of subjects and predicates, and it is clearly implied in calling judgments 'complex ideas' or 'combinations of ideas'.140 ii) The fundamental form of concept-fonnation is held to be abstraction from experience. Concepts may be broken down into simpler concepts by analysis, namely by means of definitions per genus et differentiam, Le., by specifying characteristic marks (lrlerkmale). The atoms left after this mental chemistry will be "internal images arising from memories of sense impressions which I have had and acts, both internal and external, which I have performed."141 These images are held to be fonned from particular experiences by selective inattention to their specific individuating characteristics. To arrive at the concept 'green', one must start from having perceptions of leaves, blades of grass, yew trees, etc.; one abstracts from (or disregards) features other than color (e.g., shape, size, texture) and thereby obtains an idea associated with ' green, (perhaps a composite picture, perhaps a picture of a particular shade of green which is used to represent the whole range of shades of green). The idea of a concept may differ only in degree from the idea of an object, and more and more schematic or abstract concepts can be generated "by making one characteristic mark after another disappear."142 All concepts are held to be derived, immediately or indirectly, by this process of abstraction. Having appropriate experiences, whether perceptual or introspective, is the necessary condition for fonning simple concepts ("A congenitally blind person cannot have concepts of colors"), and the process of concept-formation is independent of, indeed
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presupposed by, making judgments. The psychological logicians inherited this doctrine of 'abstI'actionism' from classical empiricism. Frege argued that claiming all concepts to be ideas is just as abswd as claiming all singular judgments to be about ideas. His reasoning was identical in both cases. The underlying premise is manifestly false. It is not the case that judgments are ideas. Hence, even if concepts were parts of judgments, it would not follow that concepts must be ideas (or indeed any other species of subjective or psychological entity). Acknowledging the objectivity of judgments pulls the rug out from under the psychological logicians. After introducing the sense/reference distinction, Frege had to modify both his account of what the psychological logicians claimed and his rebuttal of their view. It is the sense of a sentence (a thought) which they mistakenly took to be something mental, indeed to be a complex idea. Hence, it must be the senses of proper names and of concept-words, i.e., what Frege conceived as the parts of thoughts, which they held to be ideas. (Since Frege used the term 'concept' for the reference of a concept-word, not its sense, their thesis cannot now be formulated by claiming that all concepts are ideas.) Therefore, the refutation of the psychological logicians' conception of concepts turns on proving that the senses of some conceptwords are not mental images. Frege proceeded to argue in just this way, distinguishing the sense of a sign from the associated idea. 14! But, in any case, the only argument available to 'the psychological logicians for concluding that these thought-eonstituents are uniformly ideas must start from the premise that all thoughts are subjective entities, and this claim is itself absurd. Consequently there is no prima facie case in the need of rebuttal. Once again Frege wins on the verdict nolo contendere. Once again it is crucial to note that this reasoning is a coda on a reductio ad absurdum. The underlying conclusion was the thesis that not all thoughts or judgments are ideas. Consequently, in Frege's view, t)lere is no support for the claim that all concepts (or the senses of all concept-words) are ideas. On the contrary, it is evident that some concepts (and the senses and references of some concept-words) are not ideas. For there would be a manifest inconsistency in conjoining the objectivity of the judgment that Socrates is mortal with the claim that one part of this judgment (the concept mortal) is an idea (hence subjective). The concept mortal must be as objective as the object (Socrates) which is the subject of this singular judgmenL For a similar reason, Frege later held that the sense of the concept-word 'mortal', like the sense of the proper name 'Socrates't must be objective; otherwise the thought expressed by the sentence 'Socrates is mortal' could not be objective since the senses of its constituents are parts of the sense of the whole sentence. l44 Consequently, Frege concluded that the psychological logicians fell into absurdity by claiming that all concepts are ideas. Both before and after introducing the sense/reference distinction Frege took care to formulate his posi~o~_~_!!t~_~I!~__of _ ~_ !1Oiyersal_
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generalization. Thus he claimed that the content of a concept-word need not may like may this celebrated early passage:
be an idea, but he did not exclude the possibility that it might be. "It be that every word calls up some sort of idea in us, even a word 'only'; but this idea need not correspond to the content of the word; it be quite different in different men. "145 The same caution informs
That we can form no idea of its content is therefore no reason for denying all meaning to a word....We are only imposed on by the opposite view because we will, when asking for the meaning of a word, consider it in isolation, which leads us to accept the idea as the meaning. Accordingly, any word for which we can find no corresponding mental picture appears to have no content But we ought always to keep before our eyes a complete proposition. Only in a proposition have the words really a meaning. It may be that mental pictures float before us all the while, but these need not correspond to the logical elements in the judgment 146
In early texts which consider the thesis that the content of a concept-word (a concept) must be an idea, Frege avoided asserting that no concept could be an idea or mental image. He manifested the same circumspection in some later discussions of the senses of concept-words. In approaching the distinction between ideas and the parts of thoughts corresponding to concept-words, he remarked that: The idea is subjective: one man's idea is not that of another....This constitutes an essential distinction between the idea and a sign's sense, which may be the common property of many people.... 147
Indeed, he added, there remains a difference between the mode of of an idea and of a sense with a word: two men "are not prevented from grasping the same sense; but they cannot have the same idea."148 Frege's objection seems always the same: If the sense of every concept-word were an idea, then in principle no thought could be shared and hence any inter-subjective science would be impossible. The conclusion to be drawn is that the premise must be false, i.e., that the senses of some concept-words are not ideas. This does not exclude the possibility that the senses of some concept-words are subjective, say perhaps that the sense of 'red' cannot be ascertained exactly by any other person when this adjective is applied to phenomenal colors within the sphere of a single consciousness. 149 On the other hand, Frege sometimes veered towards a stronger thesis. This is not evident in his criticisms of the psychological logicians, but it is conspicuous in his explanations of the conception of a concept on which he rested his logical analysis of inference. In early writings he identified concepts with functions whose values are always judgeable-contents. Though he did not argue the point, it is difficult to see how an idea (mental image) could be identified with such a function (i.e., how an idea could be a law conn~tion
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for correlating each argument with a judgeable-content). Similarly, in later writings, he identified the sense of a concept-word with a function whose values are always thoughts. These functions (laws of correlation) must be as objective as their arguments (e.g., the senses of proper names of objective objects) and their values (objective thoughts), In his view, this alone would prevent the identification of such a function with any mental image. 150 This strand of thinking inclined Frege towards advancing the claims that the sense of a concept-word cannot be an idea: Certainly it is possible in making not the sense of the sentence. It and the same sense of play of logically irrelevant accompanying take for the proper object of their
a judgment...a play of may be observed that ideas can be wholly phenomenon that [the study.151
ideas occurs; but that is with the same sentence different and it is this psychological] logicians
Anyone who hears 'the word 'horse' and \D1derstands it will probably straightaway have a picture of a horse in his mind. This picture, however, is not to be confused with the sense of the word 'horse' .152
These claims rest on considerations supplementary to Frege's central reductio of the position of the psychological logicians, and the two strands of his thinking were never reconciled. In fact, he did offer supplementary arguments to support his case against the psychological logicians' conception of concepts, and some of these arguments suggest that the content or sense of a concept-word cannot be a mental image. i) In early writings Frege stressed that concepts must generally be objective entities, unlike ideas. In his view: Sensations are absolutely no concern of arithmetic. No more are mental pictures, formed from the amalgamated traces of earlier sense-impressions. All these phases of consciousness are characteristically fluctuating and indefinite, in strong contrast to the defmiteness and fixity of the concepts and objects of mathematics.153
To identify concepts with ideas would remove the objectivity of judgments and the timelessness of the truths of mathematics. For a generalization such as 'Every equilateral triangle is equiangular' expresses a relation between concepts; hence, if concepts were all ideas, it would state that two ideas in the speaker's mind stand in a certain (subjective) relation to each other,tS4 and this relation might depend on the phosphorus content of the human brain, and hence vary from person to person or be weeded out by natural selection in the struggle for existence. 155 Similarly, the proposition 'The number three falls under the concept of a prime number' is an objective truth, independent of the contents of my mind or others' minds and not subject to gradual change or historical development. l56 In short, the objectivity of mathematical judgments entails the objectivity of mathematical
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concepts. But the possibility that concepts applicable to subjective objects might be ideas is not excluded. ii) In early writings Frege also concluded that mental images are generally distinct from and irrelevant to the content of concept-words. This tmns on his limitations of conceptual content to what the cogency of inference depends on: Time and time again we are led by our thought beyond dte scope of om imagination without thereby forfeiting the support we need for our inferences.... That we can form no idea of its content is dterefore no reason for denying all meaning [content] to a word lSI
At this stage Frege did not advance the stronger conclusion that mental images have no legitimate role in determining the validity of any inference. Later he made this move in segregating sense from coloring (i.e., thoughts from their psychological trappings). For logic only sense matters; mental images, held to be variable and impossible to pin down precisely by inter-personal comparisons, are always allocated to coloring and thought to contribute only a poetic effect. Hence, he concluded that the sense of a concept-word cannot be an idea. iii) Frege queried the intelligibility of the claim that any concept is an idea. In expressing a thought by uttering the proposition 'This blade of grass is green', one predicates the concept green of an object. A psychological logician would claim that here my idea of green is asserted. of some thing (my idea of this blade of grass). But, Frege objected, it is altogether opaque how an idea can be asserted of anything. lSI A parallel argument applies to the sense of a concept-word, which a psychological logician must treat as an ingredient idea in the composition of a thought: Thoughts are fundamentally different from ideas (in the psychological sense). The idea of a red rose is something different from the thought that this rose is red. Associate ideas or run them together as we may, we shall still fmish up with an idea and never with something which could be true. lS9
By heaping associations on associations, we may arrive at a complex-idea,
but this would no more be a thought: l60 ...than an automaton, however cunningly contrived, is a living being. Put something together out of parts that are inanimate and you still have something inanimate. Combine ideas and you still have an idea and the most varied and elaborate associations can make no difference.16l
Frege here diagnosed a fundamental confusion in the psychological logicians' calling thought 'complex ideas'. For they must also apply the label 'complex idea' to the sense of a concept-expression (e.g., 'x is a red rose') and the sense of a concept-word which can be analyzed into characteristic marks (e.g., 'x is a triangle'). This obliterates the crucial
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distinction between the expressions of thoughts and all other expressions, and it generates an insoluble problem about the unity of thoughts (viz., explaining why some combinations of ideas fonnulate judgments while others do not).162 iv) Frege criticized various aspects of the doctrine that concepts are fonned by abstraction from experience. He rejected the strong thesis that all concepts are derived in this way. This would make it impossible to form a concept under which nothing fell (e.g., the concept unicorn or even prime number grater than jOOO). But there is nothing amiss with empty concepts (or even with concepts that can be proved to be empty,163 and the fonnulation of such concepts is a matter of arriving at them, not by direct abstraction, but by starting from defining characteristics. l64 Since classical empiricists and the psychological logicians typically conceded the possibility of introducing complex ideas by analytic defmitions, Frege's weak claim that not all concepts are derived by abstraction would raise little opposition. He never advanced the strong thesis that no concepts can be formed by abstraction from experience. 165 On the contrary, he regularly acknowledged the legitimacy of this form of concept-formation for many concepts. In particular, he held that we arrived by abstraction at concepts of properties of external things (e.g., concepts of color, weight and hardness l66) and of internal things (e.g., the concept red which is applicable only to the content of one's own consciousnessl ' ) . He never argued that abstraetionism is a wholly bankrupt account of concept-formation, and he never raised some of the standard difficulties that it must confront (e.g., differentiating the relational concept larger than from the converse concept smaller than).I68 But Frege did defend a thesis of intermediate strength: there are some concepts the formation of which defies explanation by abstraction from experience. In particular, he argued that the concepts of nwnbers as used in count-statements (e.g., 'Jupiter has four moons') cannot be so explained. Classical empiricists and the psychological logicians took these adjectival occurrences of numerals to signify properties of objects, and hence they explained how successive operations of abstraction generate the concept four out of the experience of seeing four cats of various breed, size and color. l69 Frege reasoned that this explanation was acceptable only if it applied to every use of numerals to answer the question 'How many.•.are there?'; hence that it must apply to the number zero. But it is manifestly absurd to try to form an idea of zero visible stars by starting from perceiving a property of something external. Seeing a sky entirely overcast with clouds would give nothing corresponding to the word 'star' or to 'zero', and a mental image of an overcast sky would be equally remote from an articulated complex idea of zero visible starS. I70 Frege offered fwther arguments to deny that any idea of number can be arrived at by selective inattention to features of what we experience. 171 In his view, this short coming is irremediable. Numerals used in count-statements do not signify properties of objects; rather, they function as parts of expressions predicating (second-level) properties of concepts (or fIrst-level properties).
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The distinction between first- and second-level concepts is one of the crucial logical distinctions annihilated by the psychological logicians' identification of concepts with ideas, and hence it is no wonder that the fonoation of the second-level concepts deployed in count-statements cannot be explained by abstraction from the experienced properties of objects. (It is an additional demerit of the abstractionist theory of concept-formation that it blurs the logical distinction between concepts and objects by presenting it as a matter of the degree of specificity in the itemizing of something's characteristics.)172 Frege's criticism did expose serious flaws in the conception of concepts as ideas in spite of the fact that he shared with his adversaries some basic misconceptions 'about the nature of ideas. He was surely correct in claiming that the psychological logicians obfuscated important logical distinctions by taking proper names, concept-words, and sentences alike to signify ideas. Serious confusion is invited by calling both thoughts and analyzable concepts 'complex ideas'. Frege was also right to exclude consideration of mental images from assessments of the validity of inferences, hence to separate the senses of the expressions from the ideas associated with words. Finally, he deserves credit for clarifying the grammar of generalizations (both existential and universal) and of count-statements by describing them as predicating properties of properties and hence as containing second-level concepts,173 and he rightly noted that the notion that all concepts are ideas is a major obstacle to achieving this insight. On the other hand, Frege was light-years away from offering a general criticism of the doctrine of concept-formation by abstraction. It would be wholly erroneous to suggest that he distinguished the sense of a concept-word from the associated mental image because he anticipated Wittgenstein's insight that it is nonsensical to suppose that mastery of the entire use of a concept-word somehow flows from correlating this expression with something static like a picture. Moreover, though he recognized a crucial logical difference between proper names and conceptwords, he did not clarify it by examining in detail how these expressions are used and explained in everyday linguistic practice, but sought to explain it by pointing to a metaphysical divide between the entities allegedly signified by these expressions, Le., the dichotomy between concepts and objects which is held to be founded deep in the nature of things. With the wisdom of hindsight, these are decisive weaknesses in his philosophical investigation of concepts. Frege was not content merely to expose the psychological logicians' misconception of concepts; he offered in its place an allegedly proper logical notion of a concept purged of all psychological excrescences. Like his positive explanation of the nature of judgments or thoughts, this explanation of what concepts really are generates further philosophical perplexities. In his early writings he arrived at the 'discovery' that concepts belong to the genus of functions. 174 In fact, a concept (in a logical sense) just is a
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function whose value is always a judgeable-content. (What he called a 'function' in Begriffsschrift is identical with what he called a 'concept' in the Foundations of Arithmetic.) This had two important corollaries. First, it involved an unorthodox extension of the application of the term 'concept'. In particular, he categorized logical expressions, both propositional connectives such as 'and'. 'or', 'ir, 'not', and quantifiers such as 'some', 'all', as concept-words (respectively of flfSt and second-level); by ttadition they had been called syncategoremata and contrasted with concepts. He also called any expression derived from a logical formula (or sentence) by functional absttaetion the name of a concept; e.g., by regarding 'Socrates' as replaceable by other expressions in the sentence 'If Socmtes is a man, he is mortal', Frege arrived at the concept expressed by the sentence-schema 'If x is a man, x is mortal'. Hence, what he acknowledged to be concepts were not restricted to what general words like 'man' and 'mortal' signify; and the judgment that all men are mortal can be analyzed by stating that a (complex) concept has the property of holding for every argument (rather than necessarily stating that a pair of concepts stand in the relation of subordination). These differences, though subtle, are of the last importance. The second corollary is the surprising claim that concept-formation (in the logical sense) must always start from judgeable-content. 17s There is no possibility of arriving at a concept in any other way, a fortiori not by any process of absttaction applied to the data of experience. 176 This idea informed one of his three fundamental logical principles: viz., "never to ask for the meaning of a word in isolation, but only in the context of a proposition. "ITI This early positive conception of a concept must be less incoherent than the conception of a judgeable-content on which it is built For, in Frege's view, the idea that a concept is a function cannot be separated from the thesis that there are objects to serve as the values of these functions, and the objectivity of concepts presupposes that these objects be objective, i.e., numerically the same objects confronting us all like the SUD. If this background makes no sense, then his description of concepts as functions whose values are judgeable-contents is itself nonsensical. In addition, his extension of the word 'concept' to include the content of logical expressions has the consequence that logic has the status of an a priori science about special logical entities; but the idea that logical propositions have a distinctive subject-matter is inconsistent with recognizing them to be tautologies which say nothing at all. After making the sense/reference distinction, Frege confined the term 'concept' (in its logical sense) to the reference of a concept-word. He defined a concept as a function whose value is always a truth value. 17! Any word or expression which is held to stand for such a function is called a concept-word, and hence one again he extended the application of the term 'concept' to cover whatever is signified by a logical expression or any sentence-schema with schematic letters. Moreover, his usage of 'concept' was now incompatible with standard practice among logicians, for he held e
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that a function must be completely defined by determining its value for every argument, and this has the consequence that the extension of any concept can be calculated from the natw'e of the concept itself! 179 The sense of a concept-word Frege thought to be a function whose value is always a thought This notion is rendered incoherent by the nonsensical presupposition that a thought is an objective object, numerically the same for different thinkers. It also demands that logical expressions have senses, and hence too that the propositions of logic express genuine thoughts distinct from one another. Consequently, the positive doctrine that Frege later juxtaposed to the psychological logicians' conception of concepts was no real improvement on his earlier one. In his criticisms of the psychological logicians' conception of concepts, Frege appeared at his philosophical best His arguments do put a finger on subtle but fundamental confusions in his opponents' thinking, and the inconsistencies in his own position are so deeply hidden that they still pass unremarked. It would be a mistake to suppose that he could be defended against serious criticism by exploiting the idea that he introduced a special semi-technical concept of a concept. Though advantageous for sidestepping objections, This would impose on him the burden to give an intelligible and consistent explanation of what he meant to be understood by 'concept', and this task is one that he did not discharge. lao Moreover, if he had succeeded in explaining his own technical notion of a concept, he would thereby deprive most of his philosophical remarks of their point. In claiming 'that logical laws are generalizations about concepts and judgments, that ' All men are mortal' expresses subordination of concepts, that 'there are prime numbers' states that the concept of a prime number has a (second-level) property, or that count-statements predicate properties of concepts, did he not intend his remarks to be understood by philosophers and logicians independently of his giving an idiosyncratic defmition of 'concept'? And would he not have imposed on himself the burden of proving that any of the expressions standardly called 'concept-words' signify what he called ,concepts'? Indeed, it is arguably unintelligible to claim that any expression stands for a function whose value is always the True or t~ False. Finally, would applying his semi-technical notion of a concept in interpreting the psychological logicians' thesis that concepts are ideas not deprive his arguments of any real targets in the thinking of Erdmann and the early Husserl? For would it be credible to take them to have held functions whose values are always judgeable-conmDts (or thoughts) are to be \identified with mental images? To fall back on a semi-technical notion of a lconcept might purchase advantage in a few local skirmishes with critics, but it would lose the overall war quite decisively.
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VII. Frege's Legacy We must now try to give a synopsis of Frege's polemic against the intrusion of psychology into logic and to evaluate his philosophical achievement in this domain with his general philosophy of logic. The focal point of his reflections was the nature of the propositions of logic, and the ramifying chains of his arguments should always be traced back to this source. This methodological principle for interpreting his antipsychologism should always be borne in mind. Having pursued his reasoning through the laws of thought down to objects and concepts, we are ourselves perhaps in danger of losing sight of the fact that our more recent investigations are subordinated to the clarification of the nature of logic. The load-bearing members of his thinking are his fundamental thoughts about logical laws, not miscellaneous and independent ideas about judgments, concepts, and objects. A second principle of interpretation is that Frege's anti-psychologistic theses must be understood as directed at very specific targets and as supported by his arguments. His arguments are, in a sense, ad homines, not contra mundum. It is ridiculous to look in his writings for a systematic refutation of idealism in all its forms. He did not undertake any examination of representative idealism in classical British empiricism, of Kant's transcendental idealism, or of the forms of Hegelian idealism that concerned Moore and Russell; nor did he embark on the refutation of scepticism about the existence of an objective domain of perceptible objects. His target was a doctrine about the nature of the truths of logic and arithmetic which was championed by Erdmann and the early Husserl. His anti-psychologism is intended to be a refutation of their case that these so-called 'necessary truths' are descriptions of contingent relations among psychological phenomena. To this misconception about logic Frege opposed the strong thesis that logical laws are significant propositions stating generalizations about special logical concepts and that they can all be deduced rigorously from an initial set of axioms stating self-evident a priori truths about entities in a logical realm. But the rest of Frege's case against the psychological logicians has the form of disproving their mistaken genemlization on which their conception of logic rested. Here, as we have emphasized, each argument is a reductio ad absurdum, and therefore Frege's antitheses to the psychological logicians' position are prima facie weak. Without supplementary evidence from his writings each antithesis should be read as a negation of a generalization, not as the assertion of a contrary genemlization. Moreover, the content of each of his counter-claims must also be related to the supporting argument. There is a strong temptation to separate his theses from the argumentative context in which they are set. But to inflate the conclusions of his reasoning in this way invites the criticism that his supporting arguments are fallacious and the scope of his reflections 100 narrow. It even opens the way to convicting him of internal
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inconsistency. To ascribe to him the central insight of Wittgenstein's arguments against the possibility of a private language would knock the props out from his argument against the psychological logicians, for it would demolish his premise that ideas, being subjective, have properties and relations which can be exactly ascertained only by their owners and it would equally render unintelligible his drawing a distinction between qualitative and numerical identity for both thoughts and mental images. Strengthening or decontextualizing Frege's anti-psychologistic theses in the name of charity has the consequence of diminishing his solid philosophical achievement Bearing in mind these two fundamental principles of interpretation, we must at last try to evaluate the achievements of Frege's anti-psychologism. It should be perspicuous that most of the general claims made on his behalf are extravagant and groundless. He did not undertake, let alone accomplish a comprehensive examination and refutation of idealism in all its forms. Far from anticipating Wittgenstein's private language argument, his reasoning against the psychological logicians depended on applying the distinction between numerical and qualitative identity to thoughts and ideas (where it is not intelligible). His distinction between content or sense and mental images (ideas) twned solely on the role of symbols in reasoning and calculation, and hence it did not amount to a refutation of imagism as a theory of meaning. Both his ambitions and the scope of his arguments were strictly limited. It is also clear that his arguments are shaped by presuppositions that he shared with his opponents and that many of these unexamined ideas are dubious at best, nonsensical at worst. His notion of subjectivity combined the quite separate strands of ownership, identification-dependence, and epistemic privacy, and he arguably fell into incoherence in affirming that it is impossible in principle to ascertain whether any judgment about something subjective is fully understood by others. He mistakenly applied the contrast between numerical and qualitative identity to ideas and thoughts, both in arguing that the ideas of different persons cannot be numerically identical, but only exactly similar, and in asserting that the thoughts of different persons may be qualitatively identical; discourse about 'inner states' lacks this conceptual articulation which Frege projected upon it from discourse about perceptible objects. He wrongly considered thinking to be a subjective mental act, the exact character of which cannot be known to anyone other than the subject himself; this was linked to a defective grasp of the concepts of having a thought, expressing a thought, making an assertion, judging something to be true, etc., since in all these cases he ignored the fact that there are behavioml criteria for performing these acts. He never shook off the influence of part/whole analysis of judgable-contents or thoughts, and this resulted in fallacious reasoning and conclusions inconsistent with his adherence to function/argument analysis in logic. All of these points must weigh heavily in the balance when we consider the value
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of his anti-psychologism as timeless answers to eternal philosophical questions. Since the clarification of the nature of logic was his overriding purpose, by far the most fundamental weaknesses of his position are mistaken propositions about logic itself. One is the idea that the propositions of logic (the Law of Identity, the Law of Excluded Middle, etc) are significant truths distinguished from all other propositions by their subject-matter. Allied with this idea is the conception of rules of inference (modus ponens, the syllogism in Barbara, universal instantiation, etc) as technical norms grounded in the truths of logic and subservient to the independent goal of truth. Both these general presuppositions Frege shared with the psychological logicians. Wittgenstein exposed the incoherence of this conception of logic in making clear that the propositions of logic are tautologies. This provides the basis for a more radical criticism of the psychological logicians' view of the nature of logic, but at the same time it shipwrecks Frege's 'Platonist' antithesis. All these reflections suggest that Frege's anti-psychologism is not a seam of pure gold. But might there not be nuggets of gold scattered in his writings, nuggets worth collecting up today and transporting to metropolitan philosophy? This seems mistaken in principle. It is unclear to what extent it makes sense to speak of his ideas independently of his reasoning and its presuppositions. But his thinking was infused with a Cartesian mythology about the realm of the psychological and a Platonist my'thology about the realm of the logical. This suggests that only somebody who shares a large measure of these Cartesian and Platonist mythologies should now find any seeds of the Tree of Knowledge scattered in his anti-psychologistic polemics. Should we then conclude that Frege's anti-psychologism is completely worthless? This would be an hysterical overreaction. He did develop telling criticisms of the influential conception of logic championed by Erdmann and the early Husser!. He argued cogently and forcefully within the limitations of a shared framework of thinking, and his arguments, fortified by his prestige as a logician, carried 'the day against 'this particular form of empiricism. His anti-psychologistic crusade affords an instructive example of how to umavel the particular knots of a specific philosophical misunderstanding. It is this skill which every philosopher must cultivate. To the extent that it is capable of transfer from one problem to another, the careful study of Frege's anti-psychologism might contribute indirectly to the elimination of misunderstandings and confusions now prevalent about the nature of logic, language, and thought.
121 ENDNOTES· • With the exception of references to section numbers, all references to Frege's publications are to pages in the original pagination. The original texts of Frege's articles are reprinted in: Gottlob Frege, Kleine Scltriften, ed. I Angelelli (Hildeshiem: G. Olms, 1967). English translations of these articles are available in: Gottlob Frege, CoUected Papers on MathemiJtics, Logic, and Philosophy, ed. B. McGuinness (Oxford: Basil Blackwell, 1984). 1. Gottlob Frege, "Review of Dr. E. Husserl's Philosophy of AritJunaic," trans. from ZEITSCHRIFT FOR PIULOSOPHIE UNO PIULOSOPIDSCHE KRITIK, 103 (1894): 313-332, p. 332. 2. Gottlob Frege, Posthumous Writings, ed. H. Hermes, F. Kambartel, F. Kaulbach, trans. P. Long, R. White (Oxford: Basil Blackwell, 1979), p. 142. 3. Gottlob Frege, The FOIUIdations of AritluMtic, a logico-mathematical enqu.iry into the concept of 1IW1Iber, 2nd revised edition, trans. I.L. Austin (Oxford: Basil Blackwell, 1959), from Die GrlUldlagen der ArithmetiJc, eine logisch mathematische Untersu,chung iber den Begriff der Zahl (Breslau: W. Koebner, 1884), p. x. 4. Gottlob . Frege, Concept#UJl Notation, a formula language of pu.re thought modelled upon the formula language of aritJunaic, in Gottlob Frege, Concept#UJl Notation and related articles, ed. and trans. Terrell Ward Bynum (Oxford: Clarendon, 1972), from Begriffsschrift, eilU! der aritJunaischen nachgebildete Formelsprache des reinen DenJcens (Halle: L. Nebert, 1879), sec. 2. 5. See: Ibid., sec. 8-10. See also: Frege, The FolUldations of Arithmetic, p. x, sec. 70. It is disputed whether the notion of a thing (Ding) in Conceptual Notation (Begriffsschrift) is identical with the notion of an object (Gegenstand) in the FolUldations of AritluMtic, and equally whether there is a parallel equivalence between the notion of a function (Funktion) and that of a concept (Begriff). A documented case in favour of these two equivalences is presented in: G.P. Baker and P.M.S. Hacker, "Dummett's Dig: Looking-Glass Archaeology," THE PIULOSOPIDCAL QUARTERLY, Vol. 37 (1987): 86-92. 6. Frege, Postluunolu Writings, p. 3. 7. Cf., Frege, Conceptual Notation, "Preface". 8. See: Frege, PosthUlllOllS Writings, p. 3. 9. Hugo Dingler objected to this thesis in correspondence with Frege. See: Gottlob Frege, Philosophical and MathemoJical Correspondence, 00. G. Gabriel, H. Hennes, F. Kambartel, C. Thiel, A. Veraart, abridged for the English edition by B. McGuinness, trans. H. Kaal (Oxford: Basil Blackwell, 1980), from Wissenschaftlicher Briefwechsel, 00. G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, A. Veraart (Hamburg: Felix Meiner, 1976), p. 18. 10. Frege, Posthumous Writings, p. 261. 11. See: Ibid., pp. 244ff. See also: Gottlob Frege, "Negation," trans. of "Die Vemeinung: Eine logische Untersuchung," BEITRAGE ZUR PHll.DSOPHIE DES DEUTSCHEN IDEAUSMUS, I (1918): 143-157, p. 145f. 12. See: Frege, Posthumous Writings, pp. 5, 142. 13. Frege had little knowledge of the ideas of the British empiricists, and his discussions of their views about nwnbers are based on an anthology, not on his reading the primary texts in full. 14. This is a major theme of Hans Siuga. See: Hans Sluga, Gottlob Frege (London: Routledge &. Kegan Paul, 1980).
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15. It is not absurd to call Frege's arguments decisive, provided that the burden of proof is judged to lie on the advocates of the claim that concepts and judgments are mental or subjective entities. 16. Frege, Philosophical and Mathematical Correspondence, p. 130. 17. Russell eventually changed his mind on this point and adopted the view that propositions are composed of images. See: Bertrand Russell, Logic and Knowledge, ed. R.C. Marsh (London: George Allen &. Unwin, 1956), pp. 283-320. See also: Bertrand Russell, The Analysis 01 Mind (London: George Allen &. Unwin, 1921). 18. Cf., Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. D.F. Pears, B.F. McGuinness (London: Routledge and Kegan Paul, 1961), pt 4.1121. 19. Ibid. 20. Ibid., pt 4.023. 21. Ibid., pt 5.55ff. 22. Russell was a notable exception; he elaborated a radically psychologistic conception of logic in defense of empiricism. See: Bertrand Russell, An Inquiry into Meaning and Truth (London: George Allen &, Unwin, 1940). 23. See: Frege, ConceptuoJ Notation, sec. 3-4. See also: Frege, 'The Thought: A Logical Inquiry," trans. of "Der Gedank:e: Eine logische Untersuchung," BEITRAGE ZUR pmLOSOPHIE DES DEUTSCHEN IDEAUSMUS, I (1918): 58-77, p. 63f. 24. This point of view is advocated by Michael Dummett. See: Michael Dummett, Frege: Philosophy of Language (London: Duckworth, 1973), pp. 88f. 25. See: Frege, PosthU11lOKS Writings, pp. 3, 261. See also: Frege, Philosophical and Mathematical CO"espoNUnce, p. 17f. 26. See: Gottlob Frege, "On Sense and Reference," trans. of "Ober Sinn und Bedeutung," ZEITSCHRIFT FOR PHILOSOPHIE UNO pmLOSOPlllSCHE KRITIK, 100 (1892): 25-50, pp. 29f. 27. See: Frege, "The Thoug~" pp. 68f. 28. Ibid., p. 66. 29. Cf., David Bell, Frege's Theory of Judgement (Oxford: Clarendon, 1979), p. 74. 30. E.H.W. Kluge, The Metaphysics of Goulob Frege (The Hague: Martinus Nijhoff, 1980), p. 16. 31. Michael Dummett, The Interpretation of Frege's Philosophy (London: Duckworth, 1981), p. 121. 32. Ibid., p. 54. 33. Ibid., p. 52. 34. P.T. Geach, "Assertion," THE PHILOSOPIDCAL REVIEW, Vol. 74 (1965): 449-465. 35. Dummett, Frege: Philosophy of Language, pp. 158ft. 36. Ibid., pp. 158 and 641. 37. Ibid., pp. 637f. 38. Michael Dumme~ "An Unsuccessful Dig," THE PIDLOSOPlllCAL QUARTERLY, Vol. 34 (1984), p. 391. 39. Dummett, Frege: Philosophy 01 Language, p. 684. 40. Cf., Edmund Hussed, Logical Investigations, trans. IN. Findlay (London: Routledge & Kegan Paul, 1970), Vol. L pp. 147ft. 41. George Boole, The MathemtJlical Analysis of Logic (Oxford: Basil Blackwell, 1948), p. 5. 42. George Boole, The Laws of Thought (Mineola: Dover, 1953), Ch. I, sec. 1. 43. B. Erdmann, Logik, quoted in translation in: Hussed, Logical Investigations, Vol. I, p. 162.
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44. Ibid., p. 162f. 45. See: Frege, Posthumous Writings, p. 128. 46. See: Gottlob Frege, GrlUldgesetze der Arithmetilc, Begriffsschriftlich abgeleitet, Band I and IT (Jena: H. Pohle, 1893 and 1903), Band I, p. xv. A translation of Frege's ''Introduction'' and Vol. I, sec. 1-52 are given in: The Basic Laws of Arithmetic: Exposition of the System, 00. and trans. Montgomery Furth (Berkeley: University of California, 1964). Translations of Vol. IT, sec. 56-67, 86-137, 139-144, 146-147, and Frege's "Appendix" are included in: Translations from the Philosophical Writings of Gottlob Frege, 00. and trans. Peter Geach, Max Black (Oxford: Basil Blackwell, 1960). 47. Frege, Posthumous Writings, p. 4. 48. Ibid., pp. 4, 128. 49. See: Frege, Gru.ndgesetze der Arithmetik, Band I, p. xv. See also: Frege, Posthumous Writings, pp. 132f. 50. See: Frege, Grundgesetze der Arilhmetik, Band I, p. xvi. 51. Ibid., Band I, pp. xvif. 53. See: Ibid., Band I, p. xvii. 54. See: Ibid. 55. See: Ibid., Band I, p. xvi. 56. Russell's demonstration that a contradiction could be derived from Axiom V of Grundgesetze led Frege to confess that this basic law of his axiomatization of the propositions of logic had always seemed to him to be lacking in the self-evidence essential to its serving as a proper foundation for the laws of truth. See: Ibid., Band II, p. 253). 57. Indeed, he emphasized the differences between these two kinds of laws. See: Ibid., Band I, p. xv. 58. See: Wittgenstein, Tractatus Logico-Philosophicus, pts. 6.1-6.113. 59. See: Ibid., pts. 6.1201. Cf., Cora Diamond, Wittgenstein's Lectures on the Foundations of Mathematics Cambridge, 1939: From the Notes of R.G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies (Hassocks, Sx.: Harvester, 1975), pp.277ff. 60. See: Diamond, Wittgenstem's Lectures on the Foundations of Mathematics, pp. 279ff. 61. See: Wittgenstein, Tractatus, pts. 6.126, 6.1263. 62. Ludwig Wittgenstein, Remarks on the Foundations of Mathematics, third 00., ed. G.H. von Wright, R. Rhees, G.EM. Anscombe (Oxford: Basil Blackwell, 1978), p.95. 63. Ibid., p. 89. 64. Frege, Posthumous Writings, p. 7. 65. See: Ibid., p. 198. See also: Frege, "Negation," pp. 151f. 66. See: Frege, Posthumous Writings, p. 253. 67. Ibid. 68. See: Ibid., pp. 132f. See also: Frege, Grundgesetze der Arithmetik, Band I, p. xv. 69. See: Frege, Grundgesetze tIer Arithmeti.k, Band I, pp. xv if; cf., Frege, Posthumous Writings, pp. 134f. 70. See: Frege, ''The Thought," p. 67. 71. See: Ibid., pp. 67f.; cf., Frege, Posthumous Writings, pp. 3f; and Frege, Philosophical and Mathematical Correspontknce, p. 67. 72. Frege, The Foundations of Arithmetic, sec. 27. 73. Frege, ''The Thought," p. 67.
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74. Frege, "On Sense and Reference," p. 30. 75. See: Frege, Posthumous Writings, p. 251. 76. Ibid., p. 133. 77. Ibid., p. 251. 78. Ibid., p. 133. 79. See: Frege, ''The Thought," p. 68. 80. Frege, Posthumous Writings, p. 133. 81. See: Frege, ''The Thought," p. 69. 82. Frege, Posthumous Writings, p. 134. 83. See: Ibid., p. 132. 84. Ibid., p. 134. 85. See: Ibid., p. 132. 86. See: Frege, ''The Thought," p. 66. 87. See: Frege, "On Sense and Reference," p. 29. 88. Frege, Posthumous Writings, p. 137. 89. Frege, "Negation," p. 146. 90. See: Frege, ''The Thought," p. 69. 91. This idea was later elaborated by M. Schlick. See: M. Schlick, "Form and Content," in Gesammelte Au/salze (Vienna: Gerold, 1938), pp. 151ff. 92. Frege, "On Sense and Reference," p. 30. 93. See: Ibid.; cf., Frege, "The Thought," p. 69; and Frege, "Review of Dr. E. Husserl's Philosophy of Arithmetic," p. 325. 94. Frege, Posthumous Writings, p. 145. 95. Ibid., p. 148. 96. Ibid., p. 7. 97. Ibid., p. 137. 98. See: Frege, The FolUldations of Arithmetic, sec. 61. 99. See: Frege, Posthumous Writings, p. 148. 100. See: Ibid., p. 135; cf., p. 251. 101. See: Ibid., p. 138. 102. Frege, ''The Thought," p. 77. 103. Frege, Posthumous Writings, p. 145. 104. See: Gottlob Frege, "On the Law of Inertia," trans. of "Ober das Trigheitsgesetz," ZEITSCHRIFr FOR PHILOSOPHIE UND PHILOSOPHISCHE KRITIK, 98 (1891): 145-161, p. 160. 105. Ludwig Wittgenstein, Philosophical Investigations, 00. G.EM. Anscombe, R. Rhees, trans. G.EM. Anscombe (Oxford: Basil Blackwell, 1953), sec. 253f., 35Off., 377ff. 106. See: Frege, Posthumous Writings, p. 135. 107. See: Frege, Grundgesetze der Arithmetik, Band I, sec. 5. 108. Cf., Frege, ''The Thought," p. 68. 109. See: Frege, Posthwnous Writings, pp. 143f. According to the doctrine of the syllogism on which the psychological logicians erected their philosophy of logic, judgments contained further elements that need not be taken to be ideas, namely syncategoremeata (signified by 'all', 'some', 'no', and 'not') and the copula (allegedly indicating assertion). 110. See: Frege, Philosophical and Mathematical Correspondence, pp. 68, 100f. 111. See: Frege, Conceptual Notation, sec. 11. See also: Frege, Grundgesetze der Arithmetik, Band L sec. 8. 112. See: Frege, Grundgesetze der Arithmetik, Band I, p. xxiv. 113. See: Ibid.
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114. See: Ibid. See also: Frege, The FOIUIdotions of Arithmetic, p. x. 115. Frege, GrUNlgesetze der Arithtnetik, Band L p. xxi.
116. Ibid. 117. Frege, "Review of Dr. E. Husser!'s Philosophy of Arithmaic," p. 318. Frege quipped tha~ on their view, no judgment could be about the Moon because this would require that the Moon be part of a state of consciousness. ''But would not.. the Moon sit a bit heavy on the stomach of one's state of consciousness?" Ibid., 316. 118. See: Frege, T~ FolUlllations of Arithmetic, sec. 27n., 61. 119. Frege, ''The Thought," p. 66. 120. See: Frege, "On Sense and Reference," p. 29f. 121. Frege, GrUNlgesetze der Arithmetik, Band L p. xix. 122. Consequently, he left himself a task in philosophy of arithmetic, namely to prove that numbers are not ideas. This required separate arguments. See: Frege, The Foundations of Arithmetic, sec. 26f. 123. Frege, GrJU&dgesetze der Arithmetik, Band L p. xxiii. 124. Frege, Posthumous Writings, p. 144. 125. See: Frege, Conceptuol Notation, sec. 2. 126. See: Ibid., sec. 2n. See also: Frege, Posthumous Writings, p. 105. 127. See: Frege, Posthumous Writings, p. 143f. 128. Ibid., p. 105 129. See: Frege, "On Sense and Reference," p. 35f. 130. See: Frege, Posthumous Writings, p. 255. 131. See: Frege, Grundgesetze der Arithmetik, Band I, sec. 32. 132. See: Ibid. 133. See: Frege, Philosophical and Mathemmical Correspondence, p. 163. 134. See: Frege, Posthumous Writings, p. 243. 135. Arguably, as we noted, the subjects of all judgments are concepts, namely if the subject of a singular judgment (e.g., that Socrates is mortal) is taken to be an individual concept 136. See: Frege, "On the Law of Inertia," p. 160. See also: Frege, "On Sense and Reference," p. 29. 137. Cf., Frege, "Review of Dr. E. Husserl's Philosophy of Arithmetic," p. 316. 138. Frege, "On the Law of !nertia," p. 160. 139. Cf., Frege, Posthumous Writings, p. 17. 140. Frege himself continued to employ this traditional terminology in early writings (See: Frege, Conceptlllll Notation, sec. 2. See also: Frege, Posthumous Writings, p. 16), although he officially denied this implication. This idiom invites misunderstanding; it is probably linked with his insistent inclination to combine the doctrine of fimction/argument analysis in logic with the idea of decomposing judgeable-contents and thoughts into parts; and this may have contributed to the emergence of his late doctrine that a thought must be built up out of thought-building-blocks (Gedanken bausteine) which correspond to the words or phrases of the sentence that expresses this thought See: Frege, Posthumous Writings, p-pe 225, 243. 141. Frege, "On Sense and Reference," p. 29. 142. Frege, "Review of Dr. E. Husser!'s Philosophy of Arithmetic," p. 316. 143. See: Frege, "On Sense and Reference," p. 29. 144. See: Frege, Philosophical and Mathemmical Co"espondence, p. 80; Frege, GrlUldgesetze der AritluMtik, Band I, sec. 32; and Frege, "On Sense and Reference," p.29.
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145. Frege, The FolUUlations of Arithmetic, sec. 59. 146. Ibid., sec. 60. 147. Frege, "On Sense and Reference," p. 29. 148. Ibid., pp. 29f. 149. Cf., Frege, ''The Thought," p. 67. 150. It does not follow, however, that the sense of a concept-word cannot be subjective. On the contrary, if there are singular thoughts limited to the sphere of a single consciousness, then the concept-words occurring in the expression of such thoughts would have senses as subjective as the value of these sense-functions (and perhaps references as subjective as the arguments of these concepts). It is disputed whether Frege treated either the content or the sense of concept-words as functions. Evidence that he made both these identifications is marshalled in: G.P. Baker and PM.S. Hacker, Frege: Logical Excavations (Oxford: Basil Blackwell, 1984), pp. 170ff., 322ff. Some criticisms are rebutted in: G.P. Baker and PM.S. Hacker, "Dummett's Dig: Looking-glass Archeology," pp. 88ff. 151. Frege, Gru.ndgesetze der Arithmetik, Band I, pp. xxif. 152. Frege, PosthU11lOUS Writings, p. 139. 153. Frege, The FolUUlations of Arithmetic, pp. vf. 154. See: Ibid., sec. 47. 155. Cf., Ibid., pp. v if. 156. See: Frege, "On the Law of Inertia," p. 158. 157. Frege, The FolUUlations of Arithmetic, sec. 60. 158. See: Frege, Gru.ndgesetze der Arithmetik, Band I, p. xxi. 159. Frege, Posthumous Writings, p. 131. 160. This objection ignores the fact that the psychological logicians would probably require every judgment to contain additional elements (namely, the copula and syncategoremata indicating 'quality' and 'quantity'). 161. Frege, Posthumous Writings, p. 145. 162. Hwne ignored the distinction in rmding no difference between the complex idea of a horse and the complex idea that horses exist (See: David Hume, A Treatise of Hwnan Nature, ed. L.A. Selby-Bigge (Oxford: Clarendon, 1978), "Appendix"), and Russell (attempting to update Hume with the addition of the sophisticated logical machinery of the predicate calculus) found difficulty in distinguishing a proposition from the mere assemblage of its components. Cf., Bertrand Russell, The Principles of Mathematics (London: George Allen & Unwin, 1903), pp. 47ff. 163. See: Frege, The FolUUlations of Arithmetic, sec. 53. 164. See: Frege, The FolUUlations of Arithmetic, sec. 49. 165. Never? He apparently argued this strong thesis in one early \D1published paper. ''1 allow the formation of concepts to proceed only from judgments....And so instead of putting a judgment together out of an individual as subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept by splitting up a judgeable-content" (Frege, Posthumous Writings, 160. Doubt might be entertained about whether this thesis is coherent in this completely general form. It might be suggested that Frege had in mind only the complex concepts required for this treatment of generality as a second-level concept (cf., Dummett, Frege: Philosophy of LanglUlg~, pp. 27ff; and Dmnmett, The Interpretation of Frege's Philosophy, pp. 292ft). 166. See: Frege, The FolUUlations of Arit~tic, sec. 45. 167. See: Frege, ''The Thought," 1?~§1~_------------ - - - - - - - - - - - - - - - - - - - - -
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168. Russell worried about this problem and tried to develop a satisfactory solution to it (See: Bertrand Russell, Theory of Knowledge: the 1913 Manuscript, -ed. E.R. Eames (London: George Allen & Unwin, 1984), pp. 85ff). The problem is claimed to be an insuperable obstacle to the general doctrine of 'abstractionism' (See: P.T. Geach. Mental Acts (London: Routledge & Kegan Paul, 1957), pp. 320. 169. Cf., Frege, "Review of Dr. E. Husserl's Philosophy of Arithmetic," pp.
316t
I
170. Cf., Frege, The Foundations of Arithmetic, sec. 58. 171. See: Frege, "Review of Dr. E. Husserl's Philosophy of Arithmetic," pp. 317, 324f. 172. Cf., Ibid., p. 316. 173. These claims mix insights with confusions. Frege obscured the difference between logical operations and material functions (concepts), and thereby misrepresented the propositions of logic as comprising the science of special logical objects (cf, Wittgenste~ Tractatus, pts. 5.2-5.254, 6.1111). 174. Cf., Frege, Posthumous Writings, p. 184. 175. See: Ibid., p. 16f. 176. Cf., Frege, The Foundations of Arithmetic, sec. 45. 177. Ibid., p. x. 178. See: Frege, Grundgesetze der Arithmetik, Band I, sec. 3. 179. In earlier writings, when he conceived of the value of a function as a judgeable-content (not as a truth-value), he did not hold this general thesis; on the contrary, he thought that only in special cases could the extension of a concept be calculated from the intrinsic nature of the concept itself (See: Ibid., sec. 53). The change is crucial, but Frege did not call attention to it 180. This accusation is substantiated in: G.P. Baker and P.M.S. Hacker, Frege: Logical Excavations, pp. 173ff., 252ff.
ANTI-PSYCHOLOGISM AND SCEPTICISM: FREGE, DESCARTES, AND WITTGENSTEIN PHILIP DWYER
I. Introduction Chapter 19 of Michael Dummett's Frege, Philosophy of Language, is entitled ttFrege's Place in the History of Philosophy." Dummett assigns Frege his place largely vis d vis Descartes: Before Descartes, it can hardly be said that anyone part of philosophy was recognized as being fundamental to all the rest: the Cartesian revolution consisted in giving this role to the theory of knowledge. Descartes made the question, 'What do we know, and what justifies our claim to this knowledge?' the starting point of all philosophy: and despite the conflicting views of the various schools, it was accepted as the starting point for more than two centuries. Frege's basic achievement lay in the fact that he totally ignored the Cartesian tradition, and was able, posthumously, to impose his different perspective on other philosophers of the analytic tradition.1
For Frege, according to Dummett, it is not the theory of knowledge, but the theory of meaning which is the fundamental part of philosophy: Because philosophy has, as its rust, if not its only task, the analysis of meanings, and because, the deeper such an analysis goes, the more it is dependent upon a correct general account of meaning, a model for what the lDlderstanding of an expression consists in, the theory of meaning, which is the search for such a model, is the fOWldation of all philosophy, and not epistemology as Descartes misled us into believing. Frege's greatness consists, in the rust place, in having perceived this. 2
I too believe that Frege's place in the history of philosophy is best worked out in connection with Descartes. However, contrary to Dummett, I believe the right account of the matler concerns Frege's positive relation to Descartes, not his lack of a relation to Descartes. The relation between Frege and Descartes is many-sided, but the aspect on which I want to concentrate concerns the connection, in the thought of both philosophers, between scepticism and a certain kind of 'anti-psychologism': the connection between scepticism and anti-psychologism is exploited by both philosophers and thereby constitutes a connection between the philosophers themselves.
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Furthennore, the connection between Frege and Descartes on the score of scepticism and anti-psychologism is mediated by a third philosopher, viz., Wittgenstein. I want to show, inter alia, that it is no accident that the considerations Wittgenstein advances against an explicitly Fregean scepticism and anti-psychologism in Remarks on the Foundations of Mathematics and Philosophical Investigations recur in On Certainty, where the target is, at least implicitly, Descartes. The story of this philosophical menage a trois, as I set it out, is parenthesized by two digressions. At the end I offer some general comments on scepticism and so-called 'methodological scepticism'. And in what follows immediately, I wish to give an indication of the exaggeration of Dummett's claim that Frege totally ignored the Cartesian tradition.
II. Frege and Descartes Given the similarities between the philosophies of Frege and Descartes to be listed shortly, the statement that Frege totally ignored the Cartesian tradition, in any broad sense of the expression, is simply wrong. Dummett, however, no doubt means 'the Cartesian tradition' in the narrow sense of a tradition concerning what he calls 'the starting point of all philosophy'. It is neither indisputable that Descartes did in fact take epistemology to be the starting-point or 'fundamental' part of philosophy rather than, say, metaphysics, or philosophical theology, or philosophy of mind, nor clear just how these are to be precisely distinguished.3 There is no less a problem, such as it is, as to what Frege took to be the starting point in philosophy, and Dummett's claim that Frege took it to be 'the theory of meaning' in no way clarifies the matter. As was seen in the second quotation in our introduction, Dummett says that the theory of meaning is the search for a model of what the understanding of an expre~ion consists in. The construction of a 'model of understanding' would normally be construed as a problem for either or both the philosophy of mind or/and the theory of knowledge. Taking the latter interpretation for example, Dummett says: ...the complex phrase on which attention needs to be concentrated is 'knowing the meaning of... ': a theory of meaning is a theory of understanding. What we have to give an account of is what a person knows when he knows what a word or expression means, that is, when he lDlderstands it4
Here a 'theory of understanding' is surely some kind of theory of knowledge, and hence, a 'theory of meaning' is too. No recourse can be made here to a distinction between knowledge of meaning and knowledge of the world. Such a distinction is quite incompatible with the truth-conditions semantics which Dummett attributes to Frege: "to grasp the sense of a sentence is, in general, to know the conditions under which that
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sentence is true and the conditions under which it is false."S The distinction between the theory of knowledge and the theory of meaning also seems to be undermined by Dummett's other remarks on Frege's notion of 'sense', a central notion, presumably, of his theory of meaning. Dummett says, "For Frege, sense is a cognitive notion: it is introduced by him in the first place to resolve a problem about the cognitive value, or information content, of true identity-statements."' In Frege, Dummett says that "it is quite wrong to think of Frege's theory of meaning as one where meaning is quite divorced from knowledge. "7 It is, in any case, not clear how seriously Dummett really means his doctrine of the starting point in philosophy. After using it as a basis for characterizing the last three hundred years of philosophy, Dummett seems to abandon it in short order. We are fll'St told that whatever part of philosophy is "fundamental to all the rest" is the "starting point for the whole subject "8 The starting point is that which "must be settled before anything else can be said."' Frege held, we are told, "that the theory of meaning is the fundamental part of philosophy which underlies all the others, "10 that "he starts from meaning by taking the theory of meaning as the only part of philosophy whose results do not depend on those of any other part, but which underlies all the rest."11 But then shortly we are told that: To say that the theory of meaning is the f01Dldation of philosophy is not to say that nothing else can be done until the main problems in the theory of meaning are resolved On the contrary, progress can be made on problems 'that arise in advance of our having a satisfactory theory of meaning, even when these are problems in the context of which the notion of meaning seems to be naturally invoked. 12
Not only is it now possible to settle some issues before we have a theory of meaning, but in some cases "it is a condition of advance in the dispute that the notion of meaning be bracketed;"l3 "in disputes of this kind, the notion of meaning must be bracketed before any progress can be made. "14 But this is not all. In this revised doctrine of the starting point, not only may we settle some issues before we have a theory of meaning; and not only, in some cases, must we settle some issues before invoking the notion of meaning, in some yet further cases, settling issues in one area may actually contribute to settling issues in the theory of meaning: It is no objection to the fundamental character of the theory of meaning that sometimes, as in the cases cited, an advance in resolving a question that arises within some other particular branch of philosophy may be made before the corresponding general question in the theory of meaning has been settled, and may, indeed, be a substantial contribution towards settling that question. IS
The question of what Frege took to be fundamental in philosophy is best construed as a question about what he took to be a very important issue in philosophy, not what he took its 'starting point' to be. Certainly he took
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epistemological issues to be fundamental, and in particular the issue of the justification of knowledge. Speculating on the effect of his The Foundations of Arithmetic, Frege says, "Someone or other, perhaps, will take this opportunity to examine afresh the principles of his theory of knowledge. n16 This would be a strange comment to come from someone who, according to Dummett, never gave us his views on knowledge. 17 Frege is clearly in the epistemological mainstream of Western philosophy. But beyond this, if his views are to be characterized as anything other than ,Fregean" they would have to be characterized as Cartesian. The following is a short list of the points of contact between Descartes' and Frege's views. (a) Both Descartes and Frege have a great concern for science - a discipline or systematic body of knowledge - taking it to be what epistemology is primarily in aid of. Descartes' Discourse on the Method of rightly conducting the Reason and seeking for Truth in the Sciences was intended as an introduction to essays on meteorology, optics, and geometry. Throughout the Discourse he refers to his method as the 'foundations of my physics'.18 In the Meditations he speaks of his doubting what were hitherto 'foundations for the sciences' ,19 while his method is "a certain Method for the resolution of difficulties of every kind in the sciences,n~ the most geneml difficulty being "to arrive at any certainty in the sciences."21 Frege's Begriffschrift opens with the sentence "In apprehending a scientific truth we pass, as a rule, through various stages of certitude. "22 The most 'secure foundation' for a proposition is provided by pure logic- "on those laws upon which all knowledge rests."23 The Begrif{schrift will have application to mathematics, Frege says, and could easily be extended to geometry. "The transition to the pure theory of motion and then to mechanics and physics could follow at this point 1124 His sample propositions in explaining his notation are not of 'the eat is on the mat' variety, but e.g., "Let a be the circumstance that the piece of iron E becomes magnetized, b the circumstance that a galvanic current flows through the wire D ete.,"2S or "the circumstance that hydrogen is lighter than carbon dioxide."26 This concern with scientific truth dominated Frege's views on logic throughout his career. Logic has the property 'true' as its object of study;27 what is true are 'thoughts', the paradigm of which is a natural law;28 the truth which is the concern of logic is "that sort of truth which it is the aim of science to discern";29 "The goal of scientific endeavor is truth."30 Descartes also speaks of his method of rightly conducting the reason in seeking truth in the sciences as his "principle rules of logic. "31 (b) Both Frege and Descartes uphold an ideal of rigour in science, whether in the broad sense of 'knowledge' or in the narrow sense of a science such as arithmetic, and take Euclid as their model (as do other Rationalists, most notably Spinoza). Descartes says that "Those long chains of reasoning, simple as they are, of which geometricians make use in order to arrive at the most difficult demonstrations, had caused me to imagine that all those things which fall under the cognizance of man might very likely
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be mutually related in the same fashion. "32 In the preface to The Basic Laws of Arithmetic, Frege introduces his method with these words: "The ideal of a strictly scientific method in mathematics which I have here attempted to realize, and which might indeed be named. after Euclid, I should like to describe as follows."33 Connected with this is an ideal of 'gaplessness' in proofs. His Begriffschrift was invented to meet the demand that every gap or "jump must be barred from our deductions."34 For Frege, it is not good enough to say, in the middle of a proof, that a certain transition is merely evident, given what has come before: "if it is a matter of gaining insight into the nature of this 'being evident', this procedure does not suffice; we must put down all of the intermediate steps, that the full light of consciousness may fall upon them. "35 Gaplessness serves to answer an epistemological question: "Because there are no gaps in the chains of inference, every ,axiom', every 'assumption', 'hypothesis', or whatever you wish to call it, upon which a proof is based is brought to light; and in this way we gain a basis upon which to judge the epistemological nature of the law that is proved. "36 This same requirement of gaplessness as the ground of true certainty, is to be found among the rules set out in Descartes' Regulae and the Discourse on Method. In the Regulae, sounding very Fregeau, Descartes says: Often people who attempt to reduce a conclusion too quickly and from remote principles do not trace the whole chaia, of intermediate conclusions with sufficient accuracy to prevent them from passing over many steps without due consideration. But it is certain that wherever the smallest link is left out the chain is broken and the whole of the certainty of the conclusion falls to the ground.37
(c) The epistemological ideal of gaplessness leads Descartes and Frege to similarities in their psychological accounts of gaplessness, Le., in their philosophies of mind. Descartes' frrst principles cannot be proved, they "are given by intuition alone," while "the remote conclusions are furnished by deduction. "31 This parallels Frege's distinction in his 'strictly scientific method in mathematics' between axioms and rules of inference on the one hand, and proved propositions on the other. The latter are not be grasped "in one single act of understanding, "39 whereas axioms are 'self-evident'.40 So for Frege and Descartes there is a psychological criterion for distinguishing logical self-evidence (Frege) or intuition (Descartes) from deduction. Frege employs a further criterion ofaxiomaticity and a rather Cartesian one at that, viz. indubitability: "The axioms are truths as are the theorems, but they are truths for which no proof can be given in our system, and for which no proof is needed. It follows from this that there are no false axioms, and that we cannot accept a thought as an axiom if we are in doubt about its bUth; for it is either false and not an axiom, or it is true but stands in need of proof and hence is not an axiom."41 Axioms (and
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laws of logic) are then clear and distinct, but what is clear and distinct to one man, another man (or Martian) may doubL42 (d) There are other similarities in the philosophies of mind of Frege and Descartes. In Descartes' official doctrine there are basically two sorts of functioning of the mind: the understanding and the will. The understanding is said to include "sense-perception, imagining, and conceiving things that are purely intelligible,"43 but sense-perception is very much the poor here, set off to one side. The utility of Descartes' method, he says, is 'that "it sets out for us a very simple way in which the mind may detach itself from the senses. tt44 The operation of the will, as opposed to the understanding, consists most importantly in judgment, i.e., assertion or denial of something.45 Frege likewise distinguishes sense perception from what he calls 'conceptual thinking', and these two are again distinguished from judgment. In The Foundations of Arithmetic Frege fmnly segregates what we come to know "through the medium of the senses" from "the fundamentally different question" of what is "given directly to our reason."46 It is "the exeICise of these higher intellectual powers that distinguish men from brutes.,,47 In the late article "The SOUICes of Knowledge in Mathematics and Mathematical Natural Sciences," Frege distinguishes three such SOUICes: (1) sense perception; (2) the logical source of knowledge; (3) the geometrical and temporal source. Section A of the article deals with peICeption and is entitled "Sense Illusions": "We must be careful not to overestimate the value of sense perception, for without the other sources of knowledge, which protect us from being deceived, we could hardly get anywhere with it 1t48 Descartes of course had a similarly sceptical opinion of perception and also viewed the correction of deceptive sense perception as an achievement of the intellect.49 According to Frege, "the logical source of knowledge, which is wholly inside us" is 'thinking'.~ The doctrine that judgment is the affIrmation of a thought, whereas thinking is the mere grasping or entertaining of a thought, occurs frrst in the Begriffschrift in his explanation of the notational difference between the content stroke and the judgment
stroke.51 (e) Both Descartes and Frege view language, as well as perception, as something that contaminates 'pure thought'. The Begriffschrift, 'a formula language for pure thought', is a contribution to one of the main tasks of philosophy, viz., "to break the domination of the word over the human spirt by laying bare the misconceptions that through the use of language almost unavoidably arise concerning the relations between concepts...."52 Frege links his Begriffschrift with Leibniz's project of an ars characteristica.53 Descartes too envisioned such a universal language "for acquiring true scientific knowledge....The greatest advantage of such a language would be the assistance it would give to men's judgment, representing matters so clearly that it would be almost impossible to go wrong. As it is, almost all our words have confused meanings, and men's minds are so accustomed to them that there is hardly anything that 'they can perfectly understand. "54
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Frege holds that "There is no contradiction in supposing there to exist beings that can grasp the same thought as we do without needing to clad it in a form that can be perceived by the senses. "ss For the contaminating effects of language are of a piece with its perceptual character: "Something by itself not perceptible by sense, the thought, is presented to the reader and I must be content with that - wrapped up in a perceptible linguistic fonn. The pictorial aspect of language presents difficulties. The sensible always breaks in and makes expressions pictorial and so improper. So one fights against language, and I am compelled to occupy myself with language although it is not my proper concern here."5C§ In The Foundations of Arithmetic Frege speaks of "achieving knowledge of a concept in its pure fonn, in stripping off the irrelevant accretions which veil it from the eyes of the mind." (geistige Auge)S7 Here he echoes Descartes' account of the clear and distinct perception of ideas and thoughts as "looking with the eyes of the mind"S' or "mental vision. ns' (t) Descartes speaks of apprehending 'ideas'fiO while Frege speaks of comprehending 'thoughts'."l Since Frege made so much of the difference between ideas (Vorstellungen) as subjective psychological entities and thoughts as abstract objective entities, this may seem to constitute a major difference between the two philosophers. However, from Begriffschrift to 'Dec Gedanke' Frege is, at any rate, right in Locke-step with Descartes in believing that there are such (mental) things as ideas or latterly 'sense data', e.g., that to see is to have 'visual ideas', to hear is to have 'auditory ideas', to feel is to have 'motor ideas', etc.62 His eventual objection to ideas in favour of thoughts was that ideas, as 'mental images' or as 'sense impressions', are private63 and, as psychological entities, have no internal relation to truth. 64 Descartes, on the other hand, sometimes denies that 'ideas' are images or sense impressions,6S and in one of their chief incarnations they are propositional in nature; they are what is apprehended by the understanding and affmned or denied by the will in making a judgment" Moreover, the gain in objectivity which Frege thought was achieved by twning token thoughts in persons' minds into type thoughts in a platonic realm, is, in the end, vitiated by the fact that ultimately the public thoughts are connected with the public signs (names and sentences) by a private process of association." (g) Whatever the differences between Frege and Descartes on the count of ideas versus thoughts, Descartes was not averse to recognizing mind-independent platonic objects. In the interview with Bunnan he says: All the demonstrations of mathematics are concerned with true beings and objects; and so the whole object of mathematics, and whatever mathematics considers in it, is a true and real being, and has a true and real nature, no less than the objects of physics. The only difference is that physics considers its object not only as a true and real being but also as actual, ~ as such existing, whereas mathematics considers its objects only as possible, not actually existing in space, but still able to exist.'"
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This could have been written by Frege. He too distinguishes "what is handleable or spatial or actual" from what is "objective," or "self-subsistent," "but not in space," such as numbers and thoughts.69 The above is by no means a full account of the links between the thought of Descartes and that of Frege, but it should serve to establish that Frege is fmnly rooted in the traditions of Cartesian rationalism, against which the later philosophy of Wittgenstein is, in good part, directed.
III. An Ambiguity about 'Psychologism' Scepticism plays an explicit and central role in Descartes' philosophy, and anti-psychologism plays an explicit and central role in Frege's philosophy. However, Descartes' employment of sceptical arguments implicitly relies on a kind of anti-psychologism, while Frege's anti-psychologism gives expression to a kind of scepticism. The connection between scepticism and anti-psychologism provides a further link between Descartes and Frege. It is with this latter link in particular that Wittgenstein enters the discussion. However, before setting this out, something must be said, by way of avoiding confusions, about the expression 'psychologism'. Dummett, in the essay "Frege's Philosophy" speaks of Frege's "strong attack on what he called 'psychologism'- the thesis that an account of the meanings of words must be given in terms of the mental processes which they arouse in speaker or hearer or which are involved in acquiring a grasp of their sense. "'0 Dummett goes on to link this hereditarily with "Wittgenstein's dictum that 'the meaning is the use'."'1 It is true that Frege argues against taking "as the meanings of words mental pictures or acts of the individual mind,",2 and asserts that to do so is to offend against the frrst of his 'three fundamental principles', viz., "always to separate sharply the psychological from the logical, the subjective from the objective."'3 It is also true that Wittgenstein's dictum about meaning as use is partly directed against the view that the meanings of words are mental images.'" Nevertheless, there is something very misleading in presenting Frege's attack in psychologism in these terms. Psychologism for Frege is first and foremost a thesis about the nature of logic, viz., that logical laws are really psychological laws. The "corrupting incursion of psychology into logic" is a matter of taking logical laws to be 'laws of thought' in the sense of asserting what is, rather than what ought to be.75 The very expression 'law of thought': ...seduces us into supposing that these laws govern thinking in the same say as laws of nature govern events in the external world. In that case they can be nothing but laws of psychology: for thinking is a mental process. And if logic were concerned with these psychological laws, it would be a part of psychology."
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For Frege, logic concerns the 'laws of truth', psychology 'the laws of taking to be true'.T1 Here Frege may be punning on the German word for perception- 'Wahrnehmung' (I have not seen the original German). The latter mayor may not be in accord with the laws of truth.." Only if they are, can an inference be justified. The issue of the justification for making a judgment is the central motive for Frege's sharp distinction between psychology and logic." Just as logical laws are not be confused with psychological laws, the objects of arithmetic - numbers - are not be to confused with the objects of psychology- 'ideas': "If number were an idea then arithmetic would be psychology."80 Likewise, it is in connection with Frege's ontology of absttaet objects - which in effect constitutes the heart of his theory of meaning, such as it is - that the issue of meaning as a mental image comes in. In his discussion of psychologism in The Basic Laws of Arithmetic, Frege says: Surveying the whole question, it seems to me that the source of the dispute lies in a difference in our conceptions of what is true. For me, what is true is something objective and independent of the judging subject; for psychological logicians it is not.11
'What is true' for Frege, and objectively so, independently of a conscious subject, are thoughts. This, of course, rules out mental images as constituting the meaning or sense or thought behind words. But the 'subjective' for Frege includes more than mental images. Psychologism also includes any reference to 'muscular sensations', or the 'content of the brain', or human evolution.12 Not only is "the origin and evolution of ideas" ruled out as irrelevant, but also "the history either of our knowledge of concepts or of the meanings of words."83 In short, 'the subjective' includes any reference to human beings. Certainly Wittgenstein's thesis that meaning is use would be no less psychologistic for Frege than would be a mental image theory of meaning. Frege would be no less horrified at something going under the name 'anthropologism' - as Dummett describes Wittgenstein's philosophy of mathematicsM - than he would at any so-called psychologism. Indeed, as the above quote about the objectivity and independence of truth shows, even the milder forms of 'anti-realism' enunciated by DummetfS would be only so much psychologism for Frege. The only alternative to platonism, for Frege, is some form of psychologism: logic and mathematics, truth and meaning, are either person-dependent or they are not. There is more to the misleadingness of positively linking Frege's attack on psychologism with Wittgenstein than that indicated above. John McDowell writes of "the hostility to psychologism voiced by Frege in the philosophy of logic and language, and extended into the philosophy of mind by Wittgenstein."" Certainly one thinks of the philosophy of mind in
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connection with Wittgenstein being hostile to 'psychologism'. But Wittgenstein's hostility to psychologism should not be spoken of in the same breath with Frege's hostility to psychologism. Wittgenstein's anti-psychologism' is directed against mental process mongering; for example, against the thesis that thinking, as such, is a mental process. 87 But Frege was a great believer in mental processes, especially, as we've seen, with regard to thinking as a mental process. It is precisely his ontological doctrine of the thought which requires his Cartesian view of the mind: "To the grasping of thoughts there must then correspond a special mental capacity, the power of thinking."- It is then left for an 'act of judgment' to acknowledge the truth of the thought." To the extent that Wittgenstein's dictum 'meaning is use' is anti-psychologistic it is meant to undennine the view that 'meaning' - the verb - designates a mental process. For Frege this is just what meaning, as an activity, is, Le., a mental process of 'intending', or 'associating', or 'connecting'90 signs with thoughts. Again, for Frege, thinking as such involves the mind's intentional powers: "Although the thought does not belong with the contents of consciousness, there must be something in his consciousness that is aimed at the thought "91 Wittgenstein's dictum about meaning and use in directed against both the views that either mental processes or Fregean thoughts give meaning to signs.92 Crispin Wright says that one important advance of Wittgenstein's philosophy of mathematics over that of the intuitionists is this: "the case for repudiating a platonist conception of mathematical truth is no longer muddled with a psychologistic conception of mathematical understanding. "93 This passage (indexed under 'psychologism. Wittgenstein's ant-realism free from ') is ambiguous. It is precisely the case presented for platonism that is muddled with a psychologistic conception of mathematical understanding, insofar as 'psychologism' is what Wittgenstein attacked. Consider, for example, the following from Wittgenstein's Remarks on the Foundations of
Mathematics: But still, I must only infer what really follows! -Is this supposed to mean: only what follows, going by the rules of inference; or is it supposed to mean: only what follows, going by such rules of inference as somehow agree with some (sort of) reality? Here what is before our minds in a vague way is that this reality is something very abstract, very general, and very rigid. Logic is a kind of ultra-physics, the description of the 'logical structure' of the world, which we perceive through a kind of ultra-experience (with the understanding e.g.).M
On the other hand, Wittgenstein's philosophy of mathematics is riddled with 'psychologism' as Frege understood it. Indeed, Wittgenstein rubs Frege's nose in it
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IV. Wittgensteinian Psychologism Remarks such 88, "For mathematics is after all an anthropological phenomenon"" seem specifically designed to set Frege spinning in his grave. When Wittgenstein says, "We shall see contradiction in a quite different light if we look at its occmrence and its consequences anthropologically...,"" we can hear Frege saying, 'Indeed we shall!'- but this concurrence would be only superficial. Wittgenstein goes on to explain that viewing contradiction 'anthropologically' means considering how it influences 'language-games', and, as he says in On Certainty, "everything descriptive of a language-game is part of logic. "fJ7 Given that a language-game is language and the actions into which it is woven,98 this view of logic would be poison for Frege. To repeat, there are only two alternatives concerning the nature of logic and mathematics: objectivity or person-dependence. This in turn must cash out as the alternative between some form of platonism and some fonn of psychologism. To the extent that Wittgenstein's rule-following considerations advanced in Philosophical Investigations and Remarks on the Foundations of Mathematics are directed against platonism, they constitute what Frege would call 'pschologism'. That Wittgenstein implicitly had Frege in mind in his discussions of rule-following could be gathered from section 80 of Frege's The Foundations of Arithmetic, entitled 'Following (in a series) is objective'. But Wittgenstein explicitly has Frege in mind in the inevitable discussion of psychologism that attends the anti-platonistic discussion of rule-following and logical compulsion in part I of Remarks on the Foundations of Mathematics. In outline, part 1 of Remarks on the Foundations of Mathematics goes as follows: Sections 1-5 concern how a role determines what steps are taken, with the upshot that it is not a mental act of meaning which determines the steps in advance (3), but rather the importance of mathematics in our life's activities that gives rise to the 'peculiar inexorability of mathematics' (5). Sections 6-23 concern logical inference and contain various antiFregean/Russellian, i.e., anti-platonist points, in particular: that the idea that rules of inference agree with some sort of person or subject-independent reality ('logic as ultra-physics') is an illusion (8); that logical inference is a transformation of signs, and that the reality it accords with is a convention or a use (9); that when one proposition follows from another, it is not that it must, but that it does: "we perform this transition" (12); it does not 'follow' in a platonic realm, short of an actual person's actual inference (21). Sections 24-112 concern proof, calculation and experiment, and mathematical belief. Sections 113-142 treat of logical compulsion, and it is here that reference to Frege on psychologism is made. Section 113 contains the dialogue on rule-following that ends with the refrain of the Kripke-style sceptic: "However many rules you give me- I give a rule that justifies my employment of your rules. "99 Section 116 says that ~__~~~_J.!f_jnfereD~e_---
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can be said to compel us in the same sense as other laws of human society.ulo Section 118 directly addresses the issue of psychologism: "It looked at first as if these considerations were meant to show that 'what seems to be a logical compulsion is in reality only a psychological one'only here the question arose: am I acquainted with both kinds of compulsion then?!" In the final paragraph of this section, Wittgenstein writes: Now we talk of the 'inexorability' of logic; and think of the laws of logic as inexorable, as still more inexorable than the laws of nature.... [Rather] There correspond to our laws of logic very general facts of daily experience. They are the ones that make it possible for us to keep demonstrating those laws in a very simple way (with ink on paper for example). They are to be compared with facts that make measurement with a yardstick easy and useful. This suggests the use of precisely these laws of inference, and now it is we that are inexorable in applying these laws" 01
This line is precisely what Frege stood against in his attack on psychologism. Part I, sections 119-130 of Remarks on the Foundations of Mathematics discuss the picture of the 'logical machine' which cranks out propositions which 'really' do follow. These sections go with Part V, section 20: "If calculating looks to us like the action of a machine, it is the human being doing the calculation that is the machine." Sections 131-133 make reference to Frege's anti-psychologism. Section 131 goes: "The laws of logic are indeed the expression of 'thinking habits' but also of the habit of thinking. That is to say they can be said to shew: how human beings think, and also what human beings call 'thinking' ."102 Section 132 has some fun with one of Frege's examples of 'a law about what men take for true', and then in sections 133-4, Wittgenstein writes: The propositions of logic are 'laws of thought', 'because they bring out the essence of human thinking'- to put it more correctly: because they bring out or shew, the essence, the technique, of thinking. They shew what thinking is and also shew kinds of thinking. Logic, it may be said, shews us what we understand by 'proposition' and by 'language'.
The direction of Wittgenstein's discussion of the laws of logic as 'laws of thought' is clearly counter to that of Frege's discussion, In the midst of these 'psychologistic' remarks, come three sections, 135-7, on error and a deceptive demon. We shall return to these. Following this in section 142, comes the remark that fmds a place in the Investigations (145): "What we are supplying are really remarks on the natural history of man...." It goes without saying that for Frege, the last thing remarks on the foundations of mathematics should be is remarks on the natural history of man. The following sections 143-51 deal with a case of 'fictitious natural history', that of the people who calculate the price of
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wood in a peculiar way. In section 152 Wittgenstein writes "Frege says in the preface to the Grundgesetze der Arithmetic: ' ...here we have a hitherto unknown kind of insanity'- but he never said what this 'insanity' would really be like." (Frege was responding to the question: "But what if beings were even found whose laws of thought flatly contradicted ours and therefore frequently led to contrary results even in practice?ttl(3) In the section that follows, Wittgenstein suggests that this 'insanity' amounts to a cultural difference. Section 154, immediately following, contains the frrst remarks in Remarks on the Foundations of Mathematics on the requirement for surveyability of proofs (more about which later). Section 155 gives a further fictitious natural history and ends with the marginal note: "Are our laws of inference eternal and immutable?" Wittgenstein's question, which alludes to Frege's claim for the "unconditional and eternal validity" of the laws of logic in his anti-psychologistic diatribe in The Basic Laws of Arithmetic,l04 is answered in the immediately following section. Isn't it like this: so long as one thinks it can't be otherwise, one draws logical conclusions. This presumably means: so long as such and such is not brought into question at all. The steps which are not brought in question are logical inferences. But the reason why they are not brought into question is not that they certainly correspond to the 'truth' - or something of the sort, - no, it is just this that is called 'thinking', 'speaking', 'inferring" 'arguing'. There is not any question at all here of some correspondence between what is said and reality: rather is logic antecedent to any such correspondence; in the same sense, that is, as that in which the establishment of a method of measurement is antecedent to the correctness or incorrectness of a statement of length. lOS
This passage brings out the point that if one rejects a platonic realm in accordance with which we 'correctly' speak, think, infer, etc., then one is left only with speaking, thinking, inferring, as such, i.e., as paradigms, being the foundation or presupposition of correct speaking, thinking, inferring. And this, on Frege's view, is simply psychologism. Sections 157-8 deal with paradigms of sign sequences as guiding inference. These sections are thus connected with a remark in Part VII, section 66: "Logical inference is a transition that is justified if it follows a particular paradigm and its rightness is not dependent on anything else. ftlO6 This again is directed against Frege's platonistic view of logical laws, and would be for Frege, not psychologism, but something just as bad: formalism. Part I of Remarks on the Foundations of Mathematics contains one more strikingly anti-Fregean remark: "The mathematician is an inventor not a discoverer. 1m. Contrast Frege in The Foundations of Arithmetic: "...even the mathematician cannot create at will, anymore than the geographer can; he too can only discover what is there and give it a name. 't108 Remarks on the Foundations of Mathematics Part I ends with section 171 where the 'logical fI
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must' is compared to various (other) Gestalt phenomena (more about which later).
v. 'Two-Kinds' Theses Wittgenstein then is clearly what Frege would characterize as a 'psychological logician'. However, Wittgenstein must be distinguished from those Frege attacked, at least insofar as Wittgenstein had the benefit of Frege's thoughts on psychology and logic, but clearly was not swayed. Why was he unswayed? Frege's anti-psychologism arises in terms of a distinction which, being a commonplace of Western philosophy, he takes for granted, and which bears on his notion of the relation of logic to psychology. The distinction is roughly, that between the logical and the empirical, between a priori science whose laws are 'general laws' that are necessarily and eternally true, and a posteriori science whose laws are not 'general', but include an 'appeal to facts', i.e., to that which is empirical and contingent. 109 Logic and arithmetic are of the first kind, psychology is of the second The distinction between the logical and the empirical is mirrored in distinctions between the ideal and the actual, between the way things are 'in principle' and the way they are 'in fact', between the way things are 'in theory' and the way they are 'in practice', between the way things are 'in themselves' and the way they are 'for us', and between the 'possible' and the 'actual'. The flfSt one hundred and some sections of Philosophical Investigations presents a concentrated attack on a platonist view of logic which portrays logic, properly symbolized, as an ideal form of language of which actual languages only approximate. Wittgenstein's historical targets here are Frege, Russell, and his own Tractatus. From these sources comes the notion of the logically perfect language which is "of the purest crystal" in contrast to the "empirical cloudiness and uncertainty" of ordinary language.110 ("The proposition and the word that logic deals with are supposed to be something pure and clear-cut," in contrast with "what are ordinarily called 'propositions', 'words', 'signs'. "lll) On the model that Wittgenstein latterly attacks, logic is conceived of as presenting language as it is 'ideally' or 'in theory' or 'in principle'- it is "a logic for a vacuum,"112 ignoring the friction and air resistance which besets actual language 'in fact' or 'in practice'. We have already cited Wittgenstein's talk in Remarks on the Foundations of Mathematics of the conception of logic as an ideal kind of physics - an 'ultra-physics' - and this goes with his critique, in Investigations 89, of logic as "something sublime" relative to the emprical investigation of the empirical world Frege repeats this pattern as regards the relation of logic to psychology. Logic presents, as it were, the ideal a priori laws of thought, or laws of an ideal thinker, while psychology presents the empirical laws of thought, the laws of actual thinking. As Frege puts it in "Thoughts": "Neither logic nor
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mathematics has the task of investigating minds and contents of consciousness owned by individual men. Their task could perhaps be represented as the investigation of the mind; of the mind, not of minds.ttll3 The logical/empirical distinction leads to a 'two-kinds' thesis about anything which exemplifies the logical/empirical distinction. Thus, insofar as the logical/empirical distinction is exemplified by the logical/psychological distinction, there ar;e two kinds of 'mind', two kinds of thinking, speaking, inferring, or rule-following: there is logical thinking or inferring, as it were, ideal inferring or inference-in-itself, and psychological inferring, what actual people actually do; ideal or logical rule-following, objectively and in itself, and actual rule-following as it is carried out in actual cases, etc. The ideal version transcends the actual version, as theory transcends practice, as noumena transcend phenomena, as the 'in principle' transcends the 'in fact', and the logical transcends the empirical. It is any such two-kinds thesis that Wittgenstein rejects as regards language and other meaning-related or intentional phenomena. "The philosophy of logic,tt Wittgenstein says, ttspeaks of sentences and words in exactly the sense in which we speak of them in ordinary life when we say e.g. 'Here is a Chinese sentence', or 'No, that only looks like writing; it is actually just an ornament' and so on. We are talking about the spatial and temporal phenomenon of language, not about some non-spatial, non-temporal phantasm. ttl14 Wittgenstein's later philosophy consists of several ,antittanscendence', or following Dummett, 'anti-realist' arguments, to the effect that, for some given intentional phenomenon, there is no way that phenomenon is 'in itself or 'in principle' transcending the way it is 'for us' or 'in fact'. For example, taking Wittgenstein's rule-following considerations llS as comprising an anti-transcendence argument, their upshot is that a rule does not transcend its application (meaning does not transcend use). There is no abstract, objective rule-in-itself transcending what Frege would call the 'extraneous empirical, psychological matter'116 or our actual application or 'following' of a rule. One might put this in tenns of a two-kinds thesis this way: there are not two kinds of rule-following- logical or 'theoretical' rule-following which, as it were, the rules themselves accomplish, versus psychological or 'practical' rule-following, the anthropological phenomenon managed by us down here on earth. Rules and rule-following are all practice. That there is 'following', that there are actions which we all agree upon as cases of following', produces the illusion 'that there are rules independent of our actioo-in-agreement, and which guide our action and thereby produce the agreement. But roles are variously interpretable and when it comes to acting on a rule there will be no interpretation apart from my action. To put the point another way, insofar as a rule requires application, there can be no rule for that, no rule for the application of a rule: in acting on a rule, nothing further can guide me- I must simply act. Now as far as any rules (i.e., expressions of roles) go, you may act one way and I another- but for the most part this doesn't happen. Our
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widespread action-in-agreement or 'form of life' is logically primitive. It is not founded on rules, but rather the other way round: there are 'rules' because there is 'following'. The practice is the intentional phenomenon, the abode of meaning, and not some transcendent non-spatial, non-temporal rule. Intentional phenomena are exhausted by their actual manifestation. There is no language or sense in itself (nor 'simpies'),117 nor definitions (in themselves),118 or in principle, or in theory, versus language for us, or in fact, or in practice (Le., the language-game), and no understanding, or thinking, or inferring in themselves, or in principle, or in theory, versus these things as they actually occur for us, in fact, in practice, Le., again, in the language-game. Such is the message of Wittgenstein's rule-following considerations as an anti-transcendence or anti-realist argument. Wittgenstein's considerations about rule-following are, however, only part of the extended anti-transcendence argument that he pursues in undermining a two-kinds thesis about meaning, which is, to repeat, a thesis that meaning and related intentional phenomena are one way in themselves or in theory transcending the way they are for us. A further central component in Wittgenstein's account of language and meaning might best be called his 'Gestalt considerations', the upshot of which is that linguistic understanding is largely perceptual and that meaning is phenomenal or perception-andunderstanding-dependenl That is to say, there is no way that meaning or sense is - no story to tell about the nature of meaning - apart from the way meaning, or the things that have meaning, are for us perceiving subjects. There is no objective 'meaning-in-itself' transcending' meaning-for-us': meaning is essentially subject or person-dependent. Space is lacking here to document and discuss in detail this surprisingly under-discussed aspect of Wittgenstein's later philosophy.119 His discussion of music, gestures, and physiognomy in connection with language and meaning is neither incidental nor infrequent (see any of his later works, except perhaps On Certainty). Particularly important is the connection he draws between 'seeing-as' and rule-following!20 As Wittgenstein's treatment of language is of a piece with his treatment of mathematics, it is not surprising that Gestalt themes - shape, pattern, physiognomy, music, seeing an aspect, notation and signs - run throughout Remarks on the Foundations of Mathematics. Wittgenstein's claim that surveyability has to do with the essence (Wesen) 121 of proof, and that ttif you have a proof pattern that cannot be taken in, and by a change in notation you tum it into one that can, then you are producing a proof, where there was none beforettl22 is an instance of Wittgenstein's Gestalt approach and its anti-transcendence consequences. It is the claim that proof, as a matter of sense or meaning, is phenomenal, Le., understandingdependent (perception-dependent). Surveyability is just the kind of thing that Frege would pass off as an extraneous, psychological matter, and Wittgenstein addresses the issue in these terms, as he continues Remarks on the Foundations of Mathematics, Part nI, section 2:
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Now let us image a proof for a Russellian proposition stating an addition like 'a+b=c', consisting of a few thousand signs. You will say: Seeing whether this proof is correct or not is a purely external difficulty, of no mathematical interest. (One man takes in easily what someone else takes in with difficulty or not at all, etc. etc.) The assumption is that the defmitions serve merely to abbreviate the expression for the convenience of the calculator; whereas they were part of the calculation. By their aid expressions are produced which could not have been produced without them: 23
It would be quite idle here to make a distinction between a logical 'could' and a psychological or otherwise non-logical 'could' in 'expressions which could not have been produced without the definitions'. There are not two kinds of proof - the proof in itself or in theory, and the proof for us in practice - nor two kinds of understanding of a proof- that achieved by individual men, and that achieved by Frege's 'the mind'. Insofar as surveyability is of the essence of proof and, more generally, insofar as proof is subject-dependent, Wittgenstein could just as well speak of the 'logical', as of the 'psychological disadvantages' of the Russellian symbolism,l24 i.e., insofar as logic is supposed to be the essence of proof.
VI. Anti.Psychologism and Scepticism The two-kinds thesis is the basis of Frege's anti-psychologism. It is also the traditional basis of scepticism, as in Descartes. The link that the two-kinds thesis provides between anti-psychologism and scepticism is such that Frege's anti-psychologism is intimately tied to a sceptical element in his thought This is why, in the midst of the discussion of Frege and psychologism in Remarks on the Foundations of Mathematics, there should occur the sequence of three remarks concerning scepticism, Le., doubt and error. The frrst two of the remarks run as follows: Imagine the following queer possibility: we have always gone wrong up to now in multipying 12 x 12. True, it is unintelligible how this can have happened. So everything worked out in this way is wrong! - But what does it matter? It does not matter at all! - And in that case there must be something wrong in our idea of the truth and falsity of arithmetical propositions. But the~ is it impossible for me to have gone wrong in calculation? And what if a devil deceives me, so that I keep on overlooking something however often I go over the swn step by step? So that if I were to awake from the enchantment I should say: ''Why was I blind?" - But what difference does it make for me to 'assume' this? I might say: "Yes to be sure, the calculation is wrong- but that is how I calculate. And this is what I now call adding, and this 'the sum of these two numbers'. "12S
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One's immediate reaction to Remarks on the Foundations of Mathematics I, 135 is 'Why doesn't it matter if we've always gone wrong in multiplying 12 x 12?' The sense of 'not mattering' is that given in Part I, section 136 about the possibility of a deceptive demon, viz. that such a hypothesis 'makes no difference'. (Again at Remarks on the Foundations of Mathematics ill, 21, Wittgenstein says: "One might say: When it can be said: 'Even if a demon had deceived us, still everything would be all right', then the prank he wanted to play on us has simply failed on its purpose.") In what sense does the hypothesis of an evil genius make no difference? In the remark following Part I sections 135-6, Wittgenstein asks us to imagine someone "bewitched" so that in counting by threes, every third object gets counted over again as the fIrst object in the next group of three; so that foUT 'goups of three', plus two, equal ten- or, 4x3+2=10. Wittgenstein suggests that such a calculation could be applied quite happily- "he takes three nuts four times over, and then 2 more, and he divides them among 10 people and each gets one nut; for he shares them out in a way corresponding to the loops of the calculation, and as often as he gives someone a second nut, it disappears. "126 So here the person's 'bewitchment', as we see it, makes no difference in the sense of making no difference to the practice with, or application of, the calculation- in the event, everything is, so to say, copacetic. But Wittgenstein's general point is not simply that there could be cases where bewitchment or deception, as it happens, make no 'practical difference'. The general point is that the only difference that something can make in mathematics, is a practical difference. The only 'differences' in mathematics are practical differences; to make no difference to a pmctice is to make no difference at all. The practice, with its paradigmatic status (this is what I now call 'adding' and this 'the sum of these two numbers'), detennines the sense of what is called 'adding' or 'the sum of these numbers' (as well as what is called 'wrong', 'correct', 'mistake', etc.) and it is not some practice-independent sense which detennines, or perhaps fails to detennine the practice. There is only practice, only application, with no 'theory' backing up the practice. Again, this pragmatism concerning mathematics is the moral of the rule-following considemtions as an anti-tmnscendence argument. To say that there is no theory tmnscending the pmctice is to say, in Fregean tenns, that there is no 'logic' transcending the 'psychology'. But the hypothesis of the evil demon depends on this distinction. If the notion of a theoretical realm which tmnscends the practical realm is idle, then so too is this particular exploitation of that notion: the theoretical possibility of error which tmnscends what is recognized as an actual error in practice. The notion is idle, it makes no difference at all. We might put the point this way: the demon is incapable of deceiving us about the practice- without doubt it exists also if he deceives us, and let him deceive us as much as he will, he can never cause it to be nothing or illegitimate so long as we think that it is legitimate. So long as the pmctice
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exists at all, even as a dream, we have paradigms and so the means of judging or recognizing error and validity. The senses of 'wrong', 'correct', ,mistake', etc. are internally tied to our practice, and our practice to paradigms. And the judging of error and right is ever more practice, precedent, and paradigm. In its practice-cum-recognition-dependence error and right, like (and as) the practice, are autonomous. (Begone Satan!) The claim then is that error, like other intentional or meaning-related phenomena, is phenomenal or recognition-dependenl But its phenomenality is not just a matter of its being constituted by and exhausted in our practices. Mathematics and language are perceptual or Gestalt phenomena. Contrary to Frege, notation is not incidental to the possibility of thoughts, and in language and mathematics the intellect is a power of the eyes and ears, hand and tongue. Perception and understanding are one, and recognition-dependence is perception-dependence. There is no error 'in itself' apart from error 'for us', apart from what we can see as error. In part III of Remarks on the Foundations of Mathematics, Wittgenstein writes: Can we be certain that there are no abysses now that we do not see? But suppose I were to say: The abysses in a calculus are not there if I do not see them! Is no demon deceiving us at present? Well, if he is, it doesn't matter. What the eye doesn't see the heart doesn't grieve over!27
The kind of error at stake in mathematics is, of course, contradiction. Doubt about there being a contradiction lurking in mathematics is what motivates Frege's project of giving mathematics a fmn foundation in logic. It is this doubt, as opposed to, so to speak, a 'naively realistic' certainty about mathematics, that constitutes the sceptical element in Frege's thought, and links him to Cartesian scepticism. Near the end of Part III of Remarks on the Foundations of Mathematics, in section 87, Wittgenstein makes the comment about looking at contradiction 'anthropologically', i.e., in terms of language-games. But in the immediately following section he can be seen to be looking at contradiction anthropologically in another sense, when he offers the following as a possible reply to the suggestion that without a consistency proof one cannot be certain that a calculus is free of contradiction: "If my conception of the calculus should sometime alter; if its aspect should alter because of some context that I cannot see now- then we'll talk some more about it...! do not see the possibility of a conttadiction. Any more than you - as it seems - see the possibility of there being one in your consistency proof. "128 Again, the suggestion is that conuadiction is perception-dependent and this is reinforced by the comparison, in section 89 which follows, between a proof and a tune. In Part III, section 78, prior to the comment about abysses in the calculus being phenomenal, Wittgenstein compares a mistake in our rules to a mistake in a musical theme, in how it sounds.__~~~~ _ ~~,!~e~ipg
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phenomenality, he says of a game whose roles make it pointless, that it stopped being a game only when this was pointed out. In general it may be said of a contradiction that, being a matter of language, it is a matter of meaning, and meaning is always phenomenal. In section 90, which ends Part Ill, Wittgenstein says: I have not yet made the role of miscalculation clear. The role of the proposition: 'I must have miscalculated'. It is really the key to any lDlderstanding of the 'fOlDldatiOns' of mathematics.
One significant thing about 'I must have miscalculated' is that it is said only of a recognized error. And the way that the phenomenality or recognition-dependence of error relates to the 'foundations' of mathematics is this. To the extent that error is recognition-dependent, there is no such thing as 'error-in-itseIr. There are not two kinds of error, nor two kinds of correctness or consistency- the kind we recognize or acknowledge versus Frege's or God's kind Likewise there are not two kinds of error-ridden or error-free inference. There is only actual (hwnan) inference. Thus of the employment of a consistency proof, Wittgenstein earlier says, "It is - I should like to say - for practical, not for theoretical purposes that the disorder is avoided. "129 He goes on to say that no consistency proof will make it "certain that people will never want to calculate differently," "that we shall never want to look at reality differently": "It is not the eternal correctness of the calculus that is supposed to be assured, but only so to speak, the temporal."l30 Wittgenstein's notion of the 'eternal' here would be no less psychologistic for Frege than the notion of the temporal, but Wittgenstein's point is clear: what, at bottom, is at issue regarding correctness in mathematics is actual ways of thinking, actual practicesthat's all there is. In Part VII of Remarks on the Foundations of Mathematics, sections 11-15, Wittgenstein looks at contradiction anthropologically in the sense of considering people with a different calculus than ours. The discussion centers around the notion of 'a hidden contradiction'. This is an important notion for Frege; 131 one of those threads which serves to intertwine his platonism, logicism, and anti-psychologism; and, of course, it is an expression of his scepticism. In Philosophical Investigations, 125, Wittgenstein compares contradiction in mathematics to a game which turns out other than expected when we follow the rules, as he does here in Remarks on the Foundations of Mathematics Vil, 13, and as he did earlier in Remarks on the Foundations of Mathematics III, 78. In the Philosophical Investigations he concludes with the remark: "The civil status of a contradiction, or its status in civil life: there is the philosophical problem. "132 The 'civil status' of a contradiction is its phenomenal status, "for," as he goes on to say in Philosophical Investigations, 126, "what is hidden, for example, is of no interest to us." Indeed, insofar as a contradiction is phenomenal, it makes no sense to speak of its being 'hidden'. Anymore
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than it would make sense to speak of a 'hidden consistency' in a set of rules, for consistency is no less phenomenal (it is a Gestalt quality). This is brought out by Wittgenstein's comparison of the consistency of a calculus with the consistency of various musical themes. l33 There is no such thing as 'consistency-in-itself'; what 'consistency' is, is not established in advance of particular cases. 134 The phenomenality of contradiction, and of mathematics generally, is brought out in another sense with this remark: "If the contradiction is so well hidden that no one notices it, why shouldn't we call what we do now 'proper calculation'?"135 This is to say, 'proper calculation' is not something transcending our actual calculation when perceived to be proper. Such calculation is not any the less "mathematics in the fullest sense"l36 for being without some 'guarantee' that we shall never come across a contradiction. Moreover, whatever is proposed as insurance against contradiction will be no less in need of such insurance itself. Thus the deceptive demon meets up with the good angel: "Up to now a good angel has preserved us from going this way! Well, what more do you want? One might say, I believe: a good angel will always be necessary, whatever you do."137 While still in Part VIII of Remarks on the Foundations of Mathematics, Wittgenstein quotes his interlocutor: "We want, not just a fairly trustworthy, but an absolutely trustworthy calculus. Mathematics must be absolute.'''138 Again in Part VIII, 36, the interlocutor exclaims, '''But surely this isn't ideal certainty!'." With this notion of the absolutely trustworthy, of ideal certainty, we get, as it were, the subliming of our whole account of knowledge, certainty, and doubt. l39 In other words, we get a two-kinds thesis of certainty and doubt, relying on the 10gicaJ/psychological distinction. In the introduction to The Foundations of Arithmetic, shortly following his initial differentiation of logic from 'psychology', Frege says the following concerning definitions: Yet it must still be borne in mind that the rigolD' of the proof remains an illusion. even though no link be missing in the chain of our deductions, so long as the definitions are justified only as an afterthought, by our failure to come across any contradiction. By these methods we shall never have achieved more than an empirical certainty, and we must really face the possibility that we may still in the end encounter a contradiction which brings the whole edifice down in ruins. l40
The important notion here for understanding the relation between antipsychologism and scepticism is that of "an empirical certainty." The Begriffschrift opens with the remark that "in apprehending a scientific truth we pass, as a rule, through various degrees of certitude," and goes on to distinguish induction from logical proof. 141 This distinction is correlated with that between how we arrive at a proposition and how it may be justified,142 which is the basis for Frege's distinction between psychology and logic. In The Foundations of Arithmetic, induction is distinguished from
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logical proof which places "the bUth of a proposition beyond all doubt,nlH and there Frege speaks of induction as itself "a psychological phenomenon."144 The distinction between induction and deduction exemplifies the two kinds of certainty: empirical or psychological or practical certainty versus logical, absolute certainty. 'Scepticism' as I am concerned with it is something that arises in connection with a traditional epistemological project going under the name 'the search for certainty'. Or again, scepticism starts with the question 'Is there anything of which we can be certain?' As such, it depends on the above type of two-kinds thesis of certainty and doubt. For the natural response to any sceptical proposal that it is not certain that, e.g., here is a hand,!45 is: 'But I am certain that here is a hand'. And the immediate sceptical response to this is: 'Oh that's just a psychological certainty. Admittedly there is no psychological or practical doubt. but there is a theoretical or metaphysical doubt about it'. So Descartes proceeds. The 'supreme' kind of doubt which is 'metaphysical' and 'hyperbolical' is what is required to investigate bUths that are 'metaphysically certain' .146 This 'metaphysical mode of knowing' contrasts with "the moral mode of knowing, which suffices for the regulation of life."147 What is known by the latter is a matter of "long and familiar CUStom,"14' of "blind impulse,nl49 rather than reason. The practical certainties yielded, though sufficient, and necessary, for everyday life, are nevertheless "opinions in some measure doubtful. "150 They are psychologically certain, but not metaphysically certain. Wittgenstein does not accept this two-kinds thesis of certainty and doubt. In On Certainty he writes: The statement 'I know that here is a hand' may then be continued: 'for it is my hand that 1 am looking at'. Then a reasonable man will not doubt that 1 know. -Nor will the idealist; rather he will say that he was not dealing with the practical doubt which is being dismissed, but there is a further doubt behind that one. -That this is an illusion has to be shewn in a different way.151
The notions of a transcendent doubt beyond practical doubt, and of an absolute certainty beyond mere 'empirical' certainty are applications of the general notion of a logical realm which transcends the 'psychological' realm as the ideal transcends the actual. U2 In the Philosophical Investigations, (84) Wittgenstein makes the point that the logical possibility of a doubt, i.e., the possibility of imagining a doubt about such and such, does not mean that one actually doubts such and such. The possibility of a doubt does not make something doubtful. The sceptic, relying on the two-kinds thesis, will say: 'Oh no, not doubtful for you, but still doubtful'. If something is doubtful, even though no one doubts it, then it must be doubtful in itself. It is this latter notion that is an illusion. There are not two kinds of doubt. Doubt is actual doubt, i.e., doubts actually had by actual people. There is no doubt or doubtfulness in itself.
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The possibility of doubt is not a kind of doubt. However, on the two-kinds thesis it is. In the 'actual world', the realm of logical possibility is just that- the realm of possibilities. But in the logical realm 'itself' the realm of possibilities sublimed - possibilities are the actualities. In the logical realm, a doubt that is logically possible is actual, while certainty metaphysical certainty - is impossible if doubt is logically possible, i.e., metaphysically actual. This is the realm of doubt in itself. To the exclamation 'But this isn't ideal certainty', Wittgenstein replies, in Remarks on the Foundations of Mathematics, with the question "-Ideal for what purpose?" The point of bringing in the question of purpose is to challenge the idea that there is a realm of certainty and doubt in themselves, leaving us out of account The question also refers us to Philosophical Investigations 87-8, where Wittgenstein criticizes Frege's notion of ideally exact concepts, explanations, and rules, as opposed to the actual concepts, explanations, and rules in our ordinary language. It is consideration of this which brings up the problem: "In what sense is logic something sublime?"153 The two-kinds thesis about rules goes with the two-kinds thesis about doubt and certainty, and leads to the illusion that a methodological scepticism is required if 'real certainty' - certainty in itself - is to be attained. Here Wittgenstein addresses indifferently Fregeans and Cartesians: It may easily look as if every doubt merely revealed an existing gap in the foundations; so that secure lDlderstanding is only possible if we fast doubt everything that can be doubted, and then remove all these doubts. 1St
The possibility of a doubt does not reveal an existing doubt in the alleged metaphysical foundations of our actual understanding of rules. There are no such transcendent foundations; our actual understanding is self-sufficient. Against the above suggestion of a possible doubt constituting an actual gap in the 'foundations', Wittgenstein says, comparing a rule to a signpost, "The sign-post is in order,- if, under nonnal circumstances, it fulfills its purpose."155 Secure understanding - certainty - is achieved so long as we actually have no 'practical' doubts, i.e., so long as 'the rules fulfil their purpose, i.e., so long as they serve our purposes. There is no purposetranscendent order which a rule may 'ideally' attain to (ideals themselves are strictly relative to purposeS),I56 and no practice-transcendent certainty to which our knowledge of a rule may attain. Philosophical Investigations, 87 is echoed in On Certainty: What I need to show is that a doubt is not necessary even when it is possible. That the possibility of the language-game doosn't depend on everything being doubted that can be doubted. (This is connected with the role of contradiction in mathematics.)I'"
I take the fIlSt two sentences to mean: the logical possibility of a doubt doesn't yield a doubt, for the purposes of establishing the language-game.
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That is to say, possible doubtfulness isn't a kind of doubtfulness. There are not two kinds of doubtfulness and certainty. The only doubtfulness is actual, practical doubtfulness, the only certainty actual, practical certainty. For Descartes, that for which it is logically impossible to be mistaken is 'metaphysically' more certain than that for which it is logically possible to be mistaken. But 'metaphysically more certain' does not mean 'more certain'. For one's certainty to be grounded on the law of contradiction does not necessarily mean that it is more certain than one that isn't so grounded. 'Metaphysically more certain' does not mean 'more certain' because 'metaphysical certainty' is not a special kind of certainty vis vis ordinary practical certainty. The connection between On Certainty, 392 and contradiction in mathematics is this. Contradiction being phenomenal, there is no contradiction-in-itself transcending what we actually recognize as a contradiction. Correlatively, there is no doubtfulness-in-itself transcending what is actually doubtful for us or to us. The notion of a theoretical doubtfulness transcending what we actually hold to be doubtful is as idle as the notion of a hidden contradiction. Indeed, the latter is a version of the fonner. Curiously, Descartes argues in the very same way when it is suggested that his 'clear and distinct perceptions' may nevertheless be doubtful. In The Reply to the Second Set of Objections he says:
a
To begin with, directly we drink that we rightly perceive something, we spontaneously persuade ourselves that it is true. Further, if this conviction is so strong that we have no reason to doubt concerning that of the truth of which we have persuaded ourselves, there is nothing more to enquire about; we have here all the certainty that can reasonably be desired. What is it to us, though perchance someone feigns that that, of the truth of which we are so frrmly persuaded, appears false to God or to an Angel, and hence is, absolutely speaking, false? What heed do we pay to that absolute falsity, when we by no means believe that it exists or even suspect its existence? We have asswned a conviction so strong that nothing can remove it, and this persuasion is clearly the same as perfect certitude.Ut
This is exactly how I should argue against the sceptic concerning the certainty of, e.g., the Moorean 'Here is a hand'. The sceptic I should then be arguing against would, of course, be Descartes. All the arguments he used above against the notion of a certainty transcending the certainty of his 'clear and distinct perceptions', I use against the notion of a certainty transcending the certainty of 'Here is a hand'a clear and distinct perception if ever there was one. What is it to me- though perchance Descartes feigns that that, of the truth of which I am so frrmly persuaded, appears false to God or an Angel or a sceptic, and hence is, absolutely speaking, false? What heed should I pay to that absolute falsity when I by no means believe that it exists or even suspect its existence? I have
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assumed a convlctton so strong that nothing can remove it, and this persuasion is clearly the same as perfect certitude. Descartes will ask how I know that I am awake and not dreaming. The answer to the question 'How does one know one is awake?' is, I believe, 'By being awake'. If this is deemed circular, it is no more so than the answer Descartes must give to the question, 'How do you know your perceptions are clear and distinct?'I59 Alternatively, one may say that there are no criteria by which we distinguish being awake from dreaming, but that does not mean we can't and don't distinguish them. We certainly do: 60 It will be said that the point about dreaming or the evil demon is simply that a mistake about my hand is logically possible. But again, that a mistake is logically possible - that 'I was mistaken about my hand' is compatible with the laws of logic - does not mean that possibly I am mistaken (anymore than that it is logically possible for a woman to turn into a pillar of salt means that a woman could tum into a pillar of salt). The logical possibility of error in no way provides grounds for doubt, especially in the particular case, as with 'Here is a hand'. Finally, it will be said, 'The question is one about justified certainty'. But my certainty in 'Here is a hand' is justified. The only way it could fail to be is if there were two kinds of justification, one of which - 'metaphysical justification' - was the only true kind. But inasmuch as there is no such thing as metaphysical certainty (as distinct from certainty), metaphysical justification can only be justification, i.e., a version of what the notion of 'metaphysical justification' presupposes, viz., ordinary justification. And there is no question that by these basic and not unrigorous standards of justification, certainty in 'Here is a hand' is justified, and more than justified. There is really only the short way with the sceptic. He says he wants a case of something certain. We say: 'Nothing is easier: "here is a hand"'. And like Descartes above, we say "there is nothing more to enquire about; we have all the certainty that can reasonably be desired." This should be the end of the discussion, if what is sought is something that is certain. The discussion goes on, of course, because of the two-kinds thesis of certainty, which allows for a so-called 'methodological scepticism'. But on the line we have advanced, 'methodological scepticism' can be nothing other than full-blooded scepticism- for there are not two kinds of scepticism. Thus anyone who finds methodological scepticism tenable is, if unwittingly, a sceptic. And there are many such.
VIL Unwitting Sceptics The hallmark of scepticism is that it offends against commonsense or 'vulgar thought'. The vulgar hold that 'Here is a hand' is certain; the sceptic holds that it is dubious. So-called methodological scepticism,
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however it may be redeemed in the end, or whatever it may come up against that is immune to 'methodological doubt' is no less offensive to common sense than is 'outright scepticism'. Indeed, it is outright scepticism. There are not two kinds of doubt. Either 'Here is a hand' is doubtful or it is not doubtful. If it is not doubtful the game is over: we have something certain. If it is doubtful the game is over:- scepticism wins. Methodological scepticism gets its running start when it is thought that there are two kinds of doubt and certainty. Methodological doubt will be 'metaphysical doubt'. But since there are not two kinds of doubt, if metaphysical doubt is doubt at all, then it is full-blooded practical doubt To say, '1 act as though it is certain, even though it is (theoretically, ultimately, strictly speaking, etc.) doubtful, does not mitigate one's scepticism. One can't be a 'theoretical sceptic' but a 'practical believer'. H one claims to have a 'theoretical doubt', then one doubts- however one acts. Again, the only question concerning, e.g. 'Here is a hand', is whether or not it is doubtful. To say, regarding this particular case (i.e., with someone's hand stuck in your face): 'This is doubtful', is to be a full-fledged practicing sceptic. For Descartes to say, indeed insist, that propositions such as the Moorean 'Here is a hand' are "not entirely certain and indubitable,"161 are "opinions in some measure doubtful,"I62 are "merely probable,"163 and in general for Descartes to say "You can reasonably doubt of all things, the knowledge of which comes to you by the senses alone"l64 is for Descartes to be a sceptic and nothing less. Similarly, any expositor of Descartes who does not immediately pull him up short at the stage where he introduces his method of doubt, that is, anyone who accepts the project of methodological doubt, whatever else in Descartes he may reject, must be deemed a sceptic. This includes in my experience, most expositors of Descartes. A good example is Bernard Williams in his Descartes: The Project of Pure Enquiry. In his discussion of Descartes' method, Williams quotes the passage from the Discourse on Method where Descartes says, "so far as practical life is concerned, it is sometimes necessary to follow opinions which one knows to be very uncertain, just as though they were indubitable...but because I wanted to devote myself solely to the search for truth, I thought that I should reject, as though it were absolutely false, everything in which I could imagine the slightest doubt, so as to see whether after that anything remained in my belief which was entirely indubitable,"165 and the passage from the "First Meditation" which begins, "Reason persuades me already that I should withhold assent no less carefully from things which are not clearly certain and indubitable, as from things which are evidently false. "166 The things which Descartes says one 'knows to be very uncertain', or which at least are 'not clearly certain and indubitable' include such things as 'the Moorean 'Here is a hand'. Williams makes no objection to calling such things uncertain. His only objection, at this point, is that Descartes' strategy for 'fmding the truth', "is surely far from obvious: we constantly want the truth about various matters, but hardly ever demand the
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indubitable. nl67 But this is surely far from obvious. Insofar as we want the truth about various matters, we certainly don't expect to get something that is open to doubt, and for the most part, we don't. There is no need to demand the indubitable; it is the nonnal thing. Having asked the whereabouts of the cat, we are told that it is on the mat If there are any doubts about this, they can be defmitively resolved, but under normal circumstances, the infonnation is absolutely indubitable. But not, apparently, for Williams. He goes on to say that Descartes' sttategy "is to aim for certainty by rejecting the doubtful,"I. it "is to preserve, out of his present beliefs, any that are genuinely certain, and the way to do that is to set aside the ones that are not."I69 If, as seems to be the case, 'The cat is on the mat' or 'Here is a hand' are, for Williams, not genuinely certain, then Williams is a sceptic. For again, there are not two kinds of genuine certainty. Nor, again, are there two kinds of genuine doubt Williams says that there is no question "of the hyperbolical doubt playing any rational role within ordinary life."170 But there are not two kinds of rational doubt, nor in geneml, two kinds or ways of being rational. In his book Descartes Against the Skeptics, E.M. Curley says that, for Descartes, indubitability "is a matter of not having reasonable grounds for doubt, "1'71 and that for Descartes, "the ground of doubt is required to be not entirely frivolous."172 But the most striking thing about Descartes' or any sceptic's grounds for doubt - that his senses have once deceived him, that he may be dreaming, that there may be an evil genius - is that they are not reasonable and are entirely frivolous. There are not two kinds of reasonableness and frivolity. This is why, in On Certainty, Wittgenstein constantly poses the issue about doubt in terms of what 'the reasonable man' believes. 173 Curley speaks of the constraints on the classical sceptics "if their position was to have plausibility at all."174 But Curley, going along as he does with Descartes, has given up all right to demand plausibility from anyone. There are not two kinds of plausibility. In On Certainty, Wittgenstein asks, "Can I give the supposition that I have ever 1x~n on the moon serious consideration at all?"17S The notion of seriousness is really the key notion in any discussion of scepticism- that is, in any serious discussion. For again there are not two kinds of seriousness: 'practical seriousness' and 'philosophical seriousness'.176 The words 'serious', 'reasonable't 'frivolous', 'plausible', not to mention ,doubtful' and 'certain', are ordinary words of English, whose meanings do not change at the whim of a philosopher. (Certainly, William's capitalization - thus, 'Doubt'ITI - does nothing to alter the ordinary meaning of the word, Le., does nothing to establish that there is another kind of doubt than everyday 'practical' doubt) There is only one way to be serious about something, and that is, so to say, to be practically serious. If it is admitted that the 'doubt' about 'Here is a hand' is not 'practically' serious, then it is admitted that it is not serious at all, in which case it needn't be taken seriously at all. There is then no sceptical problem, as indeed there
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isn't. If the doubt about 'Here is a hand' is at all serious, then the only serious response is to get the man help!"
156 ENDNOTES 1.
Michael Dummett, Frege, Philosophy of Language (London: Duckworth,
1973), pp. 666-667. 2. Ibid., p. 669. 3. See, for example: Rene Descartes, Principles of Philosophy, in The Philosophical Worb of Descartes Vols. I and fi, trans. E.S. Haldane and G.R.T. Ross (Cambridge: Cambridge University, 1968), Vol. I, p. 211. 4. Dummett, Frege, Philosophy of LangllQ.ge, p. 92. 5. Ibid., p. 5. 6. Michael Dummett, Truth and Other Enigmas (London: Duckworth, 1978), p. 420. 7. Dummett, Frege, Philosophy of Language, pp. 589-590. 8. Ibid., p. 666. 9. Ibid., p. 667. 10. Ibid., p. 669. 11. Ibid. 12. Ibid., p. 672. 13. Ibid., p. 674. 14. Ibid., p. 675. 15. Ibid., pp. 675-676. 16. Gottlob Frege, Th£ Foundations of Arithmetic, trans. I.L. Austin (Oxford: Basil Blackwell, 1953), p. xi. 17. See: Dwnmett, Frege, Philosophy of Language, p. 665. 18. See: Rene Descartes, Discourse on the Method of rightly conducting the Reason and seeking for Truth in the Sciences, in The Philosophical Works of Descartes, Vol. I, pp. 123, 127. 19. See: Rene Descartes, Meditations on First Philosophy, in Ibid., p. 140. 20. Ibid., p. 135. 21. Ibid., p. 148. 22. Oottlob Frege, Begriffschrift, in Frege and GOdel. Two Fundamental Texts in Mathematical Logic, 00. I. van Heijenoort (Cambridge: Harvard University, 1970), p.
5. 23. Ibid. 24. Ibid., p. 7. 25. Ibid., p. 35. 26. Ibid., p. 23. 27. See: Gottlob Frege, Posthumous Writings, ed. H. Hennes, F. Kambartel, F. Kaulbach, with 'the assistance of o. Gabriel and W. Rodding, trans. P. Long and R. White (Chicago: University of Chicago, 1970), p. 3. See also: Oottlob Frege, Logical Investigations, trans. P.T. Oesch and R. Stoothoff (Oxford: Basil Blackwell, 1977), p. 1. 28. See: Gottlob Frege, Posthumous Writings, pp. 133, 258-262. See also: Gottlob Frege, Logical Investigations, p. 25. 29. Ibid., p. 2. See also: Gottlob Frege, ''The Aim of the Begriffschrift," in Conceptual Notation and Related Articles, 00. and trans. Terrel Ward Bynum (Oxford: Clarendon, 1972), p. 95.; and Gottlob Frege, The Foundations of Aritlunetic, p. 99. 30. Gottlob Frege, Posthumous Writings, p. 2. 31. Descartes, The Philosophical Worb of Descartes, Vol. I, p. 212. 32. Ibid., Vol. I, p. 92. Cf., Vol. I, p. 14; and Vol. IT, pp. 52-59.
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33. Gottlob Frege, The Basic Laws of Arithmetic, 00. and trans. Montgomery Furth (Los Angeles: University of California, 1964), p. 2. 34. Frege, The FOIUUlations of Arithmetic, p. 103. 35. Frege, The Basic Laws of Arithml!tic, pp. 4-5. 36. Ibid., p. 3. 37. Descartes, The Philosophical Works of Descartes, Vol. I, p. 20. 38. Ibid., p. 8. 39. Frege, The Basic Laws of Arithml!tic, p. 4. 40. See: Frege, PosthlUnOlLf Writings, pp. 205, 210; Frege, The Foundations of Arithmetic, p. 102; and Frege, The Basic Laws of Arithmetic, p. 121. 41. Frege, PosthlUnOlLf Writings, p. 205. 42. This lDlavoidable psychological dimension of the epistemological discussion is one which Frege is never comfortable with and ultimately, for all his explicit anti-psychologis~ never squarely faces. Thus the following: ''The question why and with what right we acknowledge a law of logic to be true, logic can answer only by reducing it to another law of logic. Where that is not possible, logic can give no answer. If we step away from logic, we may say: we are compelled to make judgments by our own natme and by external circumstances; and if we do so, we cannot reject this law- of Identity for example; we must acknowledge it unless we wish to reduce OlD' thought to confusion and finally renounce all thought whatever. I shall neither dispute nor support this view; I shall merely remark that what we have here is not a logical consequence. What is given is not a reason for something's being true, but for our taking it to be true." Gottlob Frege, The Basic Laws of Arithmetic, p. 15. 43. Descartes, The Philosophical Works of Descartes, Vol. I, p. 232. 44. Ibid., p. 140. See: p. 144, and see also the famous discussion of the wax in the "Second Meditation." 45. See: Ibid., p. 174. 46. Frege, The Foundations of Arithml!tic, p. 115. See also: pp. 36, 38; and BynWll, ed., ConceptlllJ1 Notation and Related Articles, pp. 84-86. 41. Frege, The FOIUUlations of Arithmetic, p. 42. Cf., Descartes, The Philosophical Work\- of Descartes, Vol. I, p. 156. 48. Frege, Posthwnous Writings, p. 261. 49. See: Descartes, Thi! Philosophical Worh of Descartes, Vol. L p. 161, Vol. fl,
p.253. 50. Frege, PosthltU1lOus Writings, pp. 269-270. 51. Frege, Begriffschrift, p. 11. See also: Gottlob Frege, Translations from the Philosophical Writings of Gottlob Frege, trans. P. Geach and M. Black (Oxford: Basil Blackwell, 1966), p. 64; Frege, The Basic Laws of Arithmetic, p. 31; Frege, Posthumous Writings, p. 139; and Frege, Logical Investigations, p. 1. 52. Frege, Begriffschrift, p. 7. 53. See: Ibid., p. 6. 54. R.ene Descartes, Philosophical Letters, 00. and trans. Anthony Kenny (Oxford: Clarendon, 1970), p. 6. See also: Descartes, The Philosophical Works of Descartes, '/oL I, pp. 155, 252. 55. Frege, Posthumous Writings, p. 269. 56. Frege, Logical Investigations, p. 13, n. 4. See also: Frege, Posthumous Writings, p. 270. 51. Frege, The FOIUUlations of Arithmetic, p. vii. 58. Kenny, Anthony, DescQTtes: A Study of his Philosophy (New York: Random House, 1968), p. 125.
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59. Descartes, The Philosophical Worb of Descartes, Vol. I, p. 174. 60. See: Ibid. 61. See, for example: Frege, Translations from the Philosophical Writings of Gottlob Frege, p. 64. 62. See: Frege, Posthumous Writings, p. 144. 63. See: Frege, The Foundations of Arithmetic, p. 37; and Frege, Translations from the Philosophical Writings of Gottlob Frege, pp. 60, 79. 64. See: Frege, Logical Investigations, p. 5. 65. See: Descartes, The Philosophical Works of Descartes, Vol. IT, pp. 67, 70, 217. 66. See: Ibid., Vol. I, pp. 174-175. 67. See:· Frege, Logical Investigations, p. 12. Cf., Locke's account of why one must give one's words 'a secret reference', in: Jolm Locke, An Essay Concerning Human Understanding, 00. P.H. Nidditch (New York: Oxford University, 1975), Book 2, ch. 41. 68. Curley, EM., Descartes Against the Skeptics (Cambridge, Harvard University, 1978), p. 149. See also: Kenny, Descartes, ch. 6. 69. See: Frege, The Foundations of Arithmetic, pp. 35, 68-73. See also: Frege, The Basic Laws of Arithmetic, p. 16; and Frege, Logical Investigations, p. 17. 10. Dummett, Truth and Otlu!r Enigmas, p. 88. 71. Ibid., p. 94. 72. Frege, The Foundations of Arithmetic, p. x. 73. Ibid. 74. See: Ludwig Wittgenstein, The Blue and Brown Books (Basil Blackwell, 1969), pp. 3-4. 75. See: Frege, TIu! Basic Laws of Arithmetic, p. 12. 76. Ibid., pp. 12-13. 77. See: Ibid., p. 13. See also: Frege, Logical Investigations, p. 2. 78. See: Frege, The Basic Laws of Arithmetic, p. 14. 79. See: Frege, Begriffschrift, p. 15; Frege, The Foundations of Arithmetic, pp. ix, 3; Frege, Postluunous Writings, p. 3; and Frege, Logical Investigations, p. 2. 80. Frege, The Foundations of Arithmetic, p. 37; see also: pp. 105, 115. 81. Frege, The Basic Laws of Arithmetic, p. 15. 82. See: Frege, The Foundations of Arithmetic, pp. v-vii. 83. Ibid., p. vii. 84. See: Dummett, Truth and Other Enigmas, p. 182. 85. See: Ibid., pp. xl, 211, 225, 248. 86. John McDowell, "Engaging with the Essential," TIMES LITERARY SUPPLEMENT, 16 Jan. 1981, p. 62. Cf., D. Bell, "Review of K. T. Fann, Ludwig Wittgenstein," IDSTORY AND PIDLOSOPHY OF LOGIC, 1, (1980), p. 236. 87. See: Ludwig Wittgenstein, Zettel, ed. G.E.M. Anscombe and G.H. von Wright, trans. G.E.M. Anscombe (Oxford: Basil Blackwell, 1967), pp. 92-130. 88. Frege, Logical Investigations, pp. 25-26. 89. See: Ibid., p. 7. 90. See: Frege, Translations from the Philosophical Writings of Gottlob Frege, pp. 201-202, 216. 91. Frege, Logical Investigations, p. 26. 92. Ludwig Wittgenstein, Philosophical Grammar, ed. Rush Rhees, trans. Anthony Kermy (Oxford: Basil Blackwell, 1974), p. 107. 93. Crispin Wright, Wittenstein on the Foundations of Mathematics (Cambridge: Harvard University, 1980), p. 252.
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94. Ludwig Wittgenste~ Remarks on the Folmdations of Mathematics, 3rd ed., cd. G.H. von Wright, R. Rhees, G.E.M. Anscombe, trans. G.EM. Anscombe (Oxford: Basil Blackwell, 1978) Part I, 8.
95. Ibid., Part VH, 33. 96. Ibid., Part ill, 87. 97. Ludwig Wittgenstein, On Certainty, ed. G.E.M. Anscombe and G.H. von Wright, trans. Denis Paul and G.EM. Anscombe (New York: Harper and Row, 1969), 56. Cf., 375; and Wittgenstein, Remarks on the Folmdations of Mathematics, Part VH, 20, 30, 35. 98. See: Ludwig Wittgenstein, Philosophical Investigations, 3rd ed., trans. G.E.M. Anscombe (Oxford: Basil Blackwell, 1968), 7. 99. See: Saul Kripke, Wittgenstein on Rules and Private Language (Cambridge: Harvard University, 1982). 100. Contrast: Frege, Logical Investigations, p. 1; Frege, Translations from the Philosophical Writings of Gottlob Frege, p. 206. 101. Cf., Wittgenste~ ReTNJTks on the Foundations of Mathematics, Part vn, 67. 102. Cf., Wittgenstein, Zettel, 309. 103. Frege, The Basic Laws of Arithmetic, p. 14. 104. See: Ibid. 105. Cf., Wittgenstein, Philosophical Investigations, pp. 241-242. 106. Cf., Wittgenstein, Remarks on the Foundations of Mathematics, Part I, 9. 107. Ibid., Part I, 168. 108. Frege, The Folmdations of Arithmetic, p. 108. 109. See: Frege, Begriffschrift, p. 5; Frege, The Folmdations of Arithmetic, p. 4; Frege, The Basic Laws of Arithm£tic, pp. 13-14. 110. See: Wittgenste~ Philosophical Investigations, 97. Cf., 107-108. 111. Ibid., lOS. 112. Ibid., 81. 113. Frege, Logical Investigations, p. 25. 114. Wittgenste~ Philosophical Investigations, 108. 115. See, inter alia: Ibid., 138-242; and Wittgenstein, Remorks on the Foundations of Mathematics, Parts I, VI, VIll. 116. Cf., Frege, The Foundations of Arithmetic, p. 93. 117. See: Wittgenstein, Philosophical Investigations, 48. 118. See: Ibid., 28. 119. Such documentation and detailed discussion is in my D.Phil. thesis, Sense and Subjectivity: A Study of Wittgenstein and Merleau-Ponty, Oxford University, 1983. 120. See, especially: Wittgenste~ Philosophical Investigations, 73, 74, p. 54 n., 185, 228; Wittgenstein, Remarks on the Folmdations of Mathematics, Part VI, 43, 44, Part VH, 47, 60; Wittgenstein, Zenel, 276-7; and Ludwig Wittgenste~ Remarks on the Philosophy of Psychology, Vol. I, ed. Anscombe and G.H. von Wright, trans. G.E.M. Anscombe, Vol. n, ed. G.H. von Wright and Heikki Nyman, trans. C.G. Luckhardt and M.A.E. Aue (Oxford: Basil Blackwell, 1980), Vol. I 344, 505, 874, 875, 882, Vol. 387-424. 121. See: Wittgenstein, Remarlcs on the Folmdations of Mathematics, Part ill, 43.
n
122. Ibid., Part
rn,
2.
123. Cf., Frege on defmitions in: Frege, The Basic Laws of Arithmetic, p. 2. Cf., also, Wittgenstein, Philosophical Investigations, 377" 124. See: Wittgenstein, Remarlcs on the Foundations of Mathematics, Part ill, 25. 125. Ibid., Part I, 135, 136.
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126. Ibid., Part L 137. 127. Ibid., Part ill, 78. 128. Ibid., Part m, 88. 129. Ibid., Part IlL 83. 130. Ibid., Part m, 84. 131. See: Frege, The Foundations of Arithmetic, pp. ix, 106, 108. 132. Wittgenstein, Philosophical Investigations, 125. 133. See: Wittgenstein, Re1NJTu on the Foundations of Mathematics, Part VH, 370. 134. Cf., Wittgenstein, Remarks on the Foundations of Mathematics, VH, 15; and Wittgenstem, Remarks on the Philosophy of Psychology, Vol. H, 401. 135. Wittgenstein, Remarks on the Foundations of Mathematics, Part vn, 15. 136. See: Ibid., Part VH, 11. 137. Ibid., Part VII, 16. Cf., Part ill, 88, Part VI, 6; and Wittgenstein, Philosophical Investigations, 84. This is related to the point mentioned above in note 42. A similarly related point in COlUlection with Frege is raised by Wittgenstein at the beginning of Philosophical Grammar: "In attacking the fonnalist conception of arithmetic, Frege says more or less this: these petty explanations of the signs are idle once we u.nderstand the signs. Understanding would be something like seeing a picture from which all rules followed, or a picture that makes them all clear. But Frege does not seem to see that such a picture would itself be another sign, or a calculus to explain the written one to us." Wittgenstein, Philosophical Grammar, p. 40. 138. Wittgenstein, Remarks on the Foundations of Mathematics, Part VIT, 13. 139. See: Wittgenstein, Remarks on the Philosophy of Psychology, Vol. II, 289. 140. Frege, The Foundations of Arithmetic, p. ix. 141. Frege, Begriffschrift, p. 1. 142. See: Ibid. 143. Frege, The Foundations of Arithmetic, p. 2. 144. See: Ibid., p. 4. 145. See: G.E. Moore, "A Proof of the External World," in G.E. Moore, Philosophical Papers (London: Allen and Unwin, 1959). 146. See: Descartes, The Philosophical Works of Descartes, Vol. IT, pp. 266, 279. 147. Ibid., Vol. fi, p. 266. 148. See: Ibid., Vol. L p. 148. 149. See: Ibid., Vol. I, pp. 188-189. 150. See: Ibid., Vol. I, p. 148. 151. Wittgenstein, On Certainty, 19. 152. On Wittgenstein's view this notion of 'transcendent certainty' is also the result of a certain philosophy of mind: "Forget this transcendent certainty, which is connected with your concept of spirit." Wittgenstein, On Certainty, 47. For a striking confinnation of Wittgenstein's diagnosis, see: Descartes, Principles of Philosophy, Part I, principle XII, in The Philosophical Works of Descartes, Vol. I, p.
223. 153. Wittgenstein, Philosophical Investigations, 89.
154. Ibid., 87. 155. Ibid. 156. Ibid., 88. 157. Wittgenstein, On Certainty, 392. 158. Descartes, The Philosophical Works of Descartes, Vol. 159. See: Ibid., Vol. 1, p. 237.
n,
p. 41.
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160. This is not, of course. to concede that in dreams we are, as such, mistaken or deceived about anything. One may be mistaken about being chased by a monster when awake, but in a dream there is no mistake about it- unless one goes on to dream that it was a mistake. The distinction between being awake and dreaming is absolutely fundamental, md in any everyday account of error the relevant context is always explicit. Also. dreams are not 'propositional'; they are neither true nor false. When I 'dream that...', I don't dream about something true or false. Cf., On
Certainty, 676. 161. See: Descartes, The Philosophical Worb of Descartes, Vol. I, p. 145. 162. See: Ibid.• Vol. L p. 148. 163. See: Ibid.• Vol. L pp. 145. 149. 218. 220-221; Vol. IL pp. 205-206, 266. 164. Ibid., Vol. L p. 315. 165. Bernard Williams, Descartes: The Project of PlUe Enquiry (Harmondsworth: Penguin, 1978), pp. 34-35. 166. Ibid., p. 35. 167. Ibid., p. 36.
168. Ibid. 169. Ibid., p. 49. 110. Ibid., p. 61. 171. Curley, Descartes Against the Skeptics, p. 112; see also: pp. 85, 119, 106. 172. Ibid., p. 105. 173. See, for example: Wittgenstein, On Certainty, 19, 220, 254, 323, 327. 114. See: Curley, Descartes Against the Sh!ptics, p. 89; see also: p. 116. 115. Wittgenstein, On Certainty, 226. 176. Cf., Descartes, The Philosophical Works of Descartes, Vol. IL p. 206. 177. See: Williams, Descartes: TN! Project of PlUe Enquiry, pp. 47ff. 178. I would have thought that this is what lies behind 'Moore's paradox' (statements of the form '1 believe that P and it isn't so; cf., Philosophical Investigalions, p. 191), as well.as the stories of Moore, mouth agape and eyes agog, responding to a sceptical or otherwise outrageous assertion with: 'Do you really believe that? I, For again, a person can't have it both ways: if he doesn't really believe it, then there is no further issue; the context of 'doing philosophy' doesn't somehow preserve the situation as one of serious assertion; if he does really believe it, then Moore's response is the only serious one- the context of 'doing philosophy' does not exempt anyone from the normal responses to some given assertion. I say I would have thought this lies behind this Mooreana, but for his essay 'Four Fonns of Scepticism' where he prepares and then wolfs down whole a two-kinds thesis of doubt. See especially p. 199 in Philosophical Papers. Here Moore makes assertions with no argument, which assertions moreover, in my view, are just contradictions- e.g.: ''but from the fact that he sincerely believes that it is doubtful whether he is [sitting], it certainly does not follow that he doubts whether he is." Here at any rate, Moore is no respecter of ordinary language.
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I. Introduction Psychologism is the doctrine that empirical1 psychology provides the foundations for each of the other special sciences, Le., that each of the special sciences can ultimately be derived from and justified by the results of empirical psychology. In the late nineteenth century, Gottlob Frege criticized psychologism in logic and mathematics, arguing that it results in subjectivism, idealism, relativism, scepticism, and solipsism- each of which displays a cavalier disrespect for truth and the objectivity of scientific knowledge. 2 Ever since Frege's critique, many philosophers have felt compelled to choose between psychologism and subjective knowledge on the one hand, and anti-psychologism and objective knowledge on the other. 3 Ordinarily, such a choice would not be too difficult to make. For when it comes to knowledge, philosophers almost universally prefer the objective kind.4 But when it comes to Frege, preferring the objective kind means believing in the possibility of a priori valid knowledge and in the existence of a third realm of eternal and immutable truths that serve as the objects of such knowledge.' And this, to put the matter bluntly, has become increasingly difficult to swallow. In my view, the psychologism/anti-psychologism debate can be traced to residual problems in the justified true belief theory of knowledge and revolves, ultimately, around the question 'What is the cognitive source that guarantees the truth of foundational beliefs?' Faced with this question, psychologistic philosophers traditionally answered 'a posteriori experience', and anti-psychologistic philosophers 'a priori reason'. But here, it is important to recognize that Frege's critique of psychologism presupposed a framework of Kantian epistemological categories that no longer seems tenable. In light of the great conceptual revolutions of the twentieth century, Kant's distinction between a priori knowledge that is strictly universal, necessary, and apodeictically certain and a posteriori knowledge that is not - let alone his distinction between analytic and synthetic statements - seems romantically naive. Whether it is due to the decline of Newtonian Mechanics and Euclidean Geometry or to the discovery of Russell's Paradox, to the incompleteness theorems of GOdeI, Church, and Turing or to
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Wittgenstein's attack on the law of non-contradiction- whatever the cause, we simply no longer have the faith in the possibility of a priori valid knowledge that Frege once had. But despite this loss of faith, philosophers who have been influenced by Frege still feel the need to provide some form of objective justification for their beliefs or, at the very least, for their believing them. The result is that philosophers who have been influenced by Frege feel caught in a Fregean Dilemma: they can choose either anti-psychologism and infallibly certain knowledge, or psychologism and no real knowledge at all. The Fregean Dilemma arises from the recognition that neither a priori reason nor a posteriori experience suffices to guarantee objective knowledge. A priori reason ensures the objectivity of justification. But it presupposes an infallibility that we do not seem to have. A posteriori experience does not presuppose infallibility. But it fails to provide for the objectivity of justification. Be this as it may, the force of the Fregean Dilemma depends upon the acceptance of what I will here call 'French Epistemology'- the Cartesian methodological doctrine that a statement should be regarded as false, or at least that it cannot be rationally accepted as true, unless it is either 'clear and distinct' (and hence, indubitably true) or derived as a logical consequence from other statements that are themselves clear and distinct. Now this, stated thus briefly, is both cryptic and in need of explication. But I mention it here at the outset because most of the attempts to resolve the Fregean Dilemma, Le., to salvage objectivity without appealing to a priori valid knowledge, have maintained French Epistemology by weakening their criteria for justification. Inductivist attempts, on the one hand, have reinterpreted the justification of statements as something other than logically sound argument- thereby ignoring Frege's warning that in lieu of a general principle of induction, "induction becomes nothing more than a psychological phenomenon, a procedure which induces men to believe in the truth of a proposition, without affording the slightest justification for so believing.'" Fideist attempts, on the other hand, have generally reduced justification at the foundational level to some form of creedal commitment- typically to a linguistic community, a scientific paradigm, or a form of life. But these attempts have done so, I will argue, at the cost of blurring the intuitive distinctions among being-true, being-believed-to-be-true, and being-justified-as-true. In so doing, they have issued, however unconsciously and contrary to expressed intentions, in subjectivist theories of knowledge. Contrary to these attempts, my own approach is to maintain: (1) that there are sharp distinctions between being-true, being-believed-to-be-true, and being-justified-as-true; (2) that there is an equally sharp distinction between the justification of a statement and the justification for believing that statement; (3) that a statement is justified as true if-and-only-if it can be shown to be the consequence of a logically sound argument; (4) that the justification of a statement is a1 ways a justification from assumptions that
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are not, themselves, justified; but (5) that one need not justify a statement in order to rationally accept it as true. Taken together, these points constitute a repudiation of French Epistemology and the justified true belief theory of knowledge in favor of an attitude toward cognition that I have, for lack of a better name, called 'Epistemological Buddhism'.' In so doing, they also constitute a repudiation of such time-honored epistemological values as conviction and creedal commitment In what follows, I will try to make these intuitions explicit.
II. The Role of Justification Elsewhere,8 I have identified four specific anti-psychologistic theses that can be found in Frege's philosophical writings: (1) logical anli-psychologism, or the thesis that logic is an a priori normative and not an a posteriori descriptive (or natural) science; (2) linguistic anti-psychologism, or the thesis that meanings, or senses (including thoughts), are third-realm entities and not mental entities or spatio-temporal objects; (3) mathematical anti-psychologism, or the thesis that mathematical objects are third-realm entities· and not mental entities or spatio-temporal objects; and (4) epistemological anti-psychologism, or the thesis that questions of justification are distinct from questions of discovery and that questions of discovery are not pertinent to the evaluation of the truth of a theory. There, I argued that these four theses are transcendental consequences of Frege's assumptions that truth is objective and independent of the knowing subject, i.e., that being-true is distinct from being-believed-to-be-true, and that truth is the object of human knowledge. I do not wish to deny any of this here. But thus said, it is important to emphasize that the psychologism/anti-psychologism debate, like all debates concerning the foundations of knowledge, is fIrst and foremost a debate about justification. Specifically, it is a debate about what counts as a justification, about what sorts of things can justify wha~ and about what constitutes the grounds or ultimate justification of our knowledge. Insofar as this is concerned, Frege's complaint against psychologism was that it encourages us to regard as justifications arguments and 'proofs' that really are not. Psychologism does this, according to Frege, because it purports to justify the laws of logic and mathematics with empirical observations- the latter being, by nature, far too particular, contingent, subjective, and uncertain to underwrite the reputed universality, necessity, objectivity, and certainty of the former. Contrary to psychologism, Frege maintained that the integrity of justification depends upon the existence of a third realm of eternal and immutable general principles "which themselves neither need nor admit of proof" and which can be apprehended a priori without recourse to empirical observation. Here, epistemological and logical anti-psychologism maintain (respectively) that justification should be modelled on mathematical
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proof from a priori principles, Le., on deductively sound arguments, and that logically sound arguments suffice to guamntee the truth of whatever they justify. Linguistic anti-psychologism then adds a corollary concerning the objectivity of meaning- a corollary that many regard as a necessary prerequisite for the validity (and hence soundness) of deductive arguments. to But if the psycbologism/anti-psychologism debate is a debate about justification, it would be 100 naive to regard it as a straightforward disagreement in which the use of 'justification" by psychologistic and anti-psychologistic philosophers is clearly the same. On the contrary, it is precisely what is meant by 'justification' that is at the heart of the issue. But nor would it be right to regard the dispute as merely verbal. Defming what anti-psychologistic and psychologistic philosophers mean by 'justification' will not, in and of itself, resolve the debate. For the issue, of course, is not what philosophers do mean by 'justification', but what they should. In what immediately follows, I will argue that this debate is a consequence of residual problems in the traditional justified true belief theory of knowledge- specifically, that it is the consequence of problems regarding the ambiguity of 'belief' and the foundations of justification. Getting clear about these problems will not, in and of itself, resolve either the Fregean dilemma or the psychologism/anti-psychologism debate. But it will, I hope delineate the pitfalls that any such resolution should avoid.
A. The Ambiguity of 'Belief If we conceive of knowledge as justified bUe belief, 'then the questions 'that should immediately arise (but in fact rarely do) are "What are we trying to justify when we are trying to justify true beliefl" and "What are we claiming is justified when we claim to have justified true beliefl" The obvious answer to these questions is 'a belief' But here, 'belief' is importantly ambiguous. It may refer either to the content of belief (what is believed), or to the process of belief (the believing itself). That is, it may refer to a statement (or object) that someone believes, or to a person's (or subject's) act of believing an object (or statement). I do not wish to suggest that there is anything problematic or improper about either of these senses of 'belief'. Nor do I wish to suggest that either one of these senses should, in and of itself, be preferred over the other. It is, however, essential to note that this 8IIlbiguity of 'belief' gives rise to two quite different 'justified true belief' theories of knowledge- theories that differ with regard to: (a) what sort of thing is justified in justified true belief; (b) what sort of thing can justify it; and (c) what sort of thing counts as a justification of it According to the first (henceforth 'objectivist') theory, what we are trying to justify when we are trying to justify true belief and what we are claiming is justified when we 'claim to have justified true belief is an object that someone believes, i.e., a statement According to the objectivist theory, 0
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only true statements can be known, and in order for someone to know a true statement, he must both believe it and be justified in his belief. But since it is, according to the objectivist theory, a statement that is being justified, and since justification, according to the objectivist theory, consists in showing that a statement is true, justification, itself, is construed as a logical relationship between that statement and whatever justifies it (henceforth, its 'justifiers'). Here, the objectivist theory maintains that statements can be justifted only by other statements, and that a statement is justified when-and-only-when it is shown to be the logical conclusion of other statements that are, themselves, already known to be true. For these reasons, justification, according to the objectivist theory, takes the fonn of a logically sound argument According to the second (henceforth 'subjectivist') theory, what we are trying to justify when we try to justify true belief and what we are claiming is justified when we claim to have justified true belief is not a statement (or object) that someone believes, but someone's act of believing a statement The subjectivist theory, like the objectivist theory, maintains that only true statements can be known, and that in order for someone to know a true statement, he must both believe it and be justified in his belief. But since it is, according to this theory, not a statement, but someone's act of believing a statement that is being justified, justification is, itself, not a logical relationship between statements and other statements, i.e., not a relationship dealing with logoi or words, but a psychological relationship between a subject's act of believing a statement and whatever might serve as the justifiers of that act, i.e., a relationship in which at least one of the terms is a mind, psyche, or psychological experience. Here, such justifiers need not be construed to be statements (logical things). Psychological experiences, e.g., sense perceptions, sensations, emotions, and acts of believing, may serve as well. Moreover, if psychological experiences are the things to be justified, and if psychological experiences can serve as their justifiers, then justification cannot take the form of a logical argumentnot, at least, unless psychological experiences can serve as the premisses and conclusions of logical arguments. Now 'psychologism' and 'anti-psychologism' are evaluative names for, respectively, the subjectivist and objectivist justified true belief theories of knowledge. They are, in other words, evaluative names for epistemologies whose primary concerns are, respectively, the justification of the subjects' knowing and the justification of the objects known. Insofar as this is concerned, 'psychologism' is used pejoratively - to denegrate subjectivist theories of knowledge - and 'anti-psychologism' is used amelioratively- to reaffirm the epistemological value of objectivity. Here, anti-psychologistic philosophers insist that objective knowledge is the knowledge of truth and that the sort of justification pertinent to objective knowledge is the justification of statements- for these are the sorts of things that are true or false. Any concern with the justification of the subjects who believe these statements will, accordingly, be denigrated as psychologism. Such a concern,
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according to anti-psychologistic philosophers, is either beneath the dignity of philosophy - to the extent to which it subordinates Truth to Belief and Reality to Appearance - or downright pernicious- to the extent to which it confuses being-ttue with being-believed.. to-be-true or maintains that the justification of believers is all that really matters. Now it is, I think, undoubtedly the case that epistemology's censure of psychologism has masked the need for subjective justification. For regardless of whether or not our statements can, in the [mal analysis, be objectively justified, we do want our doctors to be properly trained, our lawyers to be conversant with the law, our engineers to be accurate in their calculations, and, what is more, we want them to be held responsible for their actions when they are not or when they act contrary to accepted procedures. II It is, moreover, possible that the same sort of thing that justifies an object that is believed can, in one way or another, justify a subject who believes it, e.g., that an argument that justifies a statement also justifies the person who produces or becomes aware of it. But it is also possible that a person may be justified in believing a statement that is not justified (or justifIable) at all. And it is, in part, for this reason -that we insist that the subject who believes and the object that he believes are entirely different things. Mistaking the one for the other can only engender confusion. In particular, it engenders the confusion of mistaking the justification of the one for a justification of the other. A justification of a statement that some person believes is not necessarily a justification of that person's believing it. Conversely, a justification of a person's believing a statement is not necessarily a justification of that statement People may, by virtue of their appeal to the authority of Einstein, be justified in believing that E=MC2• But it is not the authority of Einstein that justifies the statement that E=MC2. (One might rather suppose that it is the 'justification' of E=MC2 that justifies Einstein's authority!) And relatively few who are 'justified' in believing that E=MC2 are able to reproduce the arguments and considerations used to 'justify' it (That is why they appeal to his authority!) On the other hand, a person may be able to produce (or reproduce) an argument that justifies a statement that he believes without ever understanding how or why that argument works. But all of this simply underscores the fact that the subject who believes and that object that he believes are entirely different things. Now the psychologism/anti-psychologism debate can be traced to the ambiguity of 'belier as follows. Modem epistemology (epistemology since Descartes) has been almost exclusively justificationist in nature. But while there has been a strong consensus that knowledge is justified true belief, there has, until very recently, 12 been a general failure to recognize the ambiguity of 'belier or to distinguish the two theories of knowledge that stem from it. The result is that epistemologists have generally conflated the justification of a statement with the justification of someone's act of believing that statement. I ' And they have typically done so in one of two ways. Psychologistic epistemologists have generally taken the justification
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for a subject's believing a statement to be the justification of that statement itself. And anti-psychologistic epistemologists, for their part, have generally maintained that no one is ever justified in believing a statement unless he can give a logical proof of it. 14 In this way, failure to recognize the ambiguity of 'belieft has proved detrimental to the subjectivist and objectivist theories alike. For it either makes the justification of the object too simple, or it makes the justification of the subject too hard. It is, perhaps, ironic that the same epistemologists who conflate the objectivist and subjectivist theories of knowledge genemlly denigrate psychologism and claim to be dissatisfied with anything short of objective knowledge. This, perhaps, is why Husserl regarded psychologism as being the result of a confusion- something which, "to think it out to the end, is already to have given it up."u Still, someone might suppose that if a true statement could be justified as the conclusion of a logical argument, and if someone who believed that statement knew of that argument and was able to produce it of his own accord, and understand it, then the justification of the statement he believed might also serve as a justification for his act of believing it. Indeed, one might even insist that a subject is justified in believing a statement if-and-only-if that subject can produce and understand a justification of the statement he believes. In that case, there would still be a difference between the subject who believes and the object that he believes. But the ambiguity of 'belief and the distinction between objective and subjective knowledge would have little practical consequence. For in that case, one could not have the one without having the other. It might be thought that epistemology can safeguard objective knowledge by following either of these paths, Le., by maintaining the objectivist justified true belief theory of knowledge or by making the justification of a statement a criterion for justifiably believing it. Indeed, the second path might seem especially attractive, since it joins psychology and epistemology instead of alienating them. Each of these paths, however, leads directly to the second problem with the justified true belief theory of knowledge- a problem that infects both the subjectivist and objectivist versions of the theory and which would, independent of the ambiguity of 'belief, give rise to the psychologism/anti-psychologism debate.
B. The Grounds of Justification suppose that a person has recognized the ambiguity of 'belief and has either: (a) adopted the objectivist justified true belief theory of knowledge; or (b) stipulated that a person's act of believing a statement is justified if-and-only-if he is able to produce and understand a justification of that statement In either case, and regardless of whether we are justifying an object or a subject, that person will have knowledge of a statement if-and-only-if he is able to produce and understand a justification of that
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statement Thus, it might be thought that here are two ways to avoid the threat of psychologism. But this, unfortunately, is not the case. For even if we adopt the objectivist justified true belief theory of knowledge, there is still the possibility that psychological experiences may enter into our 'justifications' of statements. In fact, there is good reason to believe that psychological experiences must enter into our justifICation of statements. Let me explain. Earlier we said that justification, according to the objectivist theory, assumes the form of a logical argument and that a statement is justified if-and-only-if it can be derived as the logical consequence of other statements that are themselves already known to be true. It is important to note that this objectivist theory of justification contains two planks: (a) the justification of a statement assumes the form of a logical argument (statements can be justifIed only by other statements); and (b) the premisses of that argument must themselves be justified as true (the justifiers of a statement must already be known to be true). But it is, in this context, also important to note the rationale for (b). For it is the introduction of (b) into the objectivist theory of justification that results in the second problem with the justified true belief theory of knowledge. Why is it necessary for the justification of a statement that the justifiers of that statement are already known to be true? Well, why does a statement need to be justified in the fast place? Ordinarily, we ask for a justification of a statement only when there is some reason to doubt the truth of that statement and we do not want to accept that statement dogmatically or as a matter of faith. Now reason to doubt the truth of a statement may range from its inconsistency with itself, to its inconsistency with the way things seem, to the mere logical possibility that it is false. But if there is no reason at all to doubt the bUth of a statement or if someone is willing to accept that statement as dogma, then there would be little point in asking for or attempting to give a justification of it. JustifICation is thus required to avoid both doubt and dogma. But if this is the reason why a justification is required, then any proposed justification that appeals to either doubt or dogma must be considered unacceptable. Now suppose that a person P believes a statement S and that P is also aware of an argument A according to which S is the logical consequence of a set of statements T. That is, suppose somebody believes something and is able to produce an argument to 'justify' it. Does A justify S? Here, one might assume that A justifies S only if A is valid, Le., only if S is true in every case in which all the members of T are. For if S could be false despite the truth of all of the members of T, then it would be difficult to see how A could or why A should count as a justification of S. Any justification of S would, presumably, suffice to show that S is true. But if A is invalid, then it does not, by definition, suffICe to show that S is true. (A might, in that case, count as a justification of P's believing S, but we are here assuming the objectivist justified true belief theory of knowledge.) Still, it is elementary that a false statement may be the logical consequence
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of a valid argument if one or more of the premisses of that argument are also false. 50 even if A is valid, P's demonstration that 5 is the logical consequence of T does not suffice to justify 5. P must know that all of the members of T are true. For if P is doubtful of 5 but also doubtful of one or more of T, then any appeal to T to justify 5 is little more than a charade. 5 may, indeed, follow logically from T, but that is small comfort unless we already have knowledge of T. IT P is willing to accept the dubious T in order to justify the dubious S, then he might as well have accepted the dubious S to begin with. Here, the rationale for (b) is clear. Without (b) justification ultimately reduces to dogmatism. For these reasons, T cannot serve as a justifier of S unless T is already known to be bUe. Hence, the rationale for (b) and, hence, 'the second problem with the justified bUe belief theory of knowledge. The second problem with the justified true belief theory of knowledge is that it leads, without modification, immediately to infinite regress (and hence to no justification at all). This is very easy to see. Suppose again that a person P believes a statement 5 and that P is also aware of an argument A according to which 5 is the logical consequence of a set of statements T. Does A justify 5? We have already seen that A does not justify Sunless T is already known to be true. But the objectivist justified true belief theory of knowledge tells us that in order to count as knowledge, T must itself be an instance of justified true belief, i.e., P must be aware of some argument A * according to which T is the logical consequence of a statement or set of statements T*. Does A * justify T? As we have just seen, T* must itself be known to be true if it is to serve as a justifier of T. Hence, T* must also be an instance of justified true belief and P must be aware of some argument A ** according to which T* is the logical consequence of a statement or set of statements T**. And so on. We have shown that the objectivist requirements (a) that justification assume the form of a logical argument and (b) that the premisses of that argument must themselves be known lead immediately to infmite regress. In order for a statement to be justified, the statements that justify it must be justified. But we have also shown that (b) is essential to the justified true belief theory of knowledge. If T is no better known than S, then the use of T to 'justify' S is a charade. Here, the lesson to be learned concerns the nature, as opposed to the possibility, of justification. The point is not that justification is impossible (in any but the special cases where: (1) justification is demanded of foundational statements; or (2) justification is demanded of all statements). The point is that every justification or proof is a justification or proof from assumptions. That is, the form and purpose of a justification is to show that a certain statement (action, belief, or what-have-you) is in accordance with and a consequence of certain assumptions. While we may indeed ask for a justification of those assumptions, it makes no sense at all to ask for the justification of foundational assumptions- Of, a fortiori, of all assumptions. But this, again,
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is not because justification is impossible. It is because the very nature of justification presupposes the existence of statements that go unjustified. So if an objectivist wants to maintain that knowledge is justified true belief but avoid infinite regress and charade, then he seems to have only one option open. 16 He must deny that statements can be justified only by other statements. In other words, the objectivist must commit himself to at least two of the three planks of the subjectivist theory of justification, or else admit that justification, and hence knowledge, is impossible. In order to avoid both infinite regress and charade, the objectivist must maintain: (1) that the justifiers of statements need not themselves be statements; and (2) that justification need not assume the form of a logical argument. Objectivists have traditionally sought to do this by: (a) distinguishing between immediate and mediate ways of acquiring knowledge, i.e., between intuition and inference; (b) developing theories regarding infallible sources of immediate knowledge; and (c) construing such infallible sources of immediate knowledge as the ultimate justifiers of statements, Le., as the foundations of knowledge. Here, the project has been to identify a set of statements, the foundations, the truth of whose members is guaranteed not by their valid derivation from other statements, but by their intuitive derivation from allegedly infallible sources. Such foundational statements are alleged to be special instances of knowledge. They do not admit of logical justification (that's why they are fountiational), but nor do they need to be logically justified. They do not need to be logically justified because their truth is (alleged to be) guaranteed as a result of their intuition from an infallible source. Thus guaranteed, these foundational statements can serve as the ground for all subsequent logical justification. Be this as it may, this concern with infallible sources of knowledge has typically resulted in psychologism of one form or another. For these cognitive sources have typically been construed to be faculties of the mind like sensibility, understanding, or reason. And thus construed, the ultimate justifiers of statements tum out to be psychological experiences. We have been discussing the role of justification in the psychologism/ anti-psychologism debate and, especially, two of the residual problems with the justified true belief theory of knowledge that have given rise to this debate. The problem posed by the ambiguity of 'belief is serious and the equivocations that have resulted from it are responsible for many of the disputes in the history of epistemology. One can still see its influence today in the prevalent belief that inductive inference and the so-called 'logic of confmnation' can provide justification for objective knowledge. "Even observation statements reporting a million white swans and no non-white swans fail to justify the statement that all swans are white," insists the deductivist "But surely, one would would be an irrational sceptic to believe otherwise," replies the inductivist. And so the debate continues. But as soon as one distinguishes between the justification of the statement and the justification of someone's believing it, it is easy to see that both the deductivist and the inductivist are righl The evidence cited may very well
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justify someone's believing that all swans are white- despite the fact that it does not justify the statement Be this as it may, the questions regarding the foundations of justification pose even greater problems for the objectivist theory of knowledge. If the grounding of justification in cognitive sources is a necessary prerequisite for the possibility of justification, and if such cognitive somces are ultimately psychological in nature, then the objectivist justified true belief theory of knowledge seems an impossible dream. For in that case, the objectivist justified true belief theory of knowledge leads either to psychologistic justification (justification by psychological experience), or to no justification at all. If epistemology insists upon a role for justification, then the ensuing psychologistic justification results in at least one of three different forms of subjectivism: (1) the subjectivism of confusing the justification of the 'knowing' subject with the justification of what the subject 'knows'; (2) the subjectivism of regarding what the subject 'knows' as being justified by the subject's private experiences; or (3) the subjectivism of equating evidence that is good enough to convince some subject with evidence that suffices to justify a statement. And if epistemology rejects a role for justification, then it is left to explain what objective knowledge is, how it is possible, and how it differs from mere opinion, faith, and other forms of subjective belief. Still, one might suppose that if infallible sources of knowledge truly do exist, then a psychologism of the sort that we have been discussing would be innocuous. For if our reason or sensibility is constructed in such a way as to intuit infallible knowledge, then whatever knowledge it yields might as well be objective- the epistemological value of objectivity resulting not from the sanctity of objects, but from the bias and fallibility of subjects. Now I do not want to deny that the existence of infallible cognitive sources would render the sort of psychologism that we have been discussing innocuous. But the fact remains that the great conceptual revolutions of the twentieth century have placed all claims to infallible cognitive sources in doubt. Of course, the mere fact that we might doubt the claim that a cognitive source is infallible does not, in and of itself, refute the infallibility of that source. If the Pope speaks infallibly when he speaks ex cathedra, then he speaks infallibly regardless of whether or not Luther agrees. But when doubt regarding the infallibility of cognitive sources arises in the context of French Epistemology, it prevents us from rationally accepting a statement on the basis of intuition and, in so doing, from accepting it on the basis of inference as well. And this, as I have said, is what gives rise to the Fregean Dilemma.
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m. French Epistemology Some people remember Descartes as a sceptic- a little bit of irony since Descartes was, according to any literal interpretation of his work, one of the greatest opponents of scepticism in the history of Western Philosophy. It is true that Descartes raised the questions 'What can we know?' and 'How can we know it?' in his Meditations on First Philosophy. And it is true that he there resolved to doubt whatever he could doubt without contradiction in order to answer them. But people who remember Descartes as a sceptic apparently remerrlber only his "First Meditation." It is important to remind them that Descartes' appeal to doubt is purely methodological, Le., that it is not the conclusion to a philosophical investigation, but a method adopted to conduct one. For while Descartes ends his "First Meditation" wondering whether there is anything that is not subject to doubt, he ends his sixth in wonder at how very little there is that is. And along the way he 'proves', beyond the shadow of a doubt, that he exists, that God exists too, that God is not an evil deceiver, that we can never make a mistake so long as we use our God-given Intellect properly, that material objects exist in essentially the way in which we perceive them, and a host of other propositions that might be regarded as even more controversial. The epistemological engine for all this 'proof is Descartes' general principle, announced at the beginning of the third meditation, that everything he clearly and distinctly perceives is true. For this reason, people who do not remember Descartes as a sceptic often remember him as being not sceptical enough. It is, however, difficult to determine whether and to what extent Descartes intended his proofs of the existence of God to be taken literally. For in discussing his own motives for writing, Descartes tells us 'that "it is well to omit things that perhaps would yield a profit to those who are living, when it is one's purpose to do other things that yields even more profit to our posterity."17 And the presence of several 'ironies' in the Meditations suggest that they should not be taken at face value. Thus, Descartes begins his "Letter of Dedication" by saying that the existence of God should be demonstrated by the aid of philosophy, as opposed to theology, since "no unbeliever seems capable of being persuaded of any religion or even any moral virtue, unless these two are f1J'St proven to him by natural reason."18 But he ends his "Letter of :Dedication" by requesting the patronage of the Faculty of Sacred Theology of Paris, since he fears that many people will not be able to follow his arguments and is confident that those who do not will -.Submit to their authority. In that same letter, Descartes explicitly criticizes the argument "that God's existence is to be believed in because it is taught in the Holy Scriptures, and...that the Holy Scriptures are to be believed because they have God as their source"20 as circular, and warns that such an argument "cannot be proposed to unbelievers because they would judge it to be a circle."21 But in his "Third Meditation," Descartes produces a 'prooft whose circularity is both notorious and but slightly less
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obvious.22 According to Descartes' 'proof', we can know that God exists and is not a deceiver, because anything we clearly and distinctly perceive is true. And we can know that anything that we clearly and distinctly perceive is bUe, because God exists and is not a deceiver.23 It is difficult to detennine whether Descartes was aware of these ironies, much less whether he intended them to be significant. But we do know that Descartes lived in an era in which a man could be executed for expressing philosophical views contrary to those of the Roman Catholic Church,24 that he was aware of the persecution of Galileo,2S and that he suppressed publication of his own La Monde for fear of suffering the same fate. 26 In light of this knowledge, Descartes' statement that it is well for a writer to omit things when doing so yields greater profit to posterity acquires new significance. And given this significance, Descartes' reminder that the Lateran Council under Leo X had condemned those philosophers who maintain that the immortality of the soul can be held on faith alone and had "explicitly enjoined Christian philosophers to refute their arguments and to use all their abilities to make the truth known"27 has a distinctly ominous ring. One cannot help but wonder how the Latemn Council would have reacted were such 'refutations' not forthcoming. For these reasons alone, we should not ignore the possibility that Descartes intended his Meditations on First Philosophy to be taken not literally, but as an attempt at indirect communication. According to this hypothesis, the intelligent reader would quickly recognize that Descartes' arguments do not suffice to prove the existence of God. But the intelligent reader would also recognize the 'ironies' mentioned above and would conclude that Descartes was too intelligent not to have intended them. Noting that Descartes had introduced his 'proofs' for the existence of God as being "such that I believe that there is no other way by which human ingenuity can find better ones, "28 the intelligent reader would then dmw the obvious conclusion. Here, the obvious conclusion would be that the Meditations is an ironical work whose true message is that the existence of God cannot be proved on rational grounds, and must be accepted on faith if it is to be accepted at all. In that case, one could no longer appeal to God as a divine foundation for science, and since no other infallible foundation is forthcoming, it would always be possible that our scientific knowledge, including our knowledge of logic and mathematics,29 is but a grand deception and another bit of irony. Now I mention all this not because I intend to defend an ironical interpretation of Descartes, but because I do not wish to lay at Descartes' grave charges that any 'intelligent' reader would attribute to misinterpretation. Again, it is very possible that Descartes intended his Meditations to be interpreted ironically, that he believed that it is impossible to prove the existence of God by rational argument, and that he did not believe that scientifIC knowledge could lay claim to the sort of absolute certainty that a divine foundation would provide. Such an ironical interpretation need not conclude that Descartes is a sceptic. For the point of Cartesian irony might be that divine foundations and absolute certainty are
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far 100 much to demand of knowledge in 'the fIrSt place. But an ironical interpretation should conclude that Descartes intended his general principle to be recognized as wishful thinking, and that the subjective certainty that we have in an idea, no matter how 'clear and distinct', is no sure criterion of its truth. Be this as it may, I will, in what follows, assume that Descartes intended his Meditations to be interpreted literally. For the fact remains that most commentators have interpreted the Meditations literally, and, interpreted literally, the Meditations has exerted an astounding influence upon the history of Western Philosophy. One may debate whether Descartes discovered epistemology or whether he discovered the mind. But it is uncontroversial that Descartes discovered Modem Philosophy. Descartes discovered Modem Philosophy by insisting upon the priority of epistemology and by introducing two methodological principles that have influenced the development of epistemology ever since. The fast of these principles is well-known as Descartes' 'methodological scepticism'. It is his resolve to call into question or doubt the truth of any belief accepted uncritically on the basis of authority, tradition, or consensus. The second of these principles, often conflated with the fast, is what I call 'French Epistemology'. It is Descartes' resolve to regard as false any belief that is neither clear and distinct (and hence indubitably true) nor justified as a logical consequence of other beliefs that are themselves clear and distinct 30 Taken together, these two principles constitute the Cartesian programmea programme which, in its attempt to derive objective certainty from methodological doubt, has dominated western philosophy for the past three hundred years. That the Cartesian Programme has dominated western philosophy for the past three hundred years can be seen in the fact that rational knowledge has, during that period, been construed almost exclusively in terms of justified true belief. Ever since Descartes, philosophers who have talked about rational knowledge have talked about the justification of true belief. In so doing, they have disagreed notoriously regarding the foundations and criteria of justification- whether rational knowledge rests upon a priori or a posteriori intuition, and whether rational knowledge requires deductive or inductive inference. They have, moreover, disagreed regarding what cOWlts as a priori and a posteriori intuition and regarding what cOWlts as deductive and inductive inference. But few philosophers in the modem period have denied that rational knowledge is justified bUe belief or that a statement must be justified before it can be rationally accepted as true. And this is significant. For the past three hundred years, cognitivists who have asserted the possibility of rational knowledge and sceptics who have denied the possibility of rational knowledge have asserted and denied not merely that such-and-such a belief is true, but that such-and-such a belief can be justified. But here, it is important to distinguish sharply between methodological scepticism and French Epistemology. Methodological scepticism asserts that we should always question or call into doubt beliefs that are not indubitably
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true, that we should always ask for a rational justification of beliefs that do not seem indubitably true, and that we should always remember that no matter how familiar or generally accepted, a belief that is neither indubitably true nor rationally justified may be false. French Epistemology, on the other hand, asserts that a statement should be regarded as false, or at least as rationally unacceptable, unless it is indubitably true or justified by other statements that are indubitably true. Methodological scepticism maintains that one should question or doubt any statement that is not justified. French epistemology, on the other hand, maintains that one should not accept as true any statement that is not justified. It is essential to realize that these are entirely different injunctions- that it is possible to call into question or doubt the truth of statements that one simultaneously accepts as bue, and hence that it is possible to simultaneously adopt methodological scepticism and repudiate French Epistemology. I call the principle that a statement should be regarded as false until proven true 'French Epistemology' partly because Descartes introduced it and Descartes was French, but primarily because the principle has a potential analogue in a French judicial principle according to which "issues of reasonable doubt in criminal cases may" contrary to Anglo-American custom "be resolved by evidence and argument bearing on prior convictions of the accused, his general behavior, even his family history. "31 But the directive that an accused must be found guilty beyond a reasonable doubt has its origin in the presumption of innocence, the principle that an accused is to be presumed innocent until proven guilty (beyond a reasonable doubt), and the two are often taken to be practically synonymous, if not legally equivalenL 32 The upshot is that an accused's prior criminal record, general behavior, or family history might, if sufficiently notorious, practically reverse the presumption of innocence. In such a case, the accused would still be presumed innocent until proven guilty, and he would still have to be proven guilty beyond a reasonable doubt But the evidence regarding his prior criminal record, etc., would be considered a sufficient rebuttal of the evidence provided by the presumption of innocence, and might, thereby, render a mere accusation a 'proof beyond reasonable doubt'. In such a case, the prosecution would not need to prove that the defendant is guilty; the defendant would need to prove that he is not. Now it seems as if something like this is at play in Descartes' resolution to doubt the veracity of his sense perceptions. Explicitly, Descartes doubts the veracity of his senses because he "noticed that they sometimes deceived me. And it is a mark of prudence never to trust wholly in those things which have once deceived us. "33 But in resolving to regard all of his former beliefs as false until proven true, Descartes in effect places the burden of proof in any epistemological proceeding upon the statement that is claimed to be true. Here, a doubter need not prove that a statement is false. Rather, those claiming to know that statement must prove that it is noL Once asserted, a cognitive claim must be proved true beyond a reasonable doubt, or be judged false.
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Here, what turns on the bmden of proof is not whether we should call into question or doubt statements that are accepted on the basis of
consensus, tradition, or authority. What turns on the burden of proof is whethez we should regard our inability to justify a statement as indicative of that statement's rational unacceptability. H we adopt French Epistemology, then an unproved statement should not be accepted as true, no matter how obvious or apparent its uuth may seem. In that case, any argument to the effect that a statement is not or cannot be justified is, in effect., an argument that that statement should be regarded as false-- or at least that it should not be accepted as true. And it is for this reason that the mere logical possibility of an omnipotent, evil deceiver caused Descartes so much worry. In the context of the "First Meditation," the mere possibility of an omnipotent, evil deceiver emerges as a reason to doubt even the most obvious and certain of our beliefs- those beliefs that could not be shaken by the possibilities that our senses may be deceiving us or that we may be dreaming. If it is possible that an omnipotent, evil deceiver exists, then it is possible that we are deceived even about the existence of extended things, size, and place,'" and "every time [we] add two and three or count the sides of a square.":u But here, it is important to remember that Descartes never believed that an omnipotent, evil deceiver actually exists,36 or even that the existence of such a deceiver is likely. Explicitly, Descartes regarded his "long-standing opinions" concerning the existence of extended things and the nature of mathematical relations as "highly probable, so that it is much more consonant with reason to believe them than to deny them."37 But what Descartes did believe (at least in the context of the "First Meditation tt ) is that the existence of an omnipotent, evil deceiver is a logical possibility. And here, it is not methodological scepticism but the burden of proof as defined by French Epistemology that led Descartes to regard this logical possibility as sufficient reason to "suppose not a supremely good God, the source of truth, but rather an evil genius, as clever and deceitful as he is powerful, who has directed his entire effort to misleading me. "38 If we adopt French Epistemology, then any argument to the effect that statements cannot be justified from indubitably true premisses is an argument that statements (including this one) cannnot be mtionally accepted as true. But if we adopt an epistemology that protects the presumption of innocence - an epistemology that simultaneously insists that we regard a statement or theory as ttue until proven false and refuses to accept 'evidence' regarding the history of that theory or its sow-ce as proof - then a statement may be rationally accepted as true without justification, provided, of course, that is does not seem false. In that case, we might even admit that statements cannot be justified and, admitting that statements cannot be justified, resolve to perpetually entertain the question whether or not they are true. And here, it is easy to see that an allegiance to methodological scepticism is entirely compatible with the repudiation of French Epistemology- that we may question whether or not a statement is true, but assume that it is unless or until we have reason to think otherwise.
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French Epistemology can, in the context of our story, be seen as an attempt to unite the objectivist and subjectivist justified true belief theories of knowledge via a seemingly innocuous psychologism that would make the justification of a statement a criterion for its justifiable acceptance. Insofar as this is concerned, adherence to French Epistemology made methodological sense so long as philosophers believed in something like an objective criterion of truth. So long as philosophers believed that the truth of a statement could be guaranteed by its being clear and distinct, or a priori, or a posteriori, or even uttered ex cathedra by the Pope, the rational acceptability of a belief could reasonably be predicated upon our ability to justify that belief- either logically, via argument, or extra-logically, by tracing it logically to an infallible source. But once the infallibility of cognitive sources is itself called into question, the mtionale for French Epistemology seems to lose its methodological appeal. Instead of functioning to insure that statements are rationally accepted only if they are troe, French Epistemology now functions to preclude the rational acceptance of statements- regardless of whether or not they are true. Adherence to French Epistemology in lieu of an objective criterion of troth does not make the mtional acceptance of a statement difficult. Adherence to French Epistemology in lieu of an objective criterion of truth makes the rational acceptance of a statement impossible. It makes the rational acceptance of a statement impossible because any logical justification or proof of a statement is, as we have seen, predicated upon some prior rational acceptance of the statement(s) that justify or prove it. The French Cognitivist may, of course, claim that the prior acceptance of such justifying statement(s) is itself rational because such justifying statement(s) are themselves logically justified by other statements. But the French Sceptic will undoubtedly counter by questioning the rational acceptance of those statements. And, as everyone since Aristotle39 has known, this sort of regress cannot continue infinitely. The French Cognitivist may stop the regress at any point, accepting statements without logical justification, and claiming that these are statements whose 'justification' consists in their derivation from a privileged cognitive source. But if he does, then the French Sceptic will undoubtedly question whether and why that sowce should be regarded as privileged and whe'ther and why the acceptance of statements derived from that source - rneditately or immediately - should be regarded as rational. Descartes, if we interpret him literally, did regard the Intellect as privileged, and the clarity and distincbless of his ideas as a sure criterion of their truth. But the clarity and distinctness of ideas has not fared well as a criterion of troth, partly because too many people claimed clarity and distincbless for too many contradictory ideas, and partly because it proved too difficult to detennine whe'ther and when any given idea is clear and distinct Nor have subsequent attempts to ground our knowledge on an objective criterion of truth fared any better. Thus, David Home, who attempted to found our knowledge on sense impressions, and who regarded
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any chain of reasoning that did not ground itself in such impressions as "entirely without foundation,"40 was forced to admit that a science based solely on sense impressions carmot determine whether anything other than those impressions exist and carmot offer our scientifIC laws any foundation other than custom and habit. And Immanuel Kant, who attempted to found scientific certainty on the universal and necessary categories of the Understanding, and who offered a transcendental deduction of those categories from the very possibility of experience, failed to anticipate that .the very sciences that he claimed to be apodeictically certain would later be regarded as false. Now Frege believed that the general principles, or axioms, that he regarded as necessary for justification but which "neither need nor admit of proof'41 could be apprehended, a priori, by the Reason, or what he called "the logical source of knowledge. ,t42 Frege, moreover, regarded such a priori intuition as infallible- writing that "an a priori error is thus as complete a nonsense as, say, a blue concept,"43 and that "we cannot accept a thought as an axiom if we are in doubt of its truth; for it is either false and hence not an axiom, or it is true but stands in need of proof and hence is not an axiom."44 That Frege did not regard this appeal to a priori intuition and the indubitability of statements as either subjectivist or psychologistic has struck some philosophers as strange.43 But it is most likely due to his construa1s: (a) of psychology as an empirical science; (b) of the psychological source of knowledge as sense perception; (c) of statements as entities of an eternal and immutable third realm; and (d) of a priori knowledge as strictly universal. necessary, apodeictically certain, and, hence, objective.46 But even Frege realized that the a priori apprehension of third realm objects would be impossible without relating those objects to a mind, and that this relationship between mind and object might be thought to compromise the objectivity of knowledge. Frege did try to explain why the apprehension of thoughts does not compromise their objectivity- saying that apprehension affects only the 'inessential properties' of the thought.47 But what Frege failed to realize was that his Basic Law V of The Fou.ndations of Arithmetic, which as an axiom was claimed to be both true and indubitable, leads, in conjunction with the other axioms of his system, directly to Russell's Paradox. It is the accumulated weight of these and other failed attempts to articulate infallible foundations that have assured many contemporary philosophers that infallible cognitive sources do not exist. This, in away, is unfortunate. For an adherence to methodological scepticism would caution doubt concerning exactly what such failed attempts mean. And here, the fact that some contemporary philosophers regard this conclusion as justified on inductive grounds is as ironic as it is unwarranted. The non-existence of infallible cognitive sources is not justified on inductive grounds. It is not justified at all. Not unless our failure to fmd a cure for cancer means that no such cure exists.4I I do not know whether infallible cognitive sources exist or not, but I think it is reasonably clear that the philosopher who
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thinks their non-existence is proven by induction has mistaken disappointment for proof. Nor should this contemporary denial of infallible sources of knowledge be confused with either a denial of the possibility of knowledge or a rejection of French Epistemology. While Descartes understood the sceptic to be one who denies 'the possibility of absolute certainty - 'probable guesses' not qualifying as knowledge, no matter how 'consonant with reason' they may be - few contemporary philosophers regard themselves as sceptics. And while most contemporary philosophers acknowledge that 'proofs' are always contingent upon foundations and foundations are never absolute, they nonetheless continue to presuppose that a statement needs to be justified, in one way or another, before it can be rationally accepted as true. Still, what such failed attempts do mean is that any future claims regarding infallible sources should, on Cartesian grounds, be subjected to doubt- it being wiser not to trust entirely to any thing by which we have once been deceived. It is this doubt regarding the infallibility of cognitive sources, as opposed to any certainty regarding their non-existence, that spells an end to the Cartesian Progmmme. The Cartesian Programme attempted to derive objective certainty from methodological doubt by showing that there exists some ' Archimedean point' that cannot, in the final analysis, be rationally doubted after all. The discovery of such an 'Archimedean point' would, in Descartes' words, allow us to do 'great things'. And if there really were some Archimedean statements that were rationally indubitable, then there would be little problem in saying that those statements can be rationally accepted without justification and that they provide the foundation for the rational acceptance of all other statements. In that case, the French epistemologist could maintain his demand for justification- the privilege of foundational statements being explained by their difference, by the fact of their rational indubitability. But in lieu of foundational statements that are rationally indubitable, French epistemology forces us into the Fregean Dilemma. We must either characterize any acceptance of beliefs that differ from a certain set as irrational, or deny the possibility of rational belief at all. Here, the prevailing contemporary attempts to found knowledge on convention or commitment, be it to a linguistic community or to a form of life, suffers from a kind of bad faith. For the myth of the foundation is like every other myth: its effectiveness as a myth depends upon its being taken for the truth. If it is really true that Archimedean points are a dime a dozen, then it may no longer be possible to do 'great things'. But if doubt regarding the infallibility of cognitive sources spells an end to the project of deriving objective certainty from methodological doubt, it need not prevent us from rationally accepting statements as true- not, at least, if we distinguish sharply between methodological scepticism and French Epistemology. In what follows, I will suggest that an epistemological approach that maintains an adherence to methodological scepticism but repudiates French Epistemology offers the best resolution to the Fregean Dilemma.
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IV. Epistemological Buddhism Earlier I said that the force of the Fregean Dilemma depends upon the acceptance of French Epistemology. There, I characterized the Fregean Dilemma as a crisis for objectivity, i.e., the problem being to salvage objective knowledge without appealing to infallible cognitive somces. But in tracing the Fregean Dilemma to French Epistemology, the terms of our discussion have changed. What was originally characterized as a crisis for obje.ctivity has now been characterized as a crisis for rationality, the problem being to salvage the rational acceptability of statements without appealing to infallible cognitive sources. Here, I hope it is obvious that if the Fregean Dilemma poses a crisis for objectivity then it also poses one for rationality- and for the same Kantian considerations that characterize what is objective as what is binding on all rational beings. Hence, Frege defended classical logic as an objective criterion for rationality, and hence Frege attacked the psychologistic tendency to regard non-classical logics as valid for those that hold them as "a heretofore unknown type of madness."·' Elsewhere50 I have argued that twentieth century philosophy is in the process of an epistemological paradigm shift in which the idea of knowledge as apodeicticly certain (what I have called 'EP1 epistemology') is gradually being replaced with the idea of knowledge as inherently fallible (what I have called 'EP2 epistemology'). There I argued that that shift in our understanding of 'knowledge' necessitates a systematically related shift in our understanding of other key epistemological teons like ' objective' , 'rational', ,scepticism', and the like. To the extent to which rational knowledge has been construed as justified true belief, this paradigm shift can be understood as an attempt to salvage rational knowledge from scepticism.. Still, the epistemological paradigm shift from EPI to EP2 has genemlly involved a weakening of the standards for justification. Where EPI sceptics had argued that: 1. Rational knowledge is justified true belief. 2. JustifICation guarantees the truth of what it justifies. 3. Logical justification guarantees the truth of what it justifies, but this guarantee is, ultimately, contingent upon the truth of premises which cannot be logically justified. 4. Extra-logical 'justification' provides no guarantee for the truth of what it 'justifies'. Therefore: S. Rational knowledge is impossible.
EP2 cognitivists have generally replied by denying that justification guarantees the truth of what it justifIeS. This weakening of the concept of justification has occurred in one of two ways. EP2 inductivists have recognized inductive inference as providing logical justification for general statements- thereby denying 2 and weakening their concept of logical
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justification. EP2 fideists have argued that the validity of general statements follows naturalistically from our commitment to their use in defining the behavior of a linguistic community- thereby denying 4 and weakening their concept of extra-logical justification. These movements sometimes go by the name of 'pragmatism', but they seem decidedly at odds with the pragmatism of Peirce, who always fought against what he called 'the frxation of belief'.51 I have already indicated that I regard each of these tendencies as a misguided form of psychologism. By weakening standards for justification, inductivism and fideism encourage us to regard as settled issues and disputes that really are not. While there is nothing in the nature of things to prevent such a weakening of standards, my own sense is that most human beings are, in their quest for certainty and security, already too inclined toward a parochial closed-mindedness and fiXity of belief which is, or should be, the purpose of epistemology to destroy. Still, the motivation for weakening the standards for justification is understandable: we all believe that we are rational; and we have all grown wary of foundations. IT there really exists a plurality of 'foundations', and no one 'foundation' is, in any non-questioning begging sense, more justified than another, then revising our concept of justification may seem our best bet to salvage rationality. The revision, however, is deceptive. It maintains a foundationalist theory of rationality without the benefit of a rational foundation. It is, moreover, both socially dangerous and scientifically sterile. For it leads, in the fmal analysis, to the same sort of unquestioning pre-judgment that has historically stifled social integration and scientific growth, and that has traditionally been the burden of rationality to combat Indeed, it not only leads to such unquestioning pre-judgment, it seems to vindicate and endorse it For these reasons, I have written elsewhere 52 that all attempts to justify a statement as true or as false are in the same epistemological boat and that rational judgments of rationality are, within a justificationalist programme, possible only given the acceptance of foundational principles (goals, values, etc.) and are made only with reference to the foundational principles accepted. All attempts to justify a statement as true or as false are in the same epistemological boat because their success or failure ultimately depends upon the acceptance or rejection of some statement(s) without justification. Rational judgments of rationality are possible within a justificationalist programme only given the acceptance of foundational principles (goals, values, etc.) and are made only with reference to the fOWldational principles accepted because the judgment that a statement (belief, action, etc.,) is rational is, within a justificationalist programme, ultimately the judgment that that statement (belief, action, etc.) is, in one way or another, justified. But all this presupposes our distinction between the objectivist and subjectivist justified true belief theories of knowledge and is, therefore, very easily misunderstood. Hence, Tom Settle write~~: ------------
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Having abandoned justificationism - roughly, the idea that there can be absolute certainty as a result of the proper use of reason - Nottumo thinks that all attempts to justify theories as true or false are in the same boat. But this presumes that justifying is an all or nothing affair and I am not willing to give up the word 'justify' to the absolutists, any more than I was willing to give up the word 'true' to the conventionalists. There is an ancient history to the notion of justifying as showing to some appropriate court that someone is innocent of some charge. I dunk this is a good cue for us. Justification, in my view, can best be seen as the act of satisfying an appropriate body of people that some belief or action is what a person should hold or do, or may hold or do. Life is full of it, though which body of people we are trying to satisfy, and what the standards are that we have to meet to do so, vary enormously.53
But as we have already seen, satisfying an appropriate body of people that a statement is true, and justifying that statement as true are two entirely different things. Satisfying an appropriate body of people that some belief or action is what a person should hold or do may count as a justification of that person's holding that belief or doing that action. And an act of justifying a statement may, simultaneously, be an act of satisfying an appropriate body of people that some belief or action is what a person should hold or do, or may hold or do. But to see justification as this, and nothing more, is to adopt what I earlier called a 'subjectivist' justified true belief theory of knowledge. But apart from this, I do not equate justificationism with the idea that there can be absolute certainty as a result of the proper use of reason (though this is what Descartes, interpreted literally, and Frege seem to have had in mind). What I mean by 'justificationism' is nothing more nor less than what I have here called 'French Epistemology' - the idea that a statement must be justified - either logically or extra-logically- in order for it to be rationally accepted as true. In my Objectivity, Rationality, and the Third Realm I sketch a quite different approach to rationality- one that maintains a suspicion of objective foundations and purported justifications without either weakening the standards for justification or denying the possibility of rational knowledge. There, I suggest that the rational man in the twentieth century
can: ...best be described as a sort of epistemological Buddhist- one deeply committed to the quest for truth, ready to entertain competing theories, and even willing to apply them in practice, but always wary of fonning deep attachments to any specific claim to truth. Such a man may be characterized as having beliefs. But what the epistemological Buddhist lacks is the commitment to belief.54
Epistemological Buddhism assumes the loss of objective or justified certainty as the epistemological problem context of the twentieth century. It acknowledges that human action in the face of WlCertainty poses deep problems for both individuals and institutions. But it argues that these problems cannot be resolved by either the proliferation of 'objective'
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standards (what might be called 'the cult of objectivism') or the denial th our actions are, in the final analysis, either meaningful or important (what might be called 'the cult of nihilism'). Rather, Epistemological Buddhism criticizes each of these contempomry tendencies as forms of self-delusion tantamount to what Sartre might have called 'epistemological bad faith' that function to illicitly reclaim the certainty and secwity they initially deny. Epistemological Buddhism also criticizes some of the consequences of the contempomry pragmatism mentioned above. One such consequence is the transformation of judgments into calculations, a transformation which camouflages the essential subjectivity of the decision-making process. Such transformation and camouflage, according to Epistemological Buddhism, are but further forms of epistemological self-delusion. Rather, Epistemological Buddhism maintains: (1) that our decisions require judgments, not calculations (that's why they are decisions); (2) that these judgments are grounded in subjectivity (that's why they are judgments); (3) that such judgments are inherently fallible (that's the lesson of the twentieth century); but (4) that such judgments are meaningful and important (because our decisions do have their consequences). In maintaining these points, Epistemological Buddhism rejects both the traditional construal of knowledge as justified true belief and its Cartesian corollary that we have here called 'French Epistemology'. But instead of embracing scepticism or the irrational, Epistemological Buddhism argues that foundational statements cannot be justified and that our rational acceptance of such statements should thus not be construed as contingent upon the quality of their justification. Contrary to French Epistemology, Epistemological Buddhism maintains that it is rational to regard a statement as true, unless or until one has good reason to believe it false. In so doing, Epistemological Buddhism maintains that we have no recourse but to trial and error (whether we wish to acknowledge it or not), and that the deep problems posed by acting in uncertainty can only be resolved by confronting our equally deep fears of error and change. Simply put, the resolution of these problems requires the acceptance of error and change as essential components of learning - as events that may be painful, but that may also lead to growth - and not, in any event, as events to be avoided, hidden, and denied at all costs. Here, Epistemological Buddhism advocates that the best way in which one can search for truth is by: (1) remaining methodologically sceptical of all claims to truth; and (2) thinking oneself into as many opposing perspectives as he possibly can. For it is only in this way that the Epistemological Buddhist will unqerstand the strength of each of the opposing candidates for truth. And without such understanding, neither genuine agreement nor genuine disagreement is possible. Here I do not want to be misunderstood I believe that quite literally any statement can be 'justified' logically provided that one is willing to accept without logical justification the statements necessary to justify it. But I also believe that the idea that we have access to an infallible source of knowledge that can give extra-logical justification for our cognitive claims
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is simply implausible. Insofar as this is concerned, I am, like Frege, opposed to psychologism because it encourages us to regard as justified statements and thec:ries that really are not. But I am also opposed to Frege's anti-psychologism- and for precisely the same reason! But despite all this, I agree with Settle" that the caricature sceptic or beginning philosopher, who refuses to be convinced by any argument provides no reason for someone to doubt his own beliefs- no more than someone's ability to convince this caricature sceptic of his beliefs would provide those 'beliefs with justifICation. But let's not leave the caricature sceptic just yet For the caricature sceptic raises a much deeper point, a point that is much more difficult to resolve, and that is ultimately at the very root of the problem with French Epistemology. Exactly why is the caricature sceptic a caricature? Presumably, because his scepticism is not real, because it is merely a stance, because he doesn't really have a different belief, but only a way with words and a logical obstinancy that renders him obnoxious to the more rermed epistemological sentiments around him. The caricature sceptic is not serious, he is merely cantankerous. Better to recognize him as such than to let him disturb the satisfaction and solidarity of Settle's appropriate body of people. Now I would not for a moment either doubt or deny that there are caricature sceptics every bit as disingenuous and cantankerous as Settle describes. But I also 'think that it is too simple to presume that every sceptic whom we find impossible to convince is such a caricature- and that it is too difficult to determine whether and when some particular sceptic is not. The caricature sceptic who refuses to be convinced by any argument gives us no reason to doubt our own beliefs. But the real sceptic who is not convinced by OUT arguments does. The caricature sceptic gives us no reason to doubt our own beliefs because our judgment that a given sceptic is a caricature is, simultaneously, the judgment that his beliefs are really no different from our own. But the real sceptic is an entirely different matter. The real sceptic gives us reason to doubt our own beliefs- not because of French Epistemology, but because of what Charles Peirce used to call 'the social impulse': namely, the recognition that other people think differently, and the thought that is "apt to occur...in some saner moment that their opinions are quite as good as [our] own."" It is this recognition that other people think differently and this thought that might occur in some saner moment that is at the root of the problem with French Epistemology. If there really were some statements that everyone believed, then there would be little opposition to saying that those statements can be rationally accepted without justification and that they provide the foundation for the rational acceptance of all other statements. In that case, the French epistemologist could defend his demand for justification- the privilege of foundational statements being explained by their difference, by the fact that no one believes them to be false. And in that case, the 'sceptic' who complained that the foundations were unjustified could be ignored as a
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caricature, and would, being a caricature, give us no reason to doubt our own beliefs. But in lieu of foundational statements that everyone believes, French Epistemology once again forces us into the Fregean Dilemma. We must either characterize any acceptance of beliefs that differ from a certain set as irrational, or deny the possibility of rational belief at all.
v. Farewell to Commitment I have characterized Epistemological Buddhism as an anti-foundationist epistemology that does not reduce rational knowledge and rationality to creedal commitment and group consensus. But some contemporary philosophers faced with the decline of foundationalism, have characterized rational knowledge - and rationality itself - as presupposing some form of commitment- either to a form of life, or a linguistic community, or a scientific paradigm. Creedal commitment, according to these philosophers, is not simply something that knowers have, it is something that they must have in order to carry out their cognitive endeavors. Hence, Thomas Kuhn, in construing so-called 'normal science' as a rational endeavor, writes that: Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, Le., for the genesis and continuation of a particular research tradition.57
And Stanley Fish, in denying the possibility of theory and value neutrality, writes that ...knowledge and conviction do not depend on such a neutrality, but on a commitment to the perspective from which one speaks, a commibnent one cannot possibly be without"
I too believe that a rational person is committed to something. But I also think that these attempts to link rationality to creedal commitment ultimately define rationality in terms of group identity- identity with the group that believes such-and-such. And this consensus approach to rationality is, I think, the very anti-thesis to the rational tradition. The contemporary concern with commibnent can be seen as an enlightened albeit fallacious move in response to the Fregean Dilemma. Frege, as we have already seen, maintained a sharp and intuitive distinction between a statement's being-true and its being-believed-to-be-true. According to Frege, someone's belief that a statement is true no more entails that statement's truth than a statement's truth entails that someone believes it. For this reason, Frege maintained an equally sharp distinction between knowledge and belief. Knowledge may be a species of belief, but it demands a stronger justification than belief alone can ever supply.S9 Thus, - - - - - - - - - - - - - - - - - - - - - - - - -
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Frege maintained that the justification for knowledge must be extrapsychological. But just because Frege also believed that such justification is possible, he argued that it is possible for humans to directly apprehend truth through extra-psychological means. Now psychologistic philosophers, like Hwne and Mill, denied that extm-psychological apprehension of truth is humanly possible. But according to contemporary psychologistic philosophers, there is no psychologically neutral perspective from which humans can objectively view the world. And just because there is no psychologically neutral perspective from which humans can objectively view the world, contemporary psychologistic philosophers maintain that the sort of justification that Frege envisioned is impossible as well. Here, psychologistic philosophers collapse the traditional distinction between knowledge and belief. If knowledge differs from belief at all, it does so by its degree of conviction and not by its quality of justification. But having collapsed the traditional distinction between knowledge and belief, psychologistic philosophers also feel obliged to deny the intuitive distinction between a statement's being-true and its being-believed-tobe-true. They feel obliged to do this because they recognize (believe?) that any assertion that a statement is true ultimately reports a belief that that statement is true. Without access to extra-psychological justification, being-true is equated with being-believed-to-be-true, and the plurality of belief with a plurality of truth. Viewed from 'within the context of this debate, the move to commitment seems enlightened in that it denies human access to any psychologically neutral perspective (or infallible cognitive source) from which to assess the validity of cognitive claims. As Fish puts it: ...facts can only be known by persons, and persons are always situated in some institutional context; therefore facts are always context relative and do not have a form independent of the structure of interest within which they emerge into noticeability. It is not simply that supra-contextual facts are unavailable to us, but that the very notion of a supra-contextual fact makes no sense since something that had no relation to the concerns of a particular hwnan situation would not be a fact and therefore could not be known by a human agent What that something might be, God only knows.-
Fish's rhetoric is apt. For it is, on the anti-psychologistic view, as if God has a library in which he keeps an encyclopedia, a dictionary, and a bible. In these books God has inscribed the laws of science, the meanings of words, and the imperatives of ethics on a medium more durable than stone. Here, the aim of cognitive inquiry is to find the key to God's library. But here, Fish's move is to deny that God's library exists. Now it is just this denial of the existence of God's library that I consider fallacious. It may well be true that facts can be known only by persons and that persons are always situated in some institutional context. But it does not follow that facts are always context relative and do not have a form independent of the
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structure of interest within which they emerge into noticeability. Rather, the most that follows is that our knowledge of facts is always context-relative and interest-dependent. Simply put, it is not the notion of supra-contextual facts, but the notion of supra-contextual albeit human knowledge of such facts that is nonsensical. Here, Fish is right Exactly what such supra-contextual facts might be, God only knows. But contrary to Fish, God's library may very well exist And it may exist despite the 'fact' that the key to God's library is locked within the library itself. For despite this 'fact', the notion of supra-contextual facts does make sense. For our knowledge of such facts would bear a relation to particular human situations- if only we knew what God only knows! Still, the Epistemological Buddhism that I advocate is a pluralist position, and Fish believes that pluralism is incoherent. Fish, moreover, seems to believe this because it is psychologically impossible for a person to simultaneously believe in the truth of inconsistent statements. It is, moreover, in this context that Fish says that knowledge and conviction do not depend upon the existence of a neutral perspective from which to describe the world, but upon a commitment to the perspective from which one actually speaks. In so doing, Fish appeals to commitment to insure the possibility of knowledge and conviction. Now commitment and conviction are time-honored epistemological virtues. But they are also the virtues of the very epistemological tradition that Fish rejects, Le., they are the virtues of an anti-psychologistic tradition that maintains the possibility of an objective knowledge free from all perspectival ambiguity. Within this tradition, one acquired knowledge by giving objective and rational justification for a belief. And within this tradition, commitment and conviction were thought to follow as psychological consequences of believing that the justification that one had given for that belief was, indeed, objective and rational. Of course, the conviction and knowledge of which Fish speaks cannot require such objective and rational justification. So objective and rational justification is not, in Fish's view, a prerequisite for knowledge and conviction. But in lieu of such objective and rational justification, Fish says that it is one's commitment to a perspective that makes knowledge and conviction possible. For it is only given such commitment that one can maintain conviction that his 'knowledge' is true. But since Fish denies the possibility of objective and rational justification, it is difficult to see what this knowledge and conviction could amount to other than 'the psychological fact that one happens to believe that a particular proposition is true. For just this reason, claims to knowledge and conviction (as opposed to belief) decline, and should decline, as soon as one recognizes that the perspective from which he speaks is not the only perspective from which one can speak. For as soon as one denies the possibility of objective and rational justification, the possibility of a human knowledge qualitatively different from human belief collapses. One could, given this recognition, maintain his claim to knowledge and conviction by believing that the perspective from which he
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speaks is the justifIably correct perspective, the perspective from which he should, in some objectively justified sense, speak. But Fish does not believe this. And neither do I. Nevertheless, Fish does say that commitment to the perspective from which one speaks is something that one cannot possibly be without. And It is with this latter statement that I take issue. Fish, of course, is not alone in this position. Many contemporary philosophers fail to distinguish between belief and commitment. Others, aware that such a distinction is sometimes maintained, deny that one can properly be drawn. For these philosophers, having a belief, performing an action, or speaking from a perspective is tantamount to being committed to that belief, action, or perspective. This denial of a distinction between belief and commitment sometimes proceeds from the psychologistic tendency to extend one's creedal obligation from the particular statement that one believes to all of its logical consequences. Here, the simple belief that P is true incurs 'commitment' not only to P, but to the infinity of statements that can be deduced from P as well. But here, the confusion is not really between belief and commitment at all. Rather, it is between creedal commitment and logical commitment. In practice, our interest in the logical consequences of P lies"' with what one should believe (if he in fact believes that P) or with what one should not believe (if he in fact doubts one or more of the logical consequences of P). And it is, in practice, only because one can be logically 'committed' to a statement that he does not believe (let alone to one that he is committed to believe) that this exercise in drawing inferences has much point. But the denial of a distinction between belief and commitment is more often bolstered by an underlying allegiance to behaviorism. And it is, with this support, more difficult to combat. For the behaviorist strategy is to determine one's ~liefs from one's actions. And since 'the behaviorist recognizes no observable differences between performing an action and being committed to that action, he likewise recognizes no difference between believing that P is true and being (creedally) committed to P. I know of no logical argument that would rationally compel the committed behaviorist to recognize a real distinction between belief and commiunent. This, however, is not because arguments do not exist, but because the 'facts' to which such argwnents appeal cannot exist as facts within 'the behaviorist framework. To argue that behavior can be interpreted as action only with reference to intentions or that commitment to belief requires a mental act over and above the belief itself will not suffice. For it is just this existence of intentions and mental acts that the committed behaviorist is committed to deny. This, nonetheless, is precisely what I will suggest- with the hope of persuading those who believe in behaviorism, but are not yet quite committOO to it Is believing that P the same thing as being committed to P? What could that mean? The sense of tcommitment' most appropriate for this discussion is that of obligation, dedication, or resolution. It is the sense of 'commitment' in which one makes a promise (of one sort or another) to
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whatever it is that he commits himself. It is in this sense that we speak of the commitment of marriage, or of the commitment undertaken when one signs a contract Promises, of course, can be broken. But it would make no sense to speak: of breaking a promise unless it were possible to make one. And it would make no sense to speak of making a promise unless making a promise differed, in some way, from not making one. But here, what differentiates making a promise from not making one is nothing more nor less than the promising itself, i.e., it is nothing more nor less than the obligation one assumes and the resolution one makes to fulftll the intention of that promise. Still, there is nothing in one's overt behavior (save, perhaps, the linguistic behavior of saying 'I promise', though one may always make a promise to oneself) that marks a distinction between promising and not promising. Two people can behave in a way indistinguishable from that of married couples without ever undertaking the marriage commitment. And two parties can engage in the activity of give and take characteristic of contractural relationships without ever entering into a contract. Still, there is a difference between making a promise and not making one. This difference, however, lies not in one's overt behavior, but in his mental actions. It lies in the obligation that one assumes and the resolution that one makes to fulftll the intention of the promise. But what sort of promise can we make and what sort of obligation can we owe to a belief or a perspective? If we claim to be committed to a belief or perspective, what are we promising to do? What the marriage vows add to the conjugal behavior of two people is simply the promise or resolution not to alter that behavior. And the same holds true for any contractural relationship. For this reason commitments are undertaken primarily to add an element of security to the relationship in question. But this element of security amounts to nothing more nor less than the resolution one makes and the obligation one assumes to remain within it. Insofar as this is concerned, believing that P is true differs from the commitment to believe that P is true in that the latter, but not the former, involves the promise to continue to believe that P. Simply put, commitment to belief involves the resolution not to change one's mind in relation to that belief. As such, commitment to a belief incurs the obligation to defend that belief (if only privately) against all criticisms oc, at least, not to consider any such criticisms seriously. In this way, creedal commitment is analogous to the marriage commitment For in committing oneself to a belief, one in effect promises to love, honor, and obey that belief and to forsake all other beliefs in order to do so. Analogously, commitment to a foundational perspective involves a resolution to continue to view the world from that perspective. As such, it is tantamount to a promise not to shift one's perspective or change one's point of view. It seems clear to me that people actually do commit themselves to beliefs and perspectives in just this way. But it seems far less clear that such creedal commitment is an appropriate response to the loss of certainty.
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Having a belief is not a voluntary matter. One can no more decide to have a belief than one can decide not to see what his eyes show. Rather, we believe a statement because that statement seems true. In this way, believing that P is true and P seeming true are one and the same thing. But if belief is not a voluntary matter, then there can be no guarantee that what seems true today will continue to seem true tomorrow. At least, there can be no such guarantee so long as we continue to entertain what others believe as serious possibilities. For so long as we regard what others believe as serious possibilities, it is a serious possibility that what seems true to them will suddenly seem true to us. But it is just here that the element of decision becomes crucial. One cannot decide not to see what his eyes show. But one can decide to close his eyes, or tum them in a different direction so as not to allow his eyes to show what he dres not want to see. Analogously, one cannot decide not to believe what seems true. But one can decide not to consider any opposing beliefs as possibly true. One can do this either by deciding not to infonn oneself of such opposing beliefs or by prejudging all such beliefs as mistaken. Hence, if it is possible to commit oneself to a belief at all, it is only because one can, and does, decide not to entertain any opposing beliefs as serious possibilities. But in this way, creedal commitment has the effect of stifling cognitive growth. Creedal commitment stifles cognitive growth by requiring that one close his mind to the consideration of opposing beliefs or perspectives as serious possibilities. In closing his mind to the consideration of opposing beliefs as serious possibilities, one may achieve a sort of confidence and secwity. He can 'rest assured' in subjective certainty. It is, however, just this 'rest' which precludes the possibility of growth. But Fish believes that creedal commitment is not only an appropriate response to objective uncertainty, but a necessary one to insure knowledge and conviction. For if it is truly impossible to justify any foundational perspective in a non-circular way, then it is only creedal commitment that allows one to rest assured in his conviction that a given statement is true. But even were truth purely dependent upon one's perspective, such commitment and conviction would seem to preclude the cognitive growth that occurs through an appreciation of the richness and strength of opposing perspectives- an appreciation that only occurs when one entertains such perspectives as serious possibilities. Were truth truly dependent upon perspective, then one might rather strive to apprehend as much truth as possible by viewing the world from as many perspectives as possible. Now pluralists like myself believe that it is impossible to objectively justify any foundational belief as true. But we do not thereby believe that objective truth does not exist. Nor do we believe that a statement's being-true is equivalent to, or entailed by, someone's belief that that statement is true. Again, we believe that God's library may very well exist And we believe this despite our denial that any person ever has access to a neutral perspective from which to read what might be written there, Le., from which a statement could be objectively justified as true. Moreover, we do
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not only believe that objective truth very possibly exists, we also believe that the discovery of objective truth should be the regulative ideal for all rational inquiry. And we believe this precisely because we believe that it is possible to be right or wrong in our belief that a statement is bUe or false even in the absence of an objective justification that that statement is true or false. While we are, in truth, not committed to this or any other belief, we are committed to the continual and relentless search for truth (despite the fact that we also acknowledge the possibility (but do not believe) that bUth does not exist!) And in the face of our denial of the possibility of objective justification, this commitment to the search for truth also commits us to the activity of considering all beliefs and foundational perspectives as if they were true. It is this commitment, rather than the commitment to any belief, that differentiates Fish's position from my own. But Fish considers pluralism, and its attendant 'critical generosity', to be incoherent. Hence, Fish writes that tt •••generosity is at once the cornerstone of the pluralist ideology and the source of its confusion tt: A pluralist wants simultaneously to make room for everyone's point of view here the motto might be Wayne Booth's commandment to pluralists, "Give your neighbor's monism a fair shake" - and to insist nevertheless that one point of view is superior to all others.61
But the consistent pluralist does give his neighbor's monism a fair shake. He gives his neighbor's monism a fair shake by admitting that monism is self-consistent and can account for all the pertinent data. In short, he acknowledges that monism is possibly true. But far from insisting that his point of view is superior to all others, the consistent pluralist simply maintains that his neighbor's monism is his neighbor's, and not his own, point of view. In so doing, the consistent pluralist pronounces his pluralism as his own point of view and claims no greater authority for it than that. The consistent pluralist does, of course, assert his belief that the monist's position is false. But it would be strange to interpret this assertion as indicating that pluralism is inconsistent or that the pluralist considers his own point of view superior to all others. For all that such superiority would amoWlt to is that the plura1ist believes that pluralism is true. And what else would one expect the consistent pluralist to believe? But what the consistent pluralist does not believe, and what his pluralism is at pains to deny, is that his position has any greater justification or authority than the monist's. This, however, is exactly what distinguishes the consistent pluralist from the monist For while the consistent pluralist and the monist both believe that their respective positions are bUe, the monist asserts that his position admits of some stronger justification than all others. And it is this belief that his position is justified as true, as opposed to the belief that it is merely true, that permits the monist to believe that his point of view is superior to all others.
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Here, the Epistemological Buddhism that I advocate contains elements of both the psychologistic and anti-psychologistic pictures outlined above. First of all, I agree with the psychologistic philosophers that there is no psychologically neutral perspective from which humans can directly apprehend what is true. And since I agree that such direct apprehension of truth is impossible, I believe 'that the sort of extra-psychological justification that philosophers like Descartes and Frege envisioned is impossible as well. H what we claim to know differs from what we believe, it does so by the degree of our conviction and not by the quality of its justification. But I also think that it is a dangerous practice to confuse what we claim to know with what is justiftably true-- even if such 'justification' is acknowledged to come only by psychological commitment.62 When it comes to knowledge, even knowledge of mathematics ,and logic, the most that we ever have to go on in any cognitve claim is our own best guess. And so long as we remain open to 'the best guesses of others, there is nothing in our own best guess to be particularly embarrassed about But this does not mean that we should claim that our own best guess is anything more than it actually is. In particular, we should always remember that our own best guess might be mistaken. And just because our own best guess might be mistaken, I maintain 'that being true is utterly distinct from being believed to be true. For these reasons, I maintain that commitment to belief is an inappropriate response to the loss of justification. The certainty of belief that results from such commitment or conviction might allow one to rest assured in those beliefs. But if one is certain of or assured in his beliefs, then he lacks the primary motivation for considering the beliefs of others as serious possibilities. Simply put, he lacks the recognition that his own beliefs might be mistaken. Again, I do not wish to be misunderstood. It may indeed be true that the ability to view an object presupposes that the viewer occupies some perspective (taken in its broadest sense). And to that extent, it seems undeniable that the perspective that one occupies at any given moment is his own, i.e., it is the perspective that he occupies. If this is all that Fish means to say, then I readily agree- one can never be without his own perspective. But it does not follow from this that a viewer needs to always occupy the same perspective or, even less, that he need be committed to the perspective that he happens at the moment to occupy. Consider, for example, Wittgenstein's famous figme of the duck-rabbit From one perspective, this figure appears as a duck, from another as a rabbit. And it is always possible that, from some third perspective, the figure appears as something else- perhaps as lines on a sheet of paper with no apparent content Seeing this figure as a duck or as a rabbit requires that one occupies a certain perspective. And some people may be so 'committed' to their perspective that they are only able to see this figure as a duck and others may be so 'committed' to their perspective that 'they are only able to see the figure as a rabbit. Now I readily acknowledge that it may be psychologically impossible for a viewer to see this figure simultaneously as
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both duck and rabbit Still, as soon as one has made the perspectival leap that permits him to see the figure now as duck, now as rabbit, the question of commitment seems ridiculous. I can well imagine that someone who has made this perspectival leap might 'commit' himself to seeing Wittgenstein's figure always as a mbbit But it is harder to imagine why he would do so. Well, that's not exactly true. I can understand that someone might make such a 'commitment' if, for example, he found the ambiguity in Wittgenstein's figure psychologically disturbing. But the suffocation that results from sticking one's head that far in the sand is, from my perspective, more disturbing still. But if the consistent pluralist does not believe that his own position has any greater justification than any other, then why does he bother to assert his position at all? And why should he bother to engage in rational criticism of the views of others? Here, part of the pluralist's motivation derives from the 'fact' that he believes that his own position is true and hopes to persuade others to adopt it. Again, there is no contradiction here. For the consistent pluralist believes not that no position is true, but that no position can be objectively justified as true. Nor is the pluralist's position an unassailable article of faith. For the simplest way to convince a pluralist that he is wrong in his pluralism is to produce a statement that is objectively justified as true! But another part of the pluralist's motivation derives from the 'facts' that he wants to understand the world around him and that included in what he wants to understand are the various ways in which others understand it This motivation, moreover, goes well beyond mere intellectual curiosity. Since the consistent pluralist commits himself to no belief, he is always able to consider the views of others as serious possibilities. As such, he is always able to alter his own beliefs without trauma when any such possibility suddenly appears more serious than his own. And here, the pluralist's attempt to view the world from the perspectives of those whose beliefs differ from his own functions as an important frrst step toward the achievement of such an understanding. Such adherence lnay well consititute critical generosity. But if it does, then we must also recognize that the critic's generosity extends as much to himself as it does to those he criticizes. For in his exercise of such critical generosity, the critic takes the frrst step toward increasing his own understanding and with it increases the possibilities for his own cognitive growth. And it is, in this way, that critical generosity promotes cognitive growth. I realize that my vision of rationality may be unsettling for some. For the decision to regard the opposing beliefs of others as serious possibilities will decidedly not issue in the sort of commitment and conviction that would allow one to 'rest assured' in his beliefs. But if Epistemological Buddhism entails a loss of confidence, it need not result in despair. For in the Epistemological Buddhist's view, the security 'that results from such commibnent and conviction is neither a virtue nor an aid in the search for bUlb.
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ENDNOTES 1. It is important to emphasize that the opponents of psychologism generally understood 'psychology' to refer to an empirical science. This explains why an anti-psychologist like Frege could appeal to self-evidence in his appraisal of axioms. But it also lDulerscores the fact that psychologism is a cousin to other attempts to 'naturalize' epistemology, e.g., sociologism, biologism, etc. 2. Frege's critique of psychologism is scattered throughout his writings. The most important sources are: Gottlob Frege, The Basic Laws of Arithmetic, ed. and trans. Montgomery Furth (Los Angeles: University of Califomi~ 1967), especially Frege's "Introduction"; Gottlob Frege, The Foundations of Arithmetic, trans. IL. Austin (Evanston: Northwestern University, 1968); Gottlob Frege, "Review of Dr. E. Russerl's Philosophy of Arithetic, trans. E. K1ug~ MIND LXXXI (July, 1972); and Gottlob Freg~ ''The Thought: A Logical Inquiry," trans. A.M. and Marcelle Quinton, MIND LXV (1956). For further discussion of the epistemological nature of Frege's critique of psychologism, see: M.A. Nottumo, Objectivity, Rationality, and the Third Realm (Boston: Martinus Nijhoff, 1985). 3. Isaac Levi, I believe, has something similar in mind when he diagnoses someone as suffering from the "curse of Frege" if he "submits to the polarization and chooses either in favor of method and against psychologism, sociologism, and historicism or chooses against method and in favor of psycho10gism, sociologism, and historicism." (Issac Levi, The Enterprise of Knowledge (Cambridge: MIT, 1980), p. 428) 4. This preference for objective knowledge undoubtedly accounts for the prevalent fear of psychologism, a fear that has made "psychologism" a philosophical term of ill-repute. As Brentano put it, "Psychologism [is a word which] when it is spoken many a pious philosopher, ... crosses himself as though the devil himself were in it." (Franz Brentano, Psychology from an Empirical Standpoint, eel. Linda L. McAlister, trans. Antos C. Rancurello, D.B. Terrel, and Linda L. McAlister (New York: Humanities, 1973), p. 306. Here the point to be made is that philosophers, by and large, do not claim to be psychologistic or to be proponents of psychologisrn; they are accused of it 5. For further discussion, see: No ttumo, Objectivity, Rationality, and the Third Realm, especially chapter 6. 6. Frege, The Foundations of Arithmetic, p. 4e. 7. See: M.A. Nottumo, "Critical Generosity or Cognitive Growth?" METAPIDLOSOPHY (1989); and Nottumo, Objectivity, Rationality, and the Third Realm, chapter 11. 8. See: Ibid., chapter 3. 9. Frege, The Foundations of Arithmetic, p. 4e. 10. The argument is simple. The validity of a deductive argument can be determined only contingent upon the condition that each of its signs retain the same meaning throughout the argwnent Freg~ in fact, insists upon this condition in introducing the signs to be used in his conceptual notation. See: Gottlob Frege, Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought, in Frege and GOdeI, 00. Jean van Heijenoort (Cambridge: Harvard University, 1970), p. 11. But it is difficult to see how the meanings of signs could be the same unless meanings were immutable objects. 11. I am indebted to Tom Settle for helping me to appreciate the importance of subjective justification: it is at the heart of every malpractice suit 12. Karl Popper is, to the best of my knowledge, the fust to have noticed these two different justified true belief theories of knowledge. See: Karl R. Popper,
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Objective Knowledge (Oxford: Oxford University, 1972), chapters 3, 4, especially pp. 108-109.
13. This conflation is, I think, what is ultimately at the root of the so-called. 'Gettier paradoxes'. See: Edmund Gettier, "Is Justified True Belief Knowledge?" ANALYSIS, 23 (1963). 14. Even Frege seemed to believe this, as is evident from this criticism that without a general principle of induction, "induction becomes nothing more than a psychological phenomenon, a procedure which induces men to believe in the truth of a proposition, withollJ affording the slightest justification for so believing." (Frege, The Foundations of Arithmetic, p. 4e, my italics) 15. Edmund Husserl, Logical Investigations, 2 vols., trans. IN. Findlay (New York: Humanities, 1970), p. 111. 16. Assuming, of course, that the objectivist intends to avoid scepticism. 17. Rene Descartes, Discourse on Method, trans. Donald A. Cress (Cambridge: Hackett, 1980), p. 35. 18. Rene Descartes, Meditations on First Philosophy, translated by Donald A. Cress (Cambridge: Hackett, 1980), p. 45. 19. See: Ibid., p. 47. There is a double irony here. On the one hand, Descartes seems to suggest that the atheists, who refuse to submit to the authority of the Holy Scriptures, will nonetheless submit to the authority of the theologians at the Sorbonne. On the other hand, the attempt to prove the existence of God by natural reason would itself seem to preclude any appeal to authority. 20. Ibid., p. 45. 21. Ibid. 22. Indeed, the circularity of Descartes' proof is so well-known that it is often referred to as 'The Cartesian Circle'. 23. These, however, are only two of the more blatant 'ironies' to be found in the Meditations. Descartes' arguments for the existence of God are replete with apparent paradoxes and logical tensions. There is, first and foremost, his self-gratuitous use of the 'light of nature', a use which seems inexplicable in light of his resolution to doubt whatever he can doubt without contradiction. Descartes, of course, drew a sharp distinction between nature and the light of nature: When I say in this meditation that I have been taught so by nature, I \D1derstand only that I am driven by a spontaneous impulse to believing this position. and not that some light of nature shows me it is true. These two positions are at considerable odds with one another. For whatever this light of nature shows me - for example, that from the fact that I doubt, it follows that I am and so on cannot in any way be doubtful, because there can be no other faculty in which I may trust as much as the light of nature that could teach which of these positions are not true. (Ibid., p. 70) But even were we to assume that the light of nature exists and is the most trustworthy of Descartes' faculties, being most trustworthy and being in no way doubtful are two different things. Still, I call Descartes' use of the light of nature ,self-gratuitous' primarily because Descartes so often appeals to it in order to legitimate his acceptance of ideas which he needs to prove the existence of God, but which would otherwise seem to be dubitable, e.g., that the cause of an idea must have at least as much formal reality as the idea has objective reality. See: Ibid., p. 71. But aside from this, there is an obvious tension between his claims: (1) that his idea of infInite Substance is "the most clear and distinct of all ideas" (Ibid., p. 74) and (2) that "the nature of the infinite is such that it is not comprehended by me,
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who am fmite." (Ibid) Descartes says that these two claims are "not inconsistent". But it is difficult to see why they are not. There is, moreover, another tension in his argument that his idea of the infmite is not compounded from his ideas of negation and the finite. Descartes says that this cannot be the case since he could not know that he is finite if he did not have the idea of something more perfect. See: Ibid. But being infinite and being more perfect are obviously two different things. Finally, there is a disturbing disanalogy in his reasoning concerning the respective causes of his ideas of God and material objects. On the one hand, Descartes maintains that he cannot be the cause of his idea of Infinite Substance (God), because he is not infmite. See: Ibid. (Were Descartes infinite, then he would have enough formal reality to cause the existence of his idea of infinite substance, and would, as a consequence, not need to conclude that some infinite substance outside himself must exist in order to cause the existence of that idea.) On the other han~ he maintains that he may well be the cause of his ideas of material objects, despite the fact fact that he is not material. Here, Descartes claims that it is possible for him to be the emi1ll!nt cause of his ideas of material substances despite the fact that he is not material, because being material is only a mode of a substance, and Descartes too is a substance. See: Ibid., pp. 73-74. So one wonders why being infmite does not count as a mode of a substance. This disanalogy is significant. Descartes' proof of the existence of God would be UIDlecessary, could he be independently certain that material objects exist And Descartes could be independently certain that material material objects exist, would he not regard himself as a possible cause of 'their ideas. 24. One need only recall Giordano Bruno, who was burnt at the stake in 1600 because of his 'heretical' philosophical views. 25. See: Ibid., p. vii. 26. See: Ibid. 27. Ibid., p. 46. 28. Descartes, Meditalions on First Philosophy, p. 46. 29. It is, of course, only the possibility of an Evil Demon that allows Descartes to doubt the obvious truths of mathematics and logic. 30. Of course, Descartes' resolution to regard a statement as false until proven true is neither a positive nor a mature doctrine of Cartesian philosophy. It is, rather, a heuristic principle that Descartes introduces toward the end of the "First Meditation" in order to facilitate his doubt by insming that there be, as he puts it, an "equal weight of }X'ejudice on both sides." (Ibid., p. 60) Thus understood, it is intended primarily to guard against Descartes' habit of assenting to and believing in those "long-standing opinions" that ''keep coming back again and again, almost against [his] will." (Ibid) Descartes' positive and mature doctrine (assuming, of course, that Descartes intended the Meditations to be interpreted literally) is announced in the 'Fourth Meditation', where Descartes suggests not that we should regard a statement as false until it is proven true, but that we should suspend our judgment on a statement entirely, avoiding all "probable guesses" until we have a proof one way or the other: Although }X'obable guesses might lead me in one direction, all it takes to move me to assent to the very opposite is the knowledge that they are merely guesswork, not certain and indubitable proofs. These last few days I have ample experience of this point, since everything that I had once believed to be as true as it possibly could be, I have now presumed to be utterly false, for the sole reason that I noticed that I could one way or another raise doubts about it
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But if I hold off from making a judgment when I do not perceive with sufficient clarity and distinctness what is in fact true, I clearly would be acting properly and would not be deceived. But were I to make an assertion or a denial, then I would not be using my freedom properly. If I tum in the direction that happens to be false, I am plainly deceived. But if I should embrace either alternative, and in so doing happen upon the truth by accident, I would still not be without fault, for it is manifest by the light of nature that the intellect's perception must always precede the will's being determined. (Ibid., p. 82) But Descartes' positive and mature doctrine is, from our perspective, just as problematic as his heuristic principle. 31. Rene David and Henry P. de Vries, The French Legal System (New York: Oceana, 1958), p. 76-77. 32. Thus, Stephen in his History of the Criminal Law writes that: "The presumption of irmocence is otherwise stated by saying the prisoner is entitled to the benefit of every reasonable doubt" (Francis A. Coffin, et al., Plffs. in Err., v. United States, U.S. REPORTS, Vol. 39 (4 March 1895) p. 493) The presumption of innocence, however, is more properly regarded as part of the evidence that an accused is innocent. And the apparently widespread tendency to identify the two in effect conflates an instrument of proof with the stale of mind that mayor may not result in an individual from that proof. For further discussion, see: Ibid. pp. 432-464. 33. Descartes, Meditalions on First Philosophy, p. 57. 34. This, I take it, allows Descartes to doubt the apparent truths of physics. 35. Ibid., p. 59. 36. On the contrary, Descartes supposes the existence of an evil genius, in the context of 'the "First Meditation," precisely because his long-standing belief in the existence of a supremely good God is so strong that it is difficult for him to doubt. See: Ibid., p. 60. 37. Ibid. 38. Ibid. 39. Aristotle put the point succinctly in: Aristotle, Analytica posteriora, in Richard McKeon, ed., The Basic Works of Aristotle (New York: Random House, 1941) p. 110: All insttuction given or received by way of argument proceeds from pre-existent knowledge. 40. David Hume, An Enquiry Concerning Human Understanding, 00. Eric Steinberg (Indianapolis: Hackett, 1977), p. 30. This, incidentally, is a beautiful statement of the psychologistic argument: In a word, if we proceed not upon some fact, present to the memory or senses, OlD' reasonings would be merely hypothetical; and however the particular links might be connected with each other, the whole chain of inferences would have nothing to support it, nor could we ever, by its means, arrive at the knowledge of any real existence. If I ask. why you believe any particular matter of fact, which you relate, you must tell me some reason; and this reason will be some other fact, connected with it But as you cannot proceed after this manner, in in[mitum, you must at last terminate in some fact, which is present to your memory or senses; or must allow that your belief is entirely without fomdation. 41. Gotdob Frege, The FOIIJIdoJions of Arithmetic, p. 4e. 42. See: Goulob Frege, "Somees of Knowledge of Mathematics and the mathematical natural Sciences," in Gottlob Frege, PosthumolU Writings, trans. Peter Long and Roger White (Chicago: The University of Chicago, 1979), pp. 266-274. 43. Frege, The FOIIJIdoJions of Arithmetic, p. 4e.
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44. Frege, Posthumous Writings; p. 205. 45. See, for example: Susan Haack, Deviant Logic (New York: Cambridge University, 1974), p. 29. 46. For further discussion of these }X>ints, see: Nottumo, Objectivity, Rationality, and the Third Realm. 47. See: Frege, '7he Thought: A Logical Inquiry." 48. Of course, there is a sense of 'exists' in which a cure for cancer does not exist- it is the sense in which such a cure does not exist because we do not know of one. But we do not need induction for that 49. Frege, The Basic Laws of Arithmetic, p. 14. 50. See: Nottumo, Objectivity, Rationality, and the Third Realm. 51. See: Charles S. Peirce, ''The Fixation of Belief," in Justus Buchler, ed., Philosophical Writings of Peirce (New York: Dover, 1955). 52. Nottumo, Objectivity, Rationality, and the Third Realm, p. 214. 53. Tom Settle, "A Complex Theory of Truth," in M.A. Notturno, ed., Perspectives on Psychologism (Leiden: EJ. Brill, 1989). 54. Nottumo, Objectivity, Rationality, and tlu! Third Realm, p. 195. 55. See: Settle, "A Complex Theory of Truth." 56. Peirce, ''The Fixation of Belief," p. 12. 57. Thomas S. Kuhn, The Structure of ScientifIC Revolutions (Chicago: University of Chicago, 1962), p. 11. 58. Stanley Fish, ''Interpretation and the Pluralist Vision," TEXAS lAW REVIEW, Vol. 60, No.3 (March, 1982), p. 501. 59. Frege insists that being true is distinct from being believed to be true. As we have seen, the act of believing is different from the object that is believed. But this, of course, is not all that Frege's slogan is meant to convey. It is also intended to say that mere belief in the truth of a pro}X>sition does not consititute a justification of that proposition, that one may believe that a statement is true and be mistaken in that belief. There are, however, difficulties with this fonnulation. It is easy to give examples of something that is false, but is, nonetheless, believed by someone to be true. The problem, however, is that every example of something that is true is, simultaneously, an example of something that we believe to be true. For how else could we propose it as an example of something that is true? 60. Fish, ''Interpretation and the Pluralist Vision," p. 497. 61. Ibid., p. 501. 62. No matter how circwnspect one is in acknowledging that his psychologistically 'justified' belief is tentative and subject to revision, those that follow are likely to be less circumspect, will tend to ignore these disclaimers, and, with time, regard the belief as true come what may.
SOCIOLOGISM JOHN HUND
I. Introduction 'Sociologism' is one of those ugly neologisms that may eventually fmd its way into the pages of the Q.E.D. The reason is that the word names a concept that is fast becoming pivotal in Anglo-American analytical philosophy. The conception I am referring to is the result of at least two streams in contemporary philosophy that seem to be coming together towards something that ' sociologism' seems best to name. What these two streams are to be called presents something of a difficulty. Let us provisionally call them 'anti-psychologism' and 'social realism', or what may be called 'social Platonism' in the philosophy of mathematics. In this note I propose to discuss two radically different versions of sociologism that are taking hold of, or influencing, philosophy today. One is an empiricist version that I attribute to Wittgenstein and the Wittgensteinians, but especially to Bloor. 1 The other is a social realist version that I attribute to such thinkers as Popper, but especially to Durkheim. In order to set the ground for my discussion I will have to describe and name two versions of psychologism that empiricist philosophers have had a habit of falling into: the fIrst is the attempt to reduce abstract, social or cultural phenomena - of varying degrees of specificity, from the most determinate to the most diffuse - to mental phenomena found in the minds of concrete individuals. The second psychologism, which has often been a reaction against the fast, is the attempt to reduce abstract cultural phenomena to patterns of behavior, often sanctioning behavior, that can be detected in the visible actions of individuals that an external observer could record. I will call these two psychologisms 'mentalism-psychologism' and 'behaviorism-psychologism' to distinguish them, respectively, from those two slippery impostors, mentalism and behaviorism. What is of greatest interest is not what distinguishes these two species of psychologism, but what it is they have in common. What they seem to have in common is an empiricist foundation that generates a nominalist impulse to reduce abstract phenomena2 to things (mental an
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The refusal to accept or to see that abstract phenomena have a reality sui generis is often based on the supposed obscwity of this claim itself. Wittgenstein is the best-known modem example that can be cited of an empiricist philosopher who regards all such talk of abstract phenomena as a mistake, or as mystif1C31ion or obfuscation. That was his very foundation, a foundation that is wholly endorsed by almost all of analytical philosophy today. The deep confusion that this view promotes, however, is only too evident from Wittgenstein's perplexed and cryptic jottings, and from the crack-up, after more than three decades of commentary, of the paradigm his later philosophy established. Today there are thousands of commentators who have published books and articles on Wittgenstein's work," and there is nothing but confusion at the top. So much has been written attempting to piece Wittgenstein's ideas together, or tear them to pieces, by the method of textual juxtaposition and commentary, that further attempts in this line seem unpromising. What seems needed is an approach that stands back from the rest to obtain an overall picture that can determine in general just what sort of method was being followed. While this may sound preposterous, it is just what has been attempted by one of Wittgenstein's new 'sociological' commentators, David Bloor. Bloor's goal has been to locate Wittgenstein's later philosophy within a tradition: the sociological tradition of Emile Durkheim. The so-called 'marriage' of Wittgenstein and Durkheim has been widely taken for gnmted lately, but as I shall argue, the marriage is a nullity: it never happened. According to Bloor, Wittgenstein thoroughly 'sociologized' philosophy by construing meaning and knowledge as social accomplishments. Bloor classifies Wittgenstein and Durkheim as writers who adopt what be calls a 'sociological' approach to meaning and necessity. Both thinkers, he claims, regarded logical necessity and conceptual constraint as categories of moral (or social) obligation. By so doing, they relativized objectivity and the foundations of knowledge by reducing them to nothing more substantial than ephemeral social constructions which can (and do) vary across cultures and over time. But, as any familiarity with Durkheim will show, many of these constructions are not arbitrary at all. Some of them, rather, can be said to be constitutive of humanity itself. Some are such that they could not be other than they are, and what we know them to be. Durkheim had a deeper insight into the nature of the social and the social foundations of knowledge than Bloor is willing to admit or perhaps able to see, an insight that Wittgenstein himself never caught hold of. The truth of the matter is that Durkheim's theory of the social is radically at odds with that of Wittgenstein's. Bloor's attempt to locate Wittgenstein's later philosophy within the sociological tradition of Durkheim is a failure, but it is an instructive failure which points the way to a better understanding of what the two sociologisms of Wittgenstein and Durkheim really are. This is important because it allows us to see just what Wittgenstein's sociologism amoWlts to, and why it cannot be sustained.
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II. Rule Anti-realism The starting point for this venture is fIXed by a radical interpretation of Wittgenstein's later philosophy that was given in 1961 by Joseph L. Cowan in an article that came in for some sharp criticism and even ridicule at the time, but has since been buried alive under the avalanche of juxtaposition commentaries that has ensued ever since. In Cowan's article, the claim is made that, for Wittgenstein, "there is no such thing as a rule."S Cowan went on to elaborate upon this remarkable claim: "there is no such thing as (or state or condition of) understanding a rule, or knowing a rule, or meaning a rule. There is no such thing as behavior guided by, or even according to, a rule."' I believe that Cowan's interpretation is quite right and that it is a fonn of blindness on the part of most contemporary commentators that prevents them from seeing that this is so. This blindness, which also afflicted Wittgenstein, prevents them from seeing that rules, whatever else they may be, are also, in part at least, abstract phenomena that cannot be reduced (without remainder) to ideas in the minds of individuals nor to actions or patterns of behavior that such individuals may display. As I will attempt to indicate below, it is precisely this blindness that has bedeviled so much of contemporary thinking about Wittgenstein's later philosophy. First there are those who have accepted Wittgenstein's role anti-realism. These writers have been led to the most absurd conclusions, such as that language use is not necessarily governed by rules. Cavell was the frrst to make this claim: he argued that, for Wittgenstein, "everyday language does not, in fact or in essence, depend 00..•8 structure and conception of roles, and yet that..absence of such a structure in no way impairs its functioning,"' and went on to endorse this view and to accept it as a liberation in thought. Then there are those writers who have not accepted, or at least have not explicitly accepted, Wittgenstein's role anti-realism. These writers have been led into the most tortuous and inconclusive attempts ever to explain what 'following' a role might amount to, or what behavior 'in accordance with a rule' might be. Part of the problem has been that no clear conception of a rule has emerged in the context of these Wittgensteinian problems. We might therefore ask: what did Wittgenstein mean by 'rule'? What emerges is that he made no distinction at all between rules and habits, or custom, and that he defmed rules in terms of habits. This comes out most clearly when considering his two-pronged theory of meaning. The frrst prong of this theory has been widely remarked upon and seems generally well-understood. It amounts to the contention, which has also been attributed (rightly) to Frege, Durkheim, and Popper, among others, that meanings cannot be identified with mental states or events in the minds of individuals. Bloor has claimed that this approach to meaning "fits snugly into the Durkheimian tradition,"8 but this betrays a misunderstanding of Durkheim that is most likely a result of the 'blindness' I mentioned above. It is true that both Wittgenstein and Durkheim rejected the view that meanings are mental, but
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while Wittgenstein adopted a form of behaviorism-psychologism, Durkheim adopted a theory of abstract collective respesentations as part of his own theory of rules. For Wittgenstein, we "strike rock bottom" when we come down to regular habitual behavior. But for Durkheim, such behavior gives us evidence for the existence of the abstract, internal dimension of rules, a dimension that is entirely missing from Wittgenstein's theory of rules-as-habits. This brings us to the second prong of Wittgenstein's theory of meaning. Wittgenstein could not identify meanings with mental phenomena because he realized that meanings were public and mental events and states were private, so the next step was to identify meanings with social phenomena, which he did regard as 'public' or external to individuals. Wittgenstein realized that without such a public or external criterion for determining, and teaching, the correct use of signs, we should have no recourse but to private languages, which he rightly regarded as impossibilities.' The second prong of his theory of meaning was the identification of this public criterion with publicly observable behavior which an observer could record. This amounted to the identification of rules with habits and comes down to a fonn of behaviorism-psychologism. Thus, his sociologism is a form of psychologism and a rejection of abstract phenomena. Curiously, Wittgenstein's theory resembles that of the jurist John Austin. Austin was not interested in meaning, but in the 'objectivity' of obligations. He recognized that binding obligations could not be reduced to subjective mental or psychological elements. Having seen the general irrelevance of a person's feelings, beliefs and wishes to the question of whether he or she was objectively under an obligation, Austin attempted to defme obligation not in terms of these subjective elements, but in terms of the objective chances or likelihood that certain officials would act in certain ways in cases of disobedience. Wittgenstein was searching for objective grounds for the possibility of human speech and communication. These grounds he found in regular usage, which was to be the criterion for correct usage. Both Austin and Wittgenstein identified rules, in other words, with what people do 'as a rule'. But these behavioristic modes of analysis obscure the fact that where rules exist, deviations from them are not merely grounds for a prediction that hostile reactions will follow, but are also a reason and a justification for such reactions. From the internal point of view of group members, rules are used as guides to social life and as the basis of claims, demands, admissions, criticism and punishment. Such rules give them reasons for behaving in one way mther than another. This, basically, has been HL.A. Hart's criticism of Austin. Indeed, the main thrust of his critique of Austin's theory of law as the command of the sovereign has been that legal obligation cannot be accounted for in terms of the simple elements of commands, habitual behavior, and sanctions- what is required is the concept of a rule, a concept that is entirely missing from both Austin's and Wittgenstein's analysis of the grounds of objective normativity.
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The core of Hart's general theory of rules is well-known: it is that a social rule has an 'internal' aspect in addition to an 'external' aspect which it shares with a mere social habit and which consists in "regular uniform behavior which an observor could record"10 Hart is quick to point out that this internal aspect of rules is sometimes misrepresented as a mere matter of feelings, but he rejects this form of psychologism. Such feelings, he says, are neither necessary nor sufficient for the existence of binding rules. What then is necessary? According to Hart, what is necessary is a "critical reflective attitude to certain patterns of behavior as a common standard ttll This language must be paid close attention to. These words were not chosen randomly or haphazardly in 'the heat of confusion, but fonn the basis of a very careful theory of normative obligation. This theory of normative obligation is a social theory of obligation, like Durheim's, and applies with equal measure to conceptual constraint and logical necessity as it does to moral and legal obligation. This can be appreciated by examining its formal features: A. External Aspect of Rules: "regular lDlifonn behavior which an observour could record"; B. Internal Aspect of Rules: (i) a "critical reflective attitude" to certain (il) "patterns of behavior" as a (iii) "common standard."
There is a radical difference between this dual conception of rules and Wittgenstein's conception of rules-as-habits. Wittgenstein's conception eliminates completely any reference to the internal aspect of rules. Notice that the third element of the internal aspect, B(iii), is abstract and apparently social in character. The attitudinal element, B(i), is mental or psychological, but notice that the object of the attitude itself is something abstract, namely standards shared by the group, and this element cannot be reduced to elements found in the mind, such as thoughts, feelings, or beliefs. This constitutes a departure from the justified true belief theory of knowledge, a theory which ultimately loqites knowledge in the mind of the believer. Hart's is a theory, like Popper's, of 'objective knowledge'.12 The common or shared standards used by the group to evaluate knowledge claims, or claims that an individual's case falls under a rule, or that someone is under an obligation, are abstracted by individuals from actual "patterns of behavior," B(ii), which amount to the regular uniform behavior that constitutes the external aspect of rules. It must be noted, however, that these patterns are not merely abstracted in idiosyncratic ways by individuals, but are, as Gellner has noted, "really there,"13 as objects to be learnt and taught and which are independent of any individual perceptions or representations of them. In other words, they are external to individuals. Where rules exist, deviations from these patterns are generally regarded as lapses or faults open to criticism. Where there are such rules, not only is criticism in fact made, but deviation from the standard imposed by the abstract category is
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generally accepted as a good reason for making it Now it must be admitted that the external aspect of rules can sometimes be difficult to distinguish from mere habitual behavior. 14 But there is a critical difference in principle between the external aspect of roles and mere habits: the external aspect of rules has something standing 'behind' it, as it were, which a mere social habit does not. What it has behind it is its collective representation as a category of behavior to be. recognized - learnt and taught - and followed by members of the group. It is precisely this element that Wittgenstein's analysis leaves out of the picture, 'the element that some commentators have loosely referred to as 'the normative'. A mere social habit or practice, taken by itself, cannot provide the external or public check that Wittgenstein sought in vain as the objective ground of meaning and knowledge, including mathematical knowledge. This is true for one very important reason: if a rule has no internal aspect, as Wittgenstein imagined. then there can be nothing to measure actual behavior against, and so no criterion for the correct application of critical behavior in cases of putative deviation from the nonnal course. Overt sanctioning behavior constitutes one part of the external aspect of rules. It is a necessary condition for the existence of binding rules in the sense that if there were no sanctioning behavior, then there could be no rules- for we should then have no way of learning and teaching the abstract categories of behavior they impose and of which, in part, they consist In one sense, rules are created by the actual critical behavior of the group, which is, after all, a fonn of observable behavior. But it would be a mistake to suppose from this, an Wittgenstein appears to suppose, that the public response is itself a sufficient condition for the existence of binding rules and objective nonnative constraint. By adopting what might be called an 'outsiders' perspective of rules,15 Wittgenstein left out of his account of the basis of group life the way members view their own regular (and irregular) behavior.. By doing this, it might have seemed plausible (but was in fact false) to suppose that the critical response of the community was a sufficient condition for the existence of roles. The mistake is the result of a failure to acknowledge the existence of a pre-existing system of abstract categories, or concepts, and 10 distinguish this from the way it is brought into existence Of, better, from the conditions of its existence. I cannot say if this error was the error that allowed Wittgenstein to identify rules with habits, but it seems likely that his doctrinaire rejection of abstract phenomena was the real cause of his identification of rules with habits.
llL Wittgenstein Perhaps enough has been said to indicate that Wittgenstein's characterizations of social rules as habits were one-sided and incomplete. Why have so many of his commentators failed to recognize this defect and
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to attempt to correct it? One reason may be that they, too, have shared Wittgenstein's almost irrational repugnance to abstract phenomena. Most of his critics seem to have been internal critics- those who have accepted as a basic ground rule of analysis the empiricist dogma, accepted by Wittgenstein, that only sensible particulars are real. Since abstract phenomena cannot be observed but concrete particulars can, they seem to have reasoned that the latter are real and the fonner are not, and that all statements about the .behavior of abstract groups, and all use of abstract concepts to describe the behavior of individuals, can ultimately be reduced to statements about the feelings, beliefs and dispositions of individuals. For what else is there? Wittgenstein's doctrine of family resemblances, which has been so widely discussed and misunderstood, was in fact nothing less than an all-out frontal attack on abstract phenomena. His remarks on rules and role-following vacillate between collateral attacks upon essences and genuine statements of perplexity at the results of his own theorizing activities. I venture to suggest that the main thrust of Wittgenstein'slater philosophy, his later work, was the denial of abstract phenomena. His mission, as he saw it, was to forever desttoy this myth. But this was bound to lead him into trouble, for as Durkheim once remarked 'man is dual'. By this, Durkheim was not alluding, in a Cartesian manner, to the duality of mind and body. He was alluding to the duality of concreteness and abstractness, a duality which is the condition of mankind. We live in two worlds: a world of abstractions and categories, and also in a world of concrete phenomena, of material bodies and mental events. These two worlds together constitute society and make it a possibility and indeed a necessity for life as we know it. I will have more to say about this later. Wittgenstein recognized, rightly, that speech and communication behavior could only be understood by seeing how these phenomena were part of the 'stream of life and 'thought' and how they fitted into 'patterns of activity' in the course of 'purposeful and shared activity'. But in speaking of these phenomena as mere 'activities', 'forms of life', or 'the given', he left a crucial dimension of social life out of his theorizing activity. Most people will agree that language and speech are considerably more than mere activities. If language and theorizing were mere activities, reflecting nothing other than their own brute existence as sounds or marks on paper and pointing to nothing beyond themselves, they would amount to no more than what Mead called a 'conversation of gestures' of the kind that ensues between infra-human creatures that have not attained to the level of symbolic interaction. The behavior of two wild dogs eyeing each other is a case in point: the sort of 'conversation' of power that precedes actual physical struggle for dominance fits into a stimulus-response paradigm of animal psychology that is ill-equipped to explain or make sense of abstract, theorizing activity. Is this the sort of paradigm that Wittgenstein's theorizing presupposes? Bloor has, in fact, been so impressed with this aspect of Wittgenstein's empiricist approach that he has attempted to develop and push these ideas to their limits by using the idiom of stimulus-response
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theory. The Skinnerian counterpart of Wittgenstein's public cntenon of custom is fOWld, he says, in the notion of a reinforcement schedule. Echoing Pavlov, Bloor says that an organism learns its behavior by a system of external checks and reinforcements. 1' Bloor is really one of Wittgenstein's most radical expositors. He seems quite faithful to Wittgenstein's position: his attempt to explain the possibility of human thought, speech and action from within the Skinnerian framework shows just how remote the theories of Durkheim and Mead really are from those of Wittgenstein. It is only a pity that Bloor fails to see that this is so. His Skinnerian account leads him to want to argue that "observable behavior provides our ultimate criterion"17 of meaning and Wlderstanding. But Bloor forgets to ask: 'observable to whom?' It is trite sociology that patterns of behavior (the external aspect of rules) become observable through participant-observation and often remain unnoticed or indeed invisible when viewed through the eyes of outsiders who lack insider's knowledge of the holistic concepts (or constitutive rules) that constitute and define the actions and patterns in question. For the anthropologist or sociologist of knowledge, for whom knowledge is 'distributed', there is recognized to be many points of view and many group perspectives, and what is externally observable to a member of one group may not be so to a member of another. The ultimate criterion for understanding the basis of human, social life is the insider's perspective,18 and this is something that individuals learn to see as they become socialized into the multifarious groups to which they belong in modem society. Indeed, we often cannot 'see' the patterns of behavior that constitute the external aspect of rules until we have acquired insider's knowledge of social structure, and this is a form of knowledge by acquaintance and not merely knowledge by description; it involves insider's apprehension of an abstract, pre-existing system of rules regarding abstract categories. Because Wittgenstein denies the existence of any such pre-existing system (the mistake alluded to at the end of section two), he is led to the hopeless view that the meaning of words is inextricable from the contexts in which they are originally learnt.19 Wittgenstein's repugnance against abstract phenomena led him to the view that there is nothing that can be treated as a standard of behavior, including categorizing behavior, and so nothing in that behavior which manifests the internal point of view characteristic of the acceptance of rules. But to argue this way impales us on the horns of a false dilemma: either rules are what they might be in a formalist's Platonic heaven - a view that Wittgenstein is at pains to reject - or there are no rules at all. The frrst part of Wittgenstein's widely discussed section 201 of the Philosophical Investigatiofli1O is a case in point: no matter what interpretation we place on this cryptic remark, its argument manque cannot be sustained. Wittgenstein's rule anti-realism is not too unlike the 'rule-scepticism' once voiced by the American legal realists. Like Wittgenstein, the realists were radical empiricists. For them, law was not an abstract system of pre-existing categories, but amounted to no more than concrete, particular decisions
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given by individual judges on particular occasions. Their contention that there is nothing to circumscribe the use of discretion by judges because of the logical possibility of a limitless number of possible classifications that may be given to any object, and that it is, as a result, false if not senseless to regard them as subject to or 'bound' to decide cases as they do, does not, however, hold water. The infinite diversity of possible classifications gives rules an open-texture to be sure, but it does not follow from the fact that rules can have exceptions incapable of exhaustive enumeration that in every case we are left to our discretion and are never bound. That is what Wittgenstein appears to be asserting. But this argument is no good. The multitude of similarities and differences that are inherent in any fact situation are circumscribed by the purposes and the nature of the activities and enterprises that individuals as participants engage in: it is this actual participation and insider's knowledge by acquaintance of the abstract standards shared by the group in that kind of activity that sets limits to the boundless possibilities of sheer logical possibility .21 These abstractions make speech, communication and society possible, yet Wittgenstein cannot see how they can be. There is another problem that must be dealt with in order to obviate a possible misunderstanding of what has been said so far: to say that rules cannot be reduced to social practices or mere conventions is not to suppose that, just because they involve abstractions, they can invariably be used deductively in the manner of a calculus. Some rules can indeed be used as a calculus, and rules of inference that constitute the propositional calculus are a case in point; but other kinds of rules, which are often of a more diffuse character, often cannot be so used. Nevertheless, we must not allow the rule-sceptic's fIXation with rules of this latter type to blind us to the fact that, in many cases, rules can be and indeed are used deductively. A legal example shows that this is so. The rules of international or constitutional law are rarely used by courts deductively, although 'artificial reasoning' may give the outward appearance of a smooth deductive procedure. Because of the diffuse and indeterminate character of the concepts used in these two branches of political/legal decision-making, the rules are often twisted and bent out of all proportion as they are used instrumentally as tools for the attainment of policy objectives. Especially in political and ideological polemics and debate, concepts often lose the specificity and determinateness required by deduction, so that a point is reached where it is true, as Wittgenstein says, that "we are clearly unable to circumscribe the concepts we use; not because we do not know their real definition, but because there is no real 'definition' to them. "22 Wittgenstein and Bloor overshoot the mark, however, when they pass from this fact to the radical conclusion that "our notion of what it is to follow the rule for generating 1t may change radically. "23 This is a hasty generalization with ruinous consequences. In the case of mathematical fonnulations, especially simple mathematical fonnutations such as 'twice two is four', there is a specificity and determinateness that is quite obviously lacking in the fuzzy
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realms of political rhetoric and the higher reaches of mathematics. When the concepts we use do have this specific and determinate character there can hardly be any reasonable doubt that we do, in fact, reason deductively and that logical necessity and conceptual constraint hold our train of reasoning together, assuring the right result from the right application of the rules. It is highly unlikely that there is no 'real' definition to most of the words we use, especially in areas of discourse where the meanings of words have been ren
IV. Bloor The case I have been attempting to present has been made to depend upon the existence of what I have called 'abstract phenomena'. What are they? This is indeed the key question to be asked, for it is precisely at this point that Wittgensteinian philosophers will be inclined to interdict "But Wittgenstein destroyed that notion long ago." It is true that Wittgenstein's later philosophy is generally, if obscurely, regarded as an attack on Platonic
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essences. Bloor calls these 'strange entities' and says of their advocates that "all they do is stress that they are different, more basic, and never change."26 He then lapses back to Wittgenstein's solution to the problem of abstract phenomena: "if you talk about essences...you are merely noting a convention."27 But is this really any sort of solution at all? Bloor makes it into a problem: he accepts that mathematics and logic are 'social', or 'conventional', and just because they are social he wants to say that there can be variation in logic and mathematics just as there is variation in social structures in different cultures and in different times. Bloor traces this relativistic sociologism back to what he calls Wittgenstein's 'sociologically orientated' Remarks on the Foundations of Mathematics, and concludes that "it is not necessary" to postulate any "vague mathematical reality"28 once we realize that mathematics is but social. There are, however, a number of serious mistakes in Bloor's analysis of mathematics and logic as social which render his overall approach defective. The frrst is that of thinking that 'the social' can be defined in terms of its external aspect alone. Wittgenstein has already been criticized on this ground, the ground that he takes no cognizance of the internal aspect of rules, and this criticism extends easily to Bloor's attempt to push Wittgenstein's extemalist analysis of rules to its Skinnerian limits. A second mistake results from Bloor's failure to distinguish social phenomena that are vague and diffuse from those that are determinate and specific. In a sense this is related to his third mistake: the failure to distinguish social phenomena that are local and temporal from those 'that are geneml and basic to the human condition. The relativism that he extracts from his sociologism is based on a faulty premise: that because there is variation is some social phenomena, there is no reason to suppose that there is not fluctuation in all social phenomena. What Bloor fails to realize is that while some social phenomena are indeed fleeting and ephemeral, there are yet others that are not so, and that some of these are so basic and unchanging to the human condition as to amount to the very conditions of human social life itself. I will have more to say about this when I tum to Durkheim's sociologism, which, as it turns out, is radically different and considerably more sophisticated than the version of it that Bloor attributes to Wittgenstein. Wittgenstein's sociologism was an attempt to get around the tendency, noticed in Frege,29 to see mathematical and logical concepts and relations as pure and detached from material objects and from the concrete field of experience. Bloor notes that Frege's tendency to ,Platonize, numbers creates a gulf between mathematics and concrete reality.30 There is truth in this. However, if we view arithmetic and logic as social phenomena with two aspects, as with Hart's model of social rules, this gulf can, perhaps, be closed, and a web of connection established between configurations of elements in nature and abstract social standards which consist of patterns or unities of meaning. Mill's theory, for example, was an empirical theory about the purely external dimension of arithmetic, but arithmetic also has an internal dimension which is abstract and not merely concrete. Once we
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realize this, Bloor's attempt to save Mill's theory from the onslaughts of Frege31 can be seen as or perhaps made into part of a larger project. His Wittgensteinian effort to explore and develop aspects of the external dimension of mathematics can be used as part of a more encompassing approach which recognizes the dual nature of social phenomena and attempts to work out their interconnections. I realize that this must sound impossibly conjectural and programmatic, especially when it is based upon such a slender theoretical formulation, but in what follows I will attempt to sketch a view of a way in which Platonic or Fregean forms might be 'sociologized'. In so doing, I will, in the main, be following the lead of Durkheim, whose theory seems badly in need of exposition. Few philosophers seem to understand its important central tenets: this is shown by the fact that the identification of Wittgenstein and Durkheim as belonging to the same sociological tradition has been allowed to stand without challenge, when it is so badly mistaken.32
v. Durkheim and Social Realism It is perhaps best to let Durkheim speak for himself, since his views seem to be so widely misunderstood. In what follows I will do just that, culling my material from his important yet widely ignored essay "Individual and Collective Representations."" Durkheim there distinguished 'individual representations', or ideas in the mind, from 'collective representations', which he regarded as abstract and social in nature. He argued that the latter, although abstract, did not just "hang in the air" as Platonists have supposed, but that they had a "definite substratum."34 What was this substratum? It was "the mass of associated individuals. The system which they form by uniting together, which varies according to their geographical disposition and the nature and number of their channels of communication."3S With regard to the relationship between abstract collective phenomena and their substratum, Durkheim's stated that "while maintaining an intimate relation with their substratum" collective representations are "to a certain extent independent of it."36 Nevertheless, "their autonomy can only be a relative one; and there is no realm of nature that is not bound to others. ,,37 "Nothing could be more absurd," he said, "than to elevate them into a sort of absolute, derived from nothing and unattached to the rest of the universe. "38 To enforce his point that abstract collective representations cannot be reduced to their substratum, Durkheim dmws an analogy between "the relationship which unites the social substratum and social life" and "that which undeniably exists between the physiological substratum and the psychic life of individuals. "39 He believes that if he can show the absurdity of reducing the mind to the brain (and the brain to its chemical elements), he will be able to show the irreducibility of abstract social phenomena to
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their behavioral or mental counterparts. His argument runs as follows: "the condition of the bmin affects all intellectual phenomena and is the immediate cause of some of them (pme sensation). But, on the other hand, representational life is not inherent in the intrinsic nature of nervous matter, since in part it exists by its own force and has its own peculiar manner of being.... A representation is not simply an aspect of the condition of a neural element at the particular moment it takes place, since it persists after the condition has passed, and since the relations of representations are different in nature from those underlying the neural elements."4O "If there is nothing extraordinary in the fact that individual representations, produced by the action and reaction between neural elements, are not inherent in these elements, there is nothing surprising in the fact that collective representations, produced by the action and reaction between individual minds that form society, do not derive directly from the latter and consequently surpass them."41 He continues with this analogy: "each mental condition is, as regards neural cells, in the same condition of relative independence as social phenomena are in relation to individual people."42 There is, he says, "no need to conceive of a soul separated from its body maintaining in some ideal milieu a dreamy or solitary existence.... The soul is 'in' the world and its life is involved with the life of thingS."43 But, he says, even though all our 'thoughts' are 'in the brain', they "cannot be rigidly localized or situated at defmite points."44 This diffusion or ubiquity, he says, "is sufficient proof that they constitute a new phenomenon.... In order that this diffusion can exist, their composition must be different from that of the cerebral mass, and consequently must have a different manner of being which is special to them."45 He thus concludes his argument: "those, then, who accuse us of leaving social life in the air because we refuse to reduce it to the individual mind have not, perhaps, recognized all of the consequences of their objection.... If it were justified it would apply just as well to the relations between mind and brain, for in order to be logical they must reduce the mind to the brain."46 "But then...following the same principle...one would be bound to say that the properties of life consist in particles of oxygen, hydrogen, carbon and nitrogen, which compose the living protoplasm, since it contains nothing beyond those particular minerals just as society contains nothing more than individuals."47 "In fact, individualistic sociology is only applying the old principles of materialistic metaphysics to social life. tt48 So here we have the core of Durkheim's social metaphysics in his own words. He rejects the Platonic vision of a heavenly realm of abstract phenomena unattached to any sort of material or psychic substratum. At the same time, he denies that abstract social phenomena can be 'reduced' to either mental or physical phenomena. He characterizes abstract social phenomena as having a reality sui generis. In this way it may be said that he 'sociologizes' Platonic and Fregean forms. This comes out most clearly when considering other aspects of Durkheim's theory. There are a number of points which Durkheim makes about collective representations which are
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of ubnost importance. He often refers to them as social facts. 49 He maintains that they continue to exist in themselves without their existence being perpetually dependent upon the disposition of anyone concrete mind He says, contentiously, that collective representations have the power of reacting directly upon each other and to combine according to their own laws. 30 They are, he says, (as we saw) external to individuals. He suggests, very importantly, that abstract social phenomena come in varying degrees of specificity and determinateness. Phenomena such as numbers, elements of logic, (X' crystallized law can be cited as examples of the most determinate of all the social forms. Social currents and movements, vague political and ideological notions, on the other hand, are some of the most indeterminate and diffuse. He also recognizes that some social phenomena are general to all of humankind whereas others are specific to local groups. Some of the former are actually general enough to be called 'constitutive of human social life. The introduction of rules of inference and the associated vocabulary of 'not', 'implies', 'therefore', 'follows from', 'and', 'or', 'if...then', and so on are cases in point. These social phenomena allow us to calculate and to think. Then there is the normative vocabulary of rules in general, consisting of 'ought', 'must', 'should', 'right' and 'wrong', and so on which constitutes the actual glue of social life. In his Primitive Classifuation Dwidleim suggests that arithmetic and counting behavior have an elementary basis in group perception, and especially in perceptions of 'us' and 'them'. Having learnt to use 'the same' and 'different' in this way, through classifying ourselves and others, we extend this abstract knowledge to other things in the natural and social environment. In this way we learn to sort and group and to count and it is on the basis of this that we learn to calculate in other ways. These are social skills. They may be said to constitute the step from the pre-social to the social world. In this way individuals become 'part of society, they preserve and perpetuate it while at the same time being held in check by it, as the grid of collective representations forces itself upon them through interaction with the collectivity. Some social phenomena are indeed specific to certain cultures, such as systems of signs (X' currency which are local and temporary phenomena which vary from one culture to another and from time to time. But there are others of a more basic and durable nature, such as the institutions of arithmetic and logic. They can hardly be called 'arbitrary' merely because they are social constructions. They have objective parameters which set their bounds, such as human physiology, the structure of the physical universe, what may be called the 'furniture' of the human mind and, according to Durkheim, laws or principles of their own association. They are so basic that they can be said to be 'timeless' and unchanging to the human condition. Because they constitute the foundations, upon which are built the edifices, of meaning, they have a 'giveness' which seems quite atemporal just because we could not imagine what it might be like without them, or if they were different than we know them to be.
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VI. To Sociologize Philosophy I have just been discussing the social foundations of human knowledge. By calling them 'social' I am indicating a movement toward sociologism. What would it be like to 'sociologize' the Kantian categories of the understanding? This is, in fact, exactly what Durkheim has suggested we do. He was not alone.. There were suggestions from some neo-Kantians along precisely these lines: some writers, like Cassirer and C.I. Lewis, reportedly thought that the categories were not fIXed by nature or by the nature of our psychological faculties, but were capable of historical and cultural variation- although it is unclear just how far they might have been prepared to go in this direction. Perhaps, like Bloor and Wittgenstein, they would have been prepared to go 'all the way' if pressed. But Durkheim would most certainly have rejected this, for reasons that have just been canvassed. A related question that might be raised, in this connection, is the extent to which a philosopher's views can be 'sociologized' as opposed to being regarded as 'proto-sociological'. My view is that a writer's theories are proto-sociological if there is a hint, even a trace, that he or she would have regarded the basic building blocks of knowledge as 'social', no matter how slight the appreciation of such a view might have been. There is no indication that I am aware of in Kant's writings that would suggest that Kant regarded his categories as social constructions, although his talk of regulative and constitutive principles is suggestive. He attempted to ground the distinction between experience and thought in different faculties of the mind, the sensibility and the understanding. But he recognized the difference between the psychological faculty of judgment, and the forms of judgment which provided for the unity of apperception, and regarded the latter as transcendental. His unity of apperception would have been regarded as social by Durkheim, in the same way that abstract collective representations are so: they transcend individual experience and pre-exist individual consciousness of them. Moreover,the particular contents of experience were recognized by Kant as having some general character, and this generality is explained by some modem commentators in terms of 'rules' and 'rules for the application of rules' which are said to constitute the empirical schematism and the categories of the understanding respectively.51 To what extent can Frege and Plato be sociologized? Or can it be said that they were proto-sociological thinkers? There are indications in Frege that he regarded his 'concepts of reason' as cultuml artefacts even though he characterized them as 'timeless'. He wrote, in the context of a discussion of the distinction between 'ideas' in the minds of individuals and the objective 'sense of a sign, that mankind "has a store of thoughts which is ttansmitted from one generation to another."52 Did Frege mean to suggest that his concepts of reason, including numbers (which he often characterized as 'objects'), were part of the storehouse of social forms, or would he have t
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placed them into another category altogether, one that, as Bloor complains, has nothing to do with the social and which he understood but poorly? The answer is not clear. Bloor's deflationary sociologism aimed to 'demystify' Frege's Platonism by construing numbers in terms of their purely external aspect alone, but what would it be like to attempt to 'sociologize' Platonic and Fregean forms as part of a Durkheimian social epistomology? What would this amount to? Here, the focus would be on analogies that can be drawn between forms as social categories or collective representations, and Plato's doctrine of 'participation' and the actual group participation that imposes the collective grid upon the individual. Patterson has said of Plato's doctrine of participation that it is impenetrable just because of the primitiveness of the notion itself, yet he gives an interpretation of Plato's metaphysics that encourages us to see it proto-sociologically: in speaking of concepts that constitute and defme society and social structures, he notes that these phenomena are 'separate from' the individuals who 'participate' in them. He gives examples of roles that it would be difficult if not impossible to reduce to the thoughts, feelings, or dispositions of individuals. He recognizes that society and societal phenemena are 'abstract' and says they are "independent of the people... "53 who participate in them as group members. He then offers the suggestion that this description seems to 'Platonize' social phenomena. But would it not be better to say that such a description 'sociologizes' Plato's original conception of them? This is of course highly speculative, but it is interestingly so: the idea has been to give some indication of what it might be like to theorize about the problems of philosophy from a Durkheimian perspective.
VIL Beyond Relativism and Absolutism Even though Durkheim's critique of Platonism has been decisive, he is still referred to as a 'social Platonist' or even a 'Platonist' by some of his commentators.54 There is a simple explanation for this: it is that Durkheim's social metaphysics contains a defmite Platonic element, namely the 'abstractness' of social phenomena and their capacity, which is sometimes fully realized, of assuming highly determinate 'forms' or 'essences' which can be - and are - used deductively in the manner of a calculus by human beings. I have already been through these arguments and there is no use in repeating them, but it is worth mentioning that these social forms constitute a transcendental reality closed to our physical senses but nonetheless accessible by other means. Their method of apprehension, the manner in which they are collectively brought into being and persist, and the nature of the constraint they exercise upon us at all levels - from the most microscopic to the most macroscopic - all constitute worthy topics of investigation. For this, if for no other reason, Durkheim's social Platonism is worth exploring further. It also raises some interesting theoretical
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problems, such as those that have already been alluded to. Most importantly, perhaps, Durkheim's sociologism establishes a fmmework for exploring the social foundations of a priori knowledge. His attempts to sociologize the categories of the understanding, his social theory of arithmetic and logic, and his overall concern with the problems of universal and necessary knowledge, give ample proof of this. Let us imagine a spectrum of theories now with Durkheim's sociologism counterpoised between the two polar opposites of relativism and dogmatic absolutism. At one end of the spectrum we have something that looks like a version of subjective idealism or what may be called 'social Berkeleyism'. This is a constructivist theory of reality not unlike the relativistic sociologism of WittgensteinSS and Bloor: when it comes to the social world, though not necessarily the physical world, most relativist-constructivist 'theorists today would accept Bishop Berkeley's fonnulation that 'to be is to be perceived'. Beauty, truth and goodness, law history and art, status, role and self, and even logic and arithmetic, are ephemeral social constructions, according to them. There is no distinction to be made between appearances and reality, they say, because reality just is a collective appearance, or
maya. Totally opposed to this relativism, at the other end of the spectrum, is something that may be called 'dogmatic Platonism', or perhaps ' vulgar Platonism', but in any case something that postulates a self-subsistent or independent realm of eternal, unchanging, abstract reality, but goes little further than this by way of attempting to explain the nature or the character of this reality.56 Could these two extreme theories, situated at either end of our imaginary spectrum, be the 'false dichotomy' supposed by Dummett to exist in the philosophy of mathematics and to be eliminable by the interposition of some middle theory which he leaves unnamed?S7 If so, then that theory can now be named: it is social realism or social Platonism or, if we like to think in terms of 'sociologisms' it is Durkheim's sociologism.S8 Wittgenstein's sociologism has been exposed as a species of psychologism and branded as social Berkeleyism. The theories of Frege, Plato, and Kant have been given proto-sociological interpretations. We can see then that there are any number of theories that can be spread across the spectrum I have been imagining, but there are certain fixed points with reference to which these theories can be given their precise location on it There are three such points of reference and they are represented by the three views that I have been discussing. Do these three views represent 'stages' in the development of philosophical thought? A speculative neo-Kantian might say so. Kant thought there were cycles in the history of philosophy and he identified three stages through which all philosophy must pass: (i) dogmatic metaphysics, and, as a reaction against this, (ii) acid scepticism, and finally (iii) the stage of pure reason, which is that of "examination, not of the facts of reason, but of reason itself, in the whole extent of its powers, and as regards its aptitude for pure a priori knowledge."S9 Since we are all agreed that reason is, at least in part, social and not merely psychological, as Kant
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seems to have imagined, does Durkheim's theory now take the place that Kant's once took between radical scepticism and dogmatic rationalism? A Durkheimian might say 'yes'. For others the answer will not be so clear, but one thing that is certain is that Durkheim's sociologism is quite unlike that of Wittgenstein's and presents a radically different way of viewing philosophy. We should take this into account: that there are two sociologisms, one that fortells the end of philosophy and another that heralds a new beginning. That is why sociologism is pivotal, because it stands at the centre of a fork in the road. It is like a signpost that points in
two directions.60. 61
218 ENDNOTES 1.
See: David Bloor, Wittgenstein: A Social Theory of Knowledge (New York: 1983). 2. The reason I call th~e phenonema 'phenomena' and not 'objects' or 'entities' is that these latter two, widely used, expressions are enormously misleading: abstract 'object' suggests that these social phenomena are objects in the physical world; abstract 'entity' suggests, worse, that they are beings or creatmes of some sort 3. See: Karl Popper, The Open Society and Its Enemies (Princeton: Princeton University, 1966), Ch. 15, sec. ill; see also: Karl Popper, ''The Mind-Body Problem:' in A Pocket Popper, ed. David Miller (Huntington, N.Y.: Fontana, 1983) pp. 265-275. References to Durkheim's works are given below. 4. A recent bibliography lists some 6000 books, articles, and reviews dealing with Wittgenstein's work. See: VA. and S.G. Shanker, 008. and comps., A Wittgenstein Bibliography (London: Croom Helm, 1986). 5. Joseph L. Cowan, "Wittgenstein's Philosophy of Logic," PIDLOSOPHICAL REVIEW, LXX (1961): 362-375, p. 364. Cowan's article was criticized on two grounds by Chihara. The first was that Cowan did not follow the usual 'juxtaposition commentary' format that has become the hallmark of commentaries on Wittgenstein's later philosophy. The second grolDld was the 'radical' interpretation given by Cowan. Chihara says: "Cowan does not cite passages which really support this remarkable interpretation, and I am at a loss to explain how he came to it" Charles S. Chihara, "Mathematical Discovery and Concept Formation," PmLOSOPIDCAL REVIEW, LXXII (1963), 17-34. p. 34. 6. Cowan, "Wittgenstein's Philosophy of Logic," p. 364. Cowan not only gave this interpretation of Wittgenstein, he also accepted it as right and concluded that logic and right thinking were without fOlDldations. 7. Stanley Cavell, ''The Availability of Wittgenstein's Later Philosophy," PmLOSOPIDCAL REVIEW, LXXI (1962), 67-93; reprinted in George Pitcher, ed., Wittgenstein (New York: Doubleday Anchor, 1966) p. 156. 8. Bloor, Wittgenstein, p. 57 9. As Ayer notes, there is nothing wrong with speaking about a private 'public' language, if by this we mean one that is shared by a limited number of people, as in a secret society with a secret code. See: A.I. Ayer, "Can There be a Private Language?" in Pitcher, ed., Wittgenstein. What is mistaken is to speak about a language that is private in the sense of being not shared or not public. 10. H.L.A. Hart, Concept of Law (New York: Oxford University, 1961), pp. 55-56. 11. Ibid. 12. See: M. A. Nottumo, Objectivity, Rationality and the Third Realm: Justification and the GrOlUlds of Psychologism (Dordrecht: Martinus Nijhoff, 1985). Nottumo's claim is that Popper's theory of objective knowledge constitutes a new epistemological paradigm, one that breaks with the old paradigm that located knowledge in belief, especially in 'justified true belier. Although it is difficult (for me) to accept Nottumo's claim (correspondence, 1 February 1987) that contemporary Wittgensteinian arguments have completely undermined the possibility of a priori knowledge, I concur whole-heartedly with him that "the ground of psychologism...is a commitment to the epistemology of empiricist justificationism. At least it [is] the consequences of this epistemological position" Ibid., p. 15. 13. Ernest Gellner, "Explanations in History," PROCEEDINGS OF THE ARISTOTELIAN SOCIETY (1956); reprinted as "Holism and Individualism in MacMill~
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History and Sociology," in Patrik Gardiner, 00., Theories of History (New York: Oxford University, 1959), p. 498. 14. This is a real methodological problem in the anthropology of law, where the question of how the researcher is to distinguish customary 'law' from mere custom is a key methodological questi~ one that has developed a small literature. I have discussed this in: John Hund., "Jurisprudence and Legal Anthropology," COMPARATIVE AND INTERNATIONAL LAW JOURNAL OF SOUTHERN AFRICA, XII (1979), 188-198. 15. For further discussion, see: John HlDld, "Insiders and Outsiders Models of Deviance and Jurisprudence," PHILOSOPHY OF THE SOCIAL SCIENCES, XV (1985), 35-44. 16. Bloor, Watgenstein, p. 59. 17. Ibid., p. 72. 18. As Jim Tiles has pointed out to me, quite rightly, if one adopts a Durkheimian metaphysics, it cannot be said that the insider's perspective is the last word when it comes to describing the influence of social forces. For Durkheim, we can be implicated in patterns of behavior and subject to currents of influence of which we are lDlaware, and sociologists and some outsiders can sometimes know things about us that we do not, and sometimes perhaps could not, know about ourselves. This was the whole point of Durkheim's Suicide, to show how, by using statistical techniques, we can become aware of patterns or currents of influence that act upon us in ways that escape our ordinary or 'lay' understanding. Do the Categories of the Understanding act upon us in such a way? What Tiles suggests is that "if there are fIXed a priori categories, we may never be able to grasp enough of our own intellectual practices fully to specify them" or alternatively "if we can specify them fully, we may not be able to understand why they are necessary," (correspondence, 4 July 1987). 19. This is sometimes referred to as Wittgenstein's 'fmitism', but it is better described by Hao Wang as 'situationalism'. See: Hao Wang, "Wittgenstein's and other Mathematical Philosophies," THE MONIST, Vol. 67 (1984), 18-28, p. 28. 20. ''This was our paradox: no course of action could be detennined by a rule, because every course of action can be made out to accord with a rule. The answer was: if everything can be made out to accord with the rule, then it can also be made to conflict with it And so there would be neither accord nor conflict here." It hardly needs to be mentioned that this passage has been infamed by Saul Kripke. See: Saul Kripke, Wittgenstein on Rules and Private Languages (Cambridge: Harvard University, 1982). Wittgenstein's so-called 'sceptical paradox' a' la Kripke reads like this: "there can be no fact as to what I mean by 'plus', or any other word at any time" or '!here is no fact about me that distinguishes between my meaning a defmite function by 'plus' ...and my meaning nothing at all," Ibid., p. 21. One searches in vain in Kripke's work for an adequate conception of rules. No wonder his arguments seem strained and inconclusive. He does not embrace Wittgenstein's rule anti-realism outright, it is true, but it seems clear that there is no place in his thinking for the internal aspect of rules. 21. Brambrough's early comments still hold water. See: Renford Brambrough, "Universals and Family Resemblances," PROCEEDINGS OF THE ARISTOTEUAN SOCIETY, LXI (1960-61). Brambrough does not accept Wittgenstein's nominalism, but he avoids falling into dogmatic Platonism. His position is Aristotelian in the sense described by Tiles in note 58 below. 22. Ludwig Wittgenstein, The Blue and Brown Books (New York: Oxford University, 1961), p. 25.
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23. Cora Diamond, ed., Wittgenstein's Lectwres on the Foundations of Mathematics, 1939: From the Notes of R.G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick. Smythies (Hassocks, Sx.: Harvester, 1975) p. 238; cited with approval in: Bloor, Wittgenstein, p. 89. This presents a good example of the kind of 'juxtaposition commentary' I have been excoriating. First I cite a passage from one work, and then one from another, and then attempt to show or assert that one passage does not 'follow from' another or was derived by some fallacious means. But now notice the passage that immediately follows the one given in the text to this note: "if you read the newspapers and see how people get around pacts you should not be surprised by this." Is there really any point in trying to show, by the juxtaposition of these passages, that the so-called 'argwnent' is fallacious? What is needed is a new method of interpretation overall, of the sort I have suggested Bloor's work attempts, but fails to achieve. 24. See: Ludwig Wittgenstein, On Certainty, edt G.EM. Anscombe and G.H. von Wright (New York: Harper & Row, 1972). See also: John W. Cook, "The Metaphysics of Wittgenstein's On Certainty," PHILOSOPHICAL INVESTIGATIONS, vrn (1985), 81-119. Wittenstein's metaphysics, i.e. his 'blindness', was driving him mad. 25. A.J. Ayer, Ludwig Wittgenstein (Harmondsworth: Penguin, 1986), p. 79. 26. Bloor, Wittgenstein, poe 84. 27. Ludwig Wittgenstein, Remarks on the Foundations of Mathematics, edt G.H. von Wright, R. Rhees, G.E.M. Anscombe (Oxford: Basil Blackwell, 1964), I, 75. Cited in: Bloor, Wittgenstein, p. 93. 28. David Bloor, Knowledge and Social Imagery (Boston: Routledge & Kegan Paul, 1977, p. 97. 29. See: Gotdob Frege, The Foundations of Arithmetic, trans. J.L. Austin (Evanston: Northwestern University, 1968). 30. Ibid., Ch. 5. 31. See: Ibid., cbs. 5, 6, and 7. 32. It really is hard to believe, as Bloor claims, that writers like Lukes and Gellner treat Wittgenstein as someone who did little more than 'rediscover' Durkheirn's insights; see: Bloor, Wittgenstein, p. 186, n. 7. 33. See: Emile Durkheim, ''Individual and Collective Representations," REVUE DE METAPHYSIQUE ET DE MORALE, VI (1898); reprinted in: Emile Durkheim, Sociology and Philosophy, trans. D.F. Pocock (New York: Free Press, 1974). All citations are to the Free Press edition. 34. Ibid., p. 23. 35. Ibid., p. 24. 36. Ibid., p. 23. 37. Ibid., p. 23. 38. Ibid. 39. Ibid., p. 24. 40. Ibid., p. 24. 41. Ibid. 42. Ibid., p. 28. 43. Ibid. 44. Ibid. 45. Ibid., p. 28. 46. Ibid., p. 28. 47. Ibid., pp. 28-29. 48. Ibid., p. 29.
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49. For further discussion, see: John Hood, "Are Social Facts Real'!" BRITISH IJOURNAL OF SOCIOLOGY, (1982), 210-278. I 50. IT Durkheim is attributing active agency to abstract theories, he seems rmistaken. Popper's view is more reasonable: he says there is a two-way causal interaction between abstract third-realm phenomena and individuals via the mind (or world two). Frege on the other hand had postulated a one-way causal projection from an abstract third-realm to individuals via the mind. For more comparisons along these lines see the lucid expository material in: Nottumo, Objectivity, RatioMlity, and the Third Realm, especially cbs. 3,5,7, and 9. 51. Robert P. Pippin, '''The Schematism and Empirical Concepts," KANT-STUDIEN, Vol. 67 (1976). Pippin does not emphasize the social character of such rules - in fact he leaves their analysis undeveloped - but it is clear that such an emphasis can be given: Kant claimed that rational creatures act not only according to laws (Gesetzen) but also according to a rep-esentation (Vorstellung) of a law. Can these laws and representations be said to represent the external and internal aspects of rules respectively? Remember, for Durkheim the internal aspect of social rules just is a 'collective representation'. 52 Gotdob Frege, 'On Sense and Reference," in Translations from the Philosophical Writings of Gonlob Frege, trans. and 00. Peter Geach and Max Black (Oxford: Basil Blackwell, 1970), p. 56; cited in: Nottmno, Objectivity, Rationality, and t~ Third Realm, p. 66. 53. Richard Patterson, Image and Reality in Plato's Metaphysics (Cambridge, Mass.: Hackett, 1985), p. 121. 54. See: Talcott Parsons, "Emile Durkheirn," in 111lerfUllional Encyclopedia of the SociDl Sciences, Vol. 4 (New York: MacMill~ 1968), pp. 311-320. See also: J.G. Peristiany, "Introduction/' in Emile Durkheim, Sociology and Philosophy, pp. xii -xxxiii. 55. Not all of Wittgenstein's commentators would agree with Bloor that Wittgenstein's sociologism is entirely relativistic. Some commentators have found the rudiments of a philosophical anthropology in his later writings, although I confess I have difficulties seeing this myself. According to a recent comment by Richard Eldridge, Wittgenstein pursued a strategy of identifying "practices" that could be "shown to be constitutive to our [hmnan] form of life and hence necessary for us [as hwnans]"; see: Richard Eldridge, "The Nonnal and the Nonnative: Wittgenstein's Legacy, Kripke and Cavell," PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH, XLVI (1986), 555-515, p. 574. 56. I do not mean these expressions to be taken as tenns of abuse or disrespect but only as metaphors for a certain style or practice of philosophy. Let me give you an example of what I mean by this: Antony Flew has recently criticized Bloor's sociologism, which Flew characterizes as the view that "what the uninstructed see as objective, logical necessities are no more than relative...and social." Antony Flew, "A Strong Programme for the Sociology of Belief," INQUIRY, Vol. 25 (1982), 365-385, p. 311. As against this view, Flew puts his own view that "it is not within the power of either man or God to decide what necessary truths are to obtain" Ibid., p. 310. But what are these 'necessary truths '? Professor Flew gives us absolutely no clue, other than to say that they are "objective and absolute logical COJDlections," "eternal, \Dlchanging," and "actually subsistent logical relations" Ibid., pp. 369, 370. 51. Michael Dummett, "Wittgenstein's Philosophy of Mathematics," THE PHILOSOpmCAL REVIEW, LXvm (1959), 324-348; reprinted in: Pitcher, 00., Wiltgenstein, p. 447. The two theories that constitute his 'false dichotomy' are called 'constructivism' and 'Platonism'.
xxxm
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58. Jim Tiles has made the valuable suggestion that Durkheim's sociologism is Aristotelian. He says that it "avoids Platonism by insisting (like Aristotle) that form must be realized in matter, and avoids nominalism by insisting (also like Aristotle) that form cannot be reduced to mattez. Matter in this context is human social interaction." (correspondence, 4 July 1987). 59. Immanuel Kant, The Critique of PlUe Reason, trans. Norman Kemp Smith (New York: MacMillan, 1963), p. 607. 60. Richard Rorty's attempt to hasten the 'end' of philosophy by using what he calls 'epistemological behaviourism' to deconstruetthe Platonic-Kantian tradition is really nothing but an application of Wittgenstein's sociologism. See, for example, his discussions of epistemological behaviourism in: Richard Rorty, Philosophy and the Mi"or of NatllTe (Oxford: Basil Blackwell, 1980), pp. 173-182, 193, 209-213, 30511, 315, 325, 373, 376, 379, 383, 385. If, however, we substitute Durkheim's sociologism for that of Wittgenstein's, a way is opened up for 'reconstructing' the Platonic-Kantian tradition that could form the basis of a new 'transcendental' departure in philosophy, one that locates 'transcendence' in society itself. 61. I would like to express my gratitude to fun Tiles and Jearmete Boers for friendly encouragement and helpful comments on this paper. I have also benefitted from friendly correspondence with Mark Nottumo.
WITTGENSTEIN'S SOCIOLOGISATION: THE FLY IN THE BOTTLE PETER MUNZ
I. The Irony of History The story of the impact of Wittgenstein on modem thought is full of bitter irony. Like a twentieth-century, intellectual Siegfried - "an Apollo who had bounded into life out of his own statue, or perhaps like the Norse God Baldur, blue-eyed and fair-haired"l - Wittgenstein set out to slay the philosophical dragon whose terror he had diagnosed correctly, oc, at least, more correctly than any other philosopher apart from Hegel. For beyond all philosophical problems about reality and perception, about universals and language and truth and meaning, there, ultimately, lies the real and ultimate philosophical problem, the meta-problem: why are people either Platonists or Aristotelians? Why are some people mtionalists and others, empiricists? Up to a point one can always explain such deep-seated and fundamental confessions of philosophical faith by looking at the psychological and/or sociological conditioning of the philosopher in question- Le., one can seek a non-philosophical explanation. Up to a point such non-philosophical explanations are indeed explanatory. But in the long run and the last analysis they always must let us down, because they involve a petitio principii. An idealist's psychological explanation why someone is a Platonist or an irrationalist must differ from an Aristotelian's explanation, thus pushing the problem merely further back instead of solving it. All such explanations must operate with theories of causality, of perception, of determinism, and so forth- thus presupposing that we know what we are setting out to discover. Wittgenstein therefore decided to find an answer to the meta-problem which would make it silly, once and for all, to take one's position with Plato or Aristotle, with Descartes or Locke, or wherever. He wanted, he said, to show the fly the way out of the bottle by the argument that philosophical positions were superfluous and had always been derived from a misunderstanding of the use of language. In the course of his life he changed his tactics, but he never changed the goal nor lost sight of the target, the meta-problem, nor faltered in his conviction that he either had or was about to show the fly the way out of the bottle. Wittgenstein never did things by halves. Already in the "Preface" to the Tractatus of 1918 he had
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expressed the opinion that he had solved all philosophical problems once and for all, though he did add, modestly, that such finality counted for little. It was an act of hybris to try his hand at a project where Hegel had failed and where Siegfried had succeeded only in Wagner's imagination. Like all acts of hybris, it was punished. In Wittgenstein's particular case, it was punished through irony, a pointedly croel punishment because irony, as indeed all humour, had been utterly foreign to Wittgenstein. For in the end, Wittgenstein came up with the proposition that the bottle in which the fly was senselessly buzzing around was hermetically sealed and made of opaque glass so that one could neither see the fly in the bottle nor compare its trajectories with those of other files in other bottles. And all of this did not matter because the fly itself, buzzing in a non-transparent medium, could not see the outside world and, therefore, could not realize that it was living in an enclosed space. Wittgenstein himself did not put it in this way. He argued instead that there was no private language, that one cannot go behind language and scrutinize it, that there are no pre-linguistic meanings, and that one cannot have meanings or intentions 'in the mind' which create or generate the uses of speech and which one could use to criticize one's speech or to determine whether one is using speech correctly or incorrectly, that is, whether one is making a blunder or not. Meaning he said, is governed by use and not by observation, and use is determined by the rules of the speech community one is living in. There are as many sets of rules as there are speech communities and each such community is the result of an act of life or of spontaneous generation. Rationalists and empiricists, Aristotelians and Platonists, idealists and realists, he said, do not disagree with each other about the same questions, but perform correctly, each ensconced in his own system. The mistake, Wittgenstein concluded, had been to think that either idealism or realism was a blunder about the world. The truth of the matter was that there were many language-games and speech communities and that in some of them the speech rules that obtained upheld idealism and in others, realism, so that at worst, an idealist could make a blunder about idealism and a realist, a blunder about realism. Thus the meta-problem was solved and never again, Wittgenstein said, could a realist reasonably object to idealism or an Aristotelian argue against Platonism. That way, the fly had not actually been shown the way out of the bottle. But since the bottle was now alleged to be made of non-transparent glass, the fly no longer knew it was inside a bottle! Wittgenstein put it by saying that all knowledge is expressed in language and language is governed by rules which are dictated by the speech-community the person who has knowledge is a member of. The heart of this argument which leads to such a conclusion is stated throughout the many collections of aphorisms that have been published to date in many different fonns, but it always comes back to one decisive form. There cannot be linguistic rules which determine the use of words for private experiences. Meaning, intention, observation - in short, all fonns of
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consciousness - are such private experiences. Even sense observation, held for so long and by so many people to be the hard rock-bottom on which all systems of knowledge are built and in tenns of which their validity is to be judged, is such a private experience from which there can be no path to a linguistically formulated expression. Since we cannot talk about private experiences, they cannot be presumed to dictate the use of words and the fonnation of our sentences. Meaning, Wittgenstein concluded, does not determine use; use determines meaning. This amounts to saying that we do not have contents or ideas or pictures in our mind and then seek words for them, but that we learn how to use words and allow them to generate meanings (in our minds, if one must keep insisting on talking of 'minds'). With these views Wittgenstein moved as far as possible from such men as William James who had confessed, after finishing his Principles 'that he had to "forge every sentence in the teeth of stubborn facts." In Wittgenstein's later world - though not in the Tractatus - we do not know of any 'stubborn facts', least of all, of stubborn facts which might compel anybody to forge sentences. If all meanings are determined by use, then whatever uses there are in any one community (the notion 'use' has no referent without the existence of or outside of a specific community) are beyond criticism because there can be no criticism or scrutiny of use. One could criticize use only if one admitted a pre-linguistic, i.e., pre-use 'meaning in the mind'. One could then scrutinize anyone particular use by looking at the meaning it is supposed to express. But since, Wittgenstein argues, there are no pre-linguistic meanings, a scrutiny of use is inconceivable. This, as we shall see, is the ultimately unacceptable and, to my mind, unrealistic implication of Wittgenstein's position. I have spoken as if 'meaning' and 'knowledge' were synonyms. They are nol But in Wittgenstein's world these two words come very' close together. "The world," writes Ernst Konrad Specht, one of his most thoughtful followers, "confronts us only within language-games"; and, more explicitly: "the ontological structure of the object is fIXed in the spontaneous drawing up of a language-game simultaneously with a specific sign usage."2 The link between knowledge and meaning follows from the rejection of subjective contents one may have in one's mind. A lot of knowledge depends on our observations, that is, on the physical impact the world makes on our nervous systems. Such impact emerges in our minds as a purely subjective awareness and, it is perfectly true, if one were to portray that subjective awareness correctly and precisely, one would have to have a 'private language'. Since we do not have a private language and since it would be a contradiction in terms if anyone claimed that he had, these subjective awarenesses, though accessible to every mind 'that has them, are not accessible to other minds and cannot be communicated to them. Hence Wittgenstein's argument 'that though we may have pre-linguistic experiences, they count for nothing. It follows, then, that whatever meanings we intend with our 'minds' are meanings derived from the manner we use language.
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This makes any knowledge and the meaning it has completely dependent on language rules, and removes it totally from observation. It may come as a surprise to find 'observation' classed with subjective awareness and inner certitude. Ever since Descartes, we have been told and told ourselves that only innate ideas and possibly introspectively gleaned emotions can be found in that class. Observations, it has been held, are, on the contrary, inter-subjectively verifiable. Hence, the Vienna Circle clutched their protocol sentences the way a drowning man reaches for the life-line. Analysis shows that there is no such life-line. What is inter-subjectively veriftable - if one has to use verification jargon - is the public pronouncement that one has made an observation. But the sensory experience alleged to stand behind the pronouncement and purported to justify it is not. It is totally private and totally subjective and, at best, accessible only through introspection: a typical instance of a pre-linguistic meaning. It is not basically distinct from Kierkegaard's famous defmition of subjective truth in the Concluding Unscientific Postscript: "an objective uncertainty held fast in an appropriation process of the most passionate inwardness. 1t3 These views or proposals are sweeping and radical and very comprehensive. Wittgenstein, with the single exception of the Tractatus, never wrote a book, but only took notes and made pronouncements. In this way, he avoided the hard task of thinking out the implications of his theories and the consequences of these proposals. The writing of books may have no intrinsic value when one is living in the center of the intellectual universe- as Wittgenstein was in Cambridge. In such a place there is no need to write books because one can reach all the people that matter by word of mouth. Ordinary mortals who do not live in such or similar charmed communities have to publish books, in the fIrSt instance, in order to communicate, to reach out for an understanding soul or intellect But over and above the communication aspect of books, there is a special value in the discipline that the composition of a book with a beginning and an ending imposes on one's thoughl This discipline was accidentally or intentionally avoided by Wittgenstein, and thus the summary implications of his ideas were not confronted for a long time. People instead preferred to imitate his 'style' and his mannerisms and deluded themselves that they were actually following in the master's foot-steps by confining themselves to this kind of imitation. When the aphoristic nature of Wittgenstein's countless pronouncements started to give rise to a massive literature about Wittgenstein - a most flowishing publishing enterprise which has now been moving at high speed for thirty-five-years - most of it remained confined to exegesis. Such criticism as crept into it was almost entirely occupied with the problems created by the fact that exegesitists sometimes disagreed on the meaning of this or that aphorism and especially on the grand question as to whether Wittgenstein's one book, the Tractatus was or was not compatible with the innumerable apho~!!l~ htL ~pin~ afte~ the T,,-actatusJ - - -
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The heart of the matter was very slow in being revealed. The heart of the matter, I take it, is that Wittgenstein went one better than Kant. Kant had proposed a Copernican Revolution in philosophy by the argument that man prescribes laws to nature rather than learns of them by observing nature. With this proposal, Kant was more right than he could have known in the 18th century. Provided one thinks of biological evolution, one can see indeed that the nervous system of man or the human mind is, through natuml selection, the adaptive product of the world it is living in. Whatever it 'prescribes' to the world was, in the frrst place, transferred from that world to the cognitive structure of man and, in 'prescribing' anything to nature, man is merely paying back or making use of what nature put into him from the start. The only fundamental criticism one has to make of Kant in this regard is his conviction that his revolution was a 'Copernican' revolution which moved man from the center to the periphery. Kant, on the contrary one might say, was perfonning a Copernican Counter-Revolution because he was stressing, against Copernicus, the central place of man- an emphasis which has since been underpinned by our knowledge of biological evolution and the so called Anthropic Principle. It is one thing to place man back into the center because one recognizes that the world he is in the center of has eliminated countless other organisms as being less well adapted to it. It is, however, a completely different thing to do what Wittgenstein's coumge prompted him to do. Wittgenstein proposed nothing less than the idea that man prescribes to himself the rules according to which he prescribes laws to nature. If the spirit of that courage may have been Kantian, the core of the argument was noL For Kant, though he could not have known this, moved along the track on which evolutionary epistemology and the Antitropic Principle were eventually to be encountered. He probably may have done so with the peculiar talent of a genuine somnambulist. For the Anthropic Principle spells out Kant's surmise: there must be a functional relationship between the nature of the universe and the constitution of the human nervous system which has been produced by it. At any rate, Kant's surmise that men are born with categories and forms of understanding 'in their minds' had a universal ring about it. For he took it that all human beings are alike in that respect and that the presence of categories and forms is completely independent of any culture, convention, language-game, or speech community. Not so Wittgenstein. In Wittgenstein's view, the conditions of life that give birth to anyone set of language rules vary enormously and arbitrarily and spontaneously so that mankind must be taken to be divided arbitrarily into countless independent cliques the taxonomy of which is, at best, Linnaean. If one leaves out the Anthropic Principle and maintains that man prescribes to himself the rules according to which he prescribes laws to nature, one must have Dutch, rather than Kan~5~!!C~~
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II. Wittgenstein's Dutch Courage and Kuhn's Spontaneity It was precisely Dutch courage that Wittgenstein was so richly endowed with. His commentators took some time in noticing it. Wittgenstein' s emphasis on the natuml practices of man and the role they played in philosophy, i.e., his anthropocentricity, was shyly referred to by both Strawson and Malcolm in their reviews of the Philosophical Investigations, which frrst appeared in 1953. Feyerabend did not mention it in his review." The frrst author to bring it out in full and to elaborate on it was Peter Winch in The Idea of a Social Science, published in 1958.s Then, in 1962, Thomas Kuhn developed his famous The Structure of Scientific Revolution!' by making avowed use of Wittgenstein's social naturalism. That same social naturalism also inspired the widely influential speech-community philosophy of Karl-Otto Apel's Transformation der Philosophie in Germany in 19757 and of Richard RoTty's Philosophy and the Mirror of Nature in America in 1979.8 This social natumlism had been critically highlighted by Ernest Gellner in "The New ldealism- Cause and Meaning in the Social Sciences"9 of 1965, and uncritically mentioned by David Pears in his Wittgenstein lO of 1971. It was referred to by P. Jones in his "Strains in Hume and Wittgenstein"ll and figures in Saul Kripke's Wittgenstein on Rules and Private Language of 1982. 12 G.H. von Wright summed it all up at the 2nd International Wittgenstein Symposium of Kirchberg by saying that "Lebensformen are embodied language-games."13 In 1983 it was finally moved into the foreground and made the subject of a special book by David Bloor, entitled Wittgenstein: The Social Theory of Knowledge. l " I think it was entirely due to Wittgenstein's aphorismic style that it took his readers so long to tumble onto the enonnity of his philosophical enterprise. Having listened myself to Wittgenstein, who even talked in aphorisms or, better, in aphorismic questions, I cannot be really sure whether Wittgenstein himself ever actually realized what it was his sayings amounted to. The progress towards a full revelation of what his many sayings amounted to was not only slow, but unsteady. There is a world of difference between Winch, Kuhn, Kripke, and Bloor. Winch suggested that since both societies and languages are rule governed, Wittgenstein's thought is a social science. Kuhn argued that theory formation in science was governed entirely by a prevailing paradigm and that the pursuit of 'normal science' could be likened therefore to Wittgensteinian pursuit of intelligible speech. Kripke used the fact that language is a rule-following activity in order to solve problems of reference. Bloor derives a social theory of knowledge from Wittgenstein in arguing that any particular knowledge system is a function of a social order. One must remain aware of the different uses to which Wittgenstein has been put. Compared with Bloor's social theory of knowledge, Winch's idea of a social science strikes one as plain commonsense, and Kuhn is halfway between Winch and Bloor. There are many worthy and valuable books on the later philosophy of Wittgenstein - I am thinking of Henry Le Roy Finch and of P.M.S. Hacker,
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D. Pole, Anthony Kenny, and E.K. Specht - but they make nothing of that social naturalism and of Wittgenstein's sociologisation of both meaning and knowledge-- even though Finch, almost alone, discusses it at some length. For that matter, one could readily ignore the enonnity of Wittgenstein's sociologisation of meaning and knowledge and enjoy his aphorisms for their own sake, were it not for the fact that it is the basis on which Kuhn has erected his famous and widely accepted philosophy of lrnowledge, and were it not for the fact that Kuhn's enterprise has been underwritten and elaborated by Karl-Ouo Apel in Germany and Richard Rorty in America. These thinkers are keeping Wittgenstein alive and force recurring preoccupation with the philosophical foundations which Wittgenstein has provided for them. Kuhn is by far the most influential propagator of Wittgenstein's later philosophy. The scope of that wide influence is largely due to the fact that Kuhn is no commentator, but has shown real originality in developing Wittgenstein's premisses. He introduced the word 'paradigm' in order to describe the set of rules which preside over and control theory fonnation in anyone community. He explicitly referred to Wittgenstein in his Chapter V of The Structure of Scientific Revolutions when he introduced the notion of paradigm. The idea 'paradigm' was implicit in Wittgenstein, and has even been articulated by him. Kuhn also introduced a really new articulation by calling the pursuit of knowledge in obedience to the rules laid down by the paradigm, 'nonnal science'. Again, the idea that theory formation is guided by and is to be judged by reference to the reigning paradigm is purest Wittgenstein. The meaning of a statement, Wittgenstein had said, depends on the use it has in a given language-game. The truth of a theory, Kuhn echoed, depends on the paradigm that is accepted in the community in which the theory is advanced. Again, wittingly or unwittingly following Wittgenstein, Kuhn insisted. that while theory formation is controlled by the prevailing paradigm (normal science), paradigm formation cannot be controlled by or accounted for by any kind of observation- not even (in an implicit aside against Karl Popper at the beginning of chapter VITI) by a falsifying observation. Falsifying observations, Kuhn might have added in that place, would be pre-linguistic or extra-paradigmatic events and can, therefore, not take place. Kuhn also developed another aspect of Wittgenstein's thought without any further reference to Wittgenstein. In his Philosophical Investigations Wittgenstein called the emergence of language-games 'spontaneous':' By this he could only mean that their emergence and their particular fonn is arbitrary and not related to anything that either precedes or surrounds anyone game and that no game is a response to or causally related to anything, least of all to a preceding game. It is true that the remark is a little cryptic. The crypticality is not dispelled by anything one fmds on the topic in Garth Hallett's A Companion to Wittgenstein's "Philosophical Investigations."l6 We fmd the notion of such 'spontaneity' again in Kuhn and there it is made to loom large. Henry Le Roy Finch enlarges lyrically on Wittgenstein's notion of spontaneity and
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explains it explicitly by using Kuhn's use of it l7 Paradigms, Kuhn says, emerge arbitrarily. They are not caused by any preceding paradigm, are not related to any other paradigm, and are not intelligible as a response to any other paradigm. They are abandoned because and when people lose interest in them, which happens in the course of nature simply because sooner or later their upholders die out The oc.casion for the emergence of a new paradigm is a growing dissatisfaction with an old paradigm. This, if one calls it that, is the 'cause' of the new paradigm. The content of the new paradigm, however, is completely unrelated to the old paradigm which it replaces. It neither contradicts nor elaborates an older paradigm. It simply replaces it arbitrarily. In this way Kuhn has elaborated Wittgenstein's conception of spontaneity into one of the corner-stones of his philosophy of knowledge. The more sober view would be that while paradigms and language-games are not 'determine(f or 'caused' by what precedes them, they are not irrational fulgurations because they: (1) emerge as responses to problem situations; and (2) are retained selectively after the critical appraisal of a whole range of comparable proposals. The Wittgenstein-Kuhn view simply states that the new paradigm is a response to a dissatisfaction with an old paradigm. But what I here mean by 'response to a problem situation' is something quite different "The response in favor of the new paradigm comes after the appraisal of comparable paradigms. The decision goes in favor of that new paradigm which explains more than the old paradigm. This is where the anti-chance factor enters and where rationality intrudes. The Wittgenstein-Kuhn view prevents such a sober evaluation of paradigm change. For, since 'meaning' is defmed in terms of paradigms, all 'meanings' are variant relative to a paradigm and cannot be compared. Hence, in the Wittgenstein-Kuhn position a rational appraisal and comparison of proposed paradigms in terms of the size of their explanatory power is impossible. I would argue against such reinforced, circular dogmatism that since the tyranny of the paradigms is what is in question, that tyranny cannot or ought not to be paraded as a reason for the denial of meaning invariance and the consequent rejection of the possibility of comparisons. In adopting Wittgenstein's almost casual remarks about the spontaneity of language games, Kuhn has introduced an irrational element into the history of knowledge. Many commentators have diagnosed an irrational element in Kuhn. They have spotted that in Kuhn's philosophy of knowledge, theories are largely immune from falsification by observation. It is true that in this regard Kuhn's philosophy contains an irrational element, but in almost all post-positivism philosophies of knowledge there is a degree of such immunity. The really irrational and original featW"e of Kuhn's philosophy consists in his adoption of Wittgenstein's concept of spontaneity. Paradigms, he is saying, succeed one another without cause or reason. They do so spontaneously. The notion that paradigms succeed one another irrationally was not unknown before Wittgenstein. The anthropologist Bronislaw Malinowski had viewed every single primitive society as a self-consistent
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whole and though, not interested in history as he was, he had never made any pronouncements as to the reasons for the origins of any particular primitive society, he would have said, had he been pressed, that they must have arisen 'spontaneously'. Similarly, Oswald Spengler, an exact contemporary of Malinowski, had argued that every circle of culture is a self-consistent whole and can be understood entirely in terms of its own 'paradigm'. Each culture, he said, arises spontaneously and its emergence is not to be understood or explained as the result of preceding conditions. Most other paradigmatists, however, had linked the emergence and demise of paradigms with the help of a developmental law. Thus, Frazer had seen human history as a progression of paradigms of magic, religion, and science; he had not admitted that these paradigms had emerged spontaneously. On the contrary, unable to explain how one had caused the next, he had simply assumed that there is a developmental law which governs the order of succession. It lies, of course, in the nature of paradigmatism that one cannot explain the rise of one paradigm as a result of anything that happened in the preceding paradigm- for that would imply that whatever happens inside anyone paradigm can have extra-paradigmatic consequences. Hence, paradigmatics are thrown back either upon the historicism of developmental laws, or upon the doctrine of spontaneity.
III. Derrida's Deconstruction and Foucault's Epistemes The question of 'the philosophical foundations provided by Wittgenstein is even more urgent because of the emergence of a philosophical movement in France which runs parallel to the Wittgenstein inspired movement in Germany, England, and America. This parallel development makes one think that Wittgenstein's sociologisation, though it unquestionably preceded similar thoughts in France, was something that 'lay in the air' and that was symptomatic of something that transcended the immediate concerns of Wittgenstein. However this may be, preoccupation with Wittgenstein is important either because he is symptomatic or because he is a seminal influence. I am not in a position to state whether Foucault and Derrida owe their idea to Wittgenstein or not. But it takes very little reflection to judge that their theories of knowledge and of literature work with the same principles. Derrida argues that we can understand a text only by deconsbUcting it into the metaphors and idioms of which it is composed. It cannot be understood by comparing it to anything outside itself, i.e., by looking at the world it purports to describe. With this doctrine that 'il n'y a pas de hors texte', Derrida echoes Wittgenstein's insistence that there are no pre-linguistic meanings and that anything we say constitutes its meaning but does not reflect or describe a pre-linguistically intuited or pictured state of affairs. The text, Derrida is telling us, is not determined by an extra-textual or
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pre-textual meaning which is pictured in the mind of its author and which the text reflects so that we might scrutinize the text and judge it by its ability to render that pre-textual meaning and compare it with that pre-textual meaning to see whether it is reflected accurately by it. One can on the contrary, Derrida says, determine the meaning of the text without regard to its author and the meanings he had in his mind, by simply examining the text's structure, Le., by asking what is implied by the fact that in the text there is a recurring opposition between 'conscious' and 'unconscious'. Such and other oppositions, though they are essential to the text's purported argument and are supposed by the author to portray pre-textual meanings, are in reality key words that give the game away because they function in ways that subvert these oppositions. Commenting on Rousseau, for example, Derrida wrote in his Of Grammatology that Rousseau considered writing a supplement to speech and masturbation a supplement to sex. 18 Thus Rousseau. Whatever meaning he wanted to convey, a purely text-bound interpretation of such passages reveals, Derrida says, that in Rousseau one cannot separate writing from onanism. There is, moreover, no way by which one can determine whether Rousseau was writing when he thought he was masturbating or whether he was masturbating when he thought he was writing. Innocent readers of Rousseau might imagine that the question could be resolved by reference to what Rousseau had had in mind, that is, by looking at his intention when he was writing. But Derrida suggests - in truly Wittgensteinian or possibly only Wittgensteinesque spirit - that we cannot look at what went on in Rousseau's mind and what his intention as the author of the text was. Therefore, Derrida concludes, we are left with nothing but the text to determine the meaning of the text. The imaginings of the innocent reader, as well as of Rousseau himself, may indeed be innocent The meaning of the text, Derrida says, exists not only in isolation from its author, but despite the author's intention and easily in flagrant contradiction to it. Jacques Moood once pointed out that if Martians approaching the earth in a space-ship saw people feeding grain into a mill, they would be unable to establish from mere observation whether the mill was being used to grind the grain or whether the grain was being used to keep the mill turning. There is, obviously a difficulty here for people who come from Mars. Derrida appears to have overlooked the fact that readers of texts are, as a rule, not Martians! If Derrida is pure Wittgenstein, Foucault seems a jump ahead in that he presents to us something very similar to Kuhn's elaboration of Wittgenstein. Kuhn argued that both truth and meaning of any theory is relative not to the world it is a theory about, but to a paradigm the validity of which depends on the fact that it is accepted or supported by a community. Foucault proposes similarly that we view any theory as a derivation from a central episteme and that epistemes come and go not in accordance with our knowledge of the world or in response to our observation of the world, but with the centuries- at least as far as western society is concerned. It may
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be correct to say that nowadays both Kuhn and Foucault as well as Derrida are greater cult figures and more influential than Wittgenstein. But if one wants to assess the enormity of the epistemological revolution here proposed, it is timely to reduce all these thinkers to their common denominaUx" and to investigate the soundness of Wittgenstein's enormity.
IV. The Hermetically Sealed Bottle The enormity of that enterprise consisted precisely in the view that the bottle in which the fly found itself was hennetically sealed and not transparent With this conclusion it is established that each speech-community is a law unto itself because it prescribes the rules which determine the meaning of the sentences permitted in it This conclusion is by itself quite stultifying, for it pennits the espousal or perpetration of any nonsense and mischief provided one can perform it within a speech-community or fmd a speech-community which has adopted rules or which is already sporting rules which will allow such acts or such thought behavior. All outside criticism and any scrutiny in terms of external standards is automatically eliminated. Moreover, the argument itself which leads to such a stultifying conclusion, is faulty. To say the least, it is based on a certain defmition of what counts as 'thought' and, at best, it is circular. For mental contents such as states of consciousness or intentions are excluded as determinants of meaning because in the speech-community in which Wittgenstein must have believed himself to have been living, the rules of language prohibited sentences in which words for mental content occurred. Wittgenstein, of course, argued that all speech-communities, since they are rule-governed, must prohibit words for such mental occWTences because, by the nature of the meaning of 'rule', there cannot be a rule which could conceivably apply to a private or inner sensation. But this additional hypothesis, which saves the argument, is only acceptable if one is willing to accept the premise that meanings and rules are functionally dependent on each other- which is precisely what many people might rightfully question. I will return to this questionability presently. It was Wittgenstein's good luck that he expressed so many aphorisms, because he thus provided an opportunity for many of his admirers to eschew this fundamental issue and to occupy themselves with less crucial matters. The fme books and papers about Wittgenstein by Anscombe, Stenius, Hacker, Finch, Pole, Specht, and many others never face up to the heart of this matter. Since Wittgenstein had never publicly committed himself to the fact that these conclusions were the heart of the matler, commentators have been able to comment on him and admire him without so much as breathing a word about the heart of the matter.
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V. Advocatus Dillboli Before embarking on a more detailed criticism of David Bloor's comprehensive claim that Wittgenstein fmally provided a basis for a total sociology of knowledge and furnished the foundations for the view that all knowledge is socially detennine.d, I would like to play the advocatus diaboli by listing the considerations which push one in the direction of the view that all knowledge is socially determined. In providing a philosophical foundation for the totalitarian claims of the sociology of knowledge, Wittgenstein was not necessarily suggesting something nobody had ever noticed before. On the contrary, his emphasis on the social nature of man and his belief that life or action preceded theoretical knowledge or meaning and was not derived from it had often been made, and Wittgenstein, aware of the cogency of these views, re-emphasizedthem and argued that they could be overlooked only at one's peril. If one peruses earlier arguments in favor of the importance of social rules for knowledge, one will often fmd that they are a little more general and more persuasive than Wittgenstein's reiterated single argument that one cannot 'talk' about mental contents and intentions because there cannot be a private 'language', and therefore not quite so exposed to weighty criticism as Wittgenstein's argument. If anything, the considerations I am going to list would strengthen Wittgenstein's conclusion, though not the special argument which led him to
it Knowledge cannot stand on its own feet Sooner or later every justification of knowledge, any appeal to evidence, even an attempt at falsification, must take something for granted that is itself not cognitive. There is no place here for a systematic survey of the non-cognitive factors involved in knowledge, and, at any mte, their nature and respective relevance will always be in dispute. Nevertheless, they are legion. If one takes 'criticizability' to be a criterion of knowledge, one must face the question as to whose criticism will be relevant and how one can decide whose criticism will be worth consideration. All knowledge involves some kind of ontology. One may demand that any ontology presupposed must be minimal, but if there is an ontology, clearly, it can itself not be the result of 'knowledge'; or, if it is, one will involve oneself in an infinite regress. One could - and this has indeed been tried - hold a 'causal' theory of knowledge in which one labels as 'knowledge' the results of causal action upon the human nervous system. But here again, there is an infmite regress: for one's detennination of what is a 'causal' action depends on one's knowledge. In such cases we would have to ~ve a theory as to what causes what before we can determine which causal action effects knowledge in our nervous system. And speaking more generally, it is hardly surprising that an analysis of knowledge always pushed one back to non-cognitive factors. For in so far as knowledge involves words and abstractions, in so far as it is verbal and general, it is obviously not a replica of what is known. If it is not a replica, it must be made of different stuff- of verbal
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abstractions, of neuronal events, etc. Then the question arises how such abstractions and events 'refer' to what is known. 'Reference' has been a notoriously difficult concept. Whichever way one turns, to speak with Hans Albert, 19 when one seeks to justify knowledge, one ends up with the Miinchhausen-Trilemma: one will have to engage either in an infinite regress, or in a vicious circle, or in some form of dogmatism. This is the reason why it has become so widely fashionable to have recourse to social rules and institutions if one is looking for a frame-work for knowledge. Or examine the matter from a more pragmatic perspective. The notion of 'plausibility' plays a crucial part in the determination of all knowledge. In one sense, at least, it is a psychological notion and is dependent on the social support one is getting and on the opinions of one's fellow-men. When an epidemic breaks out, there is an immediate search for information about the virus or bacteria involved. Lots of people are appealed to and they, in turn, appeal to others. Some speak with great authority and offer helpful advice. One has, however, to go avery, very long way before one will encounter anybody who has actually looked at the bacteria in question under a microscope; and even when one fmds somebody like that, one will be told that in so looking he has availed himself of other people's researches and theories. In short, information that is not socially mediated and supported is a long distance away and plays, in most cases, a minute role. Or take a different case. Communication is infinitely easier and more assured of success if it is taking place in a peer-group- ethnic, social, racial, religious or whatever. In such closely knit societies, one can be assured that one is being understood even though one can never quite spell out what one is saying. A gesture, a joke, an allusion is often more effective than a long-winded, articulate sentence communicated to a stranger. By the same token, in a peer-group, there can be generated a sense of intellectual euphoria on the basis of consensus. As against this, when one is alone and completely by oneself, no matter how closely and accurately one is observing nature, there remain nagging doubts. And when other people claim to have observed something that contradicts one's own observation, one requires extraordinary psychological fortitude to remain sure of what one thinks one has seen. Without any support from other people, one will, in the end, doubt one's own eyes. If one bears all these difficulties, or even only some of these difficulties, in mind, one can see how much a recourse to the argument that knowledge and meaning is determined by the rules which obtain in anyone speech-community has to recommend itself. Such recourse solves all the difficulties at once and is the perfect answer to sceptics of all ages and all complexions. First, the recommendation runs, we must have a speech-community and ascertain its rules. Such communities are a fact of human life. Their existence posits the rules of how meanings are established, and with such an appeal to the primacy of life, we can understand that the meaning of knowledge as well as the knowledge of meaning becomes a function of community. With an appeal to the primacy
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of life and the communities in which life is being lived, the recommendation hitches itself to the position advocated by many thinkers from the 18th century onward. Reason is the slave of passion; the true voice of feeling overrides the dictates of reason; 'in the beginning was the deed'; existence is prior to essence; such are the various formulations advanced before Wittgenstein. After Wittgenstein, the ultimate priority and the primacy of the speech-community has been asserted and laboriously defended in Germany by Karl-Otto Apel in Germany and by Richard Rorty in America. Given the long list of considerations which make community such an important factor in knowledge and the infinite difficulties that arise if one does not, Kuhn and Foucault, Apel and Rorty ought not to be dismissed out of hand. As mentioned, Hans Albert, a critical rationalist if there ever was one, has repeatedly shown that if one dismisses these people out of hand, one will be left with what he calls the Miinchhausen-Trilemma: either an infmite regress, or logical circularity, or dogmatism.20 Once knowledge and meaning are reduced to the rules that obtain in a speech-community, the task that lies ahead becomes henneneutical rather than epistemological. As soon as one has satisfied oneself that the meaning of one's knowledge is defmed by the use of the words the rules of one's community prescribe and permit, one can cease to worry about discovery and cognition and confme one's attention solely to the exegesis and explication of the prevailing rules. In this direction there lies a rich opportunity for the cultivation of old trnditions for celebrating them and for powing them into new shapes and formulations. Philosophers become the guardians of the rules of their community and the practice of culture will consist in the edification to be derived from the meditation upon these traditions. Given the precariousness of knowledge and the well-known difficulties of establishing meanings, the pursuit of such culture under the guardianship of hermeneutical philosophers is not a bad thing. One cuts one's losses, so to speak, and cultivates one's garden- as one of the great sceptics of the 18th century put it. Let me explore the recommendation to retreat to a speech-community as the ultimate standard bearer of one's meanings more closely with the help of Hegel. Every single individual, Hegel has argued, has private consciousness and is aware of it. But being totally alone, he is also totally free to have any content he wishes in his consciousness. The question which content is right or adequate and which is not cannot arise. He does not express it verbally and is not dependent on language. He can make himself aware of anything or in any way he choses. As soon as such an individual confronts another individual, the two of them, subject to such arbitrary determinations of the contents of their consciousness, must become locked in a battle. One consciousness must try to subdue the other. The situation is agonal, not 10 say agonizing. There is no third party, no external standard of reference, no recognized way of deciding between two conflicting contents. One may say that he is seeing a
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table in the room. The other may say that she is seeing a chair. In the absence of any coordinates, there cannot be anything but a battle. The decision whether there is a chair or a table will be left to the power of will and personality. When a third person joins, there appears the possibility of a judgment upon the two claims. The third person can side either with the man or with the woman and thus make it into a cootest between two against one. His or her decision which side to support must be cognitively arbitrary- even though it may be detennined by emotional or economic considerations. At any rate, as soon as there are more than two people involved, there is a chance for the contest to become subject to rules-- for when it is two against one, the decision of the two can become expressed as a rule. The battle will cease and a political order must arise. With the cessation of agonality, however, we come to the point where cognitive and intellectual battles are decided by non-cognitive and non-intellectual standards. For rule-making is a socio-political process and rarely controlled by epistemological considerations. Up to this point we can see that Wittgenstein's strategy followed Hegel's analysis almost word by word. Hegel's description of the vagaries of the lonely consciousness have since been underpinned by Freud. Quite early in his career Freud thought he had discovered that the hysterical behavior of many of his woman patients had been caused by the fact that they had been seduced by their fathers when they were children. Eventually he found out that most of them had actually not been seduced by their fathers, but had harbored the wish that they might be seduced by their fathers. Freud 'then concluded that hysteria can result from a wish as soon (and possibly sooner) as from a real trauma. This, in a sense, was his most important discovery and contribution to psychology. Th~ content of an individual consciousness, be had seen, is not necessarily or completely determined or induced by experiences, but can be generated and shaped by phantasy and such phantasy can produce somatic reactions. If one wants to establish a corrective to such phantasy, there must be rules of therapy. It is certainly not enough to assume that as long as little girls are not actually seduced by their fathers, hysterical symptoms will not develop. With this insight, Freud has to be placed, by the historian of ideas, half way betwePJ1 Hegel and Wittgenstein. It is a great pity that Jeffrey Masson's recent desire to create a sensation21 has made him cloud this fact Masson imagines that if hysteria is linked to seduction, there must have been individual experiences of actual seduction. IT there were not, then hysteria could not result By allegingt on the contrary, that phantasy can take the place of real seduction, Freud, Masson suggests, had detached psychoanalysis from reality and real objects. Masson got hold of the wrong end of the stick. The greatness of Freud's insight lies precisely in the opposite direction. Freud discovered that the individual consciousness t if left to itself, can be injured by phantasy and wish as soon as by a real trauma and that reality is intruded into subjective phantasy, step by step: frrst, through the somatic
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consequences of pure subjectivity and, second, through corrective action upon the lonely consciousness, i.e., from a therapeutic induction of that lonely consciousness into a rule obeying community. I rarely recommend Wittgenstein to anybody, but it might have helped Masson if he had made a proper study of Wittgenstein Of, for that matter, of Hegel. Let us return to Hegel. Unlike Wittgenstein, Hegel did not remain content with the fmding that the agonal situation which must arise when two people face each other, each equipped with nothing but their private consciousness, is fmally resolved by the emergence of a speech-community of at least three, and preferably more than three, people. He continued his analysis by noting that allover the earth such communities have arisen and that sooner or later they must come into contact with each other. There was no use arguing that, though in contact, they must keep away from each other and agree to differ. While the rules of each community are an ultimate standard to that community, Hegel argued, there must be a way in which one can compare the standards of one community to those of another. Relativism, he admitted, was a fact of life. But relativism has to be attenuated by standards of comparison which are based on the consideration that there is commensurability and that there must be at least some 'meanings' which are invariant, Le., not derived from and subject to the usage prevailing in anyone community. Wittgenstein, as is well known, had denied such invariance because he could only imagine that if there were such meanings, they would have to be culled from private subjectivity- something which he said, and Hegel would have agreed, was impossible. I do not wish to go into Hegel's way of attenuating relativism and meaning variance. For all I know, Hegel's recommendations as to how this can be done may be untenable. But I wanted to stress that he endeavored to move beyond the fmding that when speech-community meets speech-community, there can be nothing but an agreement to differ or a continuation of the agonal situation which must arise when two lonely individuals come to face each other.
VI. The Grand Bifurcation I cannot disagree with Bloor's reading of Wittgenstein. I believe that it is entirely correct and that Bloor's reading merely dots the i's which have already been made by those Wittgenstein commentators who have elaborated upon Wittgenstein's sociological orientation in general and upon his reduction of knowledge to its social, non-cognitive dimension in particular. My quarrel with Bloor is that he has failed to offer a criticism of Wittgenstein's analysis of subjective Of private consciousness. Had he done so, he would have seen that Wittgenstein's retreat to sociology is not nearly as compelling as Wittgenstein imagined, and that it is much more questionable to establish the theory of knowledge on a sociology oriented
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Wittgenstein basis than Bloor lets OD. Let me take these two criticisms of Bloor in turn. Wittgenstein's retreat is based on his argument that we cannot be aware of our intentions as mental events apart from a linguistic expression about them. Since linguistic expressions are rule governed and since it makes no sense to think: of rules apart from cOl-nmunities of people who obey rules, it follows that we cannot be aware of intentions or meanings other than those we can express linguistically and that, therefore, we cannot presume that the rules of any community are determined by mental contents, be they meanings or intentions or thoughts or whatever. On the contrary, we must conclude that whatever mental events we can be aware of must be mental events which are detennined by the uses that prevail in the community we are members of. Wittgenstein is here bifurcating nature. On one side there are subjective, mental events. On the other side there is language. This bifurcation is no mere repretition of the bifurcation that was attacked earlier this century by Alfred North Whitehead Whitehead complained that science, supported by many philosophers, was bifurcating nature by distinguishing between primary and secondary qualities. By this distinction, substance was stripped of all emotional qualities such as color, love or beauty, the latter being located entirely in the perceiving mind. On one side, he said, there is dead, quantified matter; on the other, mental contents and human feelings. Whitehead complained of such bifurcation and then developed a very intricate cosmology and methodology to overcome it, i.e., to show that feelings are located in matter. Whitehead was not very successful and found little support The bifurcation he had complained of eventually led, as he had predicted, to vulgar behaviorism and/or the theory of the identify of mental and material events. Wittgenstein's bifurcation was very different. He thought he had detected a total dualism in every person. His dualism was so complete and unbridgeable that it has often been mistaken for or identified with the linguistic usage based attack on dualism by Gilbert Ryle. Ryle indicated that, provided we avoid category mistakes, linguistic usage, at least for English speaking people, simply prohibits the fonnation of sentences that look as if dualism between mental and non-mental events were a correct account. Although Ryle was widely read at the time, there was something utterly jejune in his argument. If he meant by linguistic usage the actual words spoken in English by averagely competent users of the English language, he was doing lexicography and, by, any standards, his argument was incorrect For correct English is full of sentences which appear to indicate that mental and non-mental events are different. If, on the other hand, he did not lexicographically idolise actual English as spoken but was making a normative proposal, he ought to have provided at least some evidence why his proposed norms that would prohibit sentences about 'mental' events are valid. Wittgenstein was much more sophisticated, for he did not rule out sentences about mental events. He merely insisted that they could not be forged because of prior mental events. There are
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language-games, he added, in which sentences about mental events are allowed by the rules and, therefore, perfectly acceptable. Moreover, he never maintained that there are no subjective mental events. He merely argued that they are forever isolated from the roles that govern speech and that the insulation of speech from them is absolute. Nonnative or lexicographical, Ryle considered only one single universal community of English speakers. Wittgenstein realized that all rules are relative to special cliques and that the world is full of lots of cliques. Nevertheless, the mistake made by people who confused and keep on confusing Ryle's rejection of dualism and Wittgenstein's extreme dualism, is excusable. For if there is no conceivable bridge between private subjectivity and public language, public language utterances stand alone and isolated and are indistinguishable from that linguistic behaviorism which seems one step further along by denying that subjective awareness actually 'exists'. In a sense, the difference is truly 'academic'. For what is the point of either denying or asserting the presence of events which cannot make themselves felt and which, therefore, cannot be taken into account? However this may be, Wittgenstein did not seek to deny that there are mental, subjective events in our consciousness. He merely insisted that one cannot speak of them. Whereof one cannot speak, thereof one must remain silent, he had said quite early in his career. The bifurcation he envisaged was absolutely total for he could see no way by which one can speak of subjective mental events. For that matter, Wittgenstein simply repeated what the Gennan poet Schiller had remarked on hundred and fifty years ago: "If the soul speaks, alas! the soul is no longer speaking." Resting content with such bifurcation, Wittgenstein considered it impossible for any pre-linguistic meaning to influence a linguistic expression, and so it followed that the meaning of all linguistic expressions must be controlled from the inside, so to speak. They must be their own meanings and cannot be held to 'express' meanings; nor can they be judged or criticized as to whether they succeed in expressing meanings. Bloor fully endorses this argument. Wittgenstein's argument, however, is false. One can demonstrate the falsity in a variety of ways; I will here confme myself to two particular arguments against Wittgenstein's reasoning, one taken from biology and the other from psychology and literature. As we are all living in communities, there is an adaptive advantage for every single human being in the ability to gauge the actions and behavior of the other members of that community. The obvious way of doing so is by observing one's own self or one's own mind and one can do that in a way in which one is privileged. Nobody else can observe my mind in that manner. Wittgenstein himself, to the best of my knowledge, never denied this. Having engaged in self-observation and of selecting some and of holding others back. However - and this is equally crucial for evolution every organism must be capable of a minimum of abstraction so that it can recognize those organisms which are sufficiently similar to itself and refrain from eating them and chose them as sexual partners. In other words,
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speciation depends on the ability to abstract and disregard gross individual charactaristics in other organisms so that every organism can distinguish between those organisms which are sufficiently similar to make speciation possible and those which are so dissimilar that they can either be eaten or sexually avoided. In short, in spite of the reality of individualism, the supposition that other individuals at least of the same spe.cies are suffICiently similar for one's own subjective inner feelings to be used as a model for their behavior is by no mean arbitrary, as Humphrey seems to imply, but is grounded in biology. Let us continue beyond Humphrey with this biological perspective. Using again the Anthropic Principle, we can say that the world must be of a certain type and have certain qualities, otherwise we would not have evolved and would not be sitting here to think about the world. Since we are sitting here, thinking about the world, there must be a relation between such thinking and the world we are thinking about. In thinking, we start with the most private, most subjective content of consciousness. Then we proceed to the plausible assumption that other people are similar and not unique and that we can proceed further to modelling their private thoughts on our private thoughts. Thus, privacy is at frrst somewhat abated and, a litde later, attenuated and eventually threaded into the web of communication. From this point on, we can recognize why human beings have developed 'rules' for communal life. These rule systems are far from 'spontaneous' in Wittgenstein's sense. On the contrary, they satisfy a need for orderly communication of private thought contents and can be evaluated and scrutinized. If they satisfy that need well, they are good or correct; if not, they are not correct- or, correct to the degree to which they respond to that need. Here we arrive at Wittgenstein's position that all statements of knowledge are governed by language use. But we are arriving at this position via biology. And in doing so, we can see that rule systems are capable of being criticized. Wittgenstein had thought that they cannot be criticized because criticism, he took it, would have to consist in comparing a subjective intention or meaning (pre-linguistic event) with the rule system. Now we can see that there is an alternative possibility of criticism, because we have arrived at our rule systems from biology- i.e., we do not see them as supposed linguistic expressions of pre-linguistic meanings.
VIL Cartesian and Freudian Dreams Since the development of .biological thinking on which these arguments against Wittgenstein's bifurcation are based took place after Wittgenstein's death, it may seem a little Wlfair to advance them against him, though they must be taken to affect one's evaluation of Wittgenstein's impact on contemporary thought in general and upon Kuhn, Foucault, and Derrida in particular. They also ought to cool Bloor's ardour. However, since subject
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feelings and private, inner awareness have of old been the special concern of poets, one might seek the opinion of poetry and eschew the views of literary critics like Derrida. Wittgenstein's position was that one cannot bridge the gap between subjective awareness and linguistic expressions because we are unable to express the former linguistically. However, when one shifts the perspective even slightly, one can arrive at a different viewo The gap between subjective awareness and what can be expressed in language derives from the fact that we cannot make meaningful statements about subjective awareness, but can make meaningful statements about meaningful statements, Le., one cannot 'talk' about subjective awareness, but one can 'talk' about linguistic expressions. Though both formally and substantially different, this distinction between what one can and what one cannot talk about echoed a much older and more naive distinction between sense and nonsense. It certainly rons parallel to the old verificationism of the Vienna Circle, and of Wittgenstein's own Tractatas, that Bible of positivism, as it has been called. However, it all depends on what one means by 'meaning'. Let us suppose that we mean by 'meaning' 'critisisability'. With such a supposition, the gap is narrowed and might even disappear, for we now have a criterion of meaning which links subjective awarenesses to linguistic expressions. If, on the other hand, one uses 'sayability' as a criterion of 'meanings', one is driving a wedge between intro-spectively available subjective inwardness and public declarations. 'Sayability', by the way, is not all that different from 'verification', and the point on which Wittgenstein differs from the other Vienna positivists is simply that they were very naive about verification in that they held that a subjective stale such as 'observation' could become 'sayable' as a protocol-sentence. Wittgenstein, more realistic, realized that no subjective state, not even a sense impression, can ever be sayable. If we can show that subjective awarenesses are as criticisable as linguistic expressions, if we can show that there is a way in which something we know of only by introspection and as inward subjectivity can be compared with something else and scrutinized and can become capable of being criticized, then we can establish a link between subjectivity and public declarations and bring them together. While it is admitted that 'sayability' is no such common characteristic, 'criticizability' might be. Linguistic expressions are critisable because one can check them against the rules that prevail in the language-game one is playing. Subjective awarenesses can be criticized, at least in the flCst instance, nonverbally because one can check them against the inner images which almost invariably accompany them. While the inner subjective awareness cannot be criticized, the accompanying image it conjures up can, for it can be either adequate or inadequate. Inner awareness and a linguistic expression have, therefore, something in common. The total bifurcation appears only if one chooses a criterion of meaning which, by definition, excludes the inner awareness and includes the linguistic expression.
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Subjective meanings, that is, our innennost subjective awarenesses or feelings have an ontology, but no epistemology. We can be aware of them and know that they take place and exist But it is impossible, and here one must agree with Wittgenstein, to give a literal description of them. A literal description of my sadness would always take the grammatical and semantic form a statement about somebody else's sadness would have to take. If I say 'I am sad', I am treating my sadness as if it were somebody else's sadness about which I can say 'he is sad'. Since the two sadnesses are very different - one a subjective, obscure feeling, the other an inter-subjectively intelligible sentence governed by language rules - one and the same type of sentence cannot describe both kinds of sadness. This is why there can be no literal description of my sadness in words which we use to describe someone else's sadness. Hence, there can be no epistemology of my sadness. In principle, one cannot give a literal description of my sadness, i.e., of my subjective condition, any more than one can literally describe any emotion or, for that matter, a human face. In passing, I would add that it is altogether vary difficult to state what precisely a 'literal' description of anything would be, and one would have to be a very died-in-the wool positivist or empiricist to believe that there are some literal descriptions and that they can be distinguished without further ado from non-literal descriptions. Nevertheless - and this is the crucial point - there can be oblique statements about my sadness. As long as such an oblique 'statement' about my sadness is criticisable, it has cognitive significance and something in common with language expressions. If we can establish that 'statements' about my own darkly obscure subjective consciousness can be criticisable even though they are not literal descriptions which can be either true or false, then we can admit them to the forum of discussion and allow them an influence on the establishment of language-game rules. In order to show that subjective awarenesses can be referred to obliquely and that statements about them are not flatus sine voce, let us consider a number of possibilities. 1. If we have a subjective intention, we can find an objective correlative to it. We can point at a state of affairs and designate it as a symbol of the subjective intention. In dreams as well as in making sense observation, the first experience is an image, not a verbal description of an image. The image is a statement about the subjective experience. The experience itself is totally pre-linguistic. The image is semi-prelinguistic in that it can be described but neither accurately nor sufficiently completely for other people to form the same image after hearing a verbal description of it One can describe a face, but as the recourse to identikits in police investigations proves, such descriptions are vague and ambiguous. In pointing at an image we are not performing a verbal act which could be criticized. But one is designating a state of affairs, initially only to oneself, as a symbol which refers to the subjective feeling. And such designation can be criticized. First, it can be criticized by oneself; second, when offered pictorially to others, it can be criticized vaguely by reference to an ambiguous verbal
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description it accompanies. Gradually, thus, one can wode forward toward verbal expressions. Final verbal statements can be criticized not by simple confrontation with a subjective experience, but in the light of the intervening series of pictorial images. Images which symbolize do not describe or portray the subjective event, but refer to it obliquely. The designation of a symbol can be right or wrong, or partially right. Whatever the success of the designation, it can be criticized. One can erect a whole circle of symbols around one single subjective feeling and then eliminate from the circle all those that are 'false'. This is not a question of fmding one and only one symbol for each subjective state. Even after the elimination of the false symbols, the circle will consist of more than one. Hence we speak of oblique reference to the subjective event. In any case, we have now found a method of admitting subjective feeling to the status of events about which one can speak, albeit not literally. 2. We are all familiar with involuntary memories. Suddenly, a sound or a smell can bring to our attention in the privacy of our mind, the memory of a door, a face which was linked to a similar sound or smell many years ago. If the sound or smell forces us to have a memory of an event which never was, or if any event which did take place is brought into our private mind by a sound or smell that was not linked to it, then we have made a mistake. Here again we have found a method which allows us to take up a critical attitude to very private and subjective awareness. Thus we have found a way of introducing privacy into the world of public and social communication. Such considerations show that whether we come from biology or from the world of purely subjective feelings, the bifurcation between subjective consciousness and social communication is more apparent than real. Around the things one cannot speak of, we can now vary Wittgenstein, one can make a circle of symbols. And whereof one cannot speak, thereof one can have involuntary memories mediated by sounds or smells. Such 'voicing' of subjectivity and private meanings are pre-linguistic. But this does not mean, pace Wittgenstein, that they must forever remain confmed to the sphere of silence. They can be connected by oblique routes to the linguistic statements we can make to other people. Wittgenstein's approach to the entire problem was perverse. His contention that we cannot go behind language could mean either of two things. It could mean either that we cannot use language to talk about language or it could mean that we cannot use pre-linguistic meanings to scrutinize our use of language. In the fust of these two meanings the contention is obviously correct. If thinking is equated with speaking and if one cannot allow one's speech to be controlled by anything pre-linguistic or non-linguistic, what can be the point of talking critically about talking? One could, of course, introduce a meta-language-- but Wittgenstein never did because any meta-language would have had to be shaped either by non-language criteria or by the uses of another language-game. In the latter case one would have to admit that
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not all games are of equal value-- which Wittgenstein refused to do. If our linguistic expressions are not so obviously meaningful that they have to be talked about and explained, then we cannot hope to use language to do so. And yet, this is precisely what Wittgenstein was doing all his life. He used language to talk about language and thus went behind language or tried to do so. He talked incessantly in language about language. When I used to go to his seminars in Cambridge I was almost immediately impressed by the perversity of his behavior. The other members of that seminar were not so struck by this perversity. They were, on the contrary, so impressed by the psychopompic personality he projected and now sensitively delineated by W.W. Bartley III in his Wittgenstein,22 that they failed to see the perversity of his project In the second of the two meanings the contention is false. One can go behind language to pre-linguistic meanings and link them obliquely to linguistic meanings. One can do this either by using biological considerations or by falling back on objective correlatives to subjective feelings or by scrutinizing involuntary memories- to mention but three different strategies. And yet, this second meaning of the proposition that one cannot go behind language was the one which Wittgenstein defended. The most ultimately subjective event, indeed, the archetype of subjectivity, is the dream. This was acutely observed by Descartes in his Meditations. Descartes commented that there was no way of telling whether one was dreaming to be awake or, when awake, dreaming. "How often have I dreamt," he wrote in the opening pages of the Meditations, "that I was dressed and occupied this place by the fue, when I was lying undressed in bed?" He insisted that there was no telling, given the total subjectivity of the event, whether being awake was a dream or whether dreaming, one was awake. However, he continued, the mere fact that one was having images in mind, regardless of their ontological status, proved that one was having something in mind and that there must be something or someone to have something in mind. In passing, he also mentioned that in dreams there were represented not always "those same things" one was aware of when awake, but "sometimes others less probable, which the insane think are presented to them in their waking moments." Given the purpose he had in mind, which was to distinguish between utter subjectivity and a more objectively knowable world, Descartes could afford at that time to neglect the content of dreams. Even so, it is remarkable that Descartes had not noticed that common-sense dreams are actually very me and that when they do occur one usually wakes up with a feeling that one has been wasting good dream-time in thinking what one could have been thinking when awake. However this may be, Descartes did not avail himself of the opportunity offered by introspection into the pure subjectivity of dreams to compare such subjective images with those intersubjective images we are capable of when we are what is commonly associated with 'being awake'. Instead he concentrated on subjectivity and on what such subjectivity obliged one to believe. Freud, an infmitely more observant psychologist, realized that the
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interesting thing about the pure subjectivity of dreams is not their subjectivity, but the fact that their contents or the shape of their images differ so much from those of that other, less subjective state of being awake. Unlike Descartes, Freud concentrated on their bizarre aspect, their essential unintelligibility, and on the fact that they were a disguise" He concentrated on the comparison of those 'bizarre' images with the images we have when awake, without being overmuch interested in the question as to which of those two states was the more 'real' or what one might prove or disprove by concentrating either on the one or on the other. What mattered, he argued, was the comparison of one set of images with the other set of images- how the.y related to each other. Admittedly this was a totally un-Wittgensteinian approach. In Wittgensteinian circles one inclines towards Descartes in this matter, not towards Freud, though one refrains from drawing Cartesian conclusions from this inclination. In these circles, the utter subjectivity, the fact that dreams are wholly asocial, psychic products, is dismissed. The similarity to Descartes consists in making nothing of the fact that dreams are bizarre. Since dreams can be reported linguistically it is denied that they are made up of subjective images and it is believed instead that they are consitituted in the discourse by which they are reported and understood (i.e., which constitute their "meaning") and made a public phenomenon. "Dreams," Norman Malcolm writes in his Dreaming,'13 "are [not] identical with or composed of thoughts, impressions, feelings, images and so ono..occurring in sleep:' In the world of Wittgenstein of which Nonnan Malcolm is a famous spokesman, it is considered important to establish the status of 'being awake'. There is no effort made to concentrate, as Freud did, on the comparison of 'being awake' with 'dreaming'. Freud's approach was indeed a stroke of genius. It has helped us to grasp that the world of dreams (with the few exceptions of those dreams in which we dream of ordinary events, i.e., in which we are wasting good dream-time on having images which we freely allow ourselves to have when awake) though bizarre, is related methodically to the world we experience when awake. Dream images, Freud taught us, are, in all cases, displacements, telescopings, and condensations of our everyday waking experience. The reason why we can talk about them publicly, using the same language-game we are playing when awake, is precisely because they are consbUcted by some kind of bricolage, the separate elements or units of which, though not their mode of assembly, are taken from waking life. In dreaming, Freud says, we are 'displacing' the order of things. Northrop Frye, an anima naturaliter Freudiana, has suggested that when dream events are used by story tellers as plots and characters in seemingly 'realistic' stories, another 'displacement' has to occur- a displacement of the original displacemen~ so to speak. Frye's choice of the Freudian teoo is particularly felicitous because it suggests that there is really no special merit in wondering which of the two displacements come fJrSt, that is, in wondering whether our lives are dreams or our dreams, lives. What matters is the
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relationship between the two and the fact that we should understand that relationship to be methodical. Here, then, we have, provided we do not allow ourselves to be lured by Wittgenstein's disciples into a pre-Freudian stance about dreams, a very handy technique for groping our way from the purest and most utter subjectivity, into inter-subjectivity and of lacing the most private subjectivity into our most public linguistic performance.
VIII. Art for Art's Sake The bifurcation Whitehead had complained of was rooted in a philosophically arguable distinction between primary and secondary qualities. Wittgenstein's bifurcation which irretrievably separates subjective awareness from public statements has no comparable philosophical roots. To be sure, Wittgenstein tried hard to dig up such philosophical roots. But the reasoning he used is hopelessly circular. It is based on the idea that there cannot be a private language- a contention which can be supported philosophically only if one defines 'language' as the sort of verbal gesturing that takes place in a community. Such a definition is quite acceptable, but, since it is the notion 'language' which is in question, no argument about language can be supported by such a defmition. If one defmes language as public gesturing, it follows that private gesturing is not a language. The definition is arbitrary and the logic impeccable. But since the reasoning is circular nothing is proved. This being so, one is forced to start a search for the reasons Wittgenstein might have had for adopting such an extreme bifurcation. If the philosophical reasons for it are shakey, what could the real reasons have been? In thinking about this matter and in turning the question over in my mind for years, I kept being reminded of something. At frrst, the reminiscence was vague and uncertain. It all sounded as if I had heard it before, somewhere else, and in a different context. A truly subjective feeling of deja vu! The more I thought about Wittgenstein's bifurcation, the more I felt that I had been there before. Gradually, after a long time, the subjective feeling began to take shape and eventually it slid into words, and the words it slid into - a typical case in which subjective feelings get threaded into public, inter-subjective consciousness - were the words of Stephan George, a German poet and contemporary of Wittgenstein: •••1Ind tOricht nennt als abel zu befahren, doss ihr ... ... nimmer zu versohnen wiisstet, den /cuss im traum emphangen, und den wanren.
("It is foolish to reject the fact that it is impossible to reconcile the kiss in a dream with a real kiss"- would be an unpoetic English rendering of the message of the poem.) In this poem as elsewhere, Stephan George
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expressed the heart of fin de siecle romanticism, the idea that life and art are for ever separate and unreconcilable and that art exists only for art's sake. One could docwnent the state of mind portrayed by George by countless examples. It was either Yeats and Oscar Wilde who had said a little earlier: "Living? That is something I am getting done by my servants:' The phenomenon in question is too well known to need further discussion. I believe that Wittgenstein's bifurcation had its root in this state of mind and was its philosophical articulation. The suggestion that Wittgenstein had taken his philosophical cue from fin de siecle poetry and literature must, at frrst sight, appear grotesque. Wittgenstein was not given to read poetry and there was nothing effete in his personality. If anything, he was robust and down to earth and disliked the aestheticism and preciousness on which poets Wilde and George were floating through life. It is true that his dress, his appearance, and the austerity of his life-style- his room in Trinity was furnished with nothing but a deck chair and a rickety book-shelf - and the fact that he never wore a tie when tie wearing was still universal, betrayed a certain romanticism and were reminiscent of what in Germany used to be described as jugendbewegt - a phrase pregnant with meanings that are untranslatable. But if he sported a touch of Jugendbewegung he seemed more like a man who had descended from the Hohen Meissen than like a disciple of Stephan George, even though in Germany in 1913 there was certain overlap between these two divergent trends. If one wants to understand the forces which had pushed a man like Wittgenstein who did not obviously belong with Oscar Wilde and Stephan George into the arms of aestheticism and made him its philosophical articulator, one has to go back in history and investigate the fate of the classicism which, by the end of last century, was being replaced and superseded by art for art's sake. To my knowledge, this aspect of Wittgenstein's background has so far been overlooked. Carl E. Schorske, in a book Fin-De-Siecle VienfUiA which deals with the growth of art for art's sake, does not mention Wittgenstein; and Janik and Toulmin, in their Wittgenstem's Vienna,2S make only cursory references to the drift which ended up by separating life from art, but do not connect explicitly Wittgenstein's rejection of German classicism with the special form that drift had taken in Vienna. One's investigation must begin with Goethe, that Olympian paragon of classicism. Goethe had given a serene expression of the manner in which art and life had to be interwoven, how poetry was to be laced into truth, and truth, into poetry. Such an Olympian stance had not come easily to him. 'Realism without empiricism', Goethe might have said anticipating and elaborating on one of Wittgenstein's famous remarks, 'realism linked, instead, to subjective awareness, that was really difficult' Goethe, with real effort, had succeeded in such realism. His classical poise had not been easy to achieve. Goethe had not found solace in either Descartes or Locke and, as every reader of Faust knows, he never had managed to wear his scepticism with the calm composure displayed by Home. For Goethe, the
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quest f(X' knowledge was not only boWld to be disappointing, but also involved truck with the demonic. Nevertheless, he succeeded in holding fast to the way in which he linked the subjective to the objective and saw that the most human form of consciousness is a blend of poetry with truth, of imagination with stubborn facL Had he known William James, he would have agreed that sentences have to be forged in the teeth of stubborn facts but added that stubbool facts are forged by sentences. Richard Friedenthal, in his magisterial biography of Goethe, has amply documented how hard Goethe had to struggle to achieve such serene reconciliation between subjectivity and objectivity. Nobody who looks at the famous portrait of the monumentally mature Goethe by Joseph Karl Stieler of 1928 can fail to notice that those open and penetrating eyes betrayed some anxiety, something a little Wlcertain- a doubt about the Olympian achievement, as if they were asking 'am I really right in my Olympian posture which links poetry with truth and truth with poetry?' However this may be, Goethe's serene formulation of how subjectivity is to be laced into objectivity was impressive and set a standard for both literature and mind Goethe was, above all, the great educator, and his work the standard model of classical Bildung. Goethe's perception of the link between subjective states and objective consciousness was based on a clear perception of the differences between the two. A lesser poet, the Austrian Franz Grillparzer (1791-1872) was to echo it again in famous lines which said that we "sip art from the hands of life and life, from the chalice of art." Soon after that, the distinction came to be blurred and attempts at expressing it, more and more tarnished. The tarnishing and the confusion had a lot to do with the social situation in Vienna during the last decades of the Habsburg Empire. "People who were not born then," Robert Musil wrote: ...will fmd it difficult to believe, but the fact is that even then time was moving faster than a cavahy camel...but in those days, no one knew what it was moving towards. Nor could anyone quite distinguish between what was above and what was below, between what was moving forward and what backward.26
Historians have since found ample reasons for the justice of Musil's diagnosis, and there is no need to rehearse them. The paradoxes which flowed from the incongruous efforts to keep a political organization going, which spanned not only different ethnic groups but also groups which were at very disparate stages of social and economic development, were all visible in Vienna, the capital city and metropolis. As a result, it was becoming increasingly difficult to pursue Goethe's serene classicism, and even the somewhat colloquial version in which it had appeared in Grillparzer was beginning to lack conviction. The poet Hugo von Hofmannsthal wrestled bravely to achieve a unity, a reconciliation between the outer and the inner worlds, to make objectivity and subjectivity
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coincide in the sensuous image, to use the description of the problem by Janik and Toulmin.'Z1 For a decade Hofmannsthal quietly probed the temple walls to find a secret exit. In his myriad explorations, he discovered one of particular promise for his own intellectual development: art as the awakener of instinct:ll
If Hofmannsthal's reconciliation of life with art seemed a little blurred and nebulous, it ended up in sheer confusion with artists like Klimt when the project was described in the following words: ...of the hurrying, scurrying, flickering life, whose manifold mirror image we seek in art, in order to pause for a moment of inward contemplation and dialogue with
our own soul.29
With such a formulation we are a long way from Goethe's serene description of 'the relation between poetry and life: Dem Glilcldichen kann es an nichts gebrechen, Der dies GeschenJc mit stiller Seele nimmt: AILS'Morgendu.ft gewebt und SonnenJdarheit, Der Dichtlmg Schleier aILS' der Hand der Wahrheit.
(people on whom fortune smiles will lack nothing. They will receive this gift with a calm soul: they will receive the veil of poetry, woven of the morning's scent and the sun's clarity, from the hand of truth.) With Klimt and in the Vienna of his days, the ideal had become tarnished and confused- a wordy mixture of romantic sentiment and a nebulous desire to cling to reality. In the words of one of Klimt's sober critics,30 this was a case of 'unclear ideas' presented 'through unclear forms'. The German original for 'unclear' was 'verschwommen', an adjective which drew attention not only to a lack of clarity (i.e., a departure from Goethe's clarity of the sun) but also to the fact that all these efforts were swimming around in a state of flux. The boundaries between subjective and objective had become permeable, rather than reconciled. This permeability and these attempts to swim in fluxes was anathema to Wittgenstein. If there was Romanticism in his make-up, there also was a strong tinge of intellectual Puritanism in his mind. If subjective awareness and objective statements could be reconciled only in terms of such unclarity ('Verschwommenheit') he had to cut the Gordian knot. Goethe's harmoniously classical reconciliation of subjectivity and objectivity he might have worn. But in Wittgenstein's Vienna, these harmonies had been dissolved- dissonance, as Schoenberg proudly was to announce, had become emancipated. If subjectivity and objectivity could only be linked in Verschwommenheit, Wittgenstein's austere Pwitanism and his passion for clarity forced him to sever the verschwommene link between the two.
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Sensitive as he was, he could not deny to himself the passionate truth of subjective feeling of 'what really mattered in life', as Paul Englemann put it When he nevertheless takes immense pains to delimit the unimportant, it is not the coastline of that island which he is bent on surveying with such meticulous accuracy, but the boundary of the ocean.31
It was for that reason that Wittgenstein adopted a position which was so similar to that of Stephan George and of the art for art's sake school of thought Wittgenstein became convinced that subjective emotion (the kiss in the dream) and public world (the real kiss) are irrevocably and irreversibly and eternally irreconcilable. 'Goethe was wrong', he must have said to himself, 'for the world is bifurcated'. On one side, there was the deeply important realm, the realm of the unsayable, of the things we cannot speak about On the other, the public and objective worlds of speech, and of literal descriptions of facts, and of reality, and never the twain shall meet. Thus Wittgenstein took his distance from the confusions of the Habsburg Empire and the verschwommene, confusing philosophy German classicism had degenemted into because the social world of that Empire in which nobody could distinguish the up from the down had not admitted of anything more clear. There are two important corollaries to this explanation of Wittgenstein's philosophical stance and of his assumption of a position so reminiscent of the art for art's sake movement. The frrst corollary is that, viewed in this light, Wittgenstein was a genuine revolutionary in regard to the Habsburg Empire. That Empire could only hope to survive if people could remain tolerant of the confusion between backward and forward, up and down. For the many groups and classes that had to jostle side by side if the Empire was to continue as a going concern, there was no other way of life. As soon as people were brought up short to look at the confusion and end it, the Empire would split apart To fmd fault with that confusion was a revolutionary or subversive attack. The other corollary is much stranger. It indicates that there is a long and direct, if somewhat labyrinthine path from the art for art's sake movement to Kuhn. This may, at ftrst glance, sound very surprising. Nothing could be more removed from the aestheticism of Oscar Wilde and Andre Gide, from Hysman's Against Nature in which the hero constructs an organ which emits the flavor of liqueurs rather than the sounds of music and in which the hero lives on enemas, carefully planned by menus that blend tastes which, given the method of infusion, he cannot 'taste', than the philosophy of science presented by Kuhn. And yet, we can now clearly see the distant connection. Wittgenstein was revolted by the fin de siecle attempts to link subjectivity to objectivity, attempts which he realised led to nothing but confusion- confusion of concepts as well as a confusion of life with art. Hence, his radical separation of subjective inwardness (inclusive of observations) from objectively stated discourse in
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words. In turn, Kuhn took his cue from Wittgenstein and explained the pursuit of science as an activity which had nothing to do with experience and observation (all subjective states) and everything with obedience to a 'spontaneously' established paradigm. It does not matter much what future historians will have to say of Wittgenstein's subversive attitude to the paradigm of studied confusion that might have kept the Habsburg Empire alive, for his political role was, at best, minimal. But it must be of the greatest interest to future historians of modern thought to fmd that the course leads from the aestheticism of art for art's sake to the philosophy of Kuhn and, for that matter, to the effulgent impact of Foucault
IX. Boyle's Fate One is driven back to a search for a social explanation of knowledge only if one is satisfied, reluctantly or rejoicingly as the case may be, that under no circumstances can linguistic expressions be used to convey non-linguistic experiences. If one accepts such bifurcation, knowledge can indeed only be something people say to each other; something the validity of which does not depend on its correspondence with what it purports to be knowledge of, but something which depends on the ease with which other people understand it But if the bifurcation into subjective awareness and public expression is neither as total nor as absolute as Wittgenstein alleged, there can be no need for a social theory of knowledge. If there is no need for a social theory of knowledge, no matter what the role and importance of social structures and consensus and rules in the acquisition and propagation of knowledge are, why should we resort to a social explanation of knowledge which leaves us poorer than we need to be? If we could fmd no way in which pre-linguistic meanings could be threaded into public meanings, one would have to resign oneself to such poverty. But since there is no need to have recourse to a social explanation of knowledge, the intellectual poverty it condemns us to is intolerable. The intellectual poverty of a social theory of knowledge becomes more obvious when one looks at the consequences of Wittgenstein than when one keeps looking at Wittgenstein himself. As far as Kuhn is concemed the poverty consists in 'the fact that one cannot understand the growth of knowledge at all. All one gets, when knowledge is whatever is detennined by a reigning paradigm, is a series of paradigms which follow one another without rhyme or reason. Knowledge, in this view, has no history other than the sort of history in which one damned thing follows upon another. As far as Foucault is concerned - and we should consider him as one of the 'consequences' of the Wittgenstein bifurcation, even though his own bifurcation was not explicitly derived from Wittgenstein - the ensuing poverty consists in the fact that the only history of knowledge we can get from his view that all knowledge is determined bl_t!!~~~i1!g_~~~~~ j~ _ j
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an historicist history. In such a historicist history, epistemes are strung together in obedience to a developmental law and follow each other for no reason other than that there is a developmental law which decrees that they musL Notwithstanding such impoverishment, Bloor rejoices in the bifurcation and warmly applauds the social theory of knowledge it leaves us with. Knowledge which cannot be voiced, he says, is not viable, and viability is to be determined in terms of voicing. In making voicing and viability synonymous and in not keeping them distinct. Bloor endorses Wittgenstein's bifurcation and establishes the need of a social theory of knowledge. Bloor has been well primed for a Wittgenstein reception. As far back as 1974 he had written, reviewing Karl Popper's Objective Knowledge, that: appraise an argwnent for validity is to apply the standards of a social group. to other standards..•.n •••to
It cannot be other, or more, than this because we have no access
Wittgenstein's argement that 'We have no access to other standards' must have been a God-send to Bloor. Here he found a philosophical justification of a belief which was, most probably, politically inspired, and a philosophical justification which was both fashionable and respectable. Bloor's refusal to maintain this distinction can be illustrated with the help of the example of Boyle which he introduces in Wittgenstein: A Social Theory of Knowledge." Bloor starts from the proposition, which nobody would question, that whatever theory one holds, there is never a clear compelling reason or technical compulsion embedded in observation why it should be held. In all cases, there are prior assumptions, things that are taken for granted, other theories. Boyle, Bloor tells us, introduced the theory that matter was inert or passive and that the behavior of water in a straw, when the air is sucked out, cannot be explained by the old view that nature abhors a vacuum. Matter, Boyle declared, is brute and inanimate. Bloor then proceeds to tell us why Boyle was moved to propose a different 'language game' and oppose the Aristotelian view of horror vacui.:l4 Boyle, Bloor tells us, lived at the time when Levellers and Ranters, Diggers and Familiasts were challenging the hierarchical order of society. They claimed to derive their inspiration direct from God without the mediation of church and priests. To oppose this challenge to hierarchy, Boyle insisted that matter was passive, that is, at the bottom of a hierarchy, the top of which was occupied by God, the external law-giver." Though I have never studied Boyle and do not know what might have been the reason why Boyle voiced the theory of inert matter, I am, for the sake of argument prepared to accept that he was inspired in his imagery of nature by the conception that nature as well as society must be hierarchical. It is also conceivable that the socio-political crisis of the age he was living in lent a special edge to his images and made them appear urgent so that they eventually crystalized in the form of a theory which was opposed to
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the Aristotelian horror vacui and to the view that motion is a necessary essence of matter. People, not least the greatest thinkers, are usually inspired by something and there is often a detectable reason for the urgency which makes the crystallization of an idea in the shape of a theory possible as well as plausible. Normally one would keep voicing and viability separate and add that whatever reasons Boyle had for voicing his theory and whatever the reasons for the support or consensus he got for his theory, its viability depended on some'thing else. Its viability depended in part on observations which failed to falsify any inferences from the theory, and, in part, on the fact that it had more explanatory power than the horror vacui theory of Aristotle. However, the observations that failed to falsify it as well as the observations which showed that it had greater explanatory power go back, in the last analysis, to extra-linguistic meanings, that is, to subjective observational experiences enjoyed by certain people. If one bears in mind that these subjective experiences can be laced into the public world in which the 'voicing' occurred, the distinction between viability and voicing remains important when one wants to consider the validity of Boyle's
theory. Bloor simply erodes the distinction between viability and voicing. He maintains that Boyle voiced his theory because it was part of his attempt to uphold hierarchies- a proposition which we might sensibly entertain. Bloor then goes on to argue that Boyle's theory was considered viable by many fellow-scientists - who included no less a person than Isaac Newton because they too shared Boyle's detennination that hierarchies must be upheld and the sectaries proved wrong. This is a proposition which one cannot agree with. The reason why Boyle's view was considered viable - as distinct from the reason why he voiced it - was that it helped Newton and others to link together other phenomena and other theories which, without Boyle's hypothesis about the passivity of matter, would have remained isolated pieces of knowledge. In other words, no matter what prompted the voicing, the viability was determined by the fact that Boyle's theory had greater explanatory power. The absurdity of Bloor's explanation why Boyle was considered viable is very striking. It is precisely the sort of absurdity he commits himself to when he is using Wittgenstein's parallel refusal to distinguish between voicing and viability in order to lay the foundation for a sociological explanation of knowledge. I am not suggesting that Bloor is making bad or wrong use of Wittgenstein. On the contrary, I am convinced that Bloor's reading of Wittgenstein is correct and the one thing I agree upon with Bloor is his interpretation of Wittgenstein. I am suggesting, on the contrary, that we consider Bloor's treabnent of Boyle as a reductio ad absurdum of Wittgenstein.
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x. L'Homme Moyen Wittgensteinien Boyle is dead and cannot defend himself against Bloor's imputation that one had to wait for Wittgenstein to account for the intellectual fortunes of his theory of matter. When Bloor is using Mary Douglas in order to explain how Wittgenstein can be kept 'intact',36 one may wonder whether Mary Douglas might speak up to protest or whether she might be flattered that she is being put to good use. Either way, more flagrantly than the case of Boyle, Mary Douglas reduces the social theory of knowledge to absurdity. Bloor points out that Wittgenstein himself felt uneasy about the maintenance and protection of the boundaries of anyone language-game. n This question is much more crucial than Wittgenstein ever surmised. Who indeed is a legitimate player? And how is membership of a language-game group to be determined? Are the insane and the crippled to be admitted as equal members? And if not, why not? Neither Freud nor Kraepelin had difficulty in defining what constitutes insanity. But since then, the edges have become very frayed, and when Quine discussed the matter he was a little hesitant in stating that the blind and the insane and other 'occasional deviants' ought to be excluded. But if the blind are out, why should the deaf be in? And how is one to determine 'deviance'? More recently, R.D. Laing has suggested that such decisions are wholly arbitrary and Foucault has shown that the rationale for such decisions varies from epoch to epoch. Both Laing and Foucault have therefore pointed out that in all such cases, philosophical right is determined by political might- a conclusion with which Wittgenstein, when he said "what has to be accepted, the given, is so one could say - forms of life"38 might have agreed. Bloor feels uneasy about the reduction of philosophy to politics. Understandably so. He has therefore decided to search for a sociological explanation of philosophical questions so that he can link, even as he did in the case of Boyle, knowledge to something other than naked power. The undertaking, on Wittgensteinian premisses, is hazardous, for it involves the idea that any particular language game is determined by a non-linguistic event and that there is a pre-linguistic meaning of which the game itself is the expression. Once one takes this first step beyond Wittgenstein, one comes dangerously close to the thought that one might be able to compare different language-games with one another and to stating (heaven forbid!) that any particular game might be 'wrong' because it does not accord with something outside the game. Bloor admits, as he is about to embark on this inquiry, that "the present chapter will have a distinctly un-Wittgensteinian tone. Exposition is going to give way to development"39 In choosing Mary Douglas' theory about societies and their relations to the knowledge they espouse, he has chosen wisely, for Mary Douglas is an anima naturaliter Wittgensteiniana. Where Wittgenstein had believed that the rules of a language-game cannot be determined by pre-linguistic meanings, Mary Douglas holds that any knowledge in a given society cannot be determined by non-social factors. Admittedly, this goes a little beyond
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Wittgenstein, but the idea does not stray too far from the fold and ought to be acceptable to most hommes moyen Wittgensteiniens. Hazardous or not, Bloor uses Mary Douglas in order to soften the irrationality of Wittgenstein's idea that a language-game is a form of life, and that that is that, i.e., of the idea that a philosopher cannot be held responsible for, let alone be critical of, what life chooses to throw up. If one could, with the help of Mary Douglas, establish a typology of language-games, Bloor argues, any particular language-game could then be seen as the 'expression' of a specific social order. What is more, though Bloor does not spell this out, the notion of prediction could then be introduced. Once there is a possibility of making predictions about language-games by stating that a certain order of society will produce a certain language-game and not another, one can advance to criticism and to falsification and in this way, some modicum of rationality is introduced into the argument. Ever since Plato, philosophers have used the human body as a model for understanding societies. The history of socio-political thought is replete with such organic, biological metaphors. Even when Marx introduced dialectics to show that classes are not related to each other as different parts of an organism are related to each other, Engels soon went back to biology by explaining that in organisms the different parts are related dialectically: the seed is the thesis; the plant the antithesis; and the fruit the synthesis. Mary Douglas, in her Natural Symbols of 1970,40 made a real breakthrough. She turned the modelling round and then stood it on its head. Human bodies, all over the world, are very much alike, she said To understand societies by using the body as a model, one does not account for the differences between societies. If one starts with societies, she continued, one can explain the different kinds of knowledge people have about their bodies and about the relationships between those bodies and the world. She then proceeded to improve on the classifications of society we had used. Where ever since Plato typologies of societies had operated with one single variable so that they were classified as monarchical, democratic, oligarchic, and so forth, Mary Douglas proposed that we use two variables instead She distinguished between the outer boundary of a society and the inner structure and so arrived at four types of society: High grid, low group High grid, high group Low grid, low group Low grid, high group
Where 'grid' stands for 'internal structure' and 'group' for boundary. Mary Douglas has used this classificatory scheme to account for all manner of knowledge, to explain fear of witchcraft and the cessation of witchcraft, fear, etc. Among her most celebrated explanations in terms of this scheme is her explanation of pollution fear. She points out that in low grid, high group societies there is obviously a lot of discord inside, protected by a
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strong sense of boundary against the outside world. Hence, such societies are pollution conscious because whatever is outside the group boundary is a foreign anomaly to be kept out The internal strife inside, which results from low grid (X' which is the expression of low grid, makes people think: that the enemies they have on the inside must be people who have been Contaminated from the outside. Hence, they are forever on their guard against weak points which might occur in the group boundary, lest the inside pollution increases. Such a way of argument looks attractive because it does help to explain why people often have quite irrational fears of pollution. At the same time, it is also rather vague. When grid is low and boundary high, would one not rather expect that people are confident that disturbances can not come from the outside and that it must have been generated on the inside, i.e., that disturbances are not pollution. However this may be, at the heart of the entire theory stands Mary Douglas' refusal, often explicitly expressed, of distinguishing between rational and irrational pollution fears. It is here that she reveals her anima naturaliter Wittgensteiniana. In order to hold fast to such a distinction, one would have to grant that there can be non-social reasons why people fear pollution. One would then have to admit that in some cases the fear of pollution is due to one's knowledge of chemistry and of bio-chemistry and physics and that on those occasions on which that knowledge is moved into the foreground, there can be genuine enlightenment- as, for example, when the fear of pollution by witches was destroyed by the consideration that women can in fact not ride on broom-sticks through the air. The possibility of the removal of pollution fear through such enlightenment is explicitly discounted by Mary Oooglas.41 No argument could be more Wittgensteinesque than this argument. Nevertheless, the distinction is vital. Rational pollution fear does not stand in need of a sociological explanation. When we are afraid of nuclear fall-out, we do not have to wonder whether we are so afraid because we live in a society with high group boundaries and low grid. On one side, pollution is an awesome biological phenomenon and even the most primitive protozoon is aware of it For all unicellular beings are surrounded by a membrane which protects them from and separates them from their environment, and which is highly selective in regard to those particles of the environment it will allow across its threshold It is perfectly true that in addition to those rational or ratiomorphous (to use Egon Brunswik's term) fears of pollution, people are often prey to irrational fears. In all cases, one has to start with the distinction between rational and irrational fears and hold fast to it This distinction may not be absolute, but in all cases one has to base it on techniques of investigation which precede the effort to look for a sociological explanation. Any sociological explanation can only make sense when one is certain that the fear in question is irrational. Hence the distinction between rational and irrational fear of pollution must be prior to the sociological project With Bloor's Wittgenstein, and, I suspect, with Mary Douglas, it is at best, derived from a sociological explanation and, at
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worst, wiped out by a sociological explanation. For if one starts with a sociological explanation of pollution fears, one will usually be able to substantiate it enough so as to obviate the need for any further inquiry as to whether the fear is rational (and therefore in no need of a sociological explanation) (X" irrational, and therefore crying out for another explanation. The refusal to start with the distinction between rational fear and irrational fear and abide by it is strongly reminiscent of the other refusal to distinguish between voicing and viability. The refection of the distinction condemns the fly to permanent imprisonment in the bottle. The only gain consists in the argument that the bottle is made of non-transparent glass and that the fly, though in the bottle, does not know that it is in the bottle. The protestation of such ignomnce is the net gain of the social theory of knowledge and if such and similar ignorance can be maintained, the fly could stop buzzing and come to rest inside the bottle: a sad end to the proud claim that there are ways by which the fly could be set free and shown the way out of the bottle. Bloor's extension of Wittgenstein into a social theory of knowledge is, if anything, a final reductio ad absurdum of the technique by which Wittgenstein had proposed to solve the great meta-problem of philosophy.
XI. The Anthropic Principle to the Rescue In the last analysis, all these faults go back to a root cause. The root cause is the refusal to bear in mind that man is part of the universe and that the universe has evolved. For milennia, philosophers and scientists have wondered what kind of mind and what kind of knowledge we need to have in order to understand that universe. When most inquiries had failed and nothing but scepticism was left, man came up with the suggestion that everything we know must be a social convention and that while we cannot explain what we know by reference to the world we live in, we cam explain what we believe to be true as a function of the social order we are living in or which we try to defend. As long as one keeps wondering what kind of mind might be necessary to understand the world, one will, after centuries of agonizing turns and twists, be thrown back against the societies one is living in and seek to derive what one knows from the conditions that prevail socially, thus making nonsense of knowledge, for knowledge purports to be knowledge of the world, not a projection of social customs. I suggest we tum the whole of this epistemic or cognitive project on its head. Seeing that we are here to wonder about the world, we must have evolved, for there is no o'ther way by which we could have got here. Even if we suppose we are the descendants of migrants from outer space, we must suppose that those migrants must have evolved in the environment of a distant star or gallaxy. Having evolved, the world must be the sort of entity or process which has made that evolution possible. The mere fact that
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we have evolved gives us, therefore, a clue to the nature of the unvierse: cogito ergo mundus talis est. This is the Anthropic Principle which must, from now on, stand at the beginning of every philosophical and scientific endeavor.. Instead of wondering what kind of mind we must have to understand the world, we can now face the somewhat less formidable task of wondering what kind of world could have produced the sort of mind we now have. Starting from that premise, we will be able to maintain distinctions between voicing and viability and between rational fears and irrational fears before we do sociology, and we will Dot be dependent on sociology to teach us that there are no such distinctions. Bloor is very disanning. He starts his book by reminding us that knowledge is not self-contained, that it cannot stand on its own feet, that there have to be assumptions, etc. etc. Nobody would wish to argue against such acknowledgement. Bloor, however, jumps to 'the conclusion that if an explanation of knowledge is required and that if we have to account for the fact that when there is competition between pieces of knowledge, the race is hardly ever decided by technical compulsion or by mere observation- there is only one recourse left, a recourse to sociology. A social theory of knowledge, he writes42 is no novely. Following the sketchy attempts of earlier thinkers, it was fully developed by Durkheim at the beginning of this century. But Durkheim, Bloor correctly reports, recognized the limitations of a social theory of knowledge and accepted that there are standards of truth and falsity outside those set by social customs. Bloor then -comments: "By succumbing to this seductive idea, Durkheim allowed himself to throwaway all that he had so painfully WOD. We shall see that Wittgenstein does not lose his nerve or betray himself in this way."43 I agree with Bloor that Wittgenstein went beyond Durkheim. But I would not honour him by saying that he 'did not lose his nerve'. I prefer to think that in putting forward his views on meaning and use, Wittgenstein had a nerve! Though this way of putting it is not a logical contradiction of Bloor's praise, it detracts from the applause Wittgenstein is entitled to.
260 ENDNOTES 1. J.N. Findlay, "My Encounters with Wittgenstein," PIDLOSOPIDCAL FORUM, Winter (1972-1973), p. 171. 2. Ernst Konrad Specht, The Foundations of Wittgenstem's lAte Philosophy, trans. D.E. Walford (Manchester: Manchester University, 1963), pp. 154, 185. 3. Soren Kierkegaard, Concluding Unscientific Postscript, trans. David F. Swenson and Walter Laurie (Princeton: Princeton University, 1941), p. 182. 4. All three reviews are reprinted in: George Pitcher, ed, Wittgenstein: The Philosophical Investigations (London: Macmillan, 1968). 5. See: Peter Winch, The Idea of a Social Science and Its Relation to Philosophy (London: Routledge and Kegan Paul, 1958). 6. See: Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: University of Chicago, 1962). 7. See: Karl-Otto Apel, Transformation der Philosophie (Frankfurt am Main: Surkamp, 1975). 8. See: Richard ROlty, Philosophy and the Mirror of Nature (Princeton: Princeton University, 1979). 9. See: Ernest Gellner, ItThe New ldealism- Cause and Meaning in the Social Sciences, It in Imre Lakatos and Alan Musgrave, eds., Problems in the Philosophy of Science (Amsterdam: North-Holland, 1968). 10. See: David Pears, Wittgenstein (New York: Viking, 1971). 11. See: P. Jones, "Strains in Hume and Wittgenstein," in D. Livingstone and 1. King, eds., Hume: A Re-evaluation (New York: Fordham University, 1976). 12. Saul Kripke, Wittgenstein on Rules and Private Language (Oxford: Basil Blackwell, 1982). 13. See: E. and W. Leinfellner, H. Berghel, and A. HUbner, 008., Wittgenstein and his Impact on Contemporary Thought: Proceedings of the 2nd International Wittgenstein Symposium of Kirchberg (Vienna: Holder-Pichler-Tempsky, 1978), p. 74. 14. David Bloor, Wittgenstein, A Social Theory of Knowledge (London: MacMillan, 1983), pp. xi, 213. 15. Wittgenstein, Philosophical Investigations, trans. G.E.M. Anscombe (New York: Macmillan, 1953), Part IT, xi, p. 224e. 16. Garth Hallett, A Companion to Wittgenstem's "Philosophical Investigations (Ithaca: Cornell University, 1977), p. 731. 17. Henry Le Roy Finch, Wittgenstein-- the Later Philosophy (Atlantic Highlands: Humanities, 1977), p. 76. 18. Jacques Derrida, Of Grammatology, trans. Gayatri Chakravorty Spivak (Baltimore: The Jolms Hopkins University, 1976), p. 165. 19. Hans Albert, Transzendentale Triiumereien (Hamburg: Hoffman und Campe, 1975), p. 101. 20. See: Ibid. 21. See: Jeffrey Masson, The Assault on the Truth: Freud's Suppression of the Seduction Theory (New York: Farrar, Straus and Giroux, 1984). 22. See: W.W. Bartley ill, Wittgenstein (London: Quartet, 1983). 23. Norman Malcolm, Dreaming (London: Routledge and Kegan Paul, 1962) p.
52. 24. See: Carl E. Schorske, Fin-De-Siecle Vienna (New York: Alfred A. Knopf, 1980). 25. See: A. Janik and Stephen Toulmin, Wittgenstein's Vienna (New York: Simon and Shuster, 1973).
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26. Robert Musa The M(JIJ, withollJ Qualities, trans. Eithne Wilkins and Ernst Kaisa' (New York: Coward-McCann, 1953), p. 8. 27. See: Janik and Toulmin, Witlgenstein's Vienna, p. 113. 28. Schorske, Fin-De-Sikle Vienna, p. 18. 29. Quoted in: Ibid., p. 219. 30. Quoted in: Ibid., p. 232. 31. Paul Engelmann, Letters from Wittgenstein, trans. L. Furtmuller (Oxford: Basil Blackwel~ 1967), p. 97. 32~ David Bloor, "Popper's Mystification of Objective Knowledge," SCIENCE STUDIES, (1974).
33. Bloor, Witlgenslein: A Social Theory of Knowledge, p. 152. 34. See: Ibid., p. 153. 35. See: Ibid., p. 154. 36. See: Ibid., p. 138. 37. See: Ibid., p. 138ff. 38. Wittgenstein, Philosophical Investigations, Pt. II, xi. 39. Bloor, Witlgenstem: A Social Theory of Knowledge, p. 138. 40. See: Mary Douglas, Natural Symbols (New York: Vintage, 1970).
41. See: Mary Douglas, 'Purity and Danger Revisited," TIMES UTERARY
SUPPLEMENT, 19 September 1980, p. 1045. 42. See: Bloor, Wittgenstein: A Social Theory of Knowledge, 3. 43. Ibid.
PSYCHOLOGISM, SOCIOLOGISM, AND THE MADNESS OF SOCIAL SCIENCE RICHARD W. MOODEY
I. Introduction To speak of the 'madness' of social science is, of course, to speak metaphorically, but if we grant for the moment that broad disciplines or fields of study can somehow be mad, the madness of social science seems quite different from the madness that Whitehead attributes to mathematics. Whitehead says that mathematics is to the history of thought as Ophelia is to Hamlet: Ophelia is quite essential to the play, she is very charming- and a little mad. Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings. 1 Social science is not much like Ophelia.. Some might call it 'essential', but few would call it 'charming' or 'divine'. The pursuit of social science is mundane rather than 'divine', no refuge from the 'urgency of contingent happenings', but an attempt, perhaps foolhardy, not just to make sense of these happenings, but to make a science of them. Hubert Blalock, a former president of the American Sociological Association, worries that social science is more like Dr. Frankenstein than Ophelia when he says that we might be creating a "brainless monster," whose growth is "totally beyond our oonOOI."2 Both of these literary analogies, however, suffer from a kind of misplaced personification: social science is mad, not as Ophelia or Frankenstein are mad, but as the tea party at the March Hare's is mad. Our madness is not so much a disorder of individuals as it is a quality of our
discourse. Ours is an understandable madness. Social science is broken up into different disciplines and schools of thought, and the native tools of social science are inadequate for dealing with many of the differences that divide us. First of all, we are divided by deep differences in faith, differences which can be called 'religious', in a broad sense, and which are important to our work as social scientists. Sane discussion of these differences requires a delicate balance between respect for the beliefs of others and a
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continued commitment to one's own, a balance which requires theological methods. Second, we are divided philosophically: the 'strife of systems'] in philosophy is mirrored in social science, and we must use philosophical methods in discussing our philosophical differences. Social scientists, however, tend to be biased against theology and philosophy. We prefer empirical methods, and theology and philosophy are not empirical sciences, even though they sometimes draw upon the results of empirical science. At the heart of theological method are two activities: (1) critical reflection on one's own faith; and (2) critical discussion of the results of this clarification with others who have sought to criticize and clarify their own faith. Philosophical method requires: (1) critical reflection upon one's own acts of knowing, evaluating, choosing, and communicating; and (2) critical discussion of these reflections with others who have engaged in this same kind of critical reflection. It is common for social scientists today to say that the kinds of critical reflection I have assigned to theology and philosophy are not 'empirical' activities, even though introspectionist psychologists and some varieties of empiricist philosophers once saw them as empirical. Our bias against these kinds of critical reflection prevents our discourse from being sane, for the social sciences are fragmented by the kinds of differences which can only be grasped by these kinds of reflection, and can only be discussed sanely once they have been grasped. We are too ready to treat our colleagues with whom we disagree with contempt, to reject arguments without really trying to understand them, to disguise our prescriptions and evaluations as statements of fact, and to turn away from any examination of the assumptions upon which our assertions rest. Because discussions among members of different disciplines or schools of thought are so often mad, or maddening, communication among different groups of social scientists often breaks down, resulting in ever-deeper fragmentation. According to Blalock, if we are to avoid creating a brainless monster, we must agree upon "a set of scholarly norms designed to improve communication both within and across the several social sciences."4 But such norms cannot be developed by empirical methods, and our bias against philosophical and theological methods perpetuates the chaos. This bias often takes the form of either 'psychologism', an overevaluation of empirical methods of studying individuals, or 'sociologism', a similar over-evaluation of those methods which focus upon group phenomena. Either kind of over-evaluation implies an under-evaluation, a bias against, philosophical and theological methods. That psychologism is not confined to psychologists, nor sociologism to sociologists, is evidenced by the fact that many philosophers have embraced one or the other of them, or have been accused by other philosophers of such (illicit) embraces. Philosophers who disapprove of psychologism or sociologism are likely to call them forms of empiricism, but such a designation interferes with my argument. I am not so much interested in defming or refuting empiricism in philosophy as I am in reducing social scientists' biases against those kinds of methods which I have called philosophical and theological.
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In writing of the 'divine madness' of mathematics, Whitehead says something about the ideal nature of mathematics, but in writing of the 'mundane madness' of social science, I am talking about deviation from my ideal for social scientific discourse. Mathematicians can talk about possible worlds, but social scientists need to talk about this particular world, with its contingent events. In tenns of a medieval debate, social scientists ought, with Thomas Aquinas, to reject the notion that a question becomes scientific when it is raised with respect to all possible worlds.' We have no empirical experience of all possible worlds, so if the social sciences are to be empirical, they must be about this one. And. to keep our discussions of this world sane, we must be scrupulous about distinguishing between talk about the way things are and talk about the way we think they ought to be. The practical and theoretical difficulties of maintaining this distinction do not constitute a valid argument for giving up the effort The contemporary recognition that the social sciences cannot be 'value free', that all factual statements are 'value-laden', does not excuse us from reflecting upon the sources of those values which penneate our descriptions and explanations of facts.
II. Behaviorist Psychologism When, almost a century ago, Frege said that psychologism led to a type of madness, he was speaking as a logician, concerned about the laws of thought in all possible worlds, rather than as a social scientist, narrowly focused upon this one. Today, his words suggest a science-fiction scenario, a 'close encounter of the third kind': ...what if beings were even found whose laws of thought flatly contradicted ours and therefore frequently led to contrary results even in practice? The psychological logician could only acknowledge the fact and say simply: those laws hold for them. these laws hold for us. I should say: we have here a hitherto unknown type of madness.6
If different laws of thought hold for them, then how can we carry on a sane discussion with them? The method of the psychological logician described by Frege was introspection, a method which contemporary social scientists tend to see as non-empirical. We regard behaviorist methods, however, as empirical, and there is a behaviorist form of psychologism which also leads to difficulties for discourse. The behaviorist might say: 'They have been conditioned to utter those laws; we have been conditioned to utter these laws'. How then can we make sense to them, or they to us? I first encountered behaviorist psychologism as a freshman in college, when I had a psychology professor who seemed to be a 'crazy psychologist'. On the first day of my course in general psychology, he etymologized about the name of the discipline: "Psychology," he said,
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"means 'science of the soul', but I'm going to prove to you that there is no such thing as a soul." His pronouncement made me both fearful and hopeful- fearful, because I had beard stories about young Catholics who had 'lost their faith' at college; hopeful, because if I could be convinced that I had no soul I would not have to try so hard to 'save' it. As it turned out, he failed to prove to me that I had no soul, posed no real 'threat to my religious faith, and offered no release from my struggle with the world and the flesh. His argument went something like this: 1. Everything real is empirically observable. 2. The soul is not empirically observable. Therefore, 3. The soul is not real.
The major premise is an answer to highly controversial philosophical questions, epistemological and metaphysical. The minor premise might be considered an answer to a stupid empirical question, but is really just a question of defmitions. The conclusion is an answer to an essentially theological question. And the whole argument is strongly evaluative, suggesting that those of us who believed in souls were still in the grip of outmoded superstitions. I am not claiming that myoid professor was blinded to the existence of souls, but that he was blinded to the philosophical and theological nature of his argument. As a result, his science, as well as his philosophy and theology were compromised. His presentation of empirical method was not credible, because he tried to extend it beyond its capabilities, and the philosophical and theological dimensions of his thought were unacknowledged, perhaps even 'repressed'. It is historically understandable that psychologists have often confused philosophical and theological questions about the existence and nature of the soul with questions in scientific psychology. The battle over the existence of the soul has been a part of the long war between science and theology.' For many years, theologians successfully used their political power and cultural influence to restrict freedom of scientific inquiry; they imposed theological answers to what we now recognize as scientific questions. As science became more powerful and more respected, it was only natuml that scientists would seek to carry the battle into the heart of theological territory, attempting to give scientific proof that the very subject-matter of theology is non-existent To deny the reality of souls is not the bias of psychologism. The bias lies in the blindness toward the philosophical and theological dimensions of one's own thought, combined with contempt for the philosophical arguments and theological beliefs of others. Psychologistic contempt for the beliefs of others is expressed by BF. Skinner, who claims that behaviorism has made scientific and practical advances only by "dispossessing autonomous man."· He lists a large number of fields - all of the social sciences, law, philosophy, and religion - in
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which theorists still assume that humans have autonomy, freedom, and dignity. "The result," he says, "is a tremendous weight of traditional 'knowledge', which must be corrected or displaced by a scientific analysis." He describes the reactions of those who disagree with him: What people do about such a scientific picture of man is call it wrong, demeaning, and dangerous, argue against it, and attack those who propose or defend it They do so not out of wounded vanity but because the scientific formulation has destroyed accustomed reinforcers. If a person can no longer take credit or be admired for what he does, then he seems to suffer a loss of dignity or worth, and behavior previously reinforced by credit or admiration will undergo extinction. Extinction often leads to aggressive attack.'
While I agree with Skinner's disapproval of 'aggressive attack' in social scientific discourse, I disagree emphatically with his lumping it together with arguing against a position. Skinner himself is clearly arguing against the position that humans are dignified and free when he says that this traditional view "must be corrected or displaced by a scientific analysis." It is not clear that he is engaged in an aggressive attack upon those who hold the tmditional view, but he does trivialize their position, which is even more contemptuous than aggressive attack. Skinner's trivialization of the arguments of others is not the result of a moral failing or character defect, but is the inevitable consequence of his philosophy and theology, which he mistakenly calls his 'scientific picture of man'. He rejects 'mentalism', including all explanations of behavior in terms of the intentions of the actors. It appears, however, as if he intends his arguments to persuade his readers that he is right But if he is right, then what he intended could have had no real bearing upon his writing, which was nothing more than the verbal behavior consequent upon his personal history of reinforcements. In terms of his position, whether or not his readers are persuaded is unimportant; what is important is that his readers change their verbal behavior, which they will do only if provided the proper conditioning. He must say that his words are arranged on the page so as to constitute positive reinforcers for his readers, rather than to convey persuasive arguments. To the extent that Skinner would ada-nit u~at he has tried to persuade other social scientists, he would have to say that he has been the victim of the reinforcement schedules established by our society and culture: he has been rewarded for trying to persuade his colleagues, but not for trying .to condition them. It is important to emphasize that behaviorist psychologism is not identical to behaviorist theory, even though Skinner himself would probably reject the distinction. Behaviorist theory consists of a number of propositions about the effects of reinforcement schedules upon subsequent behavior. These propositions are corrigible in the light of empirical evidence. They provide an account of part of the domain of 'the law of effect', and specify the geneml notion that rewarded behavior is more likely to be repeated than
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unrewarded behavior, whether the behaving organisms are rats or human beings. to Behaviorist psychologism, on the other hand, consists of the claim that behaviorist theory can explain all human knowing and is the basis for all rules for knowing correctly. When behaviorist theory is treated as if it were a general epistemology, it ceases to be a legitimate scientific theory, for it then contains propositions which are not corrigible on the basis of empirical evidence, propositions which can only be challenged or supported by the use of philosophical or theological methods. For Skinner, however, philosophy and theology are little more than 'mysticism' and 'superstition'. Therefore, Skinner would emphatically reject my distinction between behaviorism as a scientific theory and behaviorist psychologism as a philosophical and theological doctrine. Either I have been conditioned to make this distinction, or I make the distinction as a part of the aggressive attack which I engage in because previously reinforced behavior has become extinct We make distinctions, such as the distinction between behaviorist psychologism and behaviorist theory, because we think we ought to, and to say that prior conditioning will lead someone to make a necessary distinction is quite useless for establishing the norm that one ought to make that distinction. When Skinner confidently asserts that ..traditional 'knowledge' must be corrected or displaced by a scientific analysis," he makes a distinction between science and traditional knowledge quite similar to my distinction between the scientific and the non-scientific component of behaviorism. Unlike Skinner, however, I believe that our scientific knowledge depends upon our non-scientific knowledge. While our scientific knowledge can indeed correct specific errors in our traditional knowledge, it cannot displace it Skinner's confidence in saying that scientific knowledge must correct or displace traditional knowledge flows, not from his scientific analysis, but from his belief in the tradition of scientific naturalism. Since I am arguing for the legitimacy of 'traditional knowledge', I cannot fault Skinner for relying upon it. What I object to is his failure to acknowledge that he does so. Psychologism is found in disciplines other than psychology. George Homans, another former president of the American Sociological Association, has been arguing for a number of years that the theoretical fragmentation of the social sciences is the consequence of social scientists' failure to recognize that behavioral psychology is their basic unifying theory. Writing of sociologists, he claims that if they were willing to make their most geneml theoretical propositions explicit, they would find them to be the propositions of behavioral psychology. "The tragedy of sociology," he claims, "is that, since they do not do this (and perhaps are afraid of trying), the actual unity of our science and hence its possibilities for cumulative theoretical growth go unrecognized, and our intellectual. chaos persists. "11 While I agree that it is tragic that sociologists, and social scientists genemlly, fail to make their most general propositions explicit, I do not agree that these are predominantly propositions of behavioral psychology.
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Homans' own rule, that we ought to make our most general theoretical propositions explicit, is not a proposition of behavioral psychology. The image of social scientific discourse which emerges from behaviorist psychologism is that of social scientists from each school of thought busily hying to set up reinforcement schedules for those who belong to other schools of thought. If all of these scientists had learned (had been conditioned to act upon) the principle that positive reinforcement is more effective then negative, this might make life in the world of social science quite pleasant: we would all be engaged in providing positive reinforcers for our opponents, while enjoying the positive reinforcers provided for us by them. It might be quite pleasant, but it would also be quite mad. Psychologism is a bias which blinds the believers to the limits of empirical psychology as well as to the importance of philosophy and theology. Emile Durkheim protested against the over-extension of psychology into the realm of 'social facts', but the sociologism he inspired can also be a serious bias.
III. SOCIOLOGISM Behavioristic psychologism offers a technique, the manipulation of reinforcements, by which those who disagree with one another might seek to bring about some degree of harmony- a kind of mutual behavioral therapy. Sociologism fails to offer an analogous technique, which leaves at least some of its adherents with a sense of defeat In "Relativism, Rationalism, and the Sociology of Knowledge," Barry Barnes and David Bloor express this sense of defeat, although the general tone of their essay is not defeatist. They compare schools of thought to culturally diverse tribes. A member of one (Tl) would prefer his tribe's way of thinking to that of another (T2). A social scientist comparing these two tribes, or two schools of thought, is not in a cognitively superior position to a member of either tribe. Like the members of Tl amd 12, the investigator will prefer his own beliefs and values, will be able to offer reasons for these preferences, and will use such words as 'true', 'false', 'rational', and 'irrational' as ways of expressing them. The fact that the social scientist can point to others who have the same beliefs and values, the members of his particular school of thought in social science, does not make his position any different from the member of any other tribe. "The crucial point," say Barnes and Bloor, "is that a relativist accepts that his preferences and evaluations are as context-bound as those of the tribes Tl and Tl." Accepting this does not threaten the sanity of social scientific discourse; what threatens it is their claim that "there is no sense attached to the idea that some standards or beliefs are really rational as distinct from merely locally accepted as such. "12 Barnes and Bloor, in making this claim, contribute to the madness of social scientific discourse in two distinct ways. First, they mix up two quite
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distinct issues: whether an idea makes any sense and whether an idea is true. There is 'sense' attached to the idea that we could sail right off the edge of our flat earth, but we think (most of us, anyway) that such an idea is false. So also, there is 'sense' attached to the idea that some standards are 'really rational' and others are noL Barnes and Bloor depend upon our grasp of that sense in order to argue that the idea is incorrect. Second, it is madness f
It seems to make sense - to be sane - for the rationalist to argue with the relativist, but not for the relativist to argue with the rationalist; he ought merely to say: 'Those criteria hold for you; these criteria hold for us'. As
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Barnes and Bloor themselves say, the relativist can do nothing but "retire defeated, to gaze from some far hilltop on the celebratory rites of the Cult of Rationalism."1.S Those 'celebratory rites', from which Barnes and Bloor gratefully excuse themselves, are nothing more than the kind of conversations I have put forward as the ideal for sane social scientific discourse. Their defeatism is a direct result of 'their inability to contain their relativism within proper limits. Empirical metl:lods of studying either individual or group phenomena inexorably lead to relativistic conclusions. It is only through the recognition of non-empirical methods that relativistic social scientists can avoid the self-defeating move of asserting their relativism absolutely. Barnes and Bloor admit defeat, but do not accept it gracefully. Rather than resting on their hilltop, serenely contemplating rationalistic rituals, they use what they regard as their vantage-point on higher ground to hurl abuse on those below. They see themselves as surrounded by hordes of rationalists, and present what they call a 'plausible hypothesis' for the unpopularity of relativism: ...so many academics see it as a dampener on their moralizing. A dualist idiom, with its demarcations, contrasts, rankings and evaluations is easily adapted to the tasks of political propaganda or self-congratulatory polemic. This is the enterprise . that relativists threaten, not science.... If relativism has any appeal at all, it will be to those who wish to engage in that eccentric activity called 'disinterested research' .16
Not only does this passage demonstrate contempt, rather than respect, for those who happen to disagree with them; it also shows an amazing lack of reflective awareness. How can Barnes and Bloor not realize that this passage itself contains 'moralizing', 'demarcations', 'contrasts', 'rankings', and 'evaluations'? Although they have tried to bracket 'the good, the bad, and the ugly' along with 'the true and the false', they want to convince their readers not only of the truth of relativism and the falsity of rationalism, but also of the moral righteousness of the 'disinterested research' which they claim is possible only to relativists. They seem quite able to adapt relativism to ' self-congratulatory polemic'. When they argue, Barnes and Bloor refer approvingly to 'the balance of argumentation', far removed from the ' self-congratulatory polemic' of the rationalists. They are quite careful not to use the term 'irrationalist' to designate their anti-rationalist position. When Skinner argues, he presents himself as coolly engaged in 'scientific analysis', unlike his opponents who call his 'scientific picture of man' 'wrong, demeaning, and dangerous', and who engage in 'aggressive attack' because of the desttuetion of their 'accustomed reinforcers'. Neither Barnes and Bloor nor Skinner seem to realize that their arguments are self-defeating, that by trivializing the _ arguments of their opponents they al~_~~~!!_~~!r_Q~_n_!I!~r~iQle.
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Sociologistic bias against philosophical and theological methods appears in a less obvious way in the 'theory of action' of Talcott Parsons. Parsons' theories are widely despised, but even his critics have often admitted that he raised many of the right questions. He addressed the philosophical divisions within the social sciences, but not the theological ones. When he returned to the United States in 1926, after graduate studies in Great Britain and Germany, he found behaviorism and empiricism "so rampant" that social scientists widely rejected "the interpretation of subjective states of mind," believing that "scientific knowledge was a total reflection of the 'reality out there'."17 In 1937, Parsons saw two major 'tribes' of social scientists, but believed that there was a ' convergence' of social scientific theories originating from the traditionally opposed tribal traditions of positivism and idealism. The convergence of social scientific theories, he claimed, was toward 'a theory of action'. Simultaneously critical and appreciative of both the positivist and the idealist philosophical traditions in social science, Parsons sought to integrate what was valid in each of them into his own epistemological doctrine, which he called 'analytical realism'.11 In spite of his notoriously dense writing style, Parsons worked toward many of the elements of sane discourse in social science. He did not display open contempt for those with whom he disagreed, even though he became a popular target of abuse in the late '60's and '70's. He was, as Ritzer puts it, a "paradigm bridger,"19 who tried to bring different schools of thought together into a single 'theory of action'. Analytical realism was to be the philosophical foundation of that theory, a foundation which has been unable to support the structure erected upon it. Parsons' analytical realism fails because it is an attempt to create a philosophy without using philosophical method, and because it ignores theology almost entirely. Alexander, a leader of the current revival of interest in Parsons, writes of Parsons' "methodological ambivalence," his "confusion" between "the analytical and the concrete reference of social theory."20 This ambivalence is a direct reflection of the ambivalence in analytical realism, which is a failed attempt to integrate the philosophical positions of Kant, whom Parsons had studied both as an undergraduate and as a graduate student, and Whitehead, who was an elder colleague of Parsons at Harvard. One consequence of Parsons' failure to integrate the teachings of his two philosophical mentors is that Parsonians disagree radically about the philosophical foundations of Parsons' thought. Parsons himself changed the way he described his position. For many years, he described his position as 'Whiteheadian' ,21 and many interpreters concurred.22 Baum and Lidz expressed a common opinion in saying that "the theory of action can be regarded as a very extensive exercise in the spelling out of Whiteheadian 'analytical realism' in the domain of the social sciences."23 Bershady, however, had drawn attention to the powerful influence of Kant upon Parsons, and suggested that Parsons might be a Kantian in his epistemology and a Whiteheadian in his metaphysics.24 After a period of collaboration with Bershady, Parsons said that he had "explicitly" taken a philosophical
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position in the Kantian tradition.~ This made it possible for MUnch to claim that "Parsonsts theoretical development must be understood as a progressive elaboration and refmement" of a Kantian "central core. "2l5 Although Parsons relied upon both Kant and Whiteheadt it is incorrect to regard either his theory of action or his doctrine of analytical realism as a 'spelling out' or an 'elaboration and refinementt of a Whiteheadian or a Kantian tcentral core t. Throughout Parsons t long careert there was a fundamental inconsistency between the Whiteheadian and Kantian elements in his theory. Parsons failed to recognize that there is an irreducible contradiction betweeen Kant and Whitehead. Kant wrote: ... everything which is perceived in space and time, therefore, all objects of an experience possible to us, are nothing but phenomena, that is, mere representations which, such as they are represented, namely, as extended beings, or series of changes, have no independent existence outside our thoughts. This system I call Transcendental Idealism.'r1
Kant distinguished his position from a form of idealism which "doubts or denies the very existence of external things." In Science and the Modern World t the book of Whitehead to which Parsons repeatedly refers t Whitehead makes the same distinction as Kant t between what he calls the tsubjective idealist' and the 'objective idealisf. Unlike the subjective idealis~ he saYSt the objective idealist affmns the existence of a world of external things t but, says Whitehead, "when he comes to analyze what the reality of this world involves, finds that cognitive mentality is in some way inextricably concerned in every detail." Whitehead contrasts his own position with both forms of idealism. He claims that the principle method of the philosopher requires the "direct inspection of the nature of things as disclosed in our own immediate present experience. "28 This cannot be reconciled with Kant Parsons did not attempt to come to grips with the profoundly different notions of philosophical method which are present in the two philosophers; he simply drew selectively upon their philosophical conclusions. He used Kant's teaching about the validity of a priori knowledge to oppose the empiricist notion that knowledge is simply a reflection of a 'reality out there'. And he used Whiteheadts criticism of tthe fallacy of misplaced concreteness' to oppose the intellectual imperialism of the economists who presented their theories as if they reflected die totality of the 'reality out theret. He could thus use both philosophers in his criticism of the positivist tradition. But Parsons also wished to criticize the idealist ttadition t of which he said: "For the purposes of this studYt it is unnecessary to trace ttte idealistic tradition back to a period earlier than that of Kant tt29 So he used Whiteheadts brand of realism as a kind of antidote to the Kantian idealism he had already swallowed. Parsons' analytical realism is simply a juxtaposition of these unintegrated Kantian and Whiteheadian points. He defmes this doctrine in three passages
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in the fmal chapter of The Struetwe of Social Action. In the fIrst passage, he conb'aSts analytical realism to empiricism and to idealist 'fIctionalism'. He contends "that at least some of the general concepts of science are not fictional but adequately 'grasp' aspects of the objective esternal world." But he maintains that these "concepts correspond, not to concrete phenomena, but to elements in them which are analytically separable from other elements." No concept or system of concepts can provide a complete description of a concrete thing or event In the second passage, Parsons stresses his realism and opposition to idealism, and in the third, he stresses his opposition to the "empiricist reifIcation" of the theoretical system found in orthodox economic theory.30 There is no question about Parsons' genuine desire to avoid both empiricism and idealism, but the rejection of both of these positions does not, in itself, constitute a coherent epistemological position. Parsons avoided a discussion of philosophical method, and thereby failed to recognize the limits of empirical method, even though he insisted upon the distinction between them. In his introductory chapter to The Structure of Social Action, he stressed the vital importance of distinguishing between empirical science and philosophy, as well as the equally vital importance of not avoiding problems simply because they are philosophical: "there are no logically watertight compartments in human experience." He argued that although the methods of philosophy and empirical science differ, the conclusions and implications of each must be subjected to critical appraisal by the other. But Parsons decided that for his pwposes, "not necessarily for others," it was legitimate to defIne philosophy as a "residual category," an effort to know "by methods other than those of empirical science. "31 This defInition was seriously inadequate for his goal of developing an epistemological foundation for social scientific research and analysis. In spite of his insistence upon the distinction between philosophical and empirical method, he says in his introduction to the paperback edition both that he had "always maintained that The Struetwe of Social Action was an empirical work," and that it was always meant to be "essentially a theoretical work." He never says that it was meant to be a 'philosophical work', even though he says that it was "written under the aegis of a complex movement in the philosophy of science," the major prophet of which was, for him, Whitehead.32 Parsons maintains that the empirical and theoretical methods of social science are adequate to carrying out tasks which Whitehead described as the essential tasks of philosophy, which he called the "critic of cosmologies," "the critic of abstractions," and the harmonizer of "the various abstractions of methodological thought. "33 Of course Parsons could not endorse Whitehead's declared method of "direct inspection of the nature of things as disclosed in our own immediate present experience," because he insisted, with Kant, that "it is fundamental that there is no empirical knowledge which is not in some sense and to some degree conceptually formed."34 As a result, Parsons' criticism of the fallacy of misplaced concreteness was quite different from Whitehead's.
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Whitehead took as his main example of this fallacy the assumption that th most "concrete" things are "simply located" bits of matter, and that "the world is a succession of instantaneous configurations of matter. tt He described this as an intellectual "spatialisation" of things: ... the expression of more concrete facts under the guise of very abstract logical constructions. There is an error; but it is merely the accidental error of mistaking the abstract for the concrete. It is an example of what I will call the 'Fallacy of Misplaced Concretene8S'. This fallacy is the occasion of great confusion in philosophy.!S
Parsons was concerned, not about spatialization, but about the overgeneralization of economic theory, calling the treatment of an economic description as if it were a complete description of concrete events an instance of this fallacy. He paraphrases Whitehead, saying that "failure to see and to take account of it is what lies at the basis of many deep-rooted errors, especially in social science."36 While Parsons has a legitimate point to make about the limits of economic theory, and while the failure to recognize these limits can be taken as an example of misplaced concreteness, his attempts to transfonn what for Whitehead was a philosophical task into an empirical and theoretical task for social science cut the heart right out of Whitehead's fundamental point Whitehead held that philosophical examination of immediate experience was an essential way to criticize scientific abstractions. Parsons' sociologistic bias led to his failure to articulate any philosophical or theological method, his failure to recognize the conflict between Kant and Whitehead, and to the failure of analytical realism and the theory of action to stand as means of unifying the social sciences. Parsons recognized many of the problems of social scientific discourse and sought to reduce the fragmentation of the social sciences, but did not develop the means to accomplish this. He no more reconciles the differences between empiricists and idealists than do Barnes and Bloor the differences between relativists and rationalists. We do not need some kind of synthesis of opposing positions, but a way of conducting sane and scholarly arguments with those who disagree with us.
IV. Theological Method As members of different groups, whether tribes, nations, or schools of thought in social science, we can discuss important issues sanely to 'the extent that we maintain a balance between taking the beliefs of others seriously and remaining committed to our own beliefs. Theological method helps us to avoid trivializing either our own beliefs or the beliefs of others. It is a way of being reasonable about beliefs which cannot, ultimately, be justified by reason. Theological discussions are a means to deeper ----------------------
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understanding of my beliefs and the beliefs of others, and theological debates are an alternative to holy wars and ideological crusades. Theological debates, like any debates, make use of rhetoric, but theological method has understanding, rather than persuasion as its primary objective. Since a great part of a religious tradition is to be found in texts, theology draws heavily upon hermeneutic method, but is never 'pure' or 'objective' interpretation, since one's deepest beliefs are at stake. To 'deconstruct' these beliefs is to despair. The cultural relativism of Boas and his students was a therapeutic attack upon racist anthropology, motivated by a sincere respect for the diversity of others. But the scientific study of culture has resulted in what Rabinow calls 'humanism as nihilism.' He argues that the followers of Parsons as well as those of Boas have unintentionally belittled the deeply held beliefs of others, whose utterances become 'texts' to be translated into Western languages, and then deconstructed.37 An open admission of the necessity of theological methods, however, sounds like a return to the dark ages. Cornte's 'law of the three stages' is but one articulation of the belief that theology and metaphysics are primitive foons of knowledge, no longer needed in a scientific age. Comte's 'law', on the other hand, is part of his theology, a doctrine of the 'religion of humanity' which Comte hoped would take the place of Christianity. It is common to regard the hope that science might bring about a better world as a kind of secular counterpart to the traditional religious hope for redemption. But whether a social scientist's hopes are theistic, atheistic, or agnostic, the continued presence of such hopes among social scientists means that we need 'theological method in order to prevent our age from becoming even darker than the time prior to the enlightenment Many social scientists are, like Comte, believers in a tradition which denies the legitimacy of theology. This tradition embodies a faith in scientific method, and a hope that scientific knowledge will redeem the world. In the twentieth century, this hope that science would bring about an era of justice, freedom, equality, peace, and prosperity was severely tested by two World Wars, the depression, the holocaust, and the bomb. Nevertheless, the tradition retained its vitality. Soon after the second World War, the neo-positivist sociologist George Lundberg answered 'yes' to the question in the title of his book: Can Science Save Us? He concluded the book with the following words: When we give our undivided faith to science, we shall possess a faith more worthy of allegiance than many we vainly have followed in the past, and we also shall accelerate the translation of our faith into actuality. 31
A more recent affIrmation of the redemptive power of science is that of sociobiologist Edward O. Wilson, who explicitly recognizes the religious nature of his faith and hope although he does not use the words 'theological method'. "My own reasoning," he says, "follows a direct line from the
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humanism of the Huxleys, Waddington, Monod, Pauli, Dobzhansky, Cattell, and others." He regards traditional theistic religion and Marxism as other religious systems which are competing with ' scientific naturalism' as the source of hope and direction for human life. He, like a good Morman, Muslim or Marxist, expresses confidence that his faith will win out in the long run: The true Promethean spirit of science means to liberate man by giving him knowledge and some measure of dominion over the physical environment. But at another level, and in a new age, it also constructs the mythology of scientific materialism, guided by the corrective devices of the scientific method, addressed with precise and deliberately affective appeal to the deepest needs of human nature, and kept strong by the blind hopes that the journey on which we are now embarked will be farther and better than the one just completed.39
Lundberg and Wilson are heroes of this faith, standing fast when weaker spirits were driven into apostacy by trying times. In 1937, Pitirim Sorokin (parsons' chainnan at Harvard) described his loss of faith: I am not ashamed to confess the World War and most of what took place after it were bewildering to one who, in conformity with the dominant currents of social thought of the earlier twentieth century, had believed in progress, revolution, socialism, democracy, scientific positivism, and many other 'isms' of the same sorl~
Sorokin claimed that what Cornte had described as a law of progress in forms of knowledge - theology, metaphysics, science - was based upon too short a period of history, and that his more complete study of historical change revealed nothing but 'trendless fluctuations' among different systems of knowledge dominated by faith, reason, or sensory observation. What Cornte had celebrated, the abandonment of the fIrSt two systems in favor of the third, Sorokin deplored, claiming that this is what had led to "the crisis of our age. "41 I have smaller, but similar fish to fry; I focus upon a minor crisis of the social sciences rather than a major crisis of our age. Sorokin claimed that modern 'sensate' society was declining because it had lost contact with significant aspects of reality, aspects which can be known only through faith and reason. I claim that contemporary social scientific discourse is mad because, by reason of our rejection of theological and philosophical methods, we cannot cope with the issues which divide us. Barnes and Bloor reject both faith and reason, nicely illustrating the 'sensate' mentality criticized by Sorokin. They refuse to acknowledge that relativism as well as rationalism has a foundation in faith. They complain that "while the relativist can fight Reason, he is helpless against Faith," arguing that Faith can protect 'Reason' just as it protects gods, oracles, and ancestral spirits. They say that the relativist, when up against faith, can do nothing but inquire into the "local, contingent causes" which could account
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for the "remarkable intensity" of that faith. 42 By tacitly asserting that their position is free from any reliance upon faith, Barnes and Bloor smuggle back in one of the very rationalist doctrines they explicitly repudiate. As 'undercover rationalists', they repudiate both faith and the method by which one investigates faith, and thus contribute to the erosion of the ground upon which sane discourse in social science might be held. This is a curious failure for men who protest so loudly that what is sauce for the goose is sauce f
V. Philosophical Method The convergence Parsons celebrated in 1937 was, if not illusory, temporary. His intellectual leadership did provide a focus for a number of social scientists from different disciplines in the fifties and early sixties. Then, for a time, his theories provided a kind of negative unity, when social scientists who could agree on little else joined together in abusing Parsons. Today, there are still those who continue to work from a Parsonian perspective, but they are just one more lonely little band of disciples, similar in many ways to groups -of people who get together to talk about the writings of George Bernard Shaw or the movies of Charlie Chaplin. Action theory has become just one of many systems and perspectives in social science.
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It is important to admit that philosophical strife is an ineradicable element within social science, because without this admission social scientists will be unwilling to use philosophical method to deal with the philosophical questions which they cannot escape. In this section, I propose to concentrate upon my assertion that the issues which divide social scientists are distinctively philosophical issues, which can only be addressed by philosophical method. I shall argue that, in spite of the seemingly endless strife of philosophical systems, there is a philosophical method which can be distinguished from empirical scientific methods and from theological method. I am not going to argue that the existence of a distinctive philosophical method will eliminate philosophical diversity. On the contrary, the explicit recognition of that philosophical diversity is an essential feature of philosophical method. Philosophical method differs from theological and scientific methods in terms of what counts as evidence. In philosophical method the critical evidence is internal to the philosopher in a way which is not the case for either theological or scientific method. I have described theological method as the criticism and clarification of one's own tradition, a tradition which mayor may not define itself as 'religious', but which provides answers to questions about God, the soul, evil, the meaning of life, and the proper objects of hope. The results of efforts at criticism and clarification will be judged to be true or false insofar as they are or are not consistent with the tradition itself. This raises questions of interpretation, but not all questions of interpretation are theological. Interpretation is only theological if one is a believer in the tradition being interpreted. The tradition is external to the theologian, even though it is the theologian's belief in it that allows it to stand as the ultimate criterion of the lTUth or falsity of theological assertions. Scientific evidence is also external to the scientist On a frrst level, empirical evidence can be said to be the data of the external senses. With the development of social science, however, the meaning of 'empirical' has been extended to include publically available symbols. In the case of both symbolic data and sensible data, however, empirical evidence is 'intersubjective', capable of being examined by more than one person. The extension of the meaning of 'empirical' to symbolic data means that interpretation has become a part of empirical social scientific method. This interpretation differs from theological interpretation because it is not done from the standpoint of a believer in a tradition which the symbols are seen as expressing, representing, or somehow carrying on. This absence of an authoritative tradition presents serious problems of determining what might count as evidence for the truth of an interpretation, but, so long as empirical methods are being adhered to, the evidence must be intersubjective. Philosophical and scientific methods are both based upon the conviction that conformity to tradition is not the only criterion of truth, but philosophical evidence may be 'subjective', rather than 'intersubjective'.
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What I mean can be illustrated by Goodner's misnamed 'reflexive sociology'. In The Coming Crisis of Western Sociology, he calls upon sociologists to be clear about their 'domain assumptions', to assess the ways in which their sociological projects depend upon these assumptions, and to seek to know their innermost selves as the essential ground for their knowledge of social worlds:" I agree that sociologists, indeed, all varieties of social scientists, should do these things, but believe that Gouldner made a serious mistake in calling the activity that leads in the direction of these desirable goals 'reflexive sociology'. It is, rather, philosophy. My knowledge of my assumptions and of my innennost self is not open to intersubjective verification or falsification. I can, through the sort of reflection Gouldner describes, correct or improve my knowledge of my innennost self, but the data are inescapably private. I can talk or write about my inner life, but only I have access to the data which enable me to judge the truth or falsity of 'that which I have expressed in words. I have contrasted theological, scientific, and philosophical methods in terms of the differences in the kinds of evidence the users of each of these methods can call upon to make judgments about the degrees of truth or falsity they can assign to answers to theological, scientific, and philosophical questions. I have said the 'users of each of these methods' rather 'than 'theologians, scientists, and philosophers', because each of these three methods is properly used by all three types of investigators. Kuhn has emphasized the degree to which much 'normal science' is the criticism and clarification of a tradition, a paradigm, in which the scientist is a believer.4s Theologians draw heavily upon the speculations of philosophers and the scientific work of linguists, historians, and archaeologists, and frequently engage in philosophical and scientific work of their own. Philosophers often demand empirical data, and work out of traditions to which they are passionately committed. But the fact that no one discipline has a monopoly on the use of anyone of these methods should not obscure the fact that the methods are different After insisting again on the differences between these three methods, I want to call attention to three important similarities. First, all are based upon a realm of human experience: one experiences a tradition as an external resource and constraint, a complex 'social fact'; one experiences different realms of the human and non-human environment; and one experiences a complex inner world, a flow of images and emotions. Second, all seek answers to questions about their respective realms of experience. These questions may be about the interpretation of symbols, or they may be about relationships among sense data or elements of inner experience, but they lead to insights into some aspect of experience. Third, in all three methods, the insights are subjected to a process of testing by evidence; not every bright idea is true. These similarities suggest that experience, insight, and judgment are essential elements in the structure of human knowing. These three cognitive acts are the foundation of the epistemology articulated by Bernard Lonergan.
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Lonergan used a lengthy examination of cognitive acbvlbes in a wide variety of areas as a way of leading his readers into a reflection upon their own cognitive experieoce. At the heart of his notion of philosophical method is personal reflection, leading to a 'self-affinnation' of one's own powers of knowing through experience, understanding, and judgment. The evidence for or against such a self-affirmation is not to be found in the external world of sensible objects or symbols, but in the conscious experience of each person. The question for epistemology, "What is happening when we are knowing?" when answered, paves the way for the metaphysical question, "What is known when that is happening? ,,46 Lonergan's metaphysical position starts out from the assertion that what is real is that which can be known by experieoce, insight, and judgment He elaborates on the possibility of an ethics, based upon a similar kind of . self-affIrmation as a morally self-conscious actor. Again, the essential philosophical method is that of reflection upon one's own activity, this time the act of making a moral choice. Although I am stressing the method of philosophy rather than the conclusions reached as a result of using that method, I recognize that one can articulate a philosophical method only after one has taken a philosophical position. This interdependence of method and substance in philosophy can serve as the basis of an argument against the notion that there can be a single philosophical method: One's philosophical method is a direct and necessary consequence of one's overall philosophical position. Philosophical positions are diverse and often opposed. Therefore, philosophical methods are diverse and often opposed.
I reject the major premise as it is formulated above. It should read: One's verbal description of one's philosophical method is a direct and necessary consequence of one's overall philosophical position.
The conclusion will, therefore, be about the diversity of verbal descriptions of philosophical method, rather than about the diversity of philosophical methods. I maintain that each person arrives at some kind of articulation of his or her philosophical position only through experience, insight, and judgment A great number of factors will determine whether or not that person is able to give an accurate verbal description of the process by which he or she came to hold this philosophical position. An analogy might provide some support for my reformulation of the major premise. A person can ride a bicycle competently without being able to describe what he does to keep from falling over. Typically, what bicycle riders say is that when they start to tip, they lean the other way. Few will say that they tum in the direction they start to fall. Yet, as skilled riders, they invariably do so. This knowledge of how to keep one's balance is an example of what Polanyi calls 'tacit knowledge'.47 My claim is that just as
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one can ride a bicycle without being able to describe how, one can engage in philosophy without being able accurately to describe the method. The diversity of philosophical positions insures a continuing diversity of descriptions of philosophical method. These descriptions of philosophical method, however, can be criticized through the rather simple expedient of reflecting upon what it is we are doing, not only when we are engaged in philosophy, but also in science or theology. My reformulation of the major premise will, of course, be vigorously opposed, particularly by 'linguistic philosophers', those who, in terms of Rorty's description, take "the view that philosophical problems are problems which may be solved (or dissolved) either by reforming language, or by understanding more about the language we presently use. "41 Linguistic philosophy is a continuum of positions stretched between the empiricist pole of logical positivism and the nihilist pole of treating every intellectual endeavor as just one more literaIy genre. Both poles, and all of the positions in between, fail adequately to formulate the methods used by philosophers, deny either the validity or the importance of distinguishing philosophical method from other forms of inquiry, and fail to provide an adequate philosophical foundation for the social sciences. Rescher says that the philosophical rejection of philosophy has been, throughout Western history, a frequent reaction to the 'scandal' of philosophical diversity: From the ancient Pyrrhorian Sceptics through modem empiricists (Hume), positivists (Comte and the VieID1a Circle), JXagmatists (Dewey and Rorty) and deconstructionists (Derrida), the dismantling or dissolution of philosophy is an ever-recurrent aspiration.·
Rescher asks: "is it possible at one and the same time to acknowledge the inability to achieve consensus as an ineliminable feature of philosophy and yet maintain its validity as an intellectual endeavor?" He answers 'yes', and I agree, but go on to ask a slightly different question: 'is it possible to acknowledge that the strife of systems in philosophy is mirrored in social science and yet maintain that social science is a valid intellectual endeavor?' I answer 'yes' to that question also, but argue further that it is necessary to acknowledge that the philosophical strife is mirrored in social science. Without this recognition of the philosophical nature of many of our differences, we will fall into the error of trying to answer philosophical questions with psychological or sociological methods, or into the dogmatism of simply asserting 'the truth', without any attempt at providing either arguments or evidence. Social scientists need a philosophical method which will lead us to become keenly aware, not only of our assumptions, but of the grounds upon which we make judgments about truth and falsity, right and wrong. Philosophical self-affmnation should lead us to recognize, and affmn, our desire to know, and to know correctly. The way in which we formulate our
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philosophical position should legitimate exchanges with those with whom we disagree, and should make us able to recognize the kind of disagreement we are having - scientific, theological, political, ethical, epistemological, etc. - and willing to carry out our dispute using the arguments and evidence appropriate to the kind of dispute it is~ Our philosophical position should lead us, in other words, to being "intelligent and reasonable," mther than "stupid and silly. "50 Social scientists cannot afford to leave philosophy to the 'professional philosophers'. Philosophy is very much like brushing our teeth; if at all possible, it should be done for ourselves. Professional philosophers cannot take care of our philosophical 'teeth', in a manner analogous to dentists or oral hygenists, because philosophical reflection is upon 'that which is less accessible to another person than the deepest recesses of our mouths. After a lengthy examination of the complex interactions between psychologism and justificationism in philosophy, Notturno reflects upon an implication of his analysis for philosophy: ...the business of philosophy is not with knowledge, i.e., 1rUth, justification, and cognitive authority. Rather, it is with understanding, or, if you will, wisdom. On my view, the philosopher's task is not to adjudicate philosophical disagreement, but simply to figure out what's being said. It is not to prove that there are other minds, but to try to understand how other minds might try to prove things. To do this properly, the philosopher must think himself into a conceptual framework in which reasoning according to 'deviant' laws - logical or otherwise - is not a heretofore unknown type of madness. He must see the world in such a way that these 'deviant' laws no longer seem deviant Most importantly, it is the philosopher's task not to stifle cognitive growth by clinging priggishly to ,cognitive authority, but to promote cognitive growth by encomaging creativity. That's right- cognitive growth! For on my view, cognitive growth occurs not through judgment, but through understanding.51
While I agree with much of this passage, my analysis leads me to disagree rather sharply with certain key points. Philosophers should indeed seek wisdon, but the·se 'lovers of wisdom' do not, by reason of the name of their game, have any special advantage over social scientists or theologians in this pursuit One cannot be wise in our contemporary world unless one knows both the limitations and the uses of all three methods- philosophical, theological, and scientific. If it is a form of madness to attempt to give a psychological or sociological answer to a philosophical question, it is equally mad to attempt to give a philosophical answer to a scientific or 'theological question. Having said this, however, I have to grant a special place to philosophy. As I have said, clarifying the differences among methods and their appropriate domains is essentially a philosophical task. What Notturno says of the philosopher, I have been saying of the social scientist: both must be able to grasp and appreciate other conceptual frameworks and 'deviant' laws of thought. But neither the philosopher nor
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the social scientist can simply 'think' himself into other framworks. Not only is there a need for empirical descriptions of other ways of thinking, there is also a need for the theological task of maintaining that delicate balance between respect for the other and fidelity to one's own beliefs. Finally, 'cognitive growth' is perfectly acceptable to me as a way of expressing a terminal value, something good in itself, rather than a means to some greater good. But I cannot accept Nottumo's denigration of judgment as a means to cognitive growth. I believe that he sees an emphasis upon judgment as a sign of justificationism, but one can stress judgment without being a justificationisl In my view, judgment is one of the essential 'moments' in the structure of human knowing. Without judgment, experience and understanding remain radically incomplete. What we must remember is that our judgments are always human- fallible and contingent, never divine.
284 ENDNOTES 1. Alfred N. Whitehead, Scie1l£e and the Modern World (New York: MacMillan,
1925), p. 31. 2. Hubert M. Blalock, Jr., Basic Dilemmas in the Social Sciences (Beverly Hills: Sage, 1984), pp. 9-10. 3. See: Nicholas Rescher, The Sirife of Systems: an Essay on the Grounds and Implications of Philosophical Diversity (Pittsburgh: University of Pittsburgh, 1985). 4. Blalock, Basic Dilentml.lS in the Social Sciences, p. 171. 5. See: Bernard J.F. Lonergan, Insight, 2nd ed. (New York: Philosophical Library, 1958), p. 679. 6. Gottlob Frege, The Basic Laws of Arithmatic, trans. Montgomery Furth (Los Angeles: University of Califomi, 1967), p. 12. 7. See: Andrew White, A History of the Warfare of Science with Theology in Christendom, abridged by Bruce Mazlish (New York: Free Press, 1965). 8. B.F. Skinner, Beyond Freedom and Dignity (New York: BantarnNintage, 1972), pp. 16-17. 9. Ibid., p. 202. 10. See: Daniel Dennett, Brainstorms: Philosophical Essays on Mind and Psychology (Montgomery, Vermont: Bradford Books, 1978), p. 71. 11. George Homans, "Fifty Years of Sociology," in Annu.al Review of Sociology, Vol. 12, Ralph Turner and James Short, 008. (Palo Alto, California: Annual Reviews, 1986), pp. xix-xxii. 12. Barry Barnes and David Bloor, "Relativism, Rationalism, and the Sociology of Knowledge," in Rationality and Relativism, Martin Hollis and Steven Lukes, eds. (Cambridge: MIT Press, 1982), pp. 26-27. 13. Ibid., p. 21. 14. Mary Hesse, Revolutions and Reconstructions in the Philosophy of Science (Bloomington: Indiana University, 1980), p. 202; cf., Barnes and Bloor, "Relativism, Rationalism, and the Sociology of Knowledge," p. 23, note 6. 15. Ibid., pp. 46-47. 16. Ibid., p. 47, note 44. 17. Talcott Parsons, Social Systems and the Evolution of Action Theory (New York: Free Press, 1977), pp. 26-27. 18. See: Talcott Parsons, The Structure of Social Action (New York: McGraw-Hil~ 1937). 19. George Ritzer, Sociology: a Multiple Paradigm Science, rev. 00. (Boston: Allyn and Bacon, 1980), p. 213. 20. J.C. Alexander, Theoretical Logic in Sociology, vol. W, The Modern Reconstruction of Classical Thought: Talcott Parsons (Berkeley: University of California, 1983), p. 152-153 21. See: Talcott Parsons, The Structure of Social Action, Paperback Edition (New York: Free Press, 1968), pp. vii-viii; Talcott Parsons, Action Theory and the Human Condition (New York: Free Press, 1978), p. 247. 22. See: Thomas Fararo, "On the Foundations of the Theory of Action in Whitehead and Parsons," and Jan Loubser, "General Introduction," both in Explorations in General Theory in Social Scie1l£e: Essays in Honor of Talcott Parsons, 1.1. Loubser, R.C. Baum, A. Effrat, and V.M. Lidz, eds. (New York: Free Press, 1976). 23. Rainer Baum and Victor Lidz, ''Introduction,'' in Explorations in General Theory in Social Science: Essays in Honor of Talcott Parsons.
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24. See: Harold Bershady, Ideology and Social Knowledge (Oxford: Basil 1973), pp. 83, 91-92. 25. Parsons, Action Theory and the HIIJ1I/UI Condition, p. 5. 26. Richard Mtlnch, ''Talcott Parsons and the Theory of Action, I: The Structure of the Kantian Core," AMERICAN JOURNAL OF SOCIOLOGY 86 (1981), 709. 27. Immanuel Kant, Critque of Pwe Reason, trans. F. Max Muller (Garden City: Doubleday, 1966), p. 345 [B: 516-520]. 28. Whitehead, Science and the Modern World, pp. 131-32, 27. 29. Parsons, The StructlUe of Social Action, p. 473. 30. Ibid., pp. 730, 753, 757. 31. Ibid., pp. 20-27. 32. Ibid., paperback edition, pp. vii-viii. 33. Whitehead, Science and the Modern World, pp. ix-x, 86, 26. 34. Parsons, The StructlUe of Social Action, p. 28. 35. Whitehead, Science and the Modern World, pp. 74-75. 36. Parsons, The StructlUe of Social Action, p. 36. 37. See: Paul Rabinow, "Humanism as Nihilism: The Bracketing of Truth and Seriousness in American Cultural Anthropology," in Social Science as Moral Inquiry, R. Bellah, N. Haan, P. Rabinow, and W. Sullivan, 008. (New York: Columbia University, 1983), pp. 52-53. 38. George A. Lwulberg, Can Science Save Us? (New York: David McKay, 1947), p. 144. 39. Edward O. Wilson, On Hwnan NatlUe (New York: Bantam Books, 1978), p. 217. 40. Pitirirn A. Sorokin, Social and Cwtwal Dynamics, Vol. I (America! Book, 1937), p. ix. 41. See: Pitirirn A. Sorokin, The Crisis of DIU Age (New York: Dutton, 1941). 42. Barnes and Bloor, "Relativism, Rationalism, and the Sociology of Knowledge," pp. 46-47. 43. See: Anatole Rapoport, Fights, Games, and Debates (Ann Arbor: University of Michigan Press, 1960). 44. See: Alvin Gouldner, The Coming Crisis of Western Sociology (New York: Avon, 1970). 45. See: Thomas Kuhn, The Structwe of ScientifIC Revolutions (Chicago: University of Chicago Press, 1970). 46. Lonergan, Insight, p. xxii. 47. See: Michael Polanyi, The Tacit Dimension (Garden City: Doubleday, 1966). 48. Richard Rorty, "Metaphilosophical Difficulties of Linguistic Philosophy," in The Linguistic Twn, 00. Richard Rorty (Chicago: University of Chicago Press, 1967), p. 3. 49. Rescher~ The Strife of Systems: an Essay on the Grounds and Implications of Philosophical Diversity, p. 16. 50. Lonergan, Insight, 416. 51. Mark Nottumo, Objectivity, Rationality and the Third Realm: Justification and the Grounds of Psychologism (Dordrecht: Martinus Nijhoff, 1985), pp. 222-223.
Blackwel~
I
THE CASE AGAINST QUINE'S CASE FOR PSYCHOLOGISM DALLAS WULARD ''Whoever remains caught up within the sphere of general reflections may allow himself to be deceived by the psychologistic arguments. A mere glance at any one logical Law, at its true meaning and at the insightfulness with which it is grasped in its own right as IrUth, necessarily puts an end to the delusion." E. Husserl1
''I would almost say that psychologism lives on inconsequence. Whoever logically thinks it out to the end will have already abandoned it when he gets there." E. Husserl2
During the late 1950s and early 1960s, to make any significant association of logic with psychology was a dreadful faux pas, one almost utterly beyond redemption. It drew scorn and pity upon you. Although Dewey's influence was not totally absent, exttaordinary effort was required for dominant logicians such as Rudolph Carnap merely to be civil toward his views and treatments of (what Dewey took to be) logical matters. Defming psychologism in logic as essentially a confusion of the objective (in this case, logical relations) with the subjective (in this case, the psychological), Carnap exempted Dewey from it on the sole grounds that he consistently dealt with subjective or mentalistic processes such as 'thinking' or 'inquiry' .3 The central connection here for an understanding of the fate of psychologism in contempomry philosophy is that between the subjective and the mental. It was Frege's intetpretation of the psychological or mental as the essentially subjective, as the 'mentalistic' in a certain opprobrious sense, that overshadowed philosophical logic in the middle quarters of the twentieth century and made Carnap's view just referred to, for example, the obvious position to take. For Frege, 'psychologism' meant the misinterpretation of concepts and propositions proper to semantics and logic in such a way that they (supposedly) came to apply to 'mental' events and entities understood in his special way. Michael Dummett comments: "When Frege engages in polemic against psychologism, what he is concerned to repudiate is the invasion of the theory of meaning by notions concerned with mental processes, mental images, and the like,.... The psychological
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was for him a realm of incommunicable inner experience....".. John Skorupski remarks in this same vein of interpretation: "'Psychologism' may be the view that laws of logic are, or hold in virtue of, the laws which govern our mental processes, or again it may be the view that 'meanings' are mental entities. Frege was clearly opposed to both, and thought they were bound up with idealism.....'" I do not suggest that this is an adequate interpretation of Frege on psychologism, but it is a view of meaning and the mental that has come to be associated with him and handed on in current discussions. The general attitude toward the relationship of logic and psychology has been radically transfonned within the last decade or two. Now it is quite common to find logical laws described as laws of cognitive psychology or as aspects of the semantics of natural language or some 'deep' grammar. The return to psychologisms of these sorts all share the view that the mental, as they now interpret it, no longer falls under the reproach of subjectivism or 'mentalism' which was raised by Frege. Having supposedly come to terms with Frege through a repositioning of the 'psychological', it is thought to be safe to return logical laws to a central position in the actual processes of human life- where they in some sense obviously belong. This certainly is an inherently desirable shift One of the most serious objections to anti-psychologistic treatments of the laws of logic has always been that such treatments cannot do justice to the practical use to which logical laws are actually put, if not in the direction, then at least in the critique of everyday thinking, talking and writing.' It is unfortunate, in the light of the desirability of an appropriate reunion between logic and psychology, that a mere non-'mentalistic' interpretation of the mental (or, as would now more likely be said, of the 'linguistic', regarded as encompassing whatever of the mental should be taken seriously by philosophers) does not in fact deal with fundamental problems facing all attempted retwns to psychologistic interpretations of logical laws. Frege and Husserl are often grouped together as critics of psychologism.7 Although there is considerable overlap between them, they turn out upon examination to make quite different points- in emphasis at least. The easy return to psychologism which has occurred in the recent past has disregarded the substance of Busserl's critique of psychologism. That critique really had little to do with the 'subjectification' of logical law as Frege understood it. Instead, it focussed upon the nature of the evidence for logical laws, and rested upon the distinction between the real (the individual) and the ideal (the universal). Insofar as the new psychologism interprets the laws of logic as laws of the real, and possibly as 'natumlistic', it remains subject to his critique, indifferently of whether the real or 'natuml' events in question are opprobriously 'mentalistic' or not. If his arguments were good in the fIrst decade of this century, they are still good today. I believe that they were and that they are. We now turn to consider how those arguments apply to the position of W.V. Quine, who has strongly influenced the contemporary return to
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psychologism. On September 9, 1968, at the Fourteenth International Congress of Philosophy in Vienna, Quine read a lecture entitled, "Epistemology Naturalized: or, The Case for Psychologism." Later, stripped of its sub-title, it was published as chapter 3 of his Ontological Relativity and Other Essays,' and became a focal point of subsequent discussions concerning the nature of epistemology and logic. It is fair to say that it substantially contributed to the monumental change of attitude that has since taken place with regard to the relationship between logic and psychology. In what follows I will attempt to show that Quine's case for psychologism depends entirely upon neglecting the details of what the working logician, including Quine himself, actually does in establishing the truths - 'the Laws of Logic' - for which logic as an intellectual discipline is primarily responsible. It is such neglect and its implications that originally opened the way for Husserl's critique and that sustains its relevance today. What exactly was the main point of Husserl's critique as it concerns the new psychologism? (Here I will be very concise, referring for a more comprehensive account to pp. 143-166 of my Logic and the Objectivity of Knowledge). Addressing, in particular, thinkers such as John Stuart Mill and Theodore Lipps, who adopted the position that logic is a brnnch of psychology, Husserl raises the issue of the evidential base of the laws of logic. If logic is a subsection of psychology, then the evidence for those laws must be drawn from the psychological realm. What then are the psychological events, facts and regularities to be invoked in showing that the laws are true? Surveying the actual literature of logic, where is there so much as a single demonstration of a single logical law in a single logic text or treatise that, in the familiar manner of demonstrations in logic, rests the truth of the law upon psychological facts and regularities? It was Husserl's view that the universal absence of such demonstrations of logical laws points to a rigorous separation of logic from psychology. The evidence supporting the familiar logical laws taught in standard courses in formal logic is complete.' We are not waiting for further evidence on the Distribution Laws, for example. But this quite conclusive evidence turns out, in addition, to be completely free of statements of empirical laws or facts of any kind, including the psychological. While numerous thinkers have held the laws of logic to be psychological, their contention has no actual bearing upon the proofs of logical laws carried out by working logicians. It is therefore a mere general prejudice with no foundation in the actual conduct of logic as a field of research and teaching. Anyone is, of course, invited to overturn this claim of general prejudice by simply producing one professionally acceptable proof of an unquestionable law of logic from psychological facts interpreted in any way one wishes. Certainly no such proof is to be found in Quine's writings. But what, then, is Quine's case for psychologism? It chiefly consists in despair of anything other than psychology to guide us in understanding how evidence works in providing us with our view of reality. It is "the bankruptcy of epistemology" conceived along the lines of logical
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reconstruction. to It is "The impossibility of strictly deriving the science of the external world from sensory evidence."11 Quine points out (what is generally conceded) that Catnap's attempts at raJionaJ reconstruction of physicalistic discoW'Se in terms of sense experience, logic, and set theory, even if successful as an account of meaning, would not enable us to prove sentences about physical objects from observation sentences (plus set theory) by acceptable logic. The move to psychologism in epistemology and logic is a response to this failure: But why all this creative reconstruction, all this make believe? The stimulation of his sensory receptors is all the evidence anybody has had to go on, ultimately, in arriving at his picture of the world. Why not just see how this construction really proceeds? Why not settle for psychology?12
The project of rational reconstruction was in fact doomed, Quine holds, by, the indeterminacy of translation: "The typical statement about bodies has no fund of experiental implications it can call its own." I] All sentences incorporate a substantial mass of theory, allowing for manifold adaptations to their ' subject matter', so that "...there can be no ground for saying which of two glaringly unlike translations of individual sentences is right."14 "The indeterminacy of translation of theoretical sentences is the natural conclusion.... This conclusion..., seals the fate of any general notion of propositional meaning or, for that matter, state of affairs."U Therewith it seals the fate of logic as a theory of the structure and interrelationships of such propositional meanings, requiring that a different subject matter be settled upon for logic itself. What is left with such meanings gone? 'Empirical' meaning: the linguistic interactions of human organisms with factors present in the public environment of which they are themselves a part. The child: ...learns his rust words and sentences by hearing and using them in the presence of appropriate stimuli. These must be external stimuli, for they must act both on the child and on the speaker from whom he is learning. Language is socially inclucated and controlled; the inculcation and control turn strictly on the keying of sentences to shared stimulation. Internal factors may vary ad libitum without prejudice to communication as long as the keying of language to external stimuli is undisturbed. 16
Laws of evidence must show up in the same public arena. Epistemology is 'naturalized', and thus (supposedly) saved from total bankruptcy, when psychological laws of stimulus and response are taken to be the only possible account of "...how evidence relates to theory, and in what ways one's theory of nature transcends any available evidence."17 "Epistemology, or something like it, simply falls into place as a chapter of psychology and hence of natural science. It studies a natural phenomena, viz. a physical human subjecL.."t'- specifically, the relation between the human being's linguistic (including scientific) output and its environmental stimuli. "We are
v'
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after an understanding of science as an institution or process in the world, and we do not intend that that understanding be any better then the science which is its object."I' This completes Quine's abstract line of reasoning in support of psychologism. Although he makes a few comments about analyticity in "Epistemology NatW'8lized," details of a psychological interpretation of evidence (and the laws of logic) are lacking there. Other works offer some help on the specifics of his view. The sub-section of Word and Objecf1l on "The Intenmimation of Sentences," for example, considers a situation where someone mixes the contents of two test tubes, notes a green tint in the compound, and emits the sentence: "There was copper in it. "21 In this case chemical theory has intervened between the observation of color and the sentence emitted. The intervening theory is a "verbal network....composed of sentences associated with one another in multifarious ways," causally and logically. But whether causally or logically: ...any such intercoIUlections of sentences must finally be due to the conditioning of sentences as responses to sentences as stimuli. H some of the connections count more particularly as logical or as causal, they do so only by reference to so-called logical or causal laws which in nun are sentences within the theory. The theory as a whole - a chapter of chemistry, in this case, plus relevant adjuncts from logic and elsewhere - is a fabric of sentences variously associated to one another and to non-verbal stimuli by the mechanism of conditioned response. 22
This helps a bit with the details. It leaves no doubt, in any case, that Quine intends to interpret the evidentiating or logical relations between sentences in terms of the psychological process of stimulus and response, and that logical laws will simply be one element (indeed, as themselves sentences) in that process. A few pages later he comments that "...any realistic theory of evidence must be inseparable from the psychology of stimulus and response, applied to sentenceS."23 We take this to mean that the fundamental logical relations, such as implication and contradiction, are matters of social conditioning, and that to say A implies B, for example, is to make a statement about the conditioned responses of the relevant language community with respect to the sentences named by 'A' and 'B.' The later book, Roots 0/ Re/erence,'lA makes this even clearer, and provides a discussion of a specific logical law: the one usually called ,Addition'. This is, so far as I can tell, the only logical law of which Quine even attempts a specifically psychologistic interpretation, which surely indicates the great distance from 'the things themselves' he maintains in his philosophical speculations about logic. He remarks: "The law that an alternation is implied by its components is thus learned, we might say, with the word 'or' itself, and similarly with the other IawS."2S This clearly applies what is said here about alternation to the laws of logic generally: laws such as the familiar Modus Toliens, the Distributive Laws, and Universal Instantiation. He takes care to restate his opposition to that linguistic
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interpretation of the laws of logic according to which they rest solely on the meanings of the logical words. ·or·. ·not·. etc. "But now." he asks. "can we perhaps fmd some sense for the doctrine [just opposedl...in terms of the learning process?" Not surprizingly. the answer is affirmative: "We learn the truth functions•...by finding connections of dispositions: e.g. that people are disposed to assent to an alternation when disposed to assent to a component"26 From this. then. he proceeds to the general statement about the laws of logic quoted above. The laws of logic are laws of tendency to assert or deny. which (with a linguistic twist. of course) fits the well-known psychologistic pattern of interpretation. Now the crucial point for our discussion is the link postulated by Quine between meaning (as communalized behavioral dispositions with regard to sentences) and truth. For the laws of logic are in some indispensible sense laws of truth. The linkage is. on his view. embedded in the learning process. "We learn to understand and use and create sentences only by learning conditions for the truth of such sentences."%7 The earliest language learning. that of observation sentences. "is simply a matter of learning the circumstances in which those sentences count as true. ":Ill 'Eternal' sentences are. of course. learned differently. since their truth values do not alter with circumstances. Truth in these discussions becomes a social concept Learning a sentence. whether an observation sentence. a logical law. or an eternal sentence. is strictly a matter of developing a disposition to affirm or deny it in harmony with the linguistic community in its physical and social environment. The following comments about a particular eternal sentence makes this 'social' concept of truth clear. At least it makes clear that assent or 'counting as true' is what we learn in learning a language and is what the logical laws mediate:
·all·.
e--'
~
~
Still. the learning of 'A dog is an animal' as I represented it consisted in learning to assent to it., and this hinged upon the truth of the sentence. It hinged anyway on our having learned to assent to 'dog' only in circwnstances in which we learned also to assent to 'animal'. If we learned to use and understand 'A dog is an animal' in the way I described, then we learned at the same time to assent to it., or account it true. 29
Thus the foundation is laid for a defmitive statement about analyticity. incorporating Quine's reinterpretation of 'the linguistic theory of logic'. Language is social. and since analyticity is truth grounded in language it ,./ will be social as well: "A sentence is analytic if everybody learns that it is true by learning its words. Analyticity. like observationality. hinges on social uniformity."30 Quine thus makes "...analyticity hinge...on a community-wide uniformity in the learning of certain words. "31 We must then be clear that, for the purposes of this discussion. Quine is -..-/ not distinguishing between being true and being communally counted or accepted as true. In particular. learning a logical law is not a conditioned
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response to truth as something distinct from acceptance within the linguistic community. There are for him no meanings, no propositions, which might be bearers of truth regardless of acceptance or rejection. The 'necessity' which the laws of mathematics and logic seem to enjoy merely amounts to the psycho-social tendency toward conservation with regard to our belief system as a whole: a preference to modify our acceptances and rejections only along lines that will least disturb it as a whole.'2 There is very little more than this to Quine's discussions of how the laws of logic are psychological laws. The thinness of the account of how those laws may be so understood is due to the fact that in the works cited above he is coming to them von oben, from his speculative theory of language and mind, not von unten, from an examination of those laws themselves. When dealing with the laws themselves, on the other hand, as is done in writings which engage with logic as a field of scientific research, a quite different picture of logical law emerges. When one examines any of Quine's . /' expositions or proofs of logical laws, one finds that they are presented as . theoretically complete without a single reference to. or invocation of support from. any psychological matter of fact. We will make just a few comments about his actual procedure in the process of logical research and exposition, since his writings in this field are so well known. Those who have used Quine's Methods of Logic will recall that the primary subjects of discussion and theoretical analysis in that work are what he calls 'schemata'. "Schemata are logical diagrams of statements."" That is, they are symbols used to pick out various kinds of statements in terms of features determinative of the logical properties and relationships of those statements. "Schemata," he tells us, "are the medium of our technical work"- although our results are to be applied to sentences.'" The 'results' of the technical work will be primarily that given schemata are or are not 'valid'. "A truth-functional schema is called consistent if it comes out true under some interpretations of its letters; otherwise inconsistent. A truth-functional schema is called valid if it comes out true under every interpretation of its letters."" "One truth-functional schema is said to imply another if there is no way of so interpreting the letters as to make the first schema true and the second false. ,,36 Quan?(icational schemata submit to a similar treatment. "We can define an open [quantificational] schema as valid when, under every nonempty choice of universe V, and all interpretations of 'Fx', 'Gx', etc. within V, the schema comes out true of every object in V."" The argumentation for the validity or non-validity of truth-functional or quantificational schemata accordingly is solely a matter of examining certain possibilities of interpretation of the schemata in question. This pattern of argumentation is still followed in arguing for the validity of the schemata underlying rules for manipulating quantifiers. For example, with the schema underlying the rule of Universal Instantiation: (1). (y)[(x)Fx
~
FyJ,
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Quine comments: To see that (1) is valid, consider any universe and any interpretation, within that universe, of 'F'. Case 1: 'F' is interpreted as true of everything in the universe. Then. for each object y in the lDliverse, '(x)Fx -+ Fy' becomes true because of true consequent; so (1) comes out true. Case 2: ' F' is interpreted otherwise. Then. for each object y in the lDliverse, '(x)Fx -+ Fy' becomes true because of false antecedent; so (l) comes out true.3I
The typical language in such analyses, 'consider any universe and any interpretation of...', is of course the heart of the matter. It is precisely such / considerations of universes and interpretations that here yields insight into the validity of logical laws. Our point in relation to the attempted psychologization of those laws can be put very simply now. What is considered in the proof of a logical law has absolutely nothing to do with psychological events, facts or regularities, however the psychological is interpreted. The precise character of those things - universes, interpretations, etc. - considered in exposition and proof of logical laws need not be cleared up here. It is enough for our present purposes that logical laws are proven, and that the premisses of those proofs do not state or presuppose /"' psychological matters of any kind. The evidence for them is complete, as cited by Quine himself, but it is not psychological. What has been said here with reference to Methods of Logic, probably his most widely used book on logic proper, is equally true of his other logical treatises. In no case do we fmd theorems proved from psychlogical premisses. We would, for completeness sake, need to add some comments about principles of substitution and of derivations generally. But such additions would change nothing for the point here at issue. Thus while, in his speculative writings, Quine suggests, for example, that the validity of the schema 'p ~ (q v r)' might rest upon certain facts pertaining to how 'or' is learned and used, he never offers such considerations when he is doing research and exposition in the discipline of logic, as distinct from speculating about iL Rather, in logical work his practice completely conforms to what Husserl said about the science of pure logic. Namely, that it is a theoretical discipline which stands entirely on its own feet," and that "logical laws and forms in the pregnant sense of these words, belong to a theoretically closed round of abstract truth, that cannot in any way be fitted into previously delimited theoretical disciplines."40 Thus the really substantial point here does not concern psychology only, or the reduction of logical laws to psychological regularities. Given any domain of objects whatever, the claim that the laws of logic are laws of ~ that domain imposes the task of proving the laws of logic from statements about the objects of that domain. (Alternative strategies, such as that of treating those laws as 'rules', will, I believe, invariably generate parallel problems. The justification of 'rules', for example, or the explanation of how they accomplish what they do, can only be carried out by reference to
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some domain of entities, including the rules themselves, what they 'govern', and whatever 'governing' itself amounts to.) Moreover, any ontology places rigorous restraints upon the possible interpretation of logical law. If, for / example, one is a 'Naturalist', the problem of how to fit the laws of logic into that framework becomes urgent A Physicalist, for example, owes us an account of how Modus Toilens and the Barbara syllogism are to be derived from the facts and laws proper to Physics. With specific reference to Quine's "Case for Psychologism," we of course / do not wish to deny that there are psychological laws of linguistic assent and denial. Those laws would fmd their evidence in behavioral or other psychological facts. But they and their accompanying facts do in fact never serve as the basis for laws of logic or count as evidence to be expounded within the science of logic. Nor is it even clear how they could. From within the discipline of logic, they present themselves as simply irrelevant. This is acknowledged by Quine's practice, as well as by the practice of the logic profession generally. Hussed's case against psychologism as an interpretation of the laws of logic is as strong today as ever. It will remain so until someone demonstrates, in a professionally acceptable way, at least one law of logic from psychological premisses.
295 ENDNOTES 1. Edmund Husserl, Logische Untersuclumgen (Halle: M. Niemeyer, 1900), Vol. 1, "Prolegomena," subsec. 21, my translation. 2. Ibid., subsec. 25, my translation. 3. See: Rudolf Camap, Logical FolUJdoJions of Probability (Chicago: University of Chicago, 1950), p. 38-39. 4. Michael Dummett, Frege: Philosophy of Language, 2nd ed. (Cambridge: Harvard University, 1981), p. 204. 5. John Skorupski, "Dwnmett's Frege," in Frege: Tradition and Influence, 00. Crispin Wright (Oxford: Basil Blackwell, 1984), p. 240. 6. For a discussion of the history of this point, see: Dallas Willard, Logic and the Objectivity of Knowledge (Athens: University of Ohio, 1984), pp. 176-180. 7. See, for example: Herbert Feigl, "Physicalism, Unity of Science and the Foundations of Psychology," in The Philosophy of Rudolf Carnap, 00. Paul Arthur Schilpp (LaSalle, Ill.: Open Court, 1963), p. 250. 8. See: w.v.o. Quine, Ontological Relativity and Other Essays (New York: Columbia University, 1969), pp. 69-90. 9. See: Edm\Dld Husserl, Logical Investigations, trans. J. N. Findlay, (New York: Humanities, 1970), p. 133. 10. Quine, Ontological Relativity and Other Essays, p. 82. 11. Ibid., p. 75. 12. Ibid. 13. Ibid., p. 79; cf., p. 82. 14. Ibid., p. 80; cf., p. 2. 15. Ibid., p. 81. 16. Ibid. 17. Ibid., p. 83. 18. Ibid., p. 82. 19. Ibid., p. 84. 20. W.V.O. Quine, Word and Object (New York: Jolm Wiley & Sons, 1960). 21. Ibid., p. 11. 22. Ibid. 23. Ibid., p. 17. 24. W.V.O. Quine, Roots of Reference (LaSalle, ID.: Open Court, 1973). 25. Ibid., p. 79. 26. Ibid. 27. Ibid., pp. 78-79. 28. Ibid., p. 79. 29. Ibid. 30. Ibid. 31. Ibid., p. 80. 32. W.V.O. Quine, Methods of Logic, revised edition (New York: Henry Holt, 1959), xiii. 33. Ibid., p. 22. 34. Ibid., pp. 91-92. 35. Ibid., p. 28. 36. Ibid., p. 33. 37. Ibid., p. 97; cf. p. 136. 38. Ibid., p. 137. For printing convenience, we use the right arrow as the conditional sign, substituting it for Quine's right horseshoe. 39. Husserl, Logical Investigations, p. 76. 40. Ibid., p. 80.
MODAL KNOWLEDGE! MICHAEL LISTON
I. Introduction For philosophers of a broadly empiricist persuasion the question how we can come to know what we claim to know has considerable importance. One of the main desiderata of empiricist epistemology is that any answer to this question should be naturalistically constrained, though the nature of the constraint varies with the particular empiricist programme. Classical empiricism demanded that all knowledge ultimately be gained through the senses, and though classical empiricists all too often failed to distinguish very clearly belief generation from justification, the idea behind the constraint seems to have been that epistemic justification amounted to an ideally reconstructed series of inferences from some set of specific sensory inputs. Twentieth-century empiricists, though they did clearly distinguish discovery from justification, adopted a similar version of the constraint. More recently, epistemological naturalists require that knowledge claims be underwritten by a causal connection relating the knower's knowledge state to the facts, entities, etc., known. These naturalistic constraints pose no problems for knowledge traditionally regarded as a posteriori. 2 Such knowledge is deemed justified by, because ultimately derivable from, sensory experience. Alternatively, it can be traced causally to the fact known. For knowledge traditionally regarded as a priori, however, the naturalistic constraints prove challenging. Certain construals of a priori knowledge, usually associated with Platonism and Rationalism, are taken to be objectionable precisely because they violate naturalistic canons. According to these non-empiricist accounts, truths known a priori are truths of some special metaphysical category, inaccessible to empirical investigation, and known by means of some special intellectual faculty. Such theses lie at the heart of the differences between the British Empiricists and their opponents across the Channel, the latter proposing and the former objecting partly on the grounds that they commit one to mysterious cognitive faculties and equally mysterious theses about innateness and the like. Perhaps an example will help to clarify the parameters of these debates. Mathematical knowledge provides the paradigm example of a priori knowledge. Mathematical realism is the initially plausible doctrine that this body of knowledge is expressible by sentences having objective truth-values. In its most straightforward formulation, mathematical realism becomes
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Mathematical Platonism, the doctrine that sentences of mathematics are true (or false) in virtue of their correctly (or incorrectly) describing an abstract Platonic world of sets or numbers and their properties and relations. But such truth-conditions are problematic from the viewpoint of the epistemological naturalist, because a Platonic world of abstract objects, their properties, and relations by its very nature cannot be empirically accessible. Platonic facts are inaccessible to sensory experience (whether introspective or perceptual); nor can they figure in causal relations. The GMelian answer that we gain knowledge of this world through the operation of a quasi-perceptual, intellectual faculty of mathematical intuition exacerbates rather than allays naturalistic scruples.3 The problem of naturalistically accounting for mathematical knowledge has received much attention in recent literature.4 It seems to me, however, that the problem is generalizable to all a priori knowledge, indeed to any body of knowledge expressible by sentences whose truth-conditions seemingly require abstract subject matter. In this paper, I will examine the problems which epistemological naturalism poses for one such area of knowledge: modal knowledge. Michael Dummett tells us that any adequate treatment of necessity must account for both its source and how we recognize it.' By the former, Dummett means that for each member, A, of a class of modal statements we must be able to answer the question: in virtue of what is A true? By the latter, he means that we must be able to account for how we could come to know such facts. Dummett's closeness to the empiricist tradition makes it clear that his formulation of the problem readily fits the general schema given above and elucidated by the case of mathematics. His demand that the facts appealed to in providing truth-eonditions for a set of sentences should be facts ultimately learnable by us can be seen, I believe, as still another variant of the naturalistic constraint. It is surprising, given all the attention devoted to the source of modality over the past two decades, how little attention has been accorded the recognition problem. Clearly, if naturalism poses a problem for mathematical knowledge, it must also pose a problem for modal knowledge. Knowledge of states of affairs whose linguistic representation requires the use of modal operators generally seems to require that we be epistemically related to items which on standard construals are inaccessible to our natural epistemic capacities. The standard possible worlds method of supplying truth-eonditions for modal sentences in terms of metalinguistic quantification over worlds runs into obvious difficulties. Any objectual understanding of the metalanguage, such as that championed by David Lewis, is clearly committed to the existence of entities which are empirically inaccessible to us and thus couldn't be naturalistically known. Nor is the problem simply a problem of reference to and quantification over strange objects. Non-objectual, realist interpretations of modal discourse seems to fare no better from a naturalistic viewpoint To interpret modalities as higher-order properties of properties - e.g., being F essentially, being F and G are
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nomically related - leaves one with the problem of stating how we can come to recognize such higher order attributions. To interpret modalities in tenns of properties of state - the actual world being in a different state seems equally mysterious from an epistemological viewpoint. Finally, it is worth noting that the problems are not confmed to de re modalities. It is one thing to know of some de dicto truth that it is true, it is quite another thing to know of it that it is r.ecessarily true. And prima facie at least, there is no more reason to think that a naturalistically satisfactory answer will be forthcoming here than in the case of de re modality.' Whether the realism is de dicto or de re, objectual or DOt, modal realism seems to land us with a naturalistically problematic area of knowledge. Of course, one might argue, in analogy with the GOdelian account of our mathematical knowledge, that modal truths are truths of some special category, inaccessible to empirical investigation, and known or discovered by means of a special intellectual faculty of modal intuition. Some contemporary modal realists seem implicitly committed to some such account. 7 Indeed the only philosopher I know of even to attempt to clarify these issues, Colin McGinn, argues explicitly that: (i) modal truths concern subject matter which is inaccessible to nonnal empiricist epistemic channels of discovery; (ii) we possess modal knowledge; and (iii) we must gain such knowledge by some means other than regular empirical channels.' Certainly the postulation of a special quasi-perceptual faculty of modal intuition seems unwarranted. The difference between those of us who understand and know a lot about logical, mathematical, or physical modality and those of us who know little can hardly be explained in terms of the operation of such a faculty. McGinn's weaker claim (iii), of course, isn't committed to such extravagance. Obviously, however, McGinn's position is less than satisfactory. Apart from its being a purely negative account - it only tells us how we do not get modal knowledge - it requires clarification. In particular, we need a better account of regular empirical channels. In this paper I hope to sketch a response to McGinn's answer to Dummett's question. This response, which will be provided in section IV, can plausibly be claimed to be naturalistic. Nevertheless, it will differ in important respects from traditional empiricist responses to the problem of modal knowledge. These responses, which typically resolve the problem by endorsing a deflationary metaphysics, can usefully be categorized by a threefold division (though I make no pretence of exhaustiveness or exclusiveness): modal scepticism, modal empiricism, and modal psychologism. Discussion of these responses will occupy sections II and III. I hope to persuade the reader that the account I will offer succeeds where these standard accounts fail because of a loosening of the notion of a naturalistic constraint, a loosening, however, whose plausibility I hope to motivate by means of considerations about how we gain an understanding and knowledge of the world through the use of models in science.
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ll. Modal Empiricism In this section, I will briefly look at modal sceptICIsm and modal empiricism. Modal psychologism will be taken up in section III. The most deflationary solution to the problem, modal scepticism, is to argue that it is foolish to attempt to provide an epistemological story, naturalistic or otherwise, underwriting our modal knowledge for the simple reason that we do not have any such knowledge. Nor is this epistemic lack due to any cognitive defect on our part. Rather we have no modal knowledge because there's none to be had. Modal realism is false, since modal sentences lack objective truth-values. The most extreme version of this position is advocated by Quine,' whose assaults on modality consist of three main claims: (i) we don't need modal discourse to achieve the aims of scientific description; (ii) the most favored explanation of the source and recognition of modality - i.e., conventionalism - fails; and (iii) alternative explanations of modality are unintelligible. However, Quine's position is more a challenge to, than a conclusive argument against, modal realism. Insofar as an alternative account is available, (ii) and (iii) will be answered. Moreover, (i) seems to depend on an extremely narrow, though fairly common, understanding of theorizing in physics: the construction of hypothetico-deductive systems with true observational consequences (following from axioms describing particle interactions). I will respond to Quine's position in section IV by providing an alternative account and arguing for the need for modality given a more liberal reading of scientific theorizing. A less extreme version of modal scepticism is naturally suggested by an analogous scepticism with respect to mathematics. According to mathematical instrumentalisffi,lo mathematical sentences do not express facts; nor are they true or false. Instead, they express rules, structures, etc., which are instrumentally useful as aids to calculation, as criteria for judging certain kinds of practices, and the like. Analogously, modal instrumentalism is the view that modal sentences are neither true nor false, but instead express rules, inference tickets, and the like. Wittgenstein seems to have held this kind of view about logical and mathematical necessity, and Ramsey and Ryle seem to have had a similar view about nomological and dispositional statements. ll This attenuated modal scepticism has an advantage over extreme Quinean scepticism in that it enables us to explain why particular kinds of modal discourse ~ useful and figure importantly in our dealings with the world, despite the fact that modal discourse lacks objectivity. (This advantage, of course, is proportional to the extent to which the usefulness and applicability of modal discourse approaches that of mathematics. Consider how untenable a mathematical analogue of extreme scepticism would be, given the usefulness of mathematics!) However, only if one is already convinced that modal discourse is irrevocably mysterious, is one likely to agree to such a non-objectivist reading. We are naturally
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(and, I will argue, correctly) as inclined to think of the four color theorem and the principle of conservation of energy as expressing (necessary) truths as we are to think of them as expressing rules about topological and physical consbUctions. In the positive account in section IV I will argue that the rule or structural aspects of modality, though important, ought not to prevent us from being modal realists. Those who find scepticism about a given kind of a priori knowledge wrong yet are impressed by epistemological naturalism tend to propose a reduction of statements of the problematic class to others which do not present the same epistemological difficulties. Call a reduction empiricistic if it attempts to reduce statements of the problematic class to statements about everyday objective empirical facts. 12 Such reductions ideally would naturalistically legitimate the problematic knowledge by making it traceable via the reduction to everyday empirical facts, knowledge of which itself is legitimated by being traceable to perceptual experience. Along these lines, Mill espoused a kind of mathematical empiricism, viewing mathematical statements as high-level generalizations ultimately gleaned from perceptual experience. The analogous view for modality, modal empiricism, seems never to have been explicitly espoused, no doubt for the obvious reason that it's difficult to see how knowledge of possibility and necessity could ever boil down to perception and observation. Humean accounts of the causal and nomological modalities, however, usually partly consist of such a view. According to Hume, a causal statement has the same objective content as some related non-causal empirical generalization: there is no objective difference between 'F-events cause G-events' and 'F-events are constantly conjoined with G-events' . Similarly, the twentieth century empiricists held that a law statement has the same objective content as some corresponding universal generalization: there's no objective difference between 'it's a law that A' and 'A' (where 'A' expresses some universal claim). In each case, objective truth-eonditions are assigned to initially problematic modal sentences in such a way that one can naturalistically come to know them. On this modal empiricist account, knowledge of causal and nomological modalities reduces to knowledge of corresponding general facts which are knowable by perception, observation, and induction. Of course, there may well be problems with our epistemic access to such general facts - due to underdetermination by evidence - but these problems are supposed to be different in kind from those posed by violation of naturalistic constraints. 13 Such modal empiricist accounts, as I said above, are generally only part of the story, because in its pure form, modal empiricism destroys many important distinctions. Causal and law statements, for example, underwrite explanations and entail counterfactuals, while the corresponding universal generalizations do neither. Modal empiricism, in other words, fails precisely where modal instrumentalism succeeds, and vice versa: objective truth-eonditions are correctly to be had on the former account at the cost of rendering inexplicable some of the characteristic uses to which we put
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modal talk; the latter account reverses the exchange. This is why modal empiricism is generally supplemented with a further explanation in non-modal terms of the role played by modality. Thus Hwne, while insisting on no objective difference between a causal statement and a statement of constant conjunctio~, nevertheless attempts to account for the differences between 'the two in terms of the different psychological expectations an utterer of each may have. Similarly, empiricists have struggled with the distinction between laws and universal accidents by appending a variety of pragmatic and formal features to their modal empiricist account: law statements, unlike universal genetalizations, contain only purely qualitative predicates, are maximally deductively organizing, are known with high probability are known with low probability- to mention but a few. Each of these accounts encounters its own specific, well-known, and severe problems, which I will not pursue here. In addition most of the supplementations are broadly psychologistic in character; so they will be indirectly treated in the next section. In this section we have seen that modal scepticism and modal empiricism are less than ideal solutions to the problem of naturalism concerning modal knowledge. The former is at best a challenge, while the latter is too weak, yet satisfactory strengthening hasn't been forthcoming. Along the way, we have also unearthed some adequacy conditions which an account of modality should meet: t
C.I. It should respond to Quine's challenge by indicating why we need to appeal to modality in contexts of serious theorizing. C.2. It should, if possible, answer the source problem by providing objective truth-conditions for modal sentences. C.3. It should be able to account for the characteristic differences in role played by modal sentences. C.4. It should answer the recognition problem in a naturalistic way, however that's best understood.
HI. Modal Psychologism Traditionally, however, by far the most widespread treatments of a priori knowledge, and modal knowledge in particular, have pivoted on the notion that sentences expressing such knowledge are true in virtue of facts about us, usually facts about our means of representation. Unlike a posteriori knowledge which is arrived at by sensory and causal contacts with the world and is therefore reviseable in light of experience, a priori knowledge (apart perhaps from its conceptual raw material) is gotten independently of experience and is therefore immune to revision in light of new data. Put in this way, it is easy to see why sentences expressing the former are taken to be true in virtue of ordinary garden-variety facts, whereas sentences
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expressing the latter are true in virtue of rather special facts about how we linguistically or psychologically represent the everyday facts. To know something a priori is to recognize it as true in virtue of possessing and reflecting on one's means of representation. Thus, my a posteriori knowledge that the Eiffel Tower is in Paris required perception at some time or other; possession of the conceptual wherewithal to represent that state of affairs does not in itself underwrite my knowledge of the fact. Possession and reflection on the means of representing the fact that red is not blue is, however, all that's needed in order to know that red is not blue. Something along these lines seems central to the most common classical accounts of a priori knowledge. 14 For an empiricist, however, the facts about the means of representation which are appealed to in this account must themselves be naturalistically accessible. Consequently, empiricist construals of apriorism tend to be psychologistic in character. Following Colin McGinn, let us call a position 'psychologistic' insofar as it attempts to satisfy the constraint of naturalism by reducing statements of an epistemologically problematic class to empirically accessible facts about us involving psychological dispositions, imagination, intentions, decisions, conventions, and the like. Facts involving such items should be knowable in a fairly straightforward way. Applied to modality, this sort of view can be found in classical empiricism from Hume to Russell. "To form a clear idea of anything, is an undeniable argument for its possibility," Home tells us: imagination is the natural epistemological route to our knowledge of possibility. Implicit in Russell's theory of descriptions is a similar view: I can understand and communicate the possibility expressed by 'The President is Catholic' because I am psychologically acquainted with the universals denoted by 'is a president' and 'is Catholic'. Logical space is determined by universals, so that modal knowledge is underwritten by acquaintance with universals. Along similar lines, the set of necessary truths is sometimes taken to be that set of truths to which we bear a characteristic psychological attitude: we'll always refuse to accept counter-examples to them. Construed in a narrow fashion, however, modal psychologism fails, basically because the reduced class of modal truths generally will not be co-extensive with the reducing class of psychological truths. Thus, for example, there are doubtless logical possibilities which no one will ever entertain. And, for example, there are doubtless necessary truths counter-examples to which we'll never be in a position either to accept or to refuse. It is tempting to try to fix this failure by invoking psychological abilities and dispositions. Thus, for example, the possible truths might be equated with the imaginable, rather than the actually imagined truths. Similarly, the set of necessary truths might be reduced to that set of truths counter-examples to which we are psychologically disposed to reject. Since these abilities and dispositions are themselves modal in character, however, they fail to provide a general reduction of modality. So, we're left with the question how we could come to know them.
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In this century, particularly in the writings of the logical positivists, modal psychologism is usually construed in a broad fashion, by appeal to linguistic convention rather than to narrow mental properties. It is important to see that conventionalism is a psychologistic doctrine in the sense given above. Necessary truths are necessary in virtue of conventions we adopt about the use of our terms. In the case of logical necessity, we have adopted conventions in the form of definitional axioms, postulates, etc. that we'll use the logical constants, if, all, not, etc. in such a way that we'll refuse to accept any counter-example to modus ponens, universal instantiation, etc. This account can be extended to other forms of necessity. Extended to mathematics, the axioms of a mathematical theory, e.g., Peano's axioms, are mathematically necessary in virtue of their expressing conventions about the use of mathematical terms, e.g., 'plus', 'times', 'successor', etc. The natural extension to physics involves the conventional introduction of new definitional axioms which govern the use of new tenns, e.g., 'force', 'mass" 'velocity', etc., by associating them with elements of a mathematical theory and with empirical operations. The upshot is that the source of all necessity is conventional. Axioms of the appropriate type are necessary in the appropriate sense in virtue of our having conventionally decided to accept nothing as falsifying them. Additionally whatever follows by the conventionally chosen principles of logic from the axioms also counts as necessary. Necessity, in other words, is a feature, imposed by us, which detennines the form of our linguistic representation of the world. IS Clearly if it worked, such an account would provide a satisfactory naturalistic answer to the recognition problem, since our recognition of necessity boils down to the relatively unproblematic question of how we recognize our own decisions, intentions, and the like. Such an account also fits squarely in the tradition of classical apriorism. Our knowledge of necessity is independent of experience, and so is immune to revision in the light of new experience. We could, of course, come to change our conventions and adopt new ones, but new experience couldn't force such a revision. As such, conventional necessity is a relative matter: sentences are necessary relative to the conventions chosen, but different conventions might be chosen at any time. Furthermore, conventional accounts appear to satisfy the adequacy conditions laid down in section II. They provide naturalistically recognizable objective truth-conditions for modal sentences (C.2, C.4), and they provide a central role for modality in serious theorizing, a role which distinguishes modal and non-modal discourse (C.I,
C.3). All very nice, if it worked. It is a notorious fact, however, that such accounts are plagued with difficulties. As we have seen, according to the account conventions fix an interpretation for the language by fixing meanings for its terms in such a way that one cannot use that language without respecting the modal constraints set up by the conventions. The
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most serious difficulties are due to problems with the notion of meaning appealed to in the account. First, as Quine has repeatedly argued, examples of meaning-fixing conventions are in fact extremely rare. The evolution of language didn't need conventioneers to help it on its way. Second, a review of the best examples of conventions - axiomatizations of logic and mathematics and stipulations in physics - makes it clear that conventionality is a passing and context-dependent trait of language. Axioms conventionally chosen for one purpose may be rejected for another. And far from being the most stable and immune-from-revision sentences of the language, conventionally adopted principles, especially in physics - e.g., Newton's Second Law - turn out to be highly susceptible to revision. Given these problems, it becomes difficult to get any empirical grasp on the idea of meaning-fIXing conventions. Indeed, there seems to be little reason to accept conventionalism even as an attenuated reconstructive programme, since there seems to be nothing to underwrite the notion of an implicitly adopted convention. In this section, I frrst tried to emphasize what an attractive account of modality conventionalism provides. I then reviewed some of the more serious difficulties with the position. It is natural to wonder whether an account of modality can be constructed which will possess the virtues of conventionalism without suffering its difficulties. The task of the next section is to provide such an account
IV. Modal Naturalism In philosophical discussions, treatments of modality in physical science are very often ignored. Yet in physics one finds constant reference being made to the notion of possibility.16 Indeed modality appears to be required for an understanding of certain parts of physics. In order to see the importance of modality and how it functions in these contexts, we will need to lay some groundwork. In Newtonian presentations of mechanics, the problem of motion is fIrst solved for an isolated particle, whose position is specifiable by three mutually orthogonal Cartesian displacement values '11' r" r,. Kinematic problems are then solved by giving '11' '" " as functions of time. Dynamic problems are solved by specifying the particle's momenta and the forces acting on it along each axis. Given this infonnation, the particle's trajectory is completely determined. A general solution to the problem of motion for any physical system of N components then follows analogously. The position of the system is specifIable by 3N Cartesian positions r r" r., three values for each particle. Kinematic problems are solved by giving the ,'s as functions of time. Finally, dynamics problems are solved by specifying appropiate momenta and force values for each particle and using the force laws to compute the resulting motion. In this way the problem of ll ,
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macroscopic motion is solved, at least in principle, by straightforward genemlization of Newtonian techniques for dealing with a single particle. In practice, however, we are rarely in a position to apply Newtonian techniques. In macroscopic motions, such as those found in solids and fluids, the component particles interact, and generally the forces of interaction will be unknown. Thus we generally lack information essential to a Newtonian solution of dynamics problems. Newton, it seems, 'thought that additional postulates like his Third Law would take care of such problems. Thus, in rigid body mechanics, the internal forces of interaction between the components of the system which maintain the rigidity of the system are assumed to cancel each other out pairwise in accordance with the Third Law. Such an assumption, though generally false (since the forces must be assumed to be central), is harmless enough in the context of rigid body motions, since the internal forces can be neglected without serious consequences. However, internal forces operative in elastic solids, in fluids, or in vibrating strings, for example, cannot be so neglected, since they clearly play a non-trivial functional role in determining the temporal evolution of the system. Moreover, even if we knew the internal forces, it would probably be impossible to calculate the motion of the system due to mathematical complexity. Since for a Newtonian solution, knowledge of the internal forces and ability to calculate their effects is required, yet generally unavailable, the only alternatives are to give up or to employ ad hoc assumptions about them. Either alternative is unwelcome, the frrst from an engineering, the second from a foundational viewpoint The techniques of analytical mechanics were developed throughout the 18th and 19th centuries by d'Alembert, Euler, Lagrange, Hamilton, and others, motivated largely by the need for workable, well-founded solutions to a variety of such problems of motion. The basic idea underlying these techniques may be sketched as follows. 17 Often we know, on the basis of empirical investigation, part of the solution to a problem of motion. In the case of a rigid piston constrained to move in a cylinder, for example, we know that however it moves it will stay in the confines of its cylinder. A diatomic molecule (a dumbell of negligible dimensions along its own axis) will be constrained to move in five possible ways: translation along three axes and rotation about two. Similarly, a planar double pendulum is constrained to move in a certain way, as is a rigid body. The idea, then, is to use this known information to help solve the problem of motion without making assumptions about internal forces acting on the system, particularly assumptions about the forces maintaining the given constraints. To make the idea work, analytical mechanics diverges from Principia-style treatments in two important ways. First, it employs generalized coordinates instead of standard Cartesian coordinates. Formally, the instantaneous state of an arbitrary mechanical system composed of N free particles has 3N degrees of freedom (independent coordinates) and can be represented by N points in a Cartesian system. When constraints are present, however, the system is no longer a free system: the number of
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degrees of freedom is reduced, since some of the coordinates functionally depend on others. In such cases Lagrange showed that a set of new independent quantities, ql' ..., q,. (n < 3N) can be isolated, which can be transformed into Cartesian locations for the system and which will therefore serve to represent the system '8 motion when known as functions of time. The qi'll are called 'generalized coordinates't and the system is said to have n degrees of freedom. In principle, any quantities may be used as genemlized coordinates: which quantities, qit and the number of them, n, are suitable, will depend on the system under study. II Thus, one Cartesian displacement is best suited to our piston example above; five coordinates are suited to a diatomic molecule, six to a rigid body, etc. Polar coordinates are suited for the motion of a particle on the swface of a sphere. Energy or angular momenta coordinates may be best suited to other systems. Once a suitable class of generalized coordinates, qi,'''' q,., for the system has been isolated, an instantaneous state of the system can then be represented by a point in an n-dimensional hyperspace, the system's configuration space, whose axes correspond to the qi. All possible kinematic states of the system are represented by the set of points of the configuration space. 19 Kinematic problems are then solved by giving the qi as functions of time, t. The system's time evolution corresponds to a series of changes of the values of the qi; so the temporal evolution can be represented as a curve in configuration space. The problem now is to describe this curve without assuming anything about the unknown forces of constraint. The solution of this problem requires the second major divergence from Newtonian presentations: the general principles of analytical mechanics, used to describe the temporal evolution of the system, make no reference to force. Rather, they are principles of least action, which identify the system's evolution as that in which a certain quantity, action, is stationary. Perhaps the most fundamental principle of least action is Hamilton's Principle which states that if a system is in state A at t] and B at t2 then it will pass from A to B so that the mean value of the difference between the system's kinetic and potential energies in the interval t]-t2 is a minimum. More canonically stated, Hamilton's Principle is: (1) (S)(3Q)(Q = {~I
aIL.dt
= 0)
where L is the difference in S's kinetic and potential energies expressed in terms of the qi, and S is the operator of the calculus of variations, the integral being taken over the interval tl-~. By means of the calculus of variations this principle provides a solution of the problem of motion for S without taking into account the nature of any unknown forces. 2o We are now in a position to return to the original concerns of this paper. Modality, I will argue, is integral to these analytical approaches. Consider Hamilton's Principle above. First, it is natural to take the universal
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quantifier to range over all possible physical systems: over systems which are perfect fluids, simple pendola, isolated diatomic molecules as well as the ale in my glass, the pendulum in my clock, and the collection of helium molecules in Emmet's balloon. Ontological purists, of course, may demand that the range of the quantifier be limited to systems actually found in nature. But their entitlement to this demand is questioned by the practice of physics: possible, non-actual systems constitute the standard examples in physics books. Moreover, there is a second intrusion of modality in Hamilton's Principle, and this is going to be less easy to legislate against The variational operator ~ contains an implicit modality. The idea of the operator is that if one examines all the kinematically possible paths in the neighborhood of the actual path between t1 and ~, where these are obtained by allowing arbitrary, virtual (=possible, non-actual) infinitesimal changes in the values of the qi' then the actual path among all those is that for which the resulting change in IL.dt vanishes. To calculate the stationary-valued actual path, values of nearby possible, non-actual paths must be used. So reference must be made to non-actual kinematically possible states of the system. Indeed these will be physically impossible, if Hamilton's Principle is physically necessary! 21 To sum up, modality is central to analytical approaches to mechanics: fIrst, the variational principles range over all possible physical systems; second, the variational principles themselves make implicit reference to kinematically possible states of a system. We can now review our questions concerning the source and recognition of modality. In virtue of what is it true that a system could be in a given kinematical state (rl...rn , t)1 The brief answer to this question is that the sentence expressing the possibility is true just in case (2) (3Q)(Q = {'Ii I 'Ii is a generalized coordinate for S} & (3r1) ••• (3rn)(ql(S,t) & ...& ~(S,t) = rn»
=f1
Similarly, Hamilton's Principle is true of necessity just in case it correctly describes the temporal evolution of any possible physical system; Le., just in case it selects the extremal path of any system point in any configuration space, given initial and final states. Some may be inclined to balk at the brevity and deflationary appearance of this answer. It might be objected that at best it tells us how to answer questions about the truth-eonditions of modal sentences in tenns of mathematical representations of modal facts. When we ask for an account of the source of the physical necessity of Hamilton's Principle or the kinematic possibilities for a system S, the objection goes, we want to know what are the underlying modal facts, not some funny mathematical analogue of those facts. In the style of classical apriorism and modal psychologism broadly construed, I have made liberal appeal to our representational apparatus (in
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the form of mathematical structures) in accounting for the source of these modalities. However, I do not wish to follow van Fraassen and claim that the locus of all modality is the model. By this I take him to mean that any space of possibility is merely a mathematical entity, an artifact of our devising possessing no objective correlate. This suggests a thesis that some principled distinction can be drawn between truth-in-virtue-of-the-objectiveempirical-facts and truth-in-virtue-of-facts-about-the-model. 22 This thesis I tentatively wish to reject. The difficulties involved in van Fraassen's sorting out of the observational from the non-observational facts are well-known. Similar problems, I believe, will attend any attempt to sort out the relative semantic contributions made by actual and artifactual facts. Certainly some of our claims will be underwritten by facts about the model. What is less certain is that one can find a principled way of sorting out the two kinds of facts. The truth of Hamilton's Principle depends on its correctly describing the history of any actual system. Its necessity depends on its correctly describing the history of any possible system. Questions about the truth of each, however, may be difficult to separate from each other in principle. Moreover, we can on a case by case basis distinguish between systems which are purely mathematical and those which also have physical realityby looking at the class of applications the theorist has in mind. 23 Perhaps the difficulties involved in providing a principled separation of the relative semantic contributions made by real physical facts and mere mathematical facts can be highlighted by an example. Physical quantities such as mass seem best understood as functions from systems and times to real numbers. Thus, tfmass(S,t) = rtf is true just in case (Ef)(ErXf = mass & f(S,t) = r). In supplying truth-conditions for the sentence, I appealed to mathematical entities: functions and numbers. Yet few would deny that such a sentence could be true in virtue of physical facts about some physical system, S. Now the truth-conditions supplied by (2) above for our modal sentence should be no different in principle. They appeal to mathematical entities, genemlized coordinates and numbers, yet the sentence, if it correctly describes a system found in nature, will be true partly in virtue of real physical facts: the number of degrees of freedom possessed by the system. In view of these considerations, it is difficult to understand the contrast between 'What really are the modal facts?' and 'How are those facts mathematically represented?' The former suggests an unanswerable metaphysical question. Nevertheless, rather than identify, as van Fraassen does, modal elements in science with modeling artifacts, I think it better to adopt the weaker thesis that any clear question or claim about the fonner can be reformulated as one about its mathematical representative, in the manner indicated. I now turn to the recognitional question. In one sense, both the truth and the modal status of the claims we have been reviewing are known a priori. Insofar as the contrast between a priori and a posteriori or between transempirical and empirical is intended to indicate a difference between
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knowledge requiring a certain amount of definitional stipulation and logical and mathematical inference and knowledge merely requiring observation, measurement, straight-rule induction, and some fairly 'direct' causal contact with the fact known, then clearly knowledge of these modalities is of the fonner sort. It takes mathematical understanding to recognize these modalities of physics, while very little such understanding is required for recognition that the Eiffel Tower is in Paris. It is doubtful, however, whether any of the knowledge, modal or otherwise, acquired in physical theorizing can be arrived at by traditionally a posteriori, empirical techniques. (I will return to this theme below.) While we should acknowledge this a priority however, we should not overemphasize its importance. The kind of modal presentation of classical mechanics which we're looking at wasn't born in vacuo. To arrive at the kind of general classical theory being discussed here, it took a long series of discoveries. Newton took a variety of vaguely understood kinematic phenomena, explicitly discussed from the fourteenth century onward and widely known through the writing of Galileo, and proposed a dynamical theory which he hoped would successfully and intelligibly model such phenomena. However, Newton's Principia itself deals with a relatively limited set of physical applications, and it required the work of James Bernoulli, d'Alembert, Euler, Lagrange, Hamilton and others to extend Newton's methods to cover the notions of rigid bodies, fluids, vibrating strings, and systems of points. 24 Rarely, however, do these discoveries consist in any straightforward application of induction or the hypothetico-deductive method. Instead, to a great degree they involve coming up with new, alternative mathematical treatments which enable the mathematical derivation of new, non-trivial consequences of postulates already shown to succeed for certain domains. Moreover, the methods of Euler, Lagrange, and Hamilton, though highly abstract, are closely linked to experimentation. The discovery of a set of genemlized coordinates requires experimentation with the system. We discover, for example, that a particular beam is a rigid body with six degrees of freedom by attempting to move its component particles relative to each other in a manner which is inconsistent with the constraint: by trying to stretch, bend, or break it, for example. If our attempts fail, we assume that it can be treated mathematically as having six degrees of
freedom. If, however,
the distinctions between a priori/a posteriori, transempirical/empirical are supposed to indicate anything deeper, then it's difficult to see what they have to do with scientific modal knowledge. First, from the apriority of the knowledge (in the sense just given) it doesn't follow that it's indefeasible or irrevisible in the light of experience. We can, and do, find that the mathematical structures we had hoped and believed were adequate to represent physical and kinematic possibilities, measurements, etc. do not possess this feature. Thus, for example, our belief in the necessity of Newton's Second Law was defeasible; it came to be
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realized that some physically possible (high-velocity) systems have no Newtonian analogs. Second, from the 'ttansempirical' character of this modal knowledge, it doesn't follow that it's mysterious or non-natural in any sense. Of course a few measurements will not generate such knowledge. But figwing out whether a certain set of mathematical structures represents some physically possible situations is no different in kind than figwing out whether they adequately represent the real world. Indeed to appeal to a faculty of modal intuition makes things far too easy. This way of dealing with the question grossly undervalues the hard work expended by Newton's successors in developing a theory which would be adequate. Mysterious innate faculties seem the wrong sort of thing to invoke to explain the successes of these men. Rather, their epistemological advances seem better explained in terms of the exercise of general cognitive abilities - mathematical skills, insight into physical problems, and the like - and their having lived in an historical epoch where others were developing and publishing the mathematical and physical tools needed to provide the basis for subsequent development. At a less general level, we have seen that the modal 'discoveries' in question rely to a great extent on general reasoning and inference together with experimentation. And it is surely true that these abilities are as natural to us as our ability to walk upright. Let us now backtrack a little to see how this account compares with the more traditional attempts at naturalism which we examined in sections II and III. In section II, we saw that modal instrumentalism (moderate modal scepticism) and modal empiricism suffered from the defects involved in violating our adequacy conditions C.2 and C.3 respectively. I hope I have shown that the account of the modalities presented here satisfies these adequacy conditions. According to the account, modal sentences (of the kind examined) do possess objective bUth-conditions, as opposed to being truth-valueless, e.g., as required by C.2. Moreover those truth-conditions are reasonably clearly expressible in mathematical terms, our means of representing in physics. I have also argued (though more tentatively) that these truth-conditions should be realistically construed: there is no clear motivation for identifying modal facts with their mathematical representation. Just as there is no clear way of talking about force except in teons of its mathematical representatives, so there is no clear way of talking about the truth-conditions of modal sentences except in terms of their mathematical representatives. But the latter should no more force anti-realism about modality on us that the former does about forces. In addition, there appear to be good independent reasons for a realistic construal: the defeasibility of modal claims in light of experience, their connections with experimentation, and their deep conceptual integration with claims traditionally thought to be about the real world As required by C.3, the account offered here goes some way toward explaining the distinctive role played by modal discourse. It explains why Hamilton's Principle is necessary - in virtue of its applying to all possible
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systems - while other statements - statements of initial and final conditions, for example - are contingent We can easily understan
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e.g., fIrst-order structures, arithmetical structures, etc. If we're asked in virtue of what is some instance of a valid frrst-order schema (logically) necessarily true, surely the clearest answer we have to date is: S is logically necessary just in case S is true in every structure. Again, it seems unnecessary to view this as a reduction of the relevant modality. We need not identify logical possibility with its mathematical representation. In particular, facts about us and our language - our acceptance of counter-examples, for example - will partly determine what are the correct structures. As for our recognition of logical or mathematical necessity, we learn about it just like we learn any other theory: by experience, trial and error, observation, doing rote exercises, solving problems, etc., in other words by doing the kinds of things one hopes one's logic students will do. Thus we clarify, extend, and improve our vague intuitive grasp on logical and mathematical possibility. There's nothing mysterious requiring the operation of a special faculty here. In a less individual-centered and more community-centered vein, I think the analogy with the case of modality and theorizing in physics can be further developed. In the early part of this century, GOdel, Tarski and others did for Frege's systematic beginnings what Euler, d' Alembert, et ale did for Newton's in the eighteenth century. New discoveries were made - e.g., soundness and completeness theorems - which developed, extended, and sharpened our pretheoretical grasp of logic and mathematics. Moreover, there's a sense in which these theoretical developments were not determined by antecedent ideas and in which these theories could come to be revised. However, I leave these matters in this highly suggestive fashion. In this paper I have taken modal knowledge as a test case of a naturalistically problematic area. I have argued that the clearest account of truth-conditions for modal sentences is in terms of abstract structurespossible worlds with a mathematical flavor. Though 'this isn't a reductive identification of mathematical and modal properties, it assumes that clear views of modality can be expressed in mathematical terms. I suppose this itself is a defeasible assumption, but it at least warrants further investigation. Though this account has little of interest to say about causal contact, sensory input, and other familiar cornerstones of naturalistic epistemology, it deserves, I think, the appellation 'naturalistic'. We can no more do all epistemology at the level of causal connections than we can all physics at the level of particle mechanics. Rather, the naturalism lies in the sketch of anthropological and general learning considerations provided. Indeed in a sense I have tried to deflate the problem of naturalism by indirectly questioning the distinctions between transempirical/empirical, a priori/a posteriori, etc. on which it relies.'n These distinctions have been amply criticized in the past, particularly by Quine, but they continue to lie behind numerous philosophical problems, particularly the problem of naturalism.
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ENDNOTES 1. This paper is largely intended as a response to: Colin McGinn, "Modal Reality," in R. Healey, 00., Reduction, Time &: Reality (New York: Cambridge University, 1981), pp. 143-189, to which I'm deeply indebted. Those familiar with: Mark Wilson. "Contingent Identity," PIDLOSOPHICAL STUDIES 43 (1983), pp. 301-327; Mark Wilson, "What Is This Thing call 'Pain'']'' PACIFIC PHILOSOPIDCAL QUARTERLY 66 (1985), pp. 227-268; and Mark Wilson "Semantics Balkanized" (forthcoming) will, I hope, see the big debt I owe to these. I also wish to thank Jeff King for his comments and suggestions. Part of the research for this paper was supported by a Mellon Postdoctoral Fellowship at Johns Hopkins. 2. I'm taking the epithets a posteriori, a priori to apply primarily to knowledge and derivatively to statements. For details, see: Colin McGinn, "A Priori and A Posteriori Knowledge," PROCEEDINGS OF THE ARISTOTELIAN SOCIETY 77, pp. 195-208. 3. See: Kurt G&lel, "What is Cantor's continuum problem']" in Paul Benacerraf and Hilary Putnam, eds., Philosophy of Mathematics: Selected Readings (Englewood Cliffs: Prentice Hall, 1964), pp. 258-273. 4. Mainly prompted by: Paul Benacerraf, "Mathematical Truth," JOURNAL OF PHILOSOPHY LXX 19 (1973), pp. 661-79. 5. See: Michael Dummett, ''Wittgenstein's Philosophy of Mathematics," in Truth and Other Enigmas (Cambridge: Harvard University, 1978), p. 169. 6. lowe this point to: MdJinn, Modal Reality, p. 177, fn. 1. 7. It is tempting to read Kripke's reliance on philosophical intuition in this way. See: Saul Kripke, ''Naming and Necessity," in Donald Davidson and Gilbert Hann~ eds., Semantics of Natural Language (Dordrecht: Reidel, 1972), pp. 253-355. 8. See: MdJinn, Modal Reality. 9. See, for example: W.V.O. Quine, Word and Object (Cambridge: MIT, 1960); and W.V.O. Quine, "Reference and Modality," in Leonard Linsky, 00., Reference and Modality (Oxford: Oxford University, 1971). 10. See, for example: H. Field, Science without Numbers (Princeton: Princeton University, 1980). 11. See, for example: C. Wright, Wittgenstein on the Foundations of Mathematics (Cambridge: Harvard University, 1980); and F.P. Ramsay, Foundations of Mathematics and Other Essays (London: Routledge and Kegan Paul, 1931). 12. This way of putting things will be familiar to Dummett readers; see: Michael Dummett, "Realism," in Truth and Other Enigmas, pp. 145-65. 13. See: McGinn, Modal Reality, pp. 165-166. As MdJinn points out, different sorts of recognition-transcendence seem involved: usually the problem of induction is taken as due to our physical limitations, but the problem of naturalistically recognizing modal and mathematical truths is taken to be different in kind. 14. For a good discussion of classical apriorism, see: T. Horowitz, "A Priori Truth," JOURNAL OF PHILOSOPHY LXXXII 5 (1985), pp. 225-239. 15. For a classic presentation, see: Rudolf Carnap, Meaning and Necessity (Chicago: University of Chicago, 1947). 16. A notable exception is: A. Bressan, A General Interpreted Modal Calculus (New Haven: Yale University, 1972). 17. The discussions of mechanics in this section are modelled on the treabnents given in: H. Goldstein, Classical Mechanics (Reading: Addison Wesley, 1965); and
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C. Lanczos, The Variational Principles of Mechanics (Toronto: University of Toronto, 1966). 18. Subject to certain fonnal restrictions: they must be finite, single-valued, and differentiable. 19. In the special 'cosmological case' where the system in question is the world, the set of possible worlds could be identified with the set of its possible states representable by its configuration space, if per impossible we had available a set of generalized coordinates for lt This may be one way to understand Stalnaker's accomt of possible worlds as state-properties. See: R. Stalnaker, Inquiry (Cunbridge: ~, 1987) 20. Hamilton's Principle can be used to derive Lagrange's equations for the system, the solution of which provides the needed values of the q/. The partial derivatives in these equations will also appeal to possibilia for a calculation of their solution. 21. This seems to count against Kripke's suggestion that perhaps physical necessity is necessity in the highest degree. It is worth emphasizing here that the kinematical modalities considered in this paper differ considerably from the standard physical modalities considered in the philosophical literature. According to standard accounts, the set of physical possibilities is usually taken to be the set of worlds in which the laws of physics are true. Such accoWlts ignore the fact that some laws, like Hamilton's Principle, themselves make reference to modality. 22. See: Bas van Fraasse~ The ScientifIC Image (Oxford: Clarendon, 1980). As good empiricists, van Fraassen tells us, we should be epistemically committed only to claims about what is actual and observable. 23. For similar claims, see: C. Truesdell, An Idiot's Fugitive Essays on Science (New York: Springer, 1984), p. 509. 24. For a spirited and unique account of this history, see: C. Truesdell, Essays in the History of Mechanics (New York: Springer, 1968). 25. Goldstein, Classical Mechanics, p. 31. For the suggestion that Field's programme to nominalize physics fails because of his similarly ignoring intrinsically modal theories, see: David Malament, "Review of H. Field, Science without Numbers," JOURNAL OF pmLOSOPHY (1982), pp. 523-34, especially p. 533. 26. Psychologism, as I have interpreted the view, is a loosely knit family of theses aimed at naturalizing epistemology by reducing problematic areas of knowledge to more naturalistically amenable properties of knowers. Thus, Frege calls 'psychologistic' positions which identify numbers with ideas, mental pictures. See: Gotdob Frege, The Foundations of Arithmetic, trans. J. L. Austin (New York: Philosophical Library, 1953), pp. v·, 37·. Dummett similarly calls 'psychologistic' theories of meaning identifying meanings with psychological entities. 27. For fmther questioning of these distinctions, see: Michael Liston, ''Naturalism and Abstract Knowledge," (forthcoming). There I argue that if our mathematical knowledge is naturalistically problematic, then so is most of our knowledge of physics. This argument would be needed to undercut an objection to the present position, viz that I haven't succeeded in providing a naturalistic account of modal knowledge, since the mathematical apparatus used to give clear answers about the source of modal knowledge is itself in need of a naturalized treatment Such a treatment, however, is to be had, but it requires a long historical and anthropological story.
DEDUCTIVISM VERSUS PSYCHOLOGISM ALAN MUSGRAVB For the belief in inductive logic is largely due to the confusion of psychological problems with. epistemological ones. It may be worth noticing, by the way, that this confusion spells trouble not only for the logic of knowledge but for its psychology as well. Sir Karl Popper
II. Who Needs Inductive Logic? INaive psychologism says that the task of logic is to describe the ways in which people think. It makes logic into a branch of descriptive psychology, and the laws of logic into psychological laws, 'laws of thought'. The basic objection to this view is that it ignores the logician's concern with the validity and invalidity of arguments. People actually reason invalidly as well as validly. Logic does not just describe these different ways of reasoning, it says which of them are valid and which not. That is why logic books sometimes contain sections on fallacies, widespread but invalid ways of thinking or reasoning. Logic is not a descriptive science like psychology, and the laws of logic are not mere descriptions of the ways in which people think. This is the central point of the critique of psychologism mounted by Frege and Husser!. In the nineteenth century the point was often put by saying that logic is not a descriptive science like psychology, but a prescriptive science like ethics. The 'laws of thought' do not describe how people do think, rather they prescribe how people ought to think. This is not wrong, but it is a bit swifl 'To reason thus-and-so is to reason validly' states or describes a logical fact; it says nothing prescriptive, nothing about how one ought to reason. But cOITibined with 'One ought to reason validly', it entails 'One ought to reason thus-and-so'. Now 'One ought to reason validly' seems platitudinous. Actually, it is itself a normative principle, and one which needs careful interpretation if it is not to have absurd results. It must not, of course, be taken to mean 'Do nothing cognitive except reasoning validly'. For this tells us to believe nothing (believing being a .cognitive doing distinct from reasoning validly). Or it tells us that if, in violation of the role, we have a belief or two, we should do nothing but explore the infinitely many valid consequences of those beliefs. Both are absurd. 'One ought to reason validly' must be taken to mean no more than 'When you reason, reason validly' - it being understood that our cognitive doings (not
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to mention our non-cognitive doings) involve much more than reasoning or arguing. But enough of these platitudes - for the moment Notoriously, twentieth-century philosophy took a linguistic tum. Locke's new way of ideas gave way to an even newer way of words. Philosophical psychology ceased to occupy center-stage and was replaced by philosophy of language. The demise of psychologism was complete. Or was it? You abandon psychologism in name only if you 'think the task of logic is to describe, not the ways in which people think, but the ways in which they talk. This is merely to pour stale psychologistic wine into new linguistic bottles. The flavor of the wine is not improved. You still ignore the logician's prime concern with validity and invalidity. Psychologism, whether in its original form or in its linguistic form, is a chief source of the view that there is such a thing as non-deductive or ampliative or inductive logic. It is said that people seldom or never argue deductively. It is assumed that the logician's task is to describe the ways in which people do in fact argue. And it is concluded that non-deductive or ampliative or inductive logic must exist to describe the ways people argue most or all the time. Both premises of this (incidentally deductive) argument can be criticized. Anti-psychologists will object to the second premise: the fact (if it is a fact) that people argue non-deductively does not show that any non-deductive logic exists which describes their arguments. Perhaps those arguments are just deductive fallacies, perhaps the only valid arguments are deductively valid arguments, perhaps the only logic is deductive logic. Deductivism is the thesis that this is indeed the case. Deductivists think that whenever we argue, we argue deductively (or should be reconstructed as so doing). Accordingly, deductivists think that the only logic that we have or need is deductive logic. Deductivists are rare birds. Virtually all philosophers think that deductivism is absurd. Are not university libraries full of books about inductive logic? Are not clever people flown about the world every year at the tax-payer's expense to attend conferences on inductive logic? Has not the United States Navy, not to mention less prestigious agencies, funded research into inductive logic? And setting aside these sociological facts, is there not the well-known philosophical fact tt;at deductivism 1ands you in a barren and hopeless Humean scepticism? We will address these questions. And we will see that deductivism, far from being absurd, risks being trivial. To soften the reader up for this bizarre claim, I invite you to consider the following argument: American cars are better than Japanese cars. Therefore, Cadillacs are better than Japanese cars. You should consider this argument from the logician's point of view: do not ask whether its premise or conclusion is true; ask instead whether its
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conclusion follows from its premise, whether the argument is valid. Deductivists say that the argument is not valid. That may seem a harsh verdict. To soften it a deductivist might reflect that the arguer has perhaps not stated all of his premises, 'that he is taking for granted the fwther obvious premise 'Cadillacs are American cars'. Supply that unstated or missing or suppressed premise, a deductivist might say, and the argument becomes a valid one. (The fancy name for an argument with one or more 'suppressed premises' is, of course, 'enthymeme'.) But there is quite a different way to soften the original harsh verdict Anti-deductivists might say that the original argument, while it is admittedly deductively invalid, is a perfectly valid argument within a special non-deductive or ampliative or inductive logic. What makes it valid is a special rule of inference (or inference-license) which can be written 'From a premise of the form "x is a Cadillac," infer a conclusion of the form "x is an American car"'. This rule, unlike the boring formal 'topic-neutral' rules of the deductive logician, is an exciting material ' topic-specific' rule. It is exciting because it is ampiiative: it enables you to reach conclusions whose truth is not necessitated by the assumed truth of your premises, it enables you to get something new out of your premises. It is a rule peculiar to automobile logic, which deals with arguments about automobiles. Automobile logic, it might be argued, affords a much better description of the original argument than does deductive logic. The deductive logician is forced to treat the original argument either as invalid or as incomplete. For the automobile logician, on the other hand, the original argument is perfectly valid as it stands- within automobile logic. Automobile logic is my invention, not that of any anti-deductivist or inductive logician. I invented it in the hope that the reader will agree with me that it is silly. It is silly to validate our original argument by inventing automobile logic, when there is a simple way to do justice to it if we wish by treating it as a deductive enthymeme. Automobile logic confounds the valuable distinction between statements of fact and rules of inference. You can recast 'Cadillacs are American cars' as a 'material rule of inference'. What you get is a rule which is shown on empirical grounds not to be universally applicable. Is it not better to keep logic tidy and immune from empirical revision (at least, from empirical revision of this trivial kind)? Is it not better to eschew non-deductive or ampliative or inductive automobile logic, and to plump instead for deductive enthymemes aoout automobiles? We do not need automobile logic- and it conduces to clarity if we do not have it. l My thesis is that what goes for automobile logic goes for non-deductive or ampliative or inductive logics in general: we do not need them, and it conduces to clarity if we do not have them. (Henceforth I shall just use 'inductive' as short for 'non-deductive' or ,ampliative, or 'inductive', as has become customary.) It is better to reconstruct all arguments as deductive
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arguments, often as deductive enthymemes with suppressed premises of one kind or another. I now illustrate this thesis. Automobile logic was my own invention. Has any inductive logician advocated anything like it? They have, and chiefly for the psychologistic reason that such inductive logics better describe the ways people actually argue. Ryle claims that the most meaty and determinate general statements are not premises of arguments, but rather rules (inference-licences) in accordance with which people draw conclusions from premises. Toulmin and Harre agree, the latter's example being 'Rabbits are herbivorous'. Toulmin and Hanson take the same view of scientific theories or (putative) laws of nature, and arrive at a peculiar version of instrumentalism. Since I have discussed these examples elsewhere,2 I shall say no more about them here. Turning to more familiar ground, consider the crudest form of so-called inductive inference, inductive generalization: 'All observed emeralds were green, therefore all emeralds are green'; or generally, 'All observed A's were 8's, therefore all A's are B's'. Deductivists think that anyone who argues this way is tacitly assuming and leaving unstated a general principle to the effect that 'Unobserved cases resemble observed cases' (or perhaps 'The future will be like the past', or perhaps 'Nature is uniform'). Adding such a principle to the premise of an inductive gneralization validates it, just as adding 'Cadillacs are American cars' to the premise of our argument about automobiles validated it. The two cases seem quite symmetrical. Yet philosophers treat them differently. Philosophers who would not touch automobile logic with a barge-pole insist that 'inductive generalization' is induction rather than deduction. Why? What are the relevant differences between the two cases? One difference is that while 'Cadillacs are American cars' happens to be true, 'Unobserved cases resemble observed cases' happens to be false. Perhaps inductive logicians disguise false unstated premises as rules of inference so as to fool their readers (and themselves?) into thinking that inductive generalization has some sort of validity after all. This thought is uncharitable as well as ludicrous: no inductive logician now defends naive inductive generalization. However, the thought will become less ludicrous (though just as uncharitable) as the pattern of so-called inductive reasoning becomes more complicated. A second difference is that 'Unobserved cases resemble observed cases' is a much more geneml principle than 'Cadillacs are American cars'. It is so geneIal that it approaches rules of deductive inference in generality. It might approach them, say I, but it does not reach them. 'Unobserved cases resemble observed cases' remains a general statement about the world. It is part and parcel of the view that the world is (has been created) so that our senses are a reliable guide to its general nature. It is part and parcel of a long-discarded human-centered metaphysic. Here lies a clue to the popularity of inductive logic. Our question is: why not treat inductive generalization as a deductive enthymeme whose missing
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premise is a general metaphysical principle? (And similarly with other so-called inductive arguments.) Well, suppose you have taken in with your philosophical mother's-milk the positivist idea that the realm of the meaningful is exhausted by verifmble statements of empirical fact and logic. Then there are no meaningful general philosophical or metaphysical statements. An enthymeme whose nlissing premise is an unverifiable statement cannot be treated as such, on pain of talking nonsense. Positivists must construe (meaningless) general statements as (meaningful) rules of inference. Logic must expand beyond deductive logic to make room for what positivism deems problematic. In this respect, inductive logic is a last legacy of logical positivism. Is this not another uncharitable and ludicrous speculation, given that philosophers have outgrown logical positivism? Well, the idea that general statements and law statements must be construed as material rules of inference was frrst proposed by Schlick, Wittgenstein, and Ramsey, who based it explicitly on the verifmbility theory of meaning. Philosophers who subsequently embraced the view may have thought that they had outgrown logical positivism; actually they carried this bit of it in their bones.3 Inductive generalization is a crude form of so-called inductive inference which no inductive logician would defend. So let my second example be a currently trendy pattern of inductive inference called inference to the best explanation. Many talk of such inferences, few say precisely how they work. Their intellectual ancestor is yet another form of ampliative inference, Peirce's abduction. So let us begin there. Abduction goes like this: The surprising fact, C, is observed. But if A were true, C would be a matter of course. Hence, .. A is true."
As it stands, this is deductively invalid. Deductivists think: it conduces to clarity if, instead of saying that it is a valid inference in ampliative 'abductive logic', we say instead that it is a deductive enthymeme. Its missing premise obviously is 'Any explanation of a (surprising) observed fact is true'. This conduces to clarity because we can now see clearly that abduction is something no sane philosopher should accept. Its principle or missing premise is obviously false. Any sane philosopher can think of countless cases where an explanation of some surprising fact was false. s Returning frrst to the original abductive scheme, an obvious way to improve it is to require that the explanation of the surprising fact be the best explanation that we have. This yields inference to the best explanation, which goes like this: FI ,
•••, F. are facts. Hypothesis H explains F I , •••, F•. No available competing hypothesis explains F I , Therefore, H is true. 6
•••,
F. as well as H does.
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As it stands, this is deductively invalid. Deductivists think it conduces to clarity if, instead of saying that it is a valid inference in ampliative 'explanationist logic', we say instead that it is a deductive enthymeme. Its missing premise obviously is 'The best available explanation of any body of facts is true'. This conduces to clarity because we can now see clearly that inference to the best explanation is something no sane philosopher should accept Its principle or missing premise is obviously false.. Any sane philosopher can 'think of countless cases where the best available explanation of some body of facts was false. (What if H is the only available explanation, and is not just false but perfectly lousy in every other respect?) Here deductivism conduces to clarity in another way. It enables us to see how inference to the best explanation might be rescued from absurdity. Suppose we take a leaf out of Peirce's book and add an epistemic modifier to the conclusion and to the missing premise; and suppose we also demand that the best available explanation satisfies minimal criteria of explanatory adequacy (or is 'adequate'). We arrive at a pattern of argument which is deductively valid and whose leading principle is not obviously absurd. It goes like this: It is reasonable to accept as true (tentatively) the best available adequate explanation of any body of facts. FI , ...., F,. are facts. Hypothesis H explains Ft , •••, F,. adequately. No available competing hypothesis explains F I , •••, F,. as well as H does. Therefore, it is reasonable to accept H as true (tentatively).
To make this scheme good, the 'explanationist' owes us an account of when a hypothesis explains a body of facts, when it does so 'adequately', and when it does so better than some other hypothesis. The 'explanationist' does not owe us an account of any special ampliative explanationist logic.' Some will be thoroughly impatient with all of this. They will say that there already exists a well worked-out inductive logic, that provided by Carnap's theory of logical probability. They will say that the thesis that the only valid arguments are deductively valid arguments stands refuted by Carnap. Is this so? Carnap's theory issues, not in arguments, but in statements of logical probability. Such statements may, like any others, figure in arguments. But when they do, the arguments are deductive ones, or are best reconstructed as such. Or so the deductivist might argue. Notoriously, the use of statements of logical probability in arguments is fraught with difficulty. The natural way to start is: p(h,e) = r
e Therefore, p(h) = r.
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This is invalid. Indeed, the assumption that it is valid leads to contradiction. For let e and e* both be true, and let p(h,e) = r and p(h, e*) = s (where r ~ s) both be true also. Then two argwnents of the above form will lead from true premises to the contradictory conclusions P(h) = r and P(h) = S (where r ~ s). This is the notorious problem of detachment in inductive logic. Because of it, no one thinks that the above scheme is deductively or inductively valid. No logic, not even 'inductive logic', should yield contradictions by valid reasoning from true premises. Some say we can 'detach' an absolute probability only when e represents the 'total evidence' at our disposal. This yields the following scheme: p(h,e)
= r.
e. e is the total evidence. Therefore, p(h) = r.
This is also deductively invalid It can be recast as a valid deduction by adding the missing premise 'The unconditional probability of a hypothesis is its conditional probability o~ the total evidence'. Is this principle true? Surely not If another piece of evidence comes in tomorrow, 'the' unconditional probability of a hypothesis might well change. The principle (and the conclusion) will have to be relativized to times to avoid this. And besides, the unconditional or absolute probability of a hypothesis is surely its conditional probability on no evidence at all, not its conditional probability on the 'total evidence'. (There are also worries about the notion of 'total evidence', but I shall not digress to air them.) Some will fmd all of this question-begging. It is not a matter, they will say, of using statements of logical probability in arguments. Instead, the situation is that a valid inductive argument corresponds to every true statement of logical probability. Given the true statement p(h,e) = r, the corresponding argument might be written: e. Therefore (inductively and to degree r), h.
The situation parallels that in deductive logic, where a valid deductive argument corresponds to every logically true conditional statement Does the parallel really hold? In the deductive case we have independent accounts of validity, logical truth, and the truth-conditions of conditional statements, from which it emerges that a valid argument corresponds to every logically true conditional. In the inductive case we have no independent account of what 'inductively implies to degree r' means: the inductive argwnent scheme just given is merely a definitional rewrite of the statement of logical probability.
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More important, the parallel with deductive logic holds only if true statements of logical probability are logical truths. Yet there are different consistent systems of logical probability which yield different values for logical probabilities. Where h is a universal hypothesis, p(h, e) = 0 in Camap's system, whereas p(h,e) may be greater than 0 in systems devised by Hintikka. As is well-known, these differences arise from different a priori probability distributions which the systems contain. Without entering into any of the technicalities here, I will simply say that I agree with those who regard any a priori probability distribution as a synthetic assertion about the world. For it asserts that a certain possible state of affairs has some finite probability of obtaining. (Never mind how 'state of affairs' is to be dermed-- that is where the technicalities come in). Such assertions do not look like logical truths: they might be true of some possible worlds and not of others. But if they are not logical truths, then neither are the statements of logical probability whose truth depends upon them. And if these are not logical truths, then the 'inductive arguments' corresponding to them are not logically valid either in anyone's logic. We can put the point differently. Consider two conflicting statements of logical probability, drawn from different systems with different a priori probability distributions. We can hardly say that one of these is logically true and the other logically false. For how could a consistent 'theory of logical probability yield a logical falsehood? So the inductive logician must say that both statements are logically true. But he can only say this if he relativizes the notion of logical truth (and of 'inductive validity') to system: p(h,e) = 0 is logically true (and p(h,e) > 0 is logically false) in Carnap's system; p(h,e) > 0 is logically true (and p{h,e) = 0 is logically false) in Hintikka's system; and so forth. There seems to be no such relativism in the deductive case. It will immediately be objected that this last remark is naive. There are alternative consistent deductive logics; the same statement can be logically true in one system and not in another; the same argument can be valid in one system and not in another. The situation is perfectly symmetrical after all. This objection raises complex and fundamental issues, which cannot be discussed here, of whether alternative deductive logics of the required kind really exist. (That alternative or at least different deductive logics of some kind exist can hardly be denied.) At this point I propose to leave the question of whether the theory (or theories) of logical probability yield valid non-deductive arguments. The question has not been fully resolved, but it has, I hope, been clarified.
II. 'Justifying' Deduction- and Induction So far we have been considering an argument in favor of non-deductive logic. The argument ran:
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Logic describes the way people argue. People argue non-deductively. Therefore, there must be non-deductive logic to describe those arguments.
We objected to the naive psychologism of the frrst premise. And we objected to the second premise that so-called non-deductive arguments are better reconstructed as deductive enthymemes. Why exactly is this better? It is better because murky doubts about the 'non-deductive validity' of such arguments can be replaced by clearer doubts about the truth of the missing premises which repair them. Once we have our deductivist reconstruction, we can usually agree on the validity or invalidity of the argument and fIX our attention on whether its premises are true. And if we do not agree on the validity or invalidity of the deductivist reconstruction, we have a well-worked out deductive logic to help us settle the matter. It is different with inductive logics. Their adherents (with the }X>ssible exception of theorists of logical probability) insist that they exist, but tend to adopt a sealed-lips }X>licy on the question of what makes some non-deductive arguments valid and others nol Indeed, with descriptivist or psychologistic tendencies to the fore, interest in validity and invalidity tends to wane altogether. That is why I spoke of murky doubts about 'non-deductive validity'. But does this not uncritically assume that deductive logic is unproblematic, that there are no 'murky doubts' about deductive validity. Deductivists tirelessly demand a justification of inductive reasoning, confident that none can be provided. But what is the justification of deductive reasoning? Focus on this question, and you will see that the justifications in each case are exactly the same. This will dispose of the sup}X>sed superiority of deductive logic, and of the sup}X>sed desirability of reconstructing inductions as disguised deductions (deductive enthymemes). Or so some would argue. Nelson Goodman raises Hume's problem. From the fact that bread nowished us in the past, we infer that it will noOOsh us tomorrow. What justifies this inference? There is no contradiction in supposing that the next piece of bread we eat will poison us. So what justifies us in supposing that observed regularities will continue? Goodman frrst asks what would count as a justification of induction. If we demand a guarantee that inductive conclusions will be correct, then there can be no justification because in the nature of the case there can be no such guarantee. Goodman next asks what counts as a justification of deduction, to see whether a similar justification might also be given for induction. He answers with the theory of reflective equilibrium. A particular deductive inference is justified by appeal to a valid rule of deductive inference. How are such rules or general principles justified? Principles of deductive inference are justified by their conformity with accepted deductive practice. Their validity depends upon accordance with the particular
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deductive inferences we actually make and sanction. If a role yields unacceptable inferences, we drop it as invalid Justification of general rules thus derives from judgments rejecting or accepting particular inferences.'
Goodman admits that this account "looks flagrantly circular": particular deductions are justified by general rules, and rules by particular deductions. Yet he insists that this is the only justification we have or need: The process of justification is a delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification for either.9
Finally, Goodman claims that a similar justification can be given for induction: Predictions are justified if they conform. to valid canons of induction; and the canons are valid if they accurately codify accepted inductive practice. tO
Thus Hume receives a simple answer. We are justified in believing that tomorrow's bread will nourish us, because we infer this belief from true premises using a 'valid canon of induction' (a justified inductive rule). And the canon is valid (the rule justified) because it accurately codifies our accepted inductive practices. This looks awfully like psychologism again. It is not naive psychologism. It distinguishes, as naive psychologism does not, between valid and invalid inferences and rules of inference. But its distinction seems psychologically (or socio-psychologically) based: an inference is 'valid' if it confonns to a rule of inference we actually endorse; and a rule of inference is 'valid' if it codifies the inferences we actually make and endorse. It is not quite the naive psychologistic view that a rule is justified by showing merely that people argue in accordance with it. People must argue in accordance with the rule and think their arguments are valid. The distinction is a fine one, given the plausible assumption that people argue only in ways they think valid. But given the distinction, we can see that the method of 'reflective equilibrium' merely demands consistency between general and particular judgments of validity and invalidity. Consistency of this kind is certainly desirable. But the idea that any set of inferential principles and practices can be justifred by being shown to be consistent is not It is a species of psychologism. 11 The method of reflective equilibrium is a species of psychologism because people might make and sanction invalid inferences and codify them with invalid rules. Stephen Stitch and Richard Nisbett raise just this Fregean (or Humean) possibility. 12 They give three examples. First, there is the Gambler's Fallacy: people think that a die is more likely to tum up a six the less often a six has turned up in previous throws. They even cite an old logic text in which a rule codifying this_~~tj!_~j>!i~i!lY_Q~f~l!dM.__
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Second. people ignore regression to the mean, and think that tall parents will have tall children, and so forth. Third. people ignore the fact that the spontaneous cure-rate for a disease may be higher than the cure-rate of some treatment, and think that you are more likely to be cured if you have the treatment than if you do not. In each case, we may have empirical evidence not only that people commit these 'inductive fallacies', but also that they accept general roles codifying them. Their inductive practice is in 'reflective equilibrium' with their inductive principles. Goodman will have to say that both practice and principles are justified, at least for such people. I accept the general point. but not the description of the examples. To call them 'inductive fallacies' suggests that there is an articulated inductive logic which deems them fallacious. They can equally well be regarded just as false beliefs, or as fallacies in deductive statistical inference. But no matter. Stitch and Nisbett consider and reject two replies to their objection. The fIrst is that in such cases the 'reflective equilibrium' will not be stable: a little persuasion by a Professor of Inductive Logic will teach these invalid arguers the error their ways. Stitch and Nisbett say this can work both ways: a little persuasion by a tongue-in-cheek (or confused) Professor of Logic might also lead people to reject valid roles in favor of invalid ones. They add that there is no reason to suppose that valid rules are easier to inculcate than invalid ones. The second 'reply' is simply to concede relativism and say that the Gambler's Fallacy (say) is justifIed for people who regularly employ it and codify it in a general role. Stitch and Nisbett reply that the Gambler's Fallacy just is a fallacy, nO matter how many people happily accept it. Quite so. At this point one would expect them to explain why this fallacy just is a fallacy, in non-psychological terms, that is, making no mention of the way people in fact argue. But one would be disappointed. Stitch and Nisbett present their improvement on Goodman's solution in two stages: they fIrst give an account which is "almost right"; they then tell a "more complicated story" which is presumbably completely right. 13 The fIrst account is awful, the second disastrous. Recall the gambler addicted to the Gambler's Fallacy and quite prepared to codify it in a general principle. Given his 'reflective equilibrium', Goodman had to say that the Gah'ibler's Fallacy is valid for this gambler. For Goodman there is no "hi~er court of appeal." But for Stitch and Nisbett there is- the experts: But surely all this is quite wrong. "I:Qere is a higher court of appeal than this subject's reflective equilibrium. It is tile reflective equilibrium of his cognitive betters. There are people in our subject's society who are recognized as allthorities on one or another sort of inference. And if our subject wanted to appeal to a higher court than his own reflective equilibrium, he could do so. He need only seek out the experts and ask them. 14
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They think that the role of experts "has been all but ignored by modem epistemologists," that it is "a hallmark of an educated and reflective person" that he defers to experts, and they are doing an empirical study to show "that one of the principle effects of education is to socialize people to defer to cognitive authorities. "15 (If you thought that a principle effect, or at least aim, of education was to teach people to think for themselves, you were wrong.) To defer to experts is genemlly "the right thing to do, from a nonnative point of view": The man who persists in believing that his theorem is valid, despite the dissent of leading mathematicians, is a fool. The man who acts on his belief that a treatment, disparaged by medical experts, will cure his child's leukemia, is worse than a fool. 1'
There are many unanswered questions about "the social psychology and sociology of epistemic authority." "In virtue of what do people come to count as experts on a given issue for a society or subculture?"17 What leads experts to change their minds? Do different groups recognize different experts? What happens when a culture with one lot of experts comes into contact with a different culture with a different lot of experts? These questions aside, the first theory is clear: a rule of inference is justified not if any old Tom, Dick, or Harry accepts and employs it, but mther if the experts do: ... a rule of inference is justified if it captures the reflective practice not of the person using it but of the appropriate experts in our society. 11
My main objection to all this is that it is psychologism again. Goodman reduced validity to psychological fact: the fact that Tom, Dick, or Harry both endorse and employ the rule of inference in question. Stitch and Nisbett reduce validity to socio-psychological fact: the fact that people socially recognized as experts both endorse and employ the rule of inference in question. Hume will be turning in his grave. Emerging from his grave, Home might point out that all the psychological or socio-psychological conditions might be met and yet the rule be invalid. We can all think of our favorite case in which the experts of 'the time and place approved a rule (or a belief, or a medical treatment) which turned out to be wrong. It is hopeless to defme 'X is right' as 'X is agreed upon by the appropriate experts', simply because we can always ask 'Are the appropriate experts right?' .19 Perhaps we misunderstand. Perhaps the idea is that something is justified if it is endorsed by the experts, because the experts are (by definition) those able to justify it. Stitch and Nisbett's text tells against this interpretation. In any case, the response is unavailing. Now we have the idea that a rule R is justified if it is endorsed by experts, where an expert is (by defmition) someone who can produce a justification J of R. We might as well say that
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R is justified if there is a justification J of it, and forget the experts altogether. Besides, this defmition of the 'expert' raises the question of whether those socially recognized as experts really are experts: perhaps the system whereby 'epistemic authority' gets bestowed has broken down. The appeal to the authority of experts is either wrong (because sociallyrecognized experts can always be wrong) or redundant (because if an expert is defined as one who has a justification, it is the justification that is important, not the fact that the expert has it). There are many other objections to this frrst solution. What if two groups of socially recognized experts disagree about R - is R both justified (valid) and unjustified (invalid)? What if the experts change their mind about R was R once valid and now invalid? I will pursue none of these questions. for they concern Stitch and Nisbett's frrst account, and they have a second account to offer. The second account immerses us further into the sociological (and relativistic) mire. Stitch and Nisbett say that their frrst account "ties the notion of justified inference 100 closely to the reflective equilibrium of socially designated authorities."20 This is fme for most people, who are (well-educated?) 'cognitive conservatives' willing to defer to the experts. But what of the (ill-educated?) 'cognitive rebel' who insists that his rule is justified even when the experts say that it is nol On the first account, he contradicts himself. on the frrst account, a rule is justified, by defmition, if the experts say that it is. This is a bit hard on the cognitive rebel. So Stitch and Nisbett redefme 'Rule R is justified' to mean: Rule R accords with the reflective inferential practice of the (person or) group of people I (the speaker) think appropriate. 21
This brings US back to square one. The addict of the Gambler's Fallacy has a justified (or valid) rule after all. Or at least, he has a justified (or valid) rule if he answers the doubting Professor of Statistics thus: To Hell with Professors! Here in Las Vegas all the experts that I respect endorse what you call the 'Gambler's Fallacy' and act accordingly. When you have lost as much money at the crap table as we have, we might listen to you.
Of course, the Gambler's Fallacy will only be valid for this chap and those whose 'reflective inferential practice' he thinks it appropriate to endorse. It will remain invalid for the Professor of Statistics and his buddies. Stitch and Nisbett's 'improved account' leads directly to relativism regarding logical validity. Stitch and Nisbett actually embrace the relativism (leaving far behind them their earlier insistence, against Goodman, that the Garrlbler's Fallacy just is a fallacy). They ask whether the Fallacious Gambler and the Professor of Statistics could continue to argue rationally and resolve 'their disagreemenl They answer in the negative:
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There is something a bit radical about the view we are urging. To take some of the sting ou~ we should note that our view leaves abundant room for rational argument about justification among cognitive conservatives. Also, there may be rational argument about justification among cognitive rebels who agree about the appropriate authority group. However, if our account succeeds in capturing what we mean when we say that an inference is justified, then it is to be expected that there will be some disputes over justification that admit of no rational resolution. 22
The Fallacious Gambler and the Professor of Statistics cannot rationally argue: they mean different things by 'justified' or 'valid', and there is no further question as to which of them is right. Indeed, even where rational argument is possible, between those who recognize the same authoritygroup, it assumes a curious character.. 'Justified' or 'valid' means 'endorsed by the authority-group I recognize'. So the only matter left open for dispute is whether or not the appropriate authority-group has endorsed the rule in question. This is a sociological question- there is no philosophical or logical question left. A while back David Hume was turning in his grave because Goodman, Stitch, Nisbett, and others who think like them (Wittgenstein, Toulmin, and their followers) all overlook Hume's chief contribution to our problem. Hume was not the frrst to point out the deductive invalidity of inductive arguments: Aristotle, Sextus Empiricus, Bacon, Descartes, and countless others knew of it. So why is the problem of induction called Hwne's problem? As well as reiternting this logical triviality, Hume insisted that as a matter of psychological fact we all do reason inductively and cannot help doing so. 'Nature' or 'instinct' or 'custom' makes us inductive reasoners. No amount of philosophical reflection can make us reason otherwise for more than an hour. Hume's originality lay in stressing precisely this conflict between psychological fact ('We all reason, and cannot help reasoning, inductively') and epistemic value ('Inductive reasoning is invalid, hence unjustified, hence unreasonable'). It also lay in the fact that he embraced both of these conflicting principles and drew the obvious conclusion: We are, and cannot help being, imltional animals. The problem is: can Hwne's irrationalist conclusion be avoided?23 Enter the modem psychologists. They say that induction is justified because we use it, or because we use it and 'codify' it in general principles, or because socially-recognized experts use it and codify it. Hume's point was precisely that psychological or socio-psychological facts (or alleged facts) like these cannot settle epistemic questions about validity or justifiability. Questions of psychological or linguistic fact are one thing, questions of epistemic or logical value another. Can this Humean separation really be maintained? It is claimed that the situation with induction is the same as the situation with deduction. The only 'justification' of deduction is that people regularly argue deductively
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and accept rules of deductive inference which legitimate their arguments. There is no Hwnean separation for deduction, so it is absurd to demand one of induction. Is this correct? Induction and deduction are certainly parallel in one respect Empirical inquiry might reveal that deductive fallacies are as widespread as (alleged) inductive fallacies. We might find people systematically engaging in invalid deductions and happily accepting rules which codify them. A Goodmanesque 'justification of deduction' by the 'method of reflective equilibrium' might well justify invalid deductions and deductive rules. 24 Frege or Husserl (or Hume) would object in such a case that the argument or rule just is a fallacy, despite the 'reflective equilibrium' which exists. How then are judgments of deductive validity or invalidity justified? They are justified, not by appeal to psychological facts of any kind, but by appeal to a geneml account of deductive validity. In the case of an invalid deduction, one shows that the assumed truth of the premises does not guarantee the truth of the conclusion. In the case of a valid deduction, one shows that it does. To do this one often breaks the argument down into a series of simpler arguments; in other words, one produces a proof. All this is perfectly well-known. It is also well-known that any such 'justification' is flawed. It is itself a deductive argument A person who does not accept the validity of some argument A is supposed to be persuaded by producing an argument of the fonn: 'Any argument with feature F is a valid argumen~ argument A has feature F, therefore argument A is valid'. People can be persuaded in this way, but only if they see or accept without argument the validity of some arguments. A person who does not see or accept the validity of any argument will not, of course, be convinced by any such 'justification' of a judgment of validity. Such 'justifications' are flawed in a second way too. They immediately raise new questions about the general account of deductive validity that they invoke. Indeed, perhaps what is demanded of a 'justification of deduction' is a justification of this general accoun~ rather than of particular judgments of validity or invalidity. That account can be 'justified' (or at least explained) in terms of the fact that some arguments have a logical form which is such that the preswned truth of the premises guarantees the truth of the conclusion. But this 'justification' (explanation) leads to new questions: 'Is the notion of logical fonn unproblematic?'; and 'Is truth-preservation a sufficient or only a necessary condition for validity?' These questions lead to profound issues in the philosophy of logic, issues which may in turn be discussed. But at no point in any of those discussions is any appeal made to psychological or linguistic facts. At no point in the 'justification of deduction' is there any appeal to the fact that people are in the habit of arguing in a certain way. There is another question still, not about any particular judgment of validity, nor about the general account of validity, but about the practice of employing deductively valid arguments: what justifies this practice? (perhaps
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an answer to this question is what is demanded of a 'justification of deduction'.) An answer to this question might invoke the idea that truth is an aim of inquiry, and that valid arguments preserve truths and enable us to detect errors (because a valid argument with a false conclusion must also have a false premise). And dlis 'justification of deduction', like the others, leads immediately to new questions. It will be apparent that I think there is little future in the project of 'justifying deduction'. It cannot be justified by appealing to psychological or linguistic facts about the ways people argue- that is to fall into the errors of naive psychologism again. It cannot be justified by appealing to the fact that some sanctioned argumentative principles and practices are in 'reflective equilibrium'they might still be invalid, and anyway dIe method presupposes that we can spot deductive inconsistencies. And any 'justification' which is non-psychologistic will itself be a deductive argument of some kind, whose premises will be more problematic than the conclusion they are meant to justify. Some of these reservations are specific to the peculiar project of 'justifying deduction'- others concern the general project of justifying anything, to which I shall soon turn. But the fact, if it is a fact, that deduction cannot be justified, does not mean that deduction and induction are on a par. For as well as trying to justify things, we can also try to criticize them. Induction and deduction are defmitely not on a par when considered from a critical point of view.
III. Critical Rationalism In the preceding section we fonnuIated the problem of induction as: can Hume's imltionalist conclusion be avoided? The conclusion in question was that we are, and cannot help being, irrational animals. And why exactly was this? It was because we cannot help believing things which transcend the immediate evidence of the senses. But such beliefs are based upon inductive reasoning, and inductive reasoning is invalid Hence any such belief is unreasonable. Most have tried to avoid Humean imltionalism by attacking his second premise, by trying to show that inductive reasoning is valid after all. Deductivists, however, accept the invalidity of induction, and say that all our valid reasonings are deductive ones (or are to be reconstructed as such). How then can deductivists avoid Hume's conclusion that any belief which transcends the immediate evidence of the senses is an unreasonable belief! Does not deductivism land you squarely in a barren and hopeless Humean scepticism-cum-irrationalism? Some deductivists call themselves critical rationalists. What is rational about endorsing Hume's imltionalism? Larry Laudan once argued as follows:
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If the only rules of inference we allow ourselves are those of deductive logic, then we will never be able to establish which theories are acceptable. But, with the bizarre exception of Popper, virtually no methodologist of science has ever suggested that the rules of deductive logic exhaust the methodological repertoire of the natural scientist 25
Now not even the bizarre Popper thinks that "the rules of deductive logic exhaust the methodological repertoire of the natural scientist" Popper advocates methodological rules like 'Perform the severest tests' or ' Avoid ad hoc modifications to your theories'. Of course, these are not rules of deductive or of any other logic. More important, it is not true that "if the only rules of inference we allow ourselves are those of deductive logic, then we will never be able to establish which theories are acceptable." Laudan himself has reconstructed the way in which Newton's theory came to be preferred to Descartes' because it correctly predicted that the earth is an ablate spheroid rather than a sphere. Let us grant the historical accuracy and the methodological soundness of this reconstruction.. The argument in favor of Newton's theory can be pedantically set out thus: Newton's theory and Descartes' theory make conflicting predictions about the shape of the earth. Experiment revealed that the Newtonian prediction was true and the Cartesian prediction false. When two theories make conflicting predictions, then the theory which makes the correct prediction is to be preferred. Therefore, Newton's theory is to be preferred to Descartes'.
This is a perfectly valid deduction. The only rules of inference we are allowing ourselves here are those of deductive logic. Yet this deductive argument does establish which theory is acceptable or preferable. So Laudan's conditional proposition is obviously mistaken. A conditional proposition which is true, and the conditional which Laudan obviously had in mind, is this: 'If the only rules of inference we allow ourselves are those of deductive logic, and the only premises we allow ourselves are observational data, then we will never be able to establish which theories are acceptable'. This conditional states the deductive underdetermination of theory by data. A deductivist must accept the frrst conjunct of its anteeedent- but a deductivist need not accept the second conjunct Recall our earlier discussion of inference to the best explanation, which we reconstructed as a perfectly valid deductive argument. Can one really, as this suggests, be an explanationist and a deductivist? Explanationism yields a positive answer to Hume. How can the problem of induction be solved without providing some inductive logic? But as deductivists see it, it was a mistake to try to give a positive solution to the problem of induction by providing an inductive logic. Let us call an inductive principle anything
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which tells us the circumstances in which it is reasonable for us to believe something (tentatively) or accept it as true (tentatively) or prefer it (tentatively). The first premise of the explanationist scheme, and the last premise of Laudan's scheme, are inductive principles in this sense. 26 Now there is nothing to stop a deductivist from accepting an inductive principle. Indeed, any deductivist who is not a total irrationalist must accept some inductive principle or other. Anyone who thinks that some beliefs (acceptances, preferences) are reasonable has implicitly or explicitly adopted some inductive principle or other. Not even Hume was a total irrationalist: he thought it reasonable to believe the immediate evidence of the senses. He was (or can be interpreted as) a deductivist who advocated the following inductive principle: 'It is reasonable to believe the immediate evidence of the senses, and what is deductively entailed by the immediate evidence of the senses, but nothing else'. In Hume's hands, deductivism combined with this spartan principle yielded irrationalism about any belief which went beyond the immediate evidence of the senses. Other deductivists may be less spartan. Deductivists see so-called inductive arguments as deductive arguments whose major premises are general epistemic principles. They might even say that an inductive argument is a deductive argument containing one or more inductive principles among its premises. That would give us inductive arguments without an inductive logic. But it would probably confuse rather than clarify. For deductivists the real 'problem of induction' is not whether inductive logic exists, but rather whether any inductive principle is philosophically defensible. Hwne thought only the spartan principle of a paragraph back was defensible, and concluded that any belief which went beyond the immediate evidence of the senses was unreasonable. Other deductivists, as I said, may be less spartan. One such is Sir Karl Popper- at least as I read him. But the exegetical issues here are complicated ones, and have become more so with the passage of time. I propose to avoid them almost totally. I also propose to approach the matter of critical rationalism, for that is what Popper says he defends, rather obliquely. The problem of rationality is whether or not any of our beliefs are reasonable beliefs. Presumably, a reasonable belief is one for which there is a (good) reason. Presumably, too, a belief might be justified by citing the (good) reason for it Notoriously, however,the tenn 'belief is ambiguous: it refers both to the content of the belief (the thing believed), and to the mental act or state of believing that content Similarly, talk of a person A's reasonable or justified belief that P is ambiguous between: (1) P being reasonable or justified, A's having a (good) reason for P; and (2) A's believing that P being reasonable or justified, A's having (good) reason for believing that P.
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Is it, as in (1), the content of a belief for which there must be a good reason if that belief is to be reasonable? Or is it, as in (2), the act of believing for which there must be a good reason if that belief is to be reasonable? Obviously, in the fust instance anyway, it is the latter. We must make room for the possibility that the same belief-content might be reasonably believed by one person and not by another. This means that we must, in the fust instance anyway, direct our attention to people's believing things, rather than to the things they believe, in discussing the problem of rationality. Traditionally, however, attention is immediately redirected outwards, at the things people believe. This is, I think, because the following principle is taken for granted in traditional discussions of our problem: (A) A's believing that P is reasonable or justified if and only if P is reasonable or justified: that is, A has good reason for believing that P if and only if A has good reason for P.
(A) may seem self-evident. Justificationists accept it and think that there are justified beliefs and hence justified believings. Sceptics-cum-irrationalists accept it and think there are no justified beliefs and hence no justified believings. But critical rationalists, as I understand them, reject (A): they say that there are no justified beliefs (here the sceptic is right), but there are justified or rational believings (here the sceptic-cum-irrationaiist is wrong). Insofar as (A) is self-evident, critical rationalism is absurd. (A)'s influence is pervasive. The traditional justified-true-belief account of knowledge ought to run: A knows that P if and only if: (a) A believes that P; (b) P is true; and (c) A can justify his believing that P, that is, give a (good) reason for his believing that P.
But given (A), the crucial third condition twns into: (c*) A can justify P, that is, give a good reason for P.
If we forget that we are defining personal knowledge here, (c*) can tum further into: (c**) P is justified, that is, there is a good reason for P.
Condition (c**) is obviously absurd. It means that if there is a good reason for some true P, unbeknownst to anyone who believes P, then all those believers know P. It means that if anyone knows P, everyone else who believes it also knows it Condition (c*), 00 the other hand, is not obviously
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absurd. On the contrary, it will be regarded as self-evident by anyone who thinks (A) is self-evident David Miller is a disciple of Popper and a professed critical rationalist. In a recent paper entitled "A Critique of Good Reasons" he argues that "there are no such things as good reasons. "27 Does he mean reasons for believings or reasons for beliefs? He means both. He ignores the distinction" He ignores the distinction because he implicitly accepts (A). This lands him in an attempt to square the circle: to defend reason while asserting that there are no good reasons for anything. If there are no reasons for beliefs, then there are no reasonable beliefs. Critical rationalism as Miller understands it (and as Popper understands it if Miller has his Popper right) is irrationalism in disguise. You do not answer Home by agreeing with him. Critical rationalism is better understood as being based upon the rejection of (A). That Miller accepts (A) is easily seen. His arguments, if correct, show that there are no good reasons for belief-contents, that condition (c**) is never satisfied. From this it follows that condition (c*) is never satisfied either: if there are no good reasons for P, then nobody can have a good reason for P. But it does not follow that condition (c) can never be satisfied either: that only follows from the failure of (c*), and (A). Yet Miller slides from the failure of (c**), hence of (c*), to the failure of (c). Hence, he implicitly accepts (A). In documenting this slide, I frrst note that Miller prefers to talk, not of beliefs and believings, but of the acceptance or rejection of hypotheses, and of classifying hypotheses as true or false. Nothing hinges on these terminological preferences: to accept a hypothesis as hUe is to believe it (and to accept it tentatively is to believe it tentatively); to classify a hypothesis as true is also to believe it (and to classify it tentatively as true is to believe it tentatively).. The slide starts early. He announces that: ... there are no such things as good reasons; that is, sufficient reasons for accepting an hypothesis rather than rejecting it, or rejecting it rather than accepting it, or anything like that. 21
Here what is denied are good reasons for acceptings or rejectings (that is, for believings). But in the next but one sentence we have:
Yet the illusion persists that the rational person is the person who can supply good reasons for what M thinks....29 Here what is denied are good reasons for beliefs. In fact, Miller's paper entirely concerns reasons for beliefs. He says:
My first thesis...is that...it is impossible
to
furnish a good reason in support of any
thesis whatever.3D
His second thesis is that good reasons for beliefs are redundant, his 'third thesis is that they are unnecessary. Like all sceptical pieces, this one
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threatens to self-destruct: if there is no good reason for any thesis whatever, there is no good reason for Miller's three theses either. But let us consider Miller's argument for the crucial first thesis, for it is interesting. It goes in two stages. A conclusive reason e for h must entail h; in this case e contains h since it begs the question; a person who does not accept h is not going to accept e either. Conclusive reasons are not good reasons. A non-conclusive reason e for h must 'partially entail' h, that is, it must be the case that 0 < p(h) < p(h,e) < 1. But h is equivalent to '(h v e) & (e ~ h)', whose frrst conjunct expresses the common content of h and e, and whose second conjunct expresses the surplus content of h and e. Now e entails the frrst conjunct and is not a good reason for it, by the frrst argument. And given plausible assumptions, e will counter-support the second conjunct, that is, p(e ~ h,e) < p(e ~ h). So e is not even a non-conclusive reason for the second conjunct, let alone a good reason for it Non-conclusive reasons are not good reasons either, because they beg part of the question. 31 This is an ingenious argument If it is correct, it shows that the whole idea of conclusive or non-conclusive reasons for beliefs is fatally flawed (at least if e's being a non-conclusive reason for h is spelled out in probabilistic terms in the way suggested). I do not know whether the argument is correct. But I will suppose that it is, for my concerns are different The argument, as I said, entirely concerns reasons for beliefs. But Miller straightway proceeds to make various assertions about believings or preferrings or (as he prefers) classifyings as true. Here are some of them (the italics are all mine): reason at all is needed for classifying a statement as true....D ...in the sphere of practice...all that we actually need is a true prediction ... there is not only no need for, but also no use for, a good reason to think that the prediction is true. 33 ...we need no reason for classifying h as false....34 ...statements [which contradict 'All swans are green'] will not supply us with a reason for rejecting 'All swans are green'.:JS ...we should be prepared to classify statements as true or false without having a reason to do so. J6 ...the critical rationalist's answer to the question 'Why do you think that h is true?' ...or 'Why do you think that action a should be performed?' will normally be 'Why not?'31 •••DO
I submit that in Miller's hands so-called critical rationalism has turned into wholesale i"ationalism. Our epistemic task is described as that of sorting truth from falsehood, of classifying some hypotheses as true and others as false. Critical rationalism's basic thesis is that the best way to do this is to subject our hypotheses to the best criticisms we can (including where appropriate severe tests), then classify those that survive the ordeal as true and those that do not as false (both 'classifications' being tentative and
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fallible). Why is this critical rationalism? Surely the critical rationalist must be claiming that it is reasonable to proceed in this way. Let h} be a hypothesis that has been as soundly refuted as a hypothesis can be~ and let It" be a hypothesis that has been as strikingly corroborated as a hypothesis can be. The critical rationalist classifies ~ as true and h} as false. Surely the claim must be that the fact that hI has been soundly refuted is a good reason to classify it as false, while the fact that ~ has been strikingly corroborated is a good reason to classify it as true. Without this claim, we do not have a version of rationalism at all. Suppose a person flies in the face of the critical discussion and classifies hI as true and h2 as false. Given his professed views, Miller cannot say that these classifyings are unreasonable, while the critical rationalist ~ s classifyings are reasonable. Miller has simply overlooked the key feature of critical rationalism, its rejection of (A), and its positive contention that if a hypothesis withstands our best efforts to show that it is false~ then this is a good reason to classify it as true but not a good reason for the hypothesis itself. Perhaps he is right to ignore this: anyone who thinks (A) self-evident will find critical rationalism a peculiar position indeed. How can there be reasons for believings (classifyings as true, preferrings with respect to truth) which are not also reasons for the things believed (preferred, classified)? Well, critical rationalism asserts rightly or wrongly that our epistemic predicament is such that the former is the most that we can have. Perhaps this is an absurd position and (A) self-evidently true. My complaint is that Miller never even addresses the question. He argues against good reasons for beliefs, and concludes without argument that there are no good reasons for believings (classifyings as true) either. The result is irrationalism, despite the rationalist rhetoric. In doing this, Miller has to set aside occasional remarks of Popper's to the effect that theory-preferences can be justified by good reasons, though theories cannot Such remarks entail the falsity of (A). The remarks were only occasional ones, they were invariably cagey and hedged about with verbal qualifications, and Popper has recently retreated from them. Miller applauds the retreat and says that for Popper theory-preferences, like the theories preferred, are not justified by good reasons at all. With friends like Miller, critical rationalism does not need enemies. More could, and briefly should, be said. The single most important reason for all the caginess, and for Miller's (and Popper's?) retreat from reason~ is the so-called pragmatic problem of induction. It is alleged that if one thinks it reasonable to act on well-corroborated theories, then one must be smuggling in some metaphysical inductivist assumption. One must be assuming, it is said, that predictions from well-corroborated theories will be true, or at least more likely to be true, than predictions from refuted theories. This objection itself proceeds from tacit acceptance of (A). The objection takes for granted what the critical rationalist denies: that a good reason for believing a theory (and its consequences) must be a good reason for the theory (and its consequences). There is no smuggled-in inductivist
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metaphysics. Rather, there is simply the epistemic principle (call it an inductive principle if you like) that it is reasonable to believe and act upon hypotheses that have withstood our best efforts to show them false, even though those best efforts are no reason for those hypotheses (or their consequences) and do not show the hypotheses to be true or even probably so. This, even if it is accepted (which it seldom is), leads immediately to a further question: why is it reasonable to proceed in this way? Here we are in murky self-referential territory: we are asked f(X" a reason for critical rationalism; in particular, we are asked for a reason for the critical rationalist view about what it is reasonable to believe. The request presupposes on the meta-level precisely the principle (A) which the critical rationalist rejects. Hence the consistent critical rationalist should refuse to answer the question. The most a consistent critical rationalist might say is that it is reasonable to adopt critical rationalism by critical rationalism's standard of what it is reasonable to adopt. This is circular. But at this level of abstraction circularity is hard to avoid, and the alternatives are even more unpalatable. Critical rationalists like to talk of 'conjectural knowledge'. Some of their opponents find the notion self-contradictory. But it is not self-contradictory, as the following consistent defmition shows: A conjecturally knows that P if and only if (a) A believes that P; (b) P is true; and (c) A is justified in believing that P, that is, A has good reason for believing that
P. Why 'conjecturally knows that P' rather than 'conjectures that P' or even 'justifiably conjectures that P'? Because you can conjecture that P, even reasonably conjecture that P, even when P is not true, even when condition (b) is not met. It is the presence of the truth-condition which entitles this to be called a definition of knowledge. The critical rationalist might even regard it as a justified true belief account of conjectural knowledge, given the interpretation of condition (c) which follows from his rejection of (A). I doubt that Sir Karl Popper, my teacher in these matters, will accept this definition of conjectural knowledge. In general, he is not fond of definitions. In particular, he has developed a phobia about belief, and says that he does not believe in belief, and such things. He prefers different locutions. And he tends to see conjectural knowledge as inhabiting his 'World 3' of the objective contents of thoughts. But whatever the merits of the theory of 'World 3' in dealing with some problems, it does not help us with the problems being discussed here. Believing (or if you prefer, preferring with respect to truth, or classifying as true) is something that epistemic subjects do, a 'World 2' phenomenon. A philosopher who believes (sic) in 'epistemology without a knowing subject' has no business
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trafficking in beliefs or in theory-choices. Such a philosopher can in turn have no answer to Hornets scepticism-corn-irmtionalism. Horne said that any belief which went beyond the immediate evidence of the senses was unreasonable.. Any answer to Home must entailt at the very least, the negation of this statement- must entail, that iSt that some beliefs which go beyond the immediate evidence of the senses are not unreasonable. To fail to say this is not so much to answer Home as to change the subject A last word. I ended the preceding section of this paper expressing scepticism about the project of tjustifying deduction t. I said that as well as trying to justify things, we can also try to criticize them, and that deduction and induction are defmitely not on a par when considered from a critical point of view. This connects with our present discussion. Suppose it could be shown that deductive logic withstands criticism better than inductive logic. This would be, for the critical rationalist, a good reason for accepting deductive logic and rejecting inductive logic. It would be, in shortt a justification for adopting the deductivist thesis. This explains the connection between critical rationalism and deductivism.
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ENDNOTES 1. I am well aware that we live in a philosophical jazz-age, where the more sacred the philosophical cow the keener Harvard professors are to slaughter it The empirical unrevisability of logic is a case in point But Quine or Putnam would regard the invention of automobile logic as a cheap way to demonstrate the empirical revisability of logic. 2. See: Alan E. Musgrave, ''Wittgensteinian Instrumentalism," THEORIA, 46, (1980), pp. 65-105, where references are given. 3. See: Ibid., for details. 4. Charles S. Peirce, The Collected Papers of Charles Sanders Peirce (Cambridge: Harvard University, 1931-58), Vol. 5, p. 189. 5. Let me hasten to add that Peirce, a very sane philosopher, did not formulate abduction as I have done. The conclusion of his scheme reads 'there is reason to suspect that A is true'. The difference is very important, but not for the point of present concern. Peirce's scheme is also deductively invalid. Deductivists will repair it with the missing premise 'There is reason to suspect that any explanation of a (surprising) observed fact is true'. The important difference is that this epistemic principle, unlike its metaphysical predecessor of the last paragraph, is not obviously absurd. I shall return to this point. 6. This is how William Lycan fonnulates the scheme in: William Lycan, "Epistemic Value," SYNTHESE, 64, (1985), p. 138. 7. Incidentally, abduction and inference to the best explanation are widely regarded not only as inductive patterns of argument, but also as patterns of argument which belong to the 'context of discovery' rather than to the 'context of justification'. Indeed, Hanson is regarded as the foremost champion of the 'logic of discovery' because he proposed several inelegant variations on Peirce's abductive scheme. This is bizarre. Abduction and inference to the best explanation both contain the hypothesis H in their premises, and say nothing about how it was discovered. Both schemes belong in the 'context of justification', as is made plain above by the epistemic modifiers in their conclusions and their leading principles. As for the 'logic of discovery', in so far as it exists it is plain old deductive logic too-- but that is another story. 8. Nelson Goodman, Fact, Fiction, and Forecast (New York: Oxford University, 1965), pp. 63-64. 9. Ibid., p. 64. 10. Ibid. 11. Having just said that consistency between inferential principles and practices is a virtue, let me qualify this immediately with 'provided that consistency is deductive consistency'. Yet it seems it must be. The project of rmding out whether any non-deductive practices and principles are in reflective equilibriwn, that is, consistent, could hardly get off the ground otherwise. Why exactly is consistency a virtue, if it does not justify the system in question? Because inconsistency would be a powerful criticism of that system. There will be more on criticism and justification in the next section. 12. See: Stephen Stitch and Richard Nisbett, "Justification and the Psychology of Human Reasoning," PHILOSOPHY OF SCIENCE, 47, (1980), pp. 188-202. 13. Ibid., p. 198. 14. Ibid. 15. Ibid., pp. 188-189. 16. Ibid., p. 199. 17. Ibid.
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18. Ibid., p. 200. 19. Compare this with: it is hopeless to define 'X is good' as 'X is commanded by God', simply because we can always ask 'Are God's commands good?'. 20. Ibid. 21. Ibid., p. 201. 22. Ibid., pp. 201-202. 23. This formulation of the problem, which is due to Russell and Popper, is better than the usual formulations: 'Can induction be justified?'; or even 'How can induction be justified?'. 24. An admittedly controversial example: for some two thousand years the 'reflective equilibrium' had it that 'All A's are B's' deductively entailed 'Some A's are B's'; for some one hundred years we have disagreed. 25. This argument does not, so far as I know, appear in any of Laudan's publications- but I have his permission to cite it. 26. Note that inductive principles, thus defined, are epistemic principles rather than metaphysical ones. Metaphysical principles such as the Principle of the Uniformity of Nature have often been appealed to in order to validate induction. Epistemic inductive principles do a different job. 27. David Miller, "A Critique of Good Reasons," forthcoming in C.W. Savage and M.L. Maxwell, eds., Science, Mind, and Psychology (Minneapolis: University of Minnesota, 1988), p. 1. All page-references to this paper are to a manuscript version dated '1984'. 28. Ibid., my italics. 29. Ibid., my italics. 30. Ibid., pp. 3-4. 31. This argument is due to Popper and Miller. See: Karl R. Popper and David Miller, "A Proof of the Impossibility of Inductive Probability," NATURE, 302, (1983), pp. 687-688. 32. Miller, "A Critique of Good Reasons," p. 10.
33. 34. 35. 36. 37.
Ibid. Ibid., p. 13. Ibid. Ibid. Ibid., p. 14.
POPPER'S FORMAL CONTRmUTIONS TO PROBABILITY THEORY HUGHES LEBLANC In the Schilpp volume devoted to him, Karl Popper notes with justified regret that his axiomatizations of the calculus of probability have been neglected 1 Deeply indebted to him and, hence, anxious to see this wrong righted, I chronicle here his formal contributions of 1938 and 1955 to absolute probability theory (parts I-II of the paper) and his fonnal contributions of 1955, 1956, and 1959 to relative probability theory (part II!). I also touch on the novel accounts of truth-functional truth and truth-functional entailment that stem from these contributions: the probabilistic accounts of Harper, Field, Leblanc, etc., (part IV). Popper has of course made other significant contributions to probability theory, but I save them for another occasion or perhaps other writers. Since those of Popper's writings I study are technical ones, so perforce is this text To facilitate the reading I define any term that might be unfamiliar and provide illustrations.
I Popper's earliest contribution to absolute probability theory is A Note on Probability," MIND, vol. 47, 1938, pp. 275-277. In The Logic of ScientifiC Discovery (New York: Basic Books, 1959), p. 318, Popper reports not knowing Andrey N. Kolmogorov's Grundbegrijfe der Wahrscheinlichkeitsrechnung (Berlin, 1933)2 when ~ wrote his note. It is, nonetheless, best studied in light of that classic. By an absolute probability fzeltf Kolmogorov understands (in effect) a triple of the kind <E,F»>, where tt
(i) E is a non-empty set, (ii) F is a noo-empty subset of the power set P(E) of E such that I. F is a field of sets and II. F contains E, and (iii) P is a function from F into R (i.e. into 'the set of the reals) such that ill. For any A in F, 0 So P(A), IV. P(E) = 1, and
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HUGHES LEBLANC V. For any A and B in F, if A n B = 0, then P(A u B) = P(A) + P(B),
and - as anticipated - he talks of P(A) for arbitrary A in F as the absolute probability of A. The reader will doubtless know P(E) in (il): called the power set of E, it is the set of all the subsets of E. He will know that P in (iii), identified as a function from F into R, is thus a function with the members of F as its arguments and the reals (those in the interval [0,1], it will turn out) as its values. He will know A n B in V as the intersection of A and B, A u B as the union of A and B, and 0 as the null set. He will also know A as the complement of A, and will recall that 'A u B' and '0' can be treated as shorthands for '-(-A n -B)' and 'A n -A', respectively, a move which reduces to two the number of Boolean functions needed to characterize a probability field. What, however, is a [ielrl! Nothing very forbidding once the reader recalls that the Cartesian product S x s' of set S and set S' is the set of all the pairs <s,s'> such that s is in S and s' in S', hence that the Cartesian product S x S is the set of all the pairs of members of S. A field F, then, is but a set together with two functions, one a function from F into F and the other a function from F x F into F which meet familiar constraints known as the postulates for Boolean algebra! The functions in question are commonly designated by the foregoing '-' and 'n '. Note, however, that the members of a field F, though frequently sets as in a Kolmogorov probability field, may be whatever there is a Boolean algebra 01: sets, relations, statements, etc.' And, when the members of F are not sets, the functions denoted by ,-' and ' n' are not the set-theoretic functions of complementation and intersection, but analogues thereof. For example, when as in Illustration 4 below and on later occasions the members of F (or those of a certain set S substituting for it) are statements, '-' does duty for the negation sign '-' and 'n' for the conjunction sign '&'.6 Kolmogorov presupposes known the postulates for Boolean algebra. I fill the lacuna with postulates due the frrst three to Lee Byrne ("Two Brief Fonnulations of Boolean Algebra, tt BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 52, 1946, pp. 269-272) and the last two to Paul C. Rosenbloom (The Elements of Mathematical Logic (New York: Dover, 1950), p. 9), thus obtaining this fuller account of an absolute probability field: An absolute probability field in the sense of Kolmogorov is a quintuple of the kind <EY,-,n,p>, where (i) E is a non-empty set, (ii)F is a non-empty subset of P(E), - a function from F into F, and n one from F x F into F such that I. AI. For any A and B in F, A n B = B n A, A2. For any A, B, and C in F, A n (B n C)
= (A n
B) n C,
- - - - - - - - - - - - - - - - - - - - - - -
POPPER'S PROBABILITY THEORY
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= C n -C if, and only if, A n B = A, A4. For any A and B in F, if A = B, then -A = -B, and A5. For any A, B, and C in F, if A = B, then A n C = B n C, and II. F contains E, and (iii) P is a function from F into R such that Ill. For any A in F, 0 Sa P(A), IV. P{E) = 1, and V. For any A, B, and C in F, if A n B = C n -C, then P(-(-A n -B» = P(A) + P(B).' AJ. For any A, B, and C in F, A n -B
Illustration 1: Let E be ( a), a whatever you please. Then lP(E) is {0, (a) ) , and F must be lP(E), with 0 and (a) each other's complements and 0 the intersection of 0 and (a). P(0) must equal 0 and P({a) must equal 1. Illustration 2: Let E be (a,b) , a and b distinct from each other but otherwise whatever you please. Then lP(E) = (0,{a),{b),{a,b)). Of the fIfteen non-empty subsets of this set, only five constitute fields, to wit:
(0), (0,{a)), (0,{b)), (0, (a,b) ), and (0,(a),(b),(a,b)), and of these five sets only two contain E, to wit: (0,{a,b)) and (0,{a),(b),(a,b}), where in both cases 0 and {a,b} are each other's complements and in the second case so are {a} and {b} as well. P(0) must equal 0, P({a,b) equal 1, and P({a) and P({b}) equal any two reals in the interval [0,1] whose sum is 1. Kolmogorov's account of a probability field won quick acceptance among the mathematicians of his day and still has wide currency, be it in its original form or slightly amended ones. But Popper, when he came to know it, objected to several of its features. In "Appendix *ii" to The Logic of Scientific Discovery, for example, he remarked that the account compelled an absolute probability function to take sets as its arguments. Yet, as he had already insisted in "Two Autonomous Axiom Systems for the Calculus of Probabilities," THE BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, vol. 6, 1955, pp. 51-57, we also accord absolute probabilities to events, statements, predicates, etc. Popper's observation is of course correct: since Kolmogorov's field F is a subset of lP(E), its members - and, hence, the arguments of the probability function P - have to be sets. Popper neglects to note, however, that a host of things can be construed or have been construed as sets. Kolmogorov himself calls the members of his initial set E elementary events" and those of his field F random events; and in Sections 2-3 of his fIrst chapter he tells us what he understands by a random event, what by the complement
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of one and 'the intersection of two, and what by the probability of one. So, his account, though not compelling the arguments of P to be events ,9 nonetheless allows it. And, more recently, writers anxious to bring together probability theory and the logic of connectives, have taken (1) Kolmogorov's E to consist of the so-called state-descriptions of a language L with, say, '-' and '&' as its only logical operators, (2) Kolmogorov's F to be the power set of this E, and (3) the probability of a statement A of L to be 0 when A is logically false, otherwise the probability of the set consisting of all, and only, the state-descriptions of L in which A holds. (3) means of course adding a clause to Kolmogorov's three in either of the above formulations, and it presupposes known or given the circumstances under which a statement of L is logically false plus those under which it holds in a state-description of L. 10 But these illustrations show that Kolmogorov's account, though geared to sets, is far less restrictive than Popper suggests. However, one might well prefer an account in which the arguments of P are not of necessity sets" One is easily had. Drop the first of Kolmogorov's two sets, allow the second - relabelled S - to be an arbitrary non-empty set, and you obtain this account which meets Popper's frrst objection: An absolute probability field in the abstract sense ll is a quadruple of the kind <S,-,n»>, where (i) S is a non-empty set, - is a function from S into S, and n one from S x S into S such that AI'. For any A and B in S, A n B = B n A, A2'. For any A, B, and C in S, A n (B n C) = (A n B) n C, AJ'. For any A, B, and C in S, A n -B = C n -C if, and only if,
AnB=A, A4'. For any A and B in S, if A = B, then -A = -B, and Aj'. For any A, B, and C in S, if A = B, then A n C = B n C, and (ii) P is a function from S into R such that B1. For any A in S, 0 ~ P(A), B2. For any A in S, P(A n A) = 1, and B3. For any A, B, and C in S, if A n B = C n -C, then P(-(-A n -B» = P(A) + P(B).
Illustration 3: Let S consist of the two sets (2) and (a), a whatever you please. Then, as in Illustration 1, 0 and {a) are each other's complements, o is the intersection of 0 and {a}, P(0) must equal 0, and P({a}) equal 1. Illustration 4: Let S consist of some atomic statement or other A, the negation B (= -B) of any statement B in S, and the conjunction B n C (= B & C) of any statement B and any statement C in S. Then S partitions into four so-called equivalence classes: SI consisting of A and all its logical equivalents in S, S2 consisting of the negations of the members of St, S3 consisting of A n -A and all its logical equivalents in S, and S4 consisting
POPPER'S PROBABILITY THEORY
345
of the negations of the members of S3. For any statement A, in S3 P(A3) must equal 0, for any statement At in S. P(At) equal 1, and for any statement Al in 51 and statement A,. in 52 P(AI ) and P(AJ equal any two reals in the interval [0,1] whose sum is 1. Note by the way that the set S in a Quadruple <5,-I"''p> constitutes a field. So, when 5 (as in Illustration 3) consists of sets, the set-theoretic union of these ({a) in Illustration 3) can serve as the E and 5 serve as the F in a Kolmogorov Quintuple: 5, being the power set of that E, is a subset of that power set and one containing E. But I shall not pursue the matter here.
n The function P in a Kolmogorov quintuple <E~,-,n,p> is only partially characterized by constraints Ill-V OIl p. 343. What more there is to P we learn as in the case of P(A n B)
= P(B
n A)
from constraints I-II - Le., from constraints placed on E, F, -, and n - and this Substitution Law If A = B, then P(A)
= P(B),12
or as in the case of P(A) = P(A n B) + P(A n -B)
from constraints 111-V together with constraints I-II and the Substitution and justifiably so in my opinion - to this subordination of probability theory to the Boolean algebra of sets. Like remarks apply to the characterization of P in a quadruple of the kind last defined. Constraints Bl-82 there tell us one fact each about P. The rest of 'the story of P we learn from constraints A1'-AS' (Le., from constraints placed on S, -, and n ) and the Substitution Law or from constraints B1-B3 together with constraints Al'-A5' and the Substitution Law. Popper would object here to the subordination of probability theory to the Boolean algebra of sets when P's arguments are sets, to the Boolean algebra of statements when they are statements, etc. Popper's own accounts of an absolute probability field, already neutral as to what P's arguments are, place constraints on P only, and thereby put an end to the dependency of probability theory on the Boolean algebra of sets, that of statements, etc. Popper calls the resulting characterization of P autonomous, an apt epithet indeed. The first of these accounts appeared in Law. In "Two Autonomous Axiom Systems" Popper objected -
346
HUGHES LEBLANC
the 1938 note mentioned earlier. It was in Popper's own estimation "somewhat clumsy," marred also by misprints, and a revised version of it appeared in the "Two Autonomous Axiom Systems" paper of 1955. Edited to suit this context and include Popper's name, the revised account runs thusly: An absolute probability [reid in the sense of Popper is a quadruple of the kind <S,-,n,P>, where S is a non-empty set, - a function from S into S, n a function from S x S into S, and P a function from S into such that Cl. For any A and B in S, P(A n B) S P(A) C2. For any A in S there is a B in S such that P(B) *" 0 and P(A n B) P(A) x P(B), C3. For any A and B in S, P(A n B) S P(B n A), C4. For any A, B, and C in S, P(A n (B n C» s P«A n B) n C), C5. For any A in S, P(A) S P(A n A),t3 and C6. For any A and B in S, P(A) = P(A n B) + P(A n -B).
=
As an account of an absolute probability field the foregoing is a tour de force, and that it is so little known among mathematicians is indeed a scandal. 14 Th~ account, though, might perhaps have won more attention, among readers of Kolmogorov's at any rate, if instead of constraints Cl-C2 Popper had used these analogues of constraints III-IV: Cl'. For any A in S, 0 5. P(A) and C2'. For any A in S, P(-(A n -A»
= 1.
15
Constraint Cl is familar, to be sure, but constraint C2 is not: it takes a moment's thought to realize that that member B of S is -(A n -A). Popper was of course at pains not to use such a constraint as Cl' (trl£ so-called Lower Bound Law) or such a one as P(A) 5. 1 (the so-called Upper Bound Law) which Rudolf Camap in Logical Foundations of Probability (Chicago: University of Chicago, 1959), p. 286, had adjudged "inessential conventions," i.e., Popper slyly glosses, "non-intuitive." He rather wanted the two laws to follow from intuitive ones and thereby be shown intuitive too. 16 But, again, the decision to use constraints Cl-C2 rather than constraints Cl'-C2' may have cost him readers who could not intuit C2. 17 In what follows I shall take the constraints on P to be these six: Cl'-C2' and C3-C6.
Popper states on p. 54 of "Two Autonomous Axiom Systems" that his account "allows the derivation of all the formulae of the customary accounts of probability." He undoubtedly had a proof of this, but to my knowledge never published it. So I supply one of my own and show that constraints Al' -AS', the Substitution Law stated above, and constraint B3 follow from
POPPER'S PROBABILITY THEORY
347
Popper's autonomous constraints CI'-C2' and C3-C6. But, as the reader may verify, the function P on pp. 342-343 meets constraints C3-C6 as well as constraints CI'-C2' (= BI-B2)'" So, Popper's account of an absolute probability field allows the derivation of exactly the same "formulae" as the account on pp. 342-343, the latter a generalization of Kolmogorov's account in Foundations of the Theory of Probability. Prerequisite of course to all this is a suitable defmition of '=' (a symbol which figures in constraints AI'-AS', the Substitution Law, and constraint B3) in terms of Popper's function P. This definition: A = B =df P(A) = P(B), would not do. It delivers the Substitution Law at a stroke, and it also delivers constraints AI' -A4' and B3. But it does not deliver constraint Aj', to wit: If A = B, then A n C = B n C. Using a counterexample of Rescher's in "A Probabilistic Approach to Modal Logic," Modal and Many-Valued Logics (Helsinki: Societas Philosophica Fennica, 1963), p. 217, let P(A) and hence P(-A) equal 1/2 (-A here serving as B), in which case A *--A
by the foregoing defmition of '='. Then P(A n A) and P(-A n A) (-A here serving as C) have to respectively equal ttl and 0, and hence
A n A = A n _A. 19 However, the following definition of '=':
A = B =df P(-(A n -B) n -(-A n B» =1, delivers constraint AS' as well and hence does the job. Note, incidentally, that when A and B are statements of our earlier language L and hence '-' and 'n' do duty for '-' and '&', respectively, P(-(A
n -B) n -(-A n B»
=1
is tantamount to P(A == B) = 1, according to which A and B are what Popper would call substitutionally equivalent and I call probabilistically equivalent. Since P(A == A) = 1, P(B
348
HUGHES LEBLANC
== A) = 1 if P(A == B) = 1, and P(A == C) = 1 if P(A == B) = 1 and P(B == C) = 1, the relation of substitutional or probabilistic equivalence is reflexive, symmetrical, and transitive, the three requirements an equivalence relation must meet. I frrst establish that together with the present definition of '=' Popper's constraints CI' -e2' and C3-C6 yield the Substitution Law (= Theorem 1). The proof requires these lemmas:
Lemma 1. P(A (\ B) ~ P(A).20 Proof: P(A (\ B) = P(A) - P(A (\ -B) ~
P(A) Lemma 2. P(A (\ A) = P(A). Proof by C5 and Lemma 1. Lemma 3. P(A) = P(B n A) + P(-B n A). Proof by C6 and C3. Lemma 4. P«A (\ -A) n B) = O. Proof: P«A n -A) n B) ~ P(A n -A) ~ P(A) - P(A n A)
(C6) (C1').
(Lemma 1) (C6)
~O
(Lemma 2)
=0
(C1').
Lemma 5. P(-A) = 1 - P(A). Proof: P(-A) = P(-(A n -A) n -A) + P«A (\ -A) (\ -A)
= P(-(A (\ -A) (\ -A) = P(-(A n -A» - P(-(A n -A) (\ = 1 - P(-(A n -A) n A) = 1 - P(A) + P«A n -A) n A) = 1 - P(A)
(Lemma 3) A)
(Lemma 4) (Lemma 3) (C2) (Lemma 3) (Lemma 4).
Lemma 6. P(A) < 1. Proof by Lemma 5 and Cl'. Lemma 7. If P(A (\ B) = 1, then P(A) = P(B). Proof: If P(A (\ B) = 1, then P(A) ~ 1 by Lemma 1, and hence P(A)=1 by Lemma 6. But if P(A (\ B) = 1, then P(B n A) = 1 by C3, and hence by the same reasoning P(B) = 1. Hence Lemma 7. Theorem 1. If A = B, then P(A) = P(B). (=The Substitution Law) Proof: Suppose P(-(A (\ -B) (\ -(-A (\ B) = 1. Then by Lemma 7 P(-(A (\ -B) = P(-(-A n B», hence by Lemma 5 P(A (\ -B) = P(-A (\ B), hence P(A (\ B) + P(A (\ -B) = P(A (\ B) + P(-A (\ B), and hence by C6 and Lemma 3 P(A) = P(B). Hence Theorem 1 by the defmition of 'A = B'.
POPPER'S PROBABILITY THEORY
349
I next establish that together with the Substitution Law Popper's constraints yield constraint B3: Theorem 2. If A n B = C n -C, then P(-(-A n -B» = P(A) + P(B). Proof: Suppose A n B = C n -C. Then P(A n B) = P(C n -C) by Theorem 1, and hence P(A n B) = 0 by C2 and Lemma 5. But P(-(-A n -B» = 1 - P(-(-A n -B» (Lemma 5) = 1 - P(-A) + P(-A n B) (C6) = P(A) + P(-A n B) (Lemma 5). Hence P(-(-A n -B» = P(A) + P(A n B) + P(-A n B) = P(A) + P(B) (Lemma 3). Hence Theorem 2. And I last establish that together with my definition of ' =' Popper's constraints yield constraints AI' -AS'. The proof exploits two theorems from my "Alternatives to Standard First-Order Semantics," Handbook of Philosophical Logic, Vol. 1 (Dordrecht: Reidel, 1983), pp. 189-274. By virtue of the frrst, P.(A) = 1 for any truth-functional truth (i.e., tautology) A of our language L, p. here a function from the statements of L into R that meets the results of writing '-' for '-' and '&' for 'n' in Popper's constraints Cl' -C2' and C3-C6;21 by virtue of the second, (i) P.(B) = 1 if P.(A) = 1 and P.(A ::> B) = 1, and hence (ii) P.(A) = 1 if, and only if, p.(B) = 1 if P.(A == B) = 1, this for any statement A and any statement B of L. 22 Hence: P.«A & B) == (B & A» 1, P.«A & (B & C» == «A & B) & C» 1, P.«A & -A) = (C & = 1 if; and only if, P.«A & B) == A) = 1, If P.(A == B) = 1, then P.(-A == -B) • 1, and If P.(A == B) = 1, then P.«A & C) == (B & C» = 1. But, if so, then Popper's own constraints yield these23 P(-«A n B) n -(B n A» n -(-(A n B) n (B n A») = 1, P(-«A n (B n C» n -«A n B) n C» n -(-(A n (B n C» n «A n B) n C») = 1, P(-«A n B) n -(C n -C» n -(-(A n -B) n (C n -C») = 1 if, and only if, P(-«A n B) n -A) n -(-(A n B) n A» = 1, If P(-(A n -B» n -(-A n B» = 1, then P(-(-A n --B) n -(--A n -B» 1, and If P(-(A n -B) n -(-A n B» = 1, then P(-«A n C) n -(B n C» n -(-(A n C) n (B n C») 1. Hence, by the defmition of '=': Theorem 3. Let A, B, and C be arbitrary members of S. Then: (a) A n B = B n A,
=
-C»
=
=
=
350
HUGHES LEBLANC (b) A n (B n C) = (A n B) n C, (c) A n -B = C n -e if, and only if, A n B = A, (d) If A = B, then -A = -B, and (e) If A B, then A n C B n C.24
=
=
So, as Popper claimed, the "autonomous" characterization of P in his 1938 note and 1955 paper allows derivation of exactly the same "formulae" as Kolmogorov's characterization. Together with the definition of '=' on p. 347 Theorem 3 also shows that the Boolean algebra of sets, that of statements, etc. - far from being prerequisites to absolute probability theory - may be viewed as outgrowths of absolute probability theory. In his Logic of Scientific Discovery of 1959 Popper obtained a similar result concerning relative as opposed to absolute probability theory, and he went on to claim on p. 356 of the book that when P takes pairs of statements as its arguments relative probability theory is "a genuine genernlization of the logic of derivation." I shall return to this claim in Part IV of the paper. Two more points before we turn to Carnap's absolute probability functions. Does the set on which an absolute probability function of Popper's is defined (Le., does the set from which it draws its arguments) automatically count by virtue of Theorem 3 as a field? Yes, if in Al' -A5', the Byrne-Rosenbloom constraints characteristic of a field, = is construed as any equivalence relation one pleases, say, the probabilistic equivalence relation of pp. 347-348. No, if = there is construed as the much stronger identity relation. Note for proof that whereas fields in the equivalence relation sense come in all sizes or cardinalities, fields in the identity sense come only in some sizes, fmite ones in particular coming only in the sizes 2, 4, 8, 16, etc. As a result, a vast number of absolute probability functions in Popper's sense do not count as absolute probability functions in Kolmogorov's sense or in that of pp. 342-343.25 Are there advantages other than ending the dependency of probability theory on Boolean algebra to construing = as a mere equivalence relation rather than as identify? Yes, when the set on which an absolute probability function is defined consists, say, of statements. We know what it means for set A to be the same as set B: whatever belongs to A must belong to B and vice-versa. We also know what it means for statement A (of, say, our earlier language L) to be logically equivalent, probabilistically equivalent, etc. to statement B (of that language L). But do we know what it means for A to be the same statement as B? And if, as I suspect, we do not, then what are we to make of the Substitution Law for A and B statements of
IL?7J6
I What we call here Carnap's absolute probability fields are those among the probability fields of pp. 342-343 that meet this extra constraint:
84. For any A in S, if P(A)
= 1, then A = -(B n
-B) for some BinS,
POPPER'S PROBABILITY THEORY
351
hence - when as in Section 55 of Carnap's Logical Foundations of Probability, Chicago, 1950, P's arguments are the statements of L - this extra constraint: B4'. For any A in S, if P(A)
= 1, then A is truth-functionally true.
In the latter case Carnap's absolute probability fields are, equivalently, those among the probability fields of pp. 342-343 in which the function P accords to state-descriptions only non-zero probabilities. To elaborate on this as earlier promised, let the so-called atomic statements of L be in alphabetic order At, A2 , A3.... The state-descriptions of L in the n-tuple
(n = 1, 2, 3,...) are the 2 conjunctions D
±At & ±A2 &
& ±Au,
where for each i from through n ±~ is either ~ itself or its negation -~. State-descriptions were popularized by Ludwig Wittgenstein and Carnap. In his Tractatus Logico-Philosophicus (London: Routledge and Kegan Paul, 1922), Wittgenstein set the absolute probability of a state-description in at 1/2D. and that of a statement A of L whose alphabetically latest atomic component is A. at m/2D, m here the number of statedescriptions of L in in which A holds. Generalizing the account, Carnap allowed the absolute probabilities of the 2 state-descriptions of L in to be positive reals whose sum is 1. To my knowledge Popper nowhere attends to state-descriptions. However, under his account of an absolute probability field, the absolute probabilities of the foregoing state-descriptions would be, more generally, non-negative reals whose sum is 1. The difference is significant Under both accounts A is truth-functionally true if, and only if, P(A) equals 1 for every P. But, whereas under Camap's account P(A) equals 1 for every P (and, hence, A is truth-functionally true) if P(A) equals 1 for any P at all, under Popper's P(A) may equal 1 for one P and yet be less than 1 for another. In Part IV of the paper I shall comment briefly on this. D
m By the time Alfred Renyi published his "On a New Axiomatic Theory of Probability," ACTA MATHEMATICA ACAD. SCIENT. HUNGARICAE, vol. 6, 1955, pp. 286-335, relative (or, as they are also called,. conditional) probability functions had long been under study and in use. However, as claimed on p. 286 of the paper, his may have been the fIrst account of them as generalizations to two arguments of Kolmogorov's one-argument probability functions. As it had considerable impact on Popper's own
HUGHES LEBLANC
352
account of things, a matter Popper acknowledges in The Logic of Scientific Discovery, p. 346, footnote 12, I consider it here is some detail. By a relative probability field Renyi understands (in effect) a quadruple of the kind <E,F,G»>, where (i) E is a non-empty set, (ii) F is a non-empty subset of P(E) such that I. F is a field of sets and II. F contains E, (iii) G is a non-empty subset of F such that III. G does not contain but IV. G contains A u B if G contains both A and B, and (iv) P is a function from F x G into R such that V. For any A in F and B in G, 0 S P(A,B) VI. For any A in G, P(A,A) = 1, VII. For any A and B in F and any C in G, if A n B = D n -D for some D in F, then P(A n B,C) = P(A,C) + P(B,C), and VIII. For any A and B in F and any B n C and C in G, P(A n B,C) = P(A,B ~ C) x P(B,C).
°
Note: 0 is excluded from G for the following reason. Suppose 0 did belong to G. Then by constraint VI P(0,0) would equal 1. But, since n = 0, by constraint VII P(0 u 0,O) would equal P(0,0) + P(0,0); and, since u = 0, P(0,0) would as a result equal 2 as well as 1. Why A u B should belong to G if A and B do is immaterial here. As a matter of fact G is often taken to consist of every member of F but 0, in which case constraint IV is automatically met'J:7 Renyi's account compels the members of F and G - hence the arguments of P - to be sets. The following account, which spells out what a field is and dispenses with G by requiring C in constraint VII to be distinct from 0, allows the arguments of P to be whatever there is a Boolean algebra of. A relative probability field in the abstract sense is a quadruple of the kind <S,-,n»>, where
°
° °
°
(i) S is a non-empty set, - is a function from S into S, and n one from S x S into S such that Al' -Aj', and (ii) P is a function from S x S into R such that Dl. For any A and B in S, 0 S P(A,B), D2. For any A in S, P(A,A) = 1, D3. For any A, B, and C in S, if A n B = D n -D but C n -D for some D in S, then P(-(-A n -B),C) = P(A,C) + P(B,C), 04. For any A, B, and C in S, P(A n B,C) = P(A,B n C) x P(B,C), and D5. For at least one A and one B in S, P(A,B) "* 1.28
POPPER'S PROBABILITY THEORY
353
Illustration 5: Let S consist of these four sets: a, -a, a n -a, and -(a n -a); and let P be this function from S x S into {O,I}:
B P(A,B)
a
-a
a n-a
-(a n -a)
0 -a a n-a 0 -(a n -a) 1
I 0 1
I I 1
I 0 1
a
t is easily verified that P meets all of constraints Dl-D5 and hence that <S,-,n,P> constitutes a relative probability field in the present sense. (I borrow the illustration from "On Relativizing Kolmogorov's Absolute Probability Functions," a paper written in collaboration with Peter Roeper.) Illustration 6: Let S be as in Illustration 5 and P be this function from S x S into {O,I/2,I}:
B P(A,B) a a 0 -a a n-a 0 -(a n -a) 1
-a
a n-a
-(a n a)
1 0 1
1 1 1
1/2 0 1
It is easily verified that P meets all of constraints Dl-D5 and hence that <S,-,n,P> constitutes a relative probability field in the present sense. It is easily verified as well that P meets this extra constraint, D6. For any A and B in S, if P(A,-(B n -B»
= 1, then A =
-(B n -B),
a constraint equivalent to one of Carnap's in Section 53 of Logical Foundations of Probability. The functions defmed on p. 12 of Camap's The Continwm of Inductive Methods (Chicago: University of Chicago, 1952), are functions in the abstract sense of p. 352, with S consisting of the statements of L but P(A,B) not accorded a value when B is truth-functionally false. So, they are in effect Renyi functions with F consisting of the statements of L and G consisting of all and only those that are not truth-functionally false. The relative probability functions in Section 53 of Logical Foundations of Probability are the same functions as in the Continuum book but with P required to meet constraint 06. As a result, they match one-to-one the absolute probability functions in Section 55 of the Logical Foundations book. As shown in "On Relativizing Kolmogorov's Absolute Probability Functions," there indeed corresponds to each function P in Section 53 a
354
HUGHES LEBLANC
function P' in Section 55 and to each function P' in Section 55 a function P in Section 53 such that P(A,B) = P'(A & B)/P'(B). So, the "formulae" of Camap's relative probability theory in the Foundations book are but translations in the idiom of two-argument functions of "fonnulae" from his absolute 000.29 The counterpart here of the Substitution Law on p. 345, to wit:
H A = B, then P(A) = P(B), runs of course as follows: If A = A' and B = B\ then
P(A~)
=
P(A'~').
As in Part II of the paper, where consttaints B1-B2 told us one fact each about absolute probability functions, constraints D1-D2 and D4 here tell us one fact each about relative probability functions. The rest of the story about relative probability functions we learn from constraints A1' -AS' and the Substitution Law for relative probability functions or from constraints D1-D4 together with constraints Al' -AS' and the Substitution Law for relative probability functions. Popper's own accounts of a relative probability field are, as one would expect, neutral as to what S's members and hence P's arguments are, and they place constraints on P only, thereby ending the dependency of relative probability theory on the Boolean algebra of sets, that of statements, etc. The fIrst of these autonomous accounts appeared in the "Two Autonomous Axiom Systems" paper of 1955. What Popper calls "a slight," but I would call "a radical," improvement of the account appeared two years later on p. 191 of "Philosophy of Science: A Personal Report," British Philosophy in the Mid-Century, A.C. Mace, 00. (London: George Allen and Unwin).30 Edited to suit this context, the revised account reads thusly: A relative probability field in the sense of Popper is a quadruple of the kind <S,-,n,p>, where S is a non-empty set, - a function from S into S, n a function from S x S into S, and P a function from S into R such that E1. E2. E3. E4. E5. E6.
For any A, B, and C in S, P(A n B,C) 5. P(A,C), For any A and BinS, P(A,A) = P(B,B), For any A and BinS, if P(C,B) :F- P(B,B) for some C in S, then P(-A,B) = P(B,B) - P(A,B), For any A, B, and C in S, P(A n B,C) = P(A~ n C) x P(B,C), For any A, B, and C in S, if P(A,D) = P(B,D) for every D in S, then P(C,A) = P(C,B), and For at least one A, one B, one C, and one DinS, P(A,B) :F- P(C,D).
Like Popper's 1955 account of an absolute probability field, the foregoing account of a relative one is a tour de force. But again Popper's determination not to use the Lower Bound Law as a constraint, his use in
POPPER'S PROBABILITY THEORY
355
constraints E2 and E3 of 'P(B,B)' instead of '1', and a further concern of his which I discuss below make for constraints that are perhaps not as "pointed" as could be.:n In any event many prefer these constraints, which in the frrst six cases were already known to Popper and in the seventh soon occurred to him: Fl. F2. F3. F4 F5. F6. F7.
For any A and BinS, 0 So P(A,B), For any A in S, P(A,A) = 1, For any A and B in S, if P(C,B) 1 for some C in S, then P(-A,B) = 1 - P(A,B), = E4= For any A, B, and C in S, P(A n B,C) = P(A,B n C) x P(B,C), For any A, B, and C in S, P(A n B,C) So P(B n A,C), For any A, B, and C in S, P(A,B n C) So P(A,C n B), and For at least one A and one BinS, P(A,B) 1.
*
*
Constraints Fl-F2 and F4 are of course familiar from Renyi's account; constraint F3 follows from (but, note, is not equivalent to) Renyi's constraint D3; constraints F5-F6 follow from constraint AI' by the Substitution Law for relative probability functions; and constraint F7, also familiar from Renyi's account, is a simplification of constraint E6. As indicated earlier, Popper went on to prove in Appendix *v of The Logic of Scientific Discovery that, given this definition of '=': A = B
=cIf
P(A,C) = P(B,C) for every C in S,
postulates for Boolean algebra equivalent to AI' -Aj' and the Substitution Law for relative probability fWlctions follow from constraints E1-E6 (so, from their equivalents FI-F7 as well), and hence that Boolean algebra, far from being a prerequisite to relative probability theory, can in point of fact be viewed as an outgrowth of it. The postulates he utilized for the occasion were postulates of Huntington's in "New Sets of Postulates for the Algebra of Logic," lRANSACTIONS OF THE AMERICAN MATHEMATICAL MONTHLY, vol. 35, 1933, pp. 274-304. He also noted that the relation designated by '=' is reflexive, symmetrical, and transitive- hence, an equivalence relation and, more specifically, one of substitutional equivalence. Having established a point critical to him, the "autonomy" from Boolean algebra of relative probability theory, Popper further insisted that the constraints placed on P be "autonomously independent," i.e., independent in the presence as well as the absence of Boolean constraints such as Ai' -AS' . Constraints F5-F6 are of course not autonomously independent: as just noted, they follow from the Boolean constraint AI' by the Substitution Law for relative probability functions, and hence are in Popper's eyes vestiges of Boolean algebra. He may have overlooked, however, that certain accounts of Boolean algebra use the inclusion relation c in lieu of the identity one =,
356
HUGHES LEBLANC
and that his own constraint El would follow by dint of this Substitution Law for relative probability functions:
If A c B, then P(B,C) =5 P(A,C) from the constraints placed in such accounts on the two functions - and n. There may well be some substitute for constraint E1 that would make for an "autonomously independent" as well as "autonomous" account of Popper's relative probability functions, but some of us already alerted by Popper to the autonomy of probability theory from Boolean algebra do value the simplicity and directness of constraints FI-F7. 32 As remarked three paragraphs back, Popper's constraint F3, though following from Renyi's constraint D3, is not equivalent to and hence is weaker than it. So, all of Renyi's relative probability functions figure among Popper's, but not vice-versa. Indeed, Renyi's functions are those and only those of Popper's that meet this extra constraint: (1) If P(A,B) = 1 for every A in S, then B = C n -C for some C in S, or equivalently this one: (2) If P(A,B) = 1 for every B in S, then A -(C n -C) for some C in
S.33
=
Because of (2), a statement A of our language L proves under Renyi's account to be truth-functionally true (i.e., again, a tautology) if, and only if, P(A,B) = 1 for every statement B of L and any relative probability function P. Under Popper's account, on the other hand, A proves to be truth-functionally true if, and only if, P(A,B) = 1 for every statement B of L and every relative probability function P. (1) is also of interest. A statement A of L is sometimes called P-absurd if P(B,A) = 1 for every statement B of L, i.e., if - to phrase it in belief-theoretic terms - should you believe A you'd believe anything. Under Renyi's account only truth-functional falsehoods are P-absurd; under Popper's, on the other hand, truth-functionally indeterminate statements of L (Le., statements of L that are neither truth-functionally true nor bUth-functionally false) may also be P-absurd. Popper's constraint E6 and, more pointedly, constraint F7 reassure us, however, that there exists for each relative probability function of Popper's at least one statement of L that is not P-absurd. Note, by the way, that under Popper's account the state descriptions of L in (n = 1,2,3,...) have as their probabilities relative to -(B & -B) (B here any statement of L) non-negative reals whose sum is 1; under Renyi's they also have as their probabilities relative to -(B & -B) non-negative reals whose sum is 1, but because of (1) they themselves cannot be P-absurd for any P; and, when Renyi's functions meet the extra constraint D6, the state-descriptions in question have as their probabilities
POPPER'S PROBABILITY THEORY
357
relative to -(B & -B) only non-zero reals whose sum is I (and they themselves cannot be P-absurd f(X' any P). It was R6nyi's stated aim to construct relative probability functions that relativized Kolmogorov's absolute ones. This required, as R6nyi puts it on p. 286 of "On a New Axiomatic Theory of Probability," that the latter be "special cases" of the f
=
P'(A)
= P(A,V),
I shall say that a family 1t of relative probability functions defmed on a set S relativizes a family 1t' of absolute ones defined on that S if (i) every function in
1t'
is the V-restriction of one in
1t
and (ii) every function in
1t
has one in
1t'
as its V-restriction.
Shown in "On Relativizing Kolmogorov's Absolute Probability Functions" is that each of Kolmogorov's absolute ~bility functions defined on a field S is the V-restriction of a relative on of R6nyi's defined on that S; and proof that each of R6nyi's relative p bility functions defined on a field S has as its V-restriction an absolute 0 e of Kolmogorov's defined on that S is immediate. So, R6nyi's relatt e probability functions relativize '. Kolmogorov's absolute ones. Consider next those among Popper's 'telative probability functions that happen to be defmed on fields. Since each R6nyi function is a Popper one defined on a field. each of Kolmogorov's absolute probability functions is the V-restriction of one of the Popper functions in question. But proof that each of the Popper functions in question has as its V-restriction an absolute one of Kolmogorov's is easily had. So, those among Popper's relative probability functions that happen to be defined on fields also relativize Kolmogorov's absolute probability functions. Consider then Popper's relative probability functions as he understood them, i.e., defined on arbitrary sets rather than just fields. Proved in the Leblanc-Roeper paper mentioned earlier is that they relativize Popper's own absolute probability functions-- and proved also is that Camap's relative probability functions (defmed. we know, on fields) relativize his absolute ones.
358
HUGHES LEBLANC
So, all 'the relative probability functions studied in the paper relativize the absolute ones they should. In this respect Renyi's and Camap's functions thus perform as well as Popper's, but there is more to the story as I show next.
IV Given the defmition of '=' on p. 355, Popper's account of a relative probability field allows derivation - we saw - of "formulae" which translate into the formulae of Boolean algebra, hence when Popper's functions take the statements of L as their arguments into the formulae or laws of the Algebra of Logic. As a result, Popper concluded in 1959 that (his) relative probability theory is "a genuine generalization of the logic of derivation"to be more precise, of the logic of truth{unctional derivation, since the statements of L are just the statements that can be compounded from given atomic statements by means of negation and conjunction. Given the results on pp. 348-350 one might conclude today that both Popper's relative probability functions and his absolute ones are generalizations of the logic of truth-functional derivation.34 However, there is a second and in my opinion quite important sense in which absolute probability theory can be thought of as a generalization of, let us say, truth function theory. By a truth function understand any function T from the statements of L into {O,I} that meets these two constraints:
TI. For any A in S, T(-A)
= 1 - T(A)
and 12. For any A and B in S, T(A
n B)
= min(T(A),T(B»,
-A and A n B understood here of course as -A and A & B, respectively. I showed in "Popper's 1955 Axiomatization of Absolute Probability" that any truth function is a 2-valued absolute probability function in the sense of Popper, and vice-versa. So, truth functions are but some of Popper's absolute probability functions, the 2-valued ones. So, Popper's absolute probability theory is a genuine generalization of truth function theory, hence a genuine generalization in this sense as well of the logic of truth-functional derivation. Note by the way that anyone of Carnap's absolute probability functions must have more than two values: value 1 being reserved for the truth-functional truths of L and value 0 for its truth-functional falsehoods, any statement of L that is truth-functionally indeterminate must have a probability other than 1 and O. So, Carnap's absolute probability theory is not like Popper's (hence, Kolmogorov's) a generalization of truth function
POPPER'S PROBABILITY THEORY
359
theory. So, it is not in my opinion the best absolute probability theory on the market.35 What P(A,B) amounts to when P is a relative probability function of Popper's that is 2-valued is still an open question. Suppose P' to be what I called earlier the V-restriction (here, the -(C & -C)-restriction) of P. Since P is 2-valued, P' is 2-valued as well and hence is some truth value function or other, say T. Now it is easily shown that if T(B) = 1, then P(A,B) amounts to T(A & B) and hence to T(B).36 But exactly what P(A,B) amounts to when T(B) = 0, I simply do not know. Probabilistic semantics, however, is my main concern here. When proving that- Boolean algebra is an outgrowth of Popper's absolute probability theory, I appealed to theorem 4.31 in "Alternatives to Standard First-Order Semantics," to wit: (3) If ~ A then P(A)
= 1,
where by '~ A' I understand that A is provable in L via Rosser's axioms
and rule of inference for L in Logic for Mathematicians (New York: McGraw-Hill, 1953). The result, a Weak Soundness Theorem, if you will, holds of course for every probability function P in Popper's sense; and, as shown in my "Alternatives" paper, so does its converse, a Weak Completeness Theorem. Hence, for any statement A of L, (4) ~ A if, and only if, P(A) = 1 for every absolute probability function P in Popper's sense, and, more generally, for any set S of statements of L and any statement A of L, (5) S ~ A if, and only if, P(S) 5. P(A) for every absolute probability function P in Popper's sense,
where I understand by '5 l- A' that A is provable in L from S via Rosser's axioms and rule of inference for L and I define P(S) thusly:
P(S) =
1 when S = 0 P(AI & ~ & ... & AJ when S {AIA,... A} for some n 2: 1 glb{P(S'):S' is a finite subset of S} when S is (denumerably) infinite.37
=
But, if so, then truth-functional truth and truth-functional entailment (or, truth-functional implication, if you prefer) may be defined as follows: A is truth-functionally true function P in Popper's sense
=.
P(A)
=1
for every absolute probability
360
HUGHES LEBLANC
and S truth-functionally entails A function P in Popper's sense,
=df
P(S)
~
P(A) for every absolute probability
and you have the beginnings of a probabilistic semantics for L, one utilizing Popper's absolute probability functions where standard semantics would utilize truth functions. Like results hold true of Popper's relative probability functions, indeed were obtained earlier than (4)-(5). There are various proofs by Harper, Field, Leblanc, etc. of this Weak Soundness and Weak Completeness Theorem for L: (6) ~ A if, and only if, P(A,B) = 1 for every statement B of L and eve r y relative probability function P in Popper's sense,
and of this Strong Soundness and Strong Completeness Theorem for L: (7) S I- A if, and only if, P(S,B) ~ P(A,B) for every statement B and every relative probability function P in Popper's sense,
of
L
where P(S,B) is defmed exactly as P(S) just was, but with ',B' intercalated two obvious places.3I But, if so, then truth-functional truth and bUth-functional entailment may also be defmed as follows:
at
A is truth-functionally true =df P(A,B) = 1 for every statement B of L and every relative probability function P of Popper's and S truth-functionally entails A =df P(S,B) ~ P(A,B) for every statement B of L and every relative probability function P of Popper's, and you have the beginnings of a second probabilistic semantics for L, one utilizing this time Popper's relative probability functions where standard semantics would utilize truth functions. And like results hold of Carnap's absolute probability functions and, say, Renyi's relative probability functions. For example, according to constraint B4' on p. 351, For every absolute probability function P of Carnap's, if P(A) = 1, then A is truth-functionally true, hence,
POPPER'S PROBABILITY THEORY
361
IT P(A) = 1 for any absolute probability function P of Carnap's, then A is truth-functionally true,39 and hence by virtue again of Theorem 431 in the "Alternatives" paper, A is truth-functionally true if, and only if, P(A) probability function P of Camap's.
=1
for any absolute
And, to hurry on, constraint (2) on p. 356 and Theorem 5.24 in the "Alternatives" paper deliver in the same manner: A is truth-functionally true if, and only if, P(A,B) = 1 for every statement B of L and any relative probability function P of Renyi's.40 But the last two results, half of each ushered in by a constraint rather than a Weak Completeness Theorem, are in my opinion less intuitive than their Popper counterparts. In each case it is of course the constraint that jars. Think again of probability functions as, say, measures of rational belief. Contrary to constraint 84', can't there be some statement of L that is not troth-functionally true and yet "believable beyond doubt"? Or, contrary to (1) on p. 356, a constraint equivalent to the one that delivered our last result, can't there be some statement of L that is "utterly unbelievable," so unbelievable indeed that - should you believe it - you'd believe anything, and yet is not truth-functionally false? Carnap's understanding of rational belief and Renyi's, narrower than Popper's, are simply too narrow to accommodate cases such as these, which are hardly far-fetched.41 Work on probabilistic semantics was triggered in my case, and possibly that of Harper and Field as well, by Popper's proof that whenever A == A'
is a formula of the Algebra of Logic, hence a truth-functional truth, P(A,B) = P(A',B) for every statement B of L.
Indeed, one more step would have yielded
If A is troth-functionally true, then P(A,B)
= 1 for every statement B of L,
and hence If
l- A, then P(A,B) = 1 for every such B.
For, if A is truth-functionally true, then so is A == -(C & -C),
HUGHES LEBLANC
362
hence by Popper's own result p(A,B) = P(-(C & -C),B) for every statement B of L. But, by (74) on p. 353 of The Logic of Scientific Discovery, P(-(C & -C),B) = 1. Hence, If ~ A, then P(A,B)
= 1 for any
statement B of L.
That extra step, if you will, and (adjustments to) Harper's proof of the other half of (6) in his 1974 Counterfactuals and Representations of Rational Belief, gave birth to probabilistic semantics, a semantics for which Popper should thus receive partial credit42 As his referring to the Algebra of Logic as tithe logic of derivation" attests, Popper tended in 1959 to think: of logic as the logic of negation and conjunction, Le., as truth-functional logic. But logic is also the logic of fust-order quantification and of much else. Probabilistic accounts of fust-order logical truth and logical entailment (with as well as without identity) were supplied in the late seventies, and in the early eighties various extensions of standard first-order logic (modal logic, tense logic, etc.) as well as deviations from standard fust-order logic (intuitionistic logic, conditional logic, etc.) were provided with a probabilistic semantics. All of these contributions to probabilistic semantics used relative rather than absolute probability functions, but interest in a probabilistic semantics that uses absolute probability functions has revived, and much work has gone into absolute probability functions that take sets of statements as their arguments, P(A) being defmed there as P({A).43 Thus has Popper generalized Kolmogorov's absolute probability functions and Renyi's relative ones, characterized the resulting functions autonomously, and thereby initiated a new semantics for a nurrt'ber of today's logics.
363 ENDNOTES 1. See: Paul Arthur Schilpp, ed, The Philosophy of Karl Popper (La Salle: Open Court, 1974), pp. 1118-1119. Popper concurs there with a regret voiced by Tom Settle on pp. 732-734 of the same volume. 2. Kolmogorov's Grundbegriffe appeared in ERGEBNISSE DER MATHEMATIK UNO IHRER GRENZBEGIETE, Vol. 2, part 3. I use here Nathan Morrison's translation of the text as Foundations of the Theory of Probability (New York: Chelsea, 1950). 3. Kolmogorov's appellation for a probability field is, of course, 'Wahrscheinlichkeitsfeld'. I add the qualifier 'absolute' throughout to differentiate the present probability fields and probability functions from the relative ones of Part ill. Nowadays probability fields are often called probability spaces. 4. It is possibly because of the role played at this point by the postulates for Boolean algebra that fields are also called Boolean algebras. The usage is disconcerting to readers who think of Boolean algebra as a part of set theory rather than a certain kind of set, and I avoid it here. 5. Even individuals when the so-called calcwMS of individuals (i.e., Lesniewski's me.reology) is equipped with a null individual. 6. Writers anxious to prevent mis\D1derstandings sometimes use such functional variables as 'f' for' -' and 'g' for 'n' when they introduce the notion of a field, but they soon revert to the more customary '-' and 'n'. 7. Constraints I-IV pennit construction of quintuples <E,F,-,n,P> where F has but one member: following a suggestion of Rosenbloom's on p. 10 of The Elements of Mathematical Logic, let E be {a}, F be {{a}}, {-a} be {a} itself, {a} n {a} be as expected {a}, and P({a}) be 1, and the trick is done. To rule out oddities of this sort, Mendelson in Introduction to Mathematical Logic (Monterey: Wordsworth & Brooks, 1987), p. 8, further demands of a field that it have at least two members. Kolmogorov need not do so: because of constraint V, F is sure to contain 0 as well as (the non-empty) E. See Notes 17, 27, and 28 for more on this point Incidentally, A n A = A by constraint ..43 and A n -A = A n -A, and hence A n -A = B n B by constraint A3 again. So, constraint V could read, more compactly, For any A and B in F, if A n B = -A n ~ then P(-(-A n -B» = P(A) + P(B). But writing 'A n B = C n -C' rather than 'A n B = A n -A' (or, for that matter, 'A n B = B n -B') forestalls the occasional question: "Is A (B) the same set in A n -A (B n -B) as in A n B?" 8. Kolmogorov's choice of the letter 'E' to denote that set was surely suggested to him by the Gennan word 'Ereignisse' for events. 9. Possibly misled by Kolmogorov's phrasing of things, many alas have inferred that it does. Kolmogorov might have prevented the misunderstanding by postponing until Section 2 mention of elementary and random events. 10. For an elementary exposition of these matters see: Kemeny, Snell, and Thompson, Introduction to Finite Malh£matics (Englewood. Cliffs: Prentice-Hall, 1956), cbs. 3 and 5. The set consisting of all, and only, the state-descriptions in which a statement A of L holds is called there the truth set of A. Note that when E in a Kolmogorov quintuple <E,F,-,n,P> consists of statements and hence F of sets of statements, these sets must be construed disjunctively rather than conjunctively-{(...(AI V AJ V...) V Au} being of course the disjunctive construal of the set of statements {AI ,A2, •••,Au} and {(...(A1 & AJ & ...) & Au} its conjunctive one. Disj\D1ctively construed, the set consisting of all the state-descriptions of L would be of absolute probability 1 as in Kolmogorov's constraint V; conj1.U1ctively construed,
364
HUGHES LEBLANC
on the other hand, it would be of absolute probability 0, and so would be the truth set of any statement of L. For more on state-descriptions see p. 366. 11. Popper would say fomwl or uninterpreted where I say abstract. But, as formulated on pp. 341-342 or pp. 342-343, Kolmogorov's account is formal in the cmrent sense of the word, and it is interpreted only in that the members of F and hence arguments of P have to be sets. So, 'abstract' (or, possibly, 'generalized') would seem the more fitting appellation for the present account 12. Kolmogorov understood by = in constraint I the identity relation. Under that construal the SldJstitKlion Law holds by the very definition of a function: taking each of its arguments into exactly one real, P must obviously take B into the same real into which it takes A if B is the same as A. However, when = in constraint I is lDlderstood as a mere equivalence relation, the SldJstitution Law must be derived from the constraints on P or must be listed among those constraints. See p. 345 and pp. 346-349 for more on this matter. 13. Constraint C3 is of course tantamO\D1t to For any A and BinS, P(A n B) = P(B (1 A). As for For any A, B, and C in S, P(A (1 (B (1 C» = P«A (1 B) n C) and For any A in S, P(A (1 A) = P(A), they follow from constraints C3-C4 and constraints Cl and CS, respectively. 14. Some logicians, on the other hand, have paid considerable attention to the account, as was noted on earlier and will be documented in Part N of the paper. 15. Proof of constraint Cl - given constraints Cl' and C6 - will be found on p. 348; and, more generally, proof that - given constraints C3-C6 - constraints Cl-C2 and Cl' -C2' are equivalent will be found in my "Popper's 1955 Axiomatization of Absolute Probability," PACIFIC PIDLOSOPIDCAL QUARTERLY, vol. 63, 1982, pp. 133-145. Robert Stalnaker in "Probability and Conditionals," PHILOSOPHY OF SCIENCE, vol. 37, 1970, pp. 64-80, uses constraint Cl' in lieu of constraint Cl and this special case of constraint C6: C2". For any A in S, P(A) = 1 - P(A) in lieu of constraint C2. Proof of constraint C2" given constraints Cl' -C2' and C3-C6 will be found on pp. 348-350. 16. See: Popper, ''Two Autonomous Axiom Systems," pp. 53-54. 17. In ''Two Autonomous Axiom Systems," p. 53, note 1, Popper indicates that constraint C2 "may be split into two": C2.l. For any A in S there is a BinS such that P(B) ~ P(A) and P(A (1 B) = P(A) x P(B), and C22. There is an A in S and a BinS such that P(A) P(B). Constraint C2.1, however, is hardly more intuitive than constraint C2; and, in my opinion at any rate, constraint C22 does not really belong in an "autonomous" set of constraints on the function P since it is equivalent to a constraint on the set S, to wit: C22'. There is an A in S and a BinS such that A B. 18. In the case of C6 the reader should use B3, the Substitution Law, and these two consequences of Al' -AS': (A (1 B) (1 (A n -B) = C (1 -C and -(-(A (1 B» (1 -(A (1 -B» = A. 19. It follows from Rescher's example that '&' is not extensional in probability contexts. For further details on the probabilistic extensionality of '-' and non-extensionality of '&' and the quantifier operator 'V', see my "A New Semantics
*"
*"
POPPER'S PROBABILITY THEORY
365
for First-Order Logic, M-any-Valued and Mostly Intensional," TOPOl, vol. 3, 1984, pp.52-62. 20. Lemma 1 is of course Popper's constraint CI, and Lemma 5 Stalnaker's constraint C2". 21. The theorem in question is 431 on p. 234, one I shall again appeal to. It says that if A is provable in L, then P.(A) = 1. But by the Weak Completeness Theorem A is provable in L if truth-functional true. The subscript's' signals that P here takes statements as its arguments. 22. The theorem in question is 4.30 on p. 233. 23. Gotten from what precedes by frrst paraphrasing 'A == B' as '(A:::> B) &. (B :::> A)' and 'A :::> B' as '-(A &. -B)', and then writing '-A' for '-A' and 'A n B' for 'A &. B'. 24. Peter Roeper has pointed out to me that my defmition of '=' can be simplified to read A = B =. P(A n -B) + P(-A n B) = 0, ~ hence, A = B =. P(-(A n -B» x P(-(-A n B» = 1. It is of course because I borrow from "Alternatives to Standard First-Order Semantics" that the present proof of Theorem 3 is relatively brief. Any reader wanting a self-contained proof of the theorem should use Roeper's simplification of my definition of ':'. 25. Some mathematicians require that = in the constraints in question be construed as identity; many others - Rosenbloom among them - allow = to be an equivalence relation. To quote (in slightly edited form) from p. 9 of his book: "Here the relation "=" is taken to be part of the known syntax language. The only properties of this relation which will be used are Tl.l.l (i.e. A = A), Tl.1.2 (i.e. If A = B, then B = A), Tl.1.3 (i.e. If A = B and B = C, then A = C», and their consequences in conj\Dlction with AI' -AS'. Hence we could alternatively take "=" as an undefined term and postulate Tl.l.1-Tl.l.3. A relation satisfying the latter conditions is called an equivalence relation." The alternative suggested in the third sentence is one I cannot pursue here. 26. Statement A &. B is logically equivalent to statement B &. A, but is it the same statement as B &. A as constraint AI' would require? Or, to pass on to constraint B3, could A &. B possibly be the same statement as C &. -C for atomic A, B, and C? 27. In his 1955 paper Renyi places no restriction on G: he merely notes that in view of the contradiction reproduced in the text (2J does not belong to G, a curious handling of the matter. Restrictions ill and IV are from his "Sur les Espaces Simples des Probabilites Conditionnelles," ANNALES DE L'INSTITUT POINCARE, N Serle, Section Bl, 1964, pp. 3-21. Since F contains 0 but G is a non-empty subset of F that does not, F is sure to have at least two members. 28. This constraint: D3'. For any A and BinS, if B :I: C n -C for some C in S, then P(-A,B) = 1 P(A,B), equivalent to Renyi's constraint D3, is sometimes used in place of D3. It brings Renyi's account closer to that of Popper's on p. 354 and that of von Wright's in The Logical Problem of Induction, second revised edition (New York: Macmillan, 1957). To preserve consistency von Wright requires that A in constraint D2 rather than B in constraint D3' be distinct from 0. Few have followed him in this. Constraints DI-D4 are compatible with S having but one member. Hence D5, a constraint which will prove of considerable interest in Part IV.
366
HUGHES LEBLANC
29. Carnap's constraints in the Continwun book are a statement-theoretic version of the Substitution Law four lines further in the main text, a variant of D3, D4, and this (needlessly strong) version of D1: o So P(A,B) S. 1. The constraints are compatible with P having 0 as its one and only value, a slip I reported to Camap shortly after publication of the book. To mend matters, I suggested adoption of this further constraint: If -(B & -A) is truth-functionally true, then P(A,B) = 1, to which Carnap assented. Adoption of Renyi's constraint D2 would have done as well, but I do not recall either of us realizing it at the time. Camap's constraints in the Logical FolUJdations book are the Substitution Law, the version above of D1, the same variant of D3, pillS in effect these two constraints: H A is truth-functionally true, then P(A,B) = 1 and H A is a state-description and B is a truth-functional truth of L, then P(A,B) > o. It is of course the last of Camap's constraints that is equivalent to D6, the way this constraint: If A is a state-description of L, then P(A) > 0, would be equivalent to C7'. 30. For some reason 1956 is given by many, Popper included, as the publication year of Mace's book. Yet my copy of it says "First Published in 1957" on the back of the title page. 31. The concern in question, we shall see, denies him use of F5-F6 below as constraints on P, and ironically enough should have denied him use of E1 as well. 32. For further information on the matter of autonomy, see my paper "The 'autonomy' of probability theory: Notes on Kolmogorov, Renyi, and Popper." 33. More exactly, Renyi's functions are those only among Popper's that happen to be defUled on fields (in the identity sense) and meet, say, constraint (1). By not requiring of his set S that it be a field (in this sense) Popper acknowledges relative as well as absolute probability functions that more traditional writers such as Kolmogorov and Renyi would not 34. Given a more general algebra than Boole's the result can be made to suit all first-order statements, hence the logic of qlUJ11tiflCationai as well as truth-functional derivation. 35. At least for customers who want their logic a byproduct of absolute probability theory. The result from my "Popper's 1955 Axiomatization of Absolute Probability" is generalized in Section 5 of "Alternatives to Standard First-Order Semantics" to cover all first-order statements. 36. The result hinges on P(A,B) amoWlting by constraint F4 to P(A ("\ B,V)IP(B,V) when P(B,V) -¢ o. 37. I lDlderstand of course by glb{P(S'):S' is a finite subset of S} the greatest lower bound (or infunwn) of the set consisting of each P(S') such that S' is a finite subset of S. Since L has only denwnerably many statements, any set of statements of L is sure to be denumerable. The defmition of P(S) here and that of P(S,B) were recommended to me by Kent Bendall. The second defmition is equivalent to one by Field in "Logic, Meaning, md Conceptual Role," THE JOURNAL OF PHILOSOPHY, vol. 74, 1977, pp. 379-409. 38. The proofs in question will be found in: William H. Harper, "A Conditional Belief Semantics for Free Quantification Logic with Identity." ESSAYS IN EPISTEMOUXJY AND SEMANTICS (New York: Haven, 1983), pp. 79-94; Field, "Logic, Meaning, and Conceptual Role"; Hugues Leblanc, "Probabilistic Semantics
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for First-Order Logic," ZEITSCHRIFr FUR MATHEMATISCHE LOGIK UND GRUNDLAGEN DER MATHEMATI~ vol. 25, 1979, pp. 497-509; and Section 5 of Hugues Leblanc, "Alternatives to Standard First-Order Semantics." A Soundness and Completeness Proof already appeared in Harper's doctoral dissertation, COunlerfactlUlls and Representations of Rational Belief, University of Rochester, 1974, but it concerned conditional logic rather than standard logic. 39. The inference here is from a statement of the form '('v'x)(F(x) ::> p)' to one of the form '(3x)F(x) ::> p'. 40. The reader was prepared on p. 356 for the occurrence of 'any' rather than 'every' in these variant results. 41. For a last comment on Carnap's and Renyi's probability fimctions see note 42, where I exploit a point made in the next paragraph of lhe main text. 42. In a letter of 1979 Popper remarked that probabilistic semantics takes up some suggestions which he had published in an Appendix to The Logic of Scientific Discovery, suggestions which he originally intended to develop himself but never found time for. Note that since (i) the sets on which Camap and Renyi defme their respective probability fimctions are fields and hence meet constraints Al' -AS' and (ii) with '-', '&', and ':=' substituting for '-', 'n', and '=', respectively, constraints Al' -A5' allow derivation of the formula A:= -(C &-C) for any truth-functional truth A of L, constraints Al' -AS' deliver by dint of this defmition: A is truth-fimctionally true =df A := -(C & -C), all the truth-functional truths of L. So, Camap's and Renyi's probability fields make for two accounts of truth-fimctional truth, the foregoing one which exploits only constraints Al' -AS' and the one on p. 361 which exploits constraints Bl-B4 or Dl-D4 as well as constraints Al' -AS'. The result robs the latter account of much of its point. Why bother doing probabilistic semantics when a Boolean account of truth-functional truth can be had from constraints Al' -A5' alone? In point of fact, why bother at all with probability functions and the constraints they must meet to count as Camap functions or Renyi ones? Popper's relative probability fields make for jlUt one 8CC01D1t of truth-functional truth as he saw, and so do his absolute probability fields as others saw. 43. See: Hugues Leblanc and Peter Roeper, "Absolute Probability Functions: A Recursive and Autonomous Account," The Tasks of Contemporary Philosophy (Vienna: Holder-Pichler-Tempsky, 1986), pp. 29-49. For formulations and uses of a probabilitic semantics that employ probability relations rather than probability functions, see: C.G. Morgan, "Weak Comparative Probabilistic Semantics," ZErrSCHRIFf FUR MATHEMATISCHE LOGI~ Vol. 30, (1984), pp. 199-212; and John Serembus, Absolute Comparative Probabilistic Semantics, doctoral dissertation, Temple University, 1987.
PHYSIOLOGICAL FOUNDATIONS OF OUR KNOWLEDGE OF THE MATHEMATICAL UNIVERSE J.N. Hattiangadi
I. INTRODUCTION Hume suggested that human knowledge is based on custom or habit, and therefore proposed to found all knowledge on a science of human nature.! It seems that the teon 'psychologism' was only applied to this doctrine in the nineteenth century, by Fries and Beneke.2 At that time there was also being developed an account of all human knowledge in terms of socially developed categories, by Hegel, for example, in a relativised version of Kant's point of view, which we may call 'sociologism'.3 The two crucial areas for sociologism and psychologism to investigate are the philosophy of mathematics and the empirical basis of knowledge, as I will describe these below.4 The point of view that I will outline will not try to reduce everything to biology, but will in crucial places be 'biologistic'. Such an approach, which becomes possible only after Darwin, Mendel, and the development of modem physiology, does, I think, what psychologism and sociologism could only promise. Having agreed to write on these subjects, I had prepared a paper which carefully skirted around the issues and avoided the topic of the philosophy of mathematics as much as possible. The philosophy of mathematics is an intimidating subject. Formal metamathematics, combined with the abstruse philosophical arguments current in the field, makes it difficult to study. And, to make matters worse, I found that I could not endorse any of the philosophies of mathematics that I was willing to discuss. One night I could not fall asleep, because I discovered that for the last ten years, since certain investigations of mine regarding the empirical basis of knowledge had been completed, I did have a philosophy of mathematics, without knowing that I did. Thinking about why it was that I did not know what should have been clear to me, I realized that I was unable to articulate my belief even to myself because it is a well known belief which is easily ridiculed. On the following day, I was still surprised to hear myself admit that I am a Pythagorean, even though I had already decided that I am one, and, in fact
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have been one for over ten years.' I will have to postpone for another time the analysis of the extraordinary situation where one subscribes to beliefs concerning a subject which he holds to be of central importance and to which his thoughts tum regularly, without being aware of those beliefs. This paper is written to explain why I am a Pythagorean, and not a modernist, where philosophy of mathematics is concerned What I have to say, however, is neither very complicated nor as fonnal as those studies which commonly fall under the heading 'philosophy of mathematics'. I do, moreover, state my views with far more confidence than I feelconfidence, that is, not in the truth of what I have to say, which I do have, but in my ability to marshall and present the facts in a field that I have always held in much awe. The modified Pythagoreanism which I shall try to defend may be summarized as the doctrine that the universe has a mathematical structure. Geometrical and arithmetical truths, I believe, are not truths about intuition. Nor are they analytical. They are objective truths (or more usually falsehoods) about the physical universe, just as this is intended in the writings of Galileo or Descartes or Newton. When Descartes maintained, for example, that matter is essentially extension, which is space, he meant this quite literally. For Descartes, as for GallIeo before him, and for Newton after him, the world that the physicist describes is a mathematical structure, and its fundamental laws are mathematical laws of change, or motion. I am a Pythagorean neither in claiming that Pythagoras is right, nor in claiming that Gallleo is right, regarding the details of the mathematical structure of the Universe. On the contrary, their views have been superseded by the modem statistical conception of the universe. Rather, my Pythagorean claim is merely part of what Pythagoras proposed, which Galileo rediscovered, that the world itself has a mathematical structure- even if we are not sure which mathematics exactly it is that describes our world. But whichever mathematics it is, as we improve our understanding of the world since GaIileo's timet 'the features of the universe seem to be more certainly mathematical than ever, however uncertain we become about its details. This thesis about mathematics will be presented in three different categories, each of which has one central thesis. First of all there is a historical thesis in which I will attempt to fonnulate my view more clearly by contrasting it with other views from the philosophy of mathematics, and show how it came about that the correct view was abandoned in favor of one or other of these views. Because I am here primarily concerned to introduce my claims in the second and third theses, I make reference to a number of historical opinions - which I take to be facts - without citing texts or elaborating upon the various details of the arguments in their support. The facts alluded to are extremely well known, and were I to be thorough, this paper would be less accessible. So I shall leave for another occasion the full description of sources and state the thesis as follows. The scientific conception of the physical world from Galileo to the time of Newton and Locke was one in which the world is analyzed as an objective
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mathematical structure. Leibniz proposed a new intetpretation of mathematics which we may call 'idealist', in one good sense of that word. There followed immediately after this an empiricist critique of the Newtonian conception of the world, a critique from which 'the scientific view never fully recovered. Leibniz's beliefs seem to have triumphed on the question of the interpretation of mathematics. But my own investigations into empiricism have led me to revaluate the empirical basis of knowledge, which brings me to the second thesis. This thesis is about foundations, about how one fmds out about the world at all. 6 It is this thesis which provided the central motivation for writing this paper, for this is the thesis to which the intriguing phrase 'physiological foundations' refers. From a modem biological and physiological perspective, our perceptual appamtus cannot be what the British empiricists had thought it was, namely, a passive way of receiving impressions of the world. Rather, perception is closely related to success in action, and it is through our ability to do things that we come to know the world. This is the true foundation of human knowledge, and particularly of our knowledge of the mathematical universe. The third thesis is a description of mathematics, and our knowledge of it. According to 'this thesis, the best conception of mathematics is the one which was abandoned in the eighteenth century. The universe is mathematical. The modern twist is that we know this through our successful physical actions. This view has neither the formal elegance nor the philosophical subtlety which characterizes the so-called 'philosophies of mathematics' which I attempt to discredit in my historical thesis. But, for all its simple-mindedness, I believe that what I say is true, which is my only excuse for saying it at all.
ll. Some Historical Notes My historical thesis is this: all the issues which arise in the philosophy of mathematics are the result of a clash between a certain model for empirical knowledge, on the one hand, and the scientific conception of the world as a mathematics of motion, on the other. The clash arose because Newton claimed, with considerable merit, that his physics, though a 'mechanics' in the sense that Galileo had envisaged, was founded on experiments, or was 'empirical' .7 Interpreting empiricism as a kind of perceptual awareness, which is a model of knowledge of great antiquity, Locke tried to distinguish between the primary (mainly mathematical) properties that belong to things properly and those secondary properties that create impressions in the mind of the perceiver" This Buddhist conception of knowledge as a kind of mental awareness of what is the case, when modified to become empiricism, was the undoing of Newtonian philosophy, at least as a united system. Of course, Newton's physics continued to have widespread influence. But what came to be called 'Newtonian Physics' bore less and
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less resemblance to Newton's original thought on the subject, and, for that matter, to those of Galileo, Descartes, Huygens, or Locke. The sharp contrast between philosophy and science that has since prevailed is but one part of the attempt to pull Newton's teeth. Indeed, a study of all the different philosophers who have called themselves 'Newtonians" and the views that they have held, would yield an amusing story. But none of these stories is stranger than that of the philosopher, David Home, who undennined the entire basis of Newtonian physics with his sceptical arguments, and still called himself a Newtonian; and, it may be argued, rightly so! Arriving at this conclusion requires an interesting analysis of eighteenth century thought. For this I am grateful to Dr. Michael Haynes who has allowed me to see his unpublished writings on the subject, to which I cannot do justice in the brief sketch which follows regarding Home, the Newtonian. Haynes contends, quite astutely, that the history of philosophy of the eighteenth century cannot be studied without paying due attention to the multifaceted dispute between Newton and Leibniz. Apart from the differential and integral calculus which they both claimed to have discovered, they seemed to disagree on nearly everything else of importance-- or is it that what has come to be important to us is determined by what they could not agree upon? Newton was a materialist and an empiricist. He believed in an immanent God, in absolute space and time, and thought that logic, the tool of scholastics, was a sterile instrument. Leibniz was an idealist and a rationalist. He believed in a transcendent God, in relative space and time, and thought all truths derivable from logic. Although eventually everybody accepted Newton's system of the world as the correct scientific system, there were many who were convinced of the truth of certain other things that Leibniz maintained, which may be called things of a 'philosophical sort', such as that individuals are the only substances, or that space and time are relative. Dr. Haynes suggests that it is against this background that we must interpret Berkeley's critique of Newton's theory of gravity, of fluxions, his rejection of matter, and his ontology of a community of spirits and their percepts, as a vindication of Leibnizian thought As a critic, Berkeley turns empiricism itself against Newton, claiming that we could not know the mathematical world which lies just beyond our perceptual ken if indeed all that we can rely upon is our sense experience. While Berkeley denied the theory of matter, and the absolute reality of space and time, he did not deny the existence of objects of common sense, or of spirits, or of God. The power of Berkeley's argument as a critique of Newton's view is undeniable. If we fmd out about the world solely from our experience, how could we possibly fmd out that it is unlike our experience in any respect whatsoever? Newton's claim to have described a mechanics whose features went beyond the content of our experience, but which was nevertheless a product of induction from experience, seems to be a claim that undermines itself. On the basis of this critique, Leibniz's monads come off very well.
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It was Hume's discovery that if we apply Berkeley's critical method in a thoroughgoing way then it necessarily undermines not only matter and the reality of space and time, but also common sense objects, spirits, and even God. Hume's argument takes the form of a tu quoque: he shows that no one can do any better than Newton. He is a Newtonian in the strange sense that since there are no good reasons for accepting any philosophical point of view, he is free to adopt the Newtonian point of view without rational
ground. The rise of modem philosophy of mathematics, then, is a retreat from mathematical theories of motion, a cautious reinterpretation designed to make mechanics appear to be other than what it is. Both the great opinions on mathematics later in the eighteenth century, namely those of Hume and Kant, are Leibniz-like even while they claim to be Newtonian. Hume suggests that mathematics is empty, whereas Kant asserts that it is a feature of how the world must be conceived, which may or may not be as Newton describes -it. One makes Newton's claim innocuous, the other less than objectively true. It seems to have been settled that we cannot live in a world where change itself has a mathematical structure, quite independently of language or of perceptions. Kant's suggestion is that the world appears to us as Newtonian because this is the only way that objects can be perceived, or even contemplated. Kant thought that mathematical truths are universal because they are culled from a distilled set of experiences- arithmetic from the pure intuition of time, as he called this distilled experience of temporal phenomena, and geometry from the pure intuition of space. The idea that we necessarily contemplate space in one particular way was undermined ,by the discovery of alternatives. But the discovery of Non-Euclidean geometries was met by the claim that there is a certain study of a more abstract sort called 'projective geometry' which specified the only possible geometries, of which Kant's was one. This was the defense initially proposed by Bertrand Russell.' Later, Russell abandoned this Kantian view, noting that the kind of geometry that Einstein proposed for use in the general theory of relativity in 1916 was of a sort that he had suggested was impossible in his youthful defense of Kant lO So apart from details, he came to believe that there was nothing in his youthful defense of Kant which was correct Russell's ideas regarding the foundations of mathematics changed dramatically when he discovered modem logic, as Frege's also did, independently. 11 Russell and Whitehead later endeavored to derive mathematics from logic, together with a theory of classes. This seriously undermined the claim that arithmetic is derived from the pure intuition of time and geometry from that of space!2 Neither seems to be necessary for the derivations in Principia Mathematica. Today, two defenses of Kantian thought remain today, neither of which is satisfactory. The [rrst of these attempts to limit what is legitimate in mathematics, while the second proposes to give an expanded version of intuitions. Brouwer proposed that the intuitions which lay at the basis of
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mathematics are those concerning provability .13 On this basis it is possible to say that certain of the derivations used by mathematicians are satisfactory, but not others. Equating mathematical truth with what is provable, in a manner that conforms with intuitionism, leads to the familiar trichotomy of intuitionistic logic, according to which there are true statements (which are proved), false statements (which are disproved) and statements which are neither true nor false (which are the undecided statements). No doubt, the attempt to derive more from fewer assumptions leads to interesting mathematical derivations. If a mathematician should say that this is what he wishes to do, there is no reason why he should not But as a philosophy of mathematics it is unsatisfactory because it does not describe why some of that mathematics which is not constructivist, or not properly founded according to this criterion, works, whereas some of it does not Consequently, it is not satisfactory as a philosophy of mathematics, however nice it may be as a way of doing mathematics. Another way to defend intuition is Poincare's, who suggested that a most abstract study of space is possible, without regard to any restrictions except those that all spaces must have. This is the science of topology. Of the several different ways in which one could study spaces, he conjectured all would give equivalent results. This turned out not to be true when, in 1960, John Milnor showed that in the case of the seven sphere there are divergences. Later it was shown that the axiom of choice and the continuum hypothesis are independent of set theory, suggesting alternative set theories, and creating difficulties for any form of intuitionism that hopes to take all of mathematics into account. Since neither attempt described here can explain all of mathematics, we must conclude that mathematics is not founded on intuition, though it is interesting to note that some of it can be so founded. I take Formalism to be a constructive attempt employing the techniques of metamathematics to found all of mathematics on intuitively satisfactory principles. As was shown independently by Tarski and GMel, a metalanguage which is adequate to this task is richer than the object language. 14 This effectively disposes of the Formalist approach of doing more with less through a process of metalinguistic ascent Once Hilbert's Programme, as this ascent is called, has been abandoned, there is little plausibility in regarding mathematics as a formalism, since we cannot thereby show why the formal structures a mathematician studies, such as number, are useful in such wide domains as accounting, crystallography, and music. To say that a mathematician studies abstract structures, or formalisms, is true some of the time, but cannot be all the truth. There is some truth to the claim that the structures of pure mathematics are merely formal, as we shall see. It is the dependance upon intuitions that I take to be the difficulty for Formalism. Most philosophers in this century have been logicists. They have held that Home was basically right, that mathematics is empty, although their reason for believing this is better than Hume's, namely that mathematics is
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derivable from logic. That logic must have a theory of classes added to it in order to derive mathematics, and that this theory is beset by antinomies, can be met with the hope that they are, or at least will be, resolved. But logicism still fails because GOdel showed, using a quasi-antinomy, that if every arithmetical truth is provable in Russell's logical system (understood to include a theory of classes or sets) then arithmetic is not consistent. GMel's theorems on the incompleteness of arithmetic show that logicism cannot be true, because the assumption that arithmetical truth and provability are equivalent is not a doctrine that is consistent with arithmetic. is Platonism has recently gained in popularity in the philosophy of mathematics, mostly by default, and fmds favour among many mathematicians. 16 Plato believed that mathematics was an understanding of the eternally immutable reality which underlies the comparatively unreal world of change. Galileo's theory of a mathematics of change or of motion itself is inconsistent with such a conception of mathematics, postulating, as it does, an unchanging universe. 17 Indeed, the very possibility of a mechanics is ruled out in Plato's conception of reality. Yet, most of those who claim to be Platonists today would balk at the doctrine of the Timaeus that the world is constructed out of mathematical elements- the line and the circle. It seems impossible to modern Platonists that the real world of stuff should be made up out of these ideal elements. This implies that the doctrine of mathematical objects is about objects in the less than real world of mind. One may, indeed study number as an 'abstract object' in the same way that Arthur Conan Doyle studied Sherlock Holmes, or as Agatha Christie studied Miss. Marple's character. If we are to take mathematicians at their word regarding the infmitesimal, we fmd that it did exist once. It ceased to exist after the discovery of the epsilon delta method. But it exists again now that we have the model theory of Abraham Robinson. Mathematical objects seem to depend for their existence on mathematicians. The usual description of such objects is to call them fictions. It seems that modem Platonism would suggest then Lltat abstract mathematical objects are fictions. (It seems that the word 'abstract' is only a euphemism for the word 'fictional'.) But if this is what mathematics is all about, then it is astonishing that it can be applied to reality in so many ways by so many sciences in the last three centuries. Why novels, poetry, and short stories do not tell us as much as mathematical physics about physical reality (as even some Romantics concede) is a mystery. Fictionalism in mathematics, which is also miscalled 'Platonism', is a comfortably irresponsible way for mathematicians to evade addressing questions concerning their reasons for doing what they do. They claim the same reason that a romantic claims for being creative- namely, self-expression. How miraculously convenient for us all that the whims of Gauss, Bolyai, Lobachevsky, Riemann and others produced non-Euclidean geometries which turned out to be relevant to empirical physics in the case of relativity theory! How remarkably useful that group theory, another
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mathematical 'fiction', has such profound consequences for modem particle theory! Pure mathematics is far too closely bound up with physics (often referred to as 'applied mathematics' when not experimental) and has too much prescience to be dismissed as a mere fiction. It is not that good mathematicians do not do exactly what they like, but Guher that what they like is a product of mathematical maturity: their likes and dislikes have become implicit judgments of hewistic worth. The usefulness of mathematical techniques in investigating the world can only be the result of a close relationship between the 'Platonic' objects of mathematics, and the constitution of the physical universe. It seems to me, therefore, that Platonism, or fictionalism, is a doctrine which is false, but whose virtue lies in allowing mathematicians to avoid philosophical questions which they, I suspect rightly, cannot be bothered to answer. 18 There is another point of view which has had some influence among philosophers, and is close to my own, namely that mathematics is just another empirical science like physics, chemistry, or biology. The most famous exponent of this tradition was John Stuart Mill. Of course, his point of view is based on a theory of induction which does not work for any of the sciences, so there is nothing special about its failure with mathematics as such. 19 In the current philosophical scene Quine holds a similar view, though without appealing to a theory of induction. Quine suggests that all our views are empirical, including those of logic and mathematics, because all our views may be modified in the face of empirical difficulty, if we wish. But if logical truth is empirical, then our acquiescence to logical consequence is a contingent decision, in accordance with the deduction theorem.. What he does not give us any indication of is why, in that case, we bother to use argwnents at all, since it all boils down in the end merely to what we are inclined to accept Consequently, Quine's point of view is unsatisfactory as it stands,20 because it does not show us why mathematics is done as it is. The only empiricist philosopher of mathematics who has investigated the issue to find out why mathematicians use proofs at all was Imre Lakatos. He suggested that in informal mathematics proofs are used to make better use of information gained from refutations. He offers as an example how Cauchy proved Euler's conjecture about polyhedra, Le., that the number of edges minus the number of vertices plus the number of faces is equal to two. Euler's conjecture was nevertheless found to have numerous counterexamples. Lakatos suggests that proofs that do not prove can still improve our knowledge by incorpomting the guilty lemma (or premise) into the conjectme. (The proof would still apply to all those objects which were not disqualified by the lemma, for example.) But Lakatos' views are incomplete and unsatisfactory. Formal mathematics, presumably, does prove for the sake of proof. How is 'this to be understood from the point of view of the empiricist? Furthermore, the method of lemma-incorporation is inconsistent with the point emphasized by Quine, namely, that in any
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derivation with a false conclusion it is not logically possible to detennine which premise is the 'guilty lemma'. Taken by themselves, Lakatos' views do not work. Added to those of Quine, they are not consistent. So having already noted the inadequacy of Quine's view by itself regarding mathematics, it seems that empiricism about logic and mathematics, however much in vogue, cannot square with the way in which mathematics is done. To summarize these historical notes: The philosophy of mathematics is always described nobly, as a search for foundations, a way of making the results of mathematics more certain. But it is rare that a mathematician fmds that she has to turn to philosophy to be sure that what she says is correct By and large mathematicians do famously without the help of philosophy. The search for the foundations of mathematics, if I am right, is a disguised flight from the discoveries of mathematical physics. This is for the very good reason that it is difficult to state how we can know that mathematical physics can be literally true if it is based on experiment and observation. We must go back and see how to defend Newton's Pythagorean metaphysics from Berkeley's critique. If we can successfully do that, then perhaps we can avoid the necessity of finding that mathematics must be either subjective, that is to say based on intuitions, or innocuous, that is to saY' empty. We must tum to the empirical foundations of science.
III. Foundations of Our Knowledge Examining the Newtonian point of view, we find that it requires that we fmd an answer to the problem of knowledge. We cannot abandon the claim that mathematical physics is empirical, because nothing since Newton has shown us that experiments do not tell us about the world, or that there is another and better way to find out about it. What is the mistake that led scientists in the eighteenth century to think that the gap between the knower and the known is unbridgeable if mathematics is believed to be about the real world? It is clear to me that the error lay in thinking that our knowledge of the world comes from perceptions, as Locke proposed. A survey of modern Darwinian theory would suggest that perceptions do not play the role that was assigned to them in the tradition of British Empiricism.21 The British Empiricist tradition attempts to trace the source of all knowledge to the content of our perceptions, calling them impressions or ideas. It seems beyond doubt that we fmd out much about the world by means of our perceptions. But if we study the physiology and adaptive value of our perceptual apparatus, we derive quite a different estimate of what can and cannot be learned about the world from our percepts. Our perceptual apparatus is derived from that of our animal ancestors. According to our understanding of the course of evolution in the last four billion years or so, the fonns of life which have survived are those which
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were better able than their nearest cousins to adapt to the particular environmental niches which were available to be exploited. In these contexts, their perceptual apparatus certainly played an important part in their adaptation. For unlike plant life, animals are unable to absorb energy directly from sunlight Consequently, locomotion and the ability to track down food are vital features in the survival of any of these forms of life. Furthennore, the particular form of perception found in any species of ·animal is closely related to its foraging activity. Another important fact about animals is that they feed not only on plants but occasionally on each other. Those species which specialize in any form of hunting have evolved complex tracking systems for prey, whereas the prey have developed complex ways of hiding from predators, warding them off or fleeing from them. In a great many cases forms of perception among prey are well developed to avoid predatory attacks. Another important aspect of animal evolution is the proliferation of mechanisms which allow the sexes to make contact in order to procreate. Because animals depend on plant material and other life forms for their energy, they have to disperse to find their food. It becomes necessary, therefore, to use their perceptual apparatus to track down other members of the species, and to pick out members of the other sex, for the purposes of procreation. Many animals possess various forms of display to attract the attention of the opposite sex and to warn away members of its own. Among herds of species which intermingle, such as the ruminants of the African rift valley, for example, the different species are clearly marked, allowing for easy recognition. The perceptual apparatus, in all these cases, is well tuned to pick out important and relevant aspects of the environment on which its survival and propagation depends. In this account I have stressed the close relationship which exists between the perceptions of an organism and the characteristic actions that it perfonns in order to manoeuvre successfully around all those things which affect its ability to survive and propagate its own. It is this close relationship between perception and action in all living forms which throws doubt on the model of perception that is found in eighteenth century British Empiricism. Had God made us in order to read His or Her book of nature, as part of a larger plan, perhaps, we would no doubt have had a perceptual apparatus designed to fmd out how things truly are, at least to the extent necessary for our salvation. Adopting as we do a Darwinian explanation of our origins, we must not suppose that the content of our perceptions is veridical.. All we can conclude is that our perceptions allow us to act moderately successfully in various circumstances. As we shall see shortly, it is most important to know those circumstances in which we can act successfully. Life among mammals is never easy. During most of the history of mammmalia, most individuals have been on the verge of starvation. Nearly all the species that have come to be have become extinct, leaving but a small percentage behind. In this respect mammals are quite like other life
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foons. To imagine in these circumstances that they could have diverted energy to the formation of a veridical perceptual system is highly unlikely. The most that such species could hope to evolve would be some perceptual apparatus as adequate as, or slightly superior to, the apparatus of its nearest rivals in responding to the opportunities and the dangers in its environment22 On the other hand, in its own normal environnlent where it is most successful, an organj~m could not be systematically deceived to such an extent that it responds inappropriately to its environment in a systematic way. Students of animal behavior have adopted a model, which was found to be of great value in physiology, to describe how organisms perceive the world as part of their adaptation. This is the 'trigger' model of action and perception. It represents organisms as repositories of stored action patterns which are by and large characteristic of the species. These action patterns are elicited by simple cues in the environment, and allow the organism to respond appropriately to them. The model of organism being assumed is a trifle mechanical. I do not want to enter into the discussion here whether such a model is good enough to capture what we mean by 'mind'. My own view is that if it does, it cannot do so without several mechanisms which do not conform to the robot-like model that I am considering. My claim here is not that human, or for that matter animal, consciousness can be reduced to the 'trigger' model of action. It is rather the claim that even if it is not sufficient to explain our perceptual apparatus, the trigger model is necessary for its understanding. We have evolved from creatures which were robot-like. We preserve a great many of the characteristic physiological arrangements of our ancestors. Even if we have developed an organ called the 'mind' which, according to some, escapes description, our physiology is still basically that of apes. It is nevertheless an important part of my thesis that our knowledge is not part of the mind, but is diffused more generally in our physiognomy. With the trigger model, an organism never perceives the whole environment, which is far too complex to be grasped by any being which is not omniscient. Rather, what the organism perceives is a simple feature of the environment which the perceptual apparatus is designed to pick out, and this acts as a trigger which releases a complex action pattern. A hungry bird of prey is coasting along lazily in the sky, or so it seems to us, until it spots a tiny rodent moving a quarter of a mile away, whereupon it swoops in a precipitous dive, landing on top of the rodent- which is itself moving. Grasping the rodent in its talons, with the same motion, it disappears into the sky. Its dive is extraordinary, because if it is a few inches 100 long, it will destroy the bird, and if a few inches too short, or off its mark, the bird goes hungry. We do not believe that the mind of a hawk is capable of calculating its flight path, but we do recognize the extraordinary skill and adaptation exhibited by this feat The bird responds to a simple cue which elicits the dive and which consists of a response to a
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characteristic movement of the rodent. As it dives, it approaches its prey by manoeuvring adroitly in response to simple aerodynamic cues. We would search in vain among the percepts of the bird for all the information which it must presuppose in its flight to successfully hunt a field mouse. Human beings are built on the same general principles. Driving on a highway with a colleague, discussing a philosophical point, one responds to the movement of other cars and to the signs as they pass by with extraordinary skill even for a relatively unskilled driver like me. 23 A slight twist of the steering wheel, or a wrong pedal pushed, could lead to a serious accident. What one perceives on the road acts only to elicit the complex learned action patterns called 'driving' that are stored in one. An illustration of the robot-like elicitation of actions is when one is sent out to pick up groceries, and fmds oneself, bewildered, in one's office at the University, having driven there automatically along the route to which he has become daily accustomed. The extremely complex actions which we perform are so often appropriate to the circumstances not because we are omniscient, but merely because the simple cues that elicit our actions are accurate as indicators of the environment. In extremely complex and fast moving environments we can learn to pick out just those transitory features in our perceptual field which allow us to deal adequately with our tasks. When we adequately respond to a complex environment E of a particular kind by an equally complex action A, the existence of a predilection in us to respond to a simple cue S which elicits the appropriate action A may be described as an implicit knowledge of the statement 'Whenever S obtains, E obtains'. In action we exhibit a propositional attitude which, if true, may be described as the knowledge that is expressed in such a statement of universal form. Because environments are complex, we can be mistaken about them. The farther we get from our natural habitat the less trustworthy are our estimates of the environment. We are consequently much more confident in or near familiar surroundings than we are far away from them.24 Our percepts, then, give us no propositional knowledge of the world, except to the extent that they too are involved in skillful actions. Our understanding of the world comes to us not in our percepts, but with them. We know about our world to the extent that the propositional presuppositions of our actions, presuppositions of the form 'whenever S obtains E obtains, in familiar surroundings', are true. H we look at all the remarkable skills we possess, then all of them attest to a rich general knowledge of local conditions. Our knowledge of the world comes with simple cues regarding when we may and when we may not trust our presuppositions, but even these cues work better in our natural habitat than they do in environments far from our own. When Bacon suggested that we experiment to fmd out about the world, he suggested this to facilitate perceptual knowledge of forms or natures. As it happens, the experimental tradition has given us new practical knowledge of
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the world which far exceeds anything which can be represented in our senses, or was imagined by Bacon. The connection between science and technology is primarily through the establishment of new experimental skills which are found useful, and not in the application of discovered truth, as Bacon had hoped. Technologists have to find uses for routines that are found trustworthy in the pursuit of science. The reason why an experiment can be relied upon to test a theory is not because it leads us to perceive something veridical, but rather because, as a routine performance, we can rely upon the knowledge embodied in that skill. To the extent that we can learn anything about the world from them we must reinterpret even simple observations as skills, or as elementary experiments. From this biological perspective it is not at all necessary that the world appear to us as it truly is. The cue which allows us to act appropriately is merely a device, not a representation of the world. But in those organisms which monitor their environments constantly (like us) such perceptions are part of an ovemll pictorial space which must bear some structural resemblance to the space of the environment if the cues are reliable. 25 But seeing is not believing. We believe what we must believe in order to do what we do when we do it successfully. In a sentence, my claim is that we rely upon routines which are well tried. If these routines are perceptual we may call them 'observations'. If motor, then 'actions'. And if intellectual, then 'procedures'. But in all cases what we rely upon are well tried routines, or well honed skills. The gap which Berkeley and Hume found between our perceptions and the world led to two hundred years of scepticism about Galileo's, Descartes' and Newton's conception of the mathematical world for a reason which was at least partially sound: no matter how deeply we inquire into the content of our perceptions we will not fmd there any feature which goes beyond the perceptual, suggesting the 'primary' qualities that GaIileo proposed. We do, however, know much about the world that goes beyond its perceptible features, though the knowledge is restricted to genernl features of local conditions in familiar habitats. It seems that we need not give up the scientific conception of a real mathematics of motion on the basis of the attack from the empiricist critique. All we need to do is to reinterpret empiricism as the experimental tradition, and we will have reinstated both of the claims of the seventeenth centwy physicists: that the world is mathematical, and that our knowledge of it is founded on contact with it in experiments.
IV. On Mathematics and Our Knowledge Thereof We live in a mathematical world, and we are mathematical creatures in it. Our spatial physiological structure and our ability to get about in the world show us to be of a piece with the world. Being adapted to our local environment we exhibit in our successful and routine actions an implicit
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understanding of the mathematical sbUcture of the local niche. It is this which is the foundation of all knowledge that we possess concerning mathematics. There are three subsidiary theses that I will defend in this section: First of all, that mathematics and axiomatics are not the same thing. Logical truth, I claim, is either subjective or empty, where mathematical truth is neither. Axiomatics is a logical marshalling of mathematics, which gives mathematics an air of triviality, not because the content is trivial, but because the fonn is trivial, being logical. Secondly, I suggest that prior and familiar mathematical skills are the 'laboratory' in which the conjectures of pure mathematics are empirically tested. Since mathematical skills are eventually grounded in our ability to manoeuvre in the physical world, pure mathematics is just as much 'about this world' as is 'applied mathematics', though the latter is a foundation for the fonner. Thirdly I examine the amazing fact that so many mathematical skills are interrelated. To believe, as is common, that this is a sign of logical connection merely confuses logic and mathematics. Rather, this should be taken as a remarkable fact about the world in which we live- its mathematics infuses and stamps itself on so many of our skills, in much the same way that it manifests itself in the symmetries of a crystal. Consequently many of our computational skills can also be seen as manifestations of aspects of the world that we inhabit Our primary understanding of the world comes to us through the routines that we can successfully perform. Jean Piaget got this point exactly right, though he came to it while attempting to develop a Kantian conception of our spatial intuitions among children as they develop their understanding. But if we study how a frog tracks a fly, or a rattlesnake a rodent, we find that perceptual systems have very different a priori presuppositions which make organisms better or worse in their adaptation to their environment We conclude that the mathematical knowledge that any life form possesses cannot be true generally, but is a general understanding merely of its local habitat or territory or its ecological niche or that aspect of its environment which it successfully exploits. But this kind of implicit mathematical knowledge that we possess as part of our adaptation to our local niche does not constitute our knowledge of mathematics as we ordinarily understand it. Mathematics is a subject that we can smdy in a University. If all organisms have the basic implicit knowledge of some aspects of the mechanical universe, it does not follow that they are all mathematicians. It is only among humans that we fmd mathematics journals, or a dedicated group of worker-humans whose main product is new mathematical results. To understand the relationship between the- physiological foundations of mathematics and the discipline of mathematics, we must make an important distinction that is frequently neglected. Mathematics as a statement of facts, such as the ratio of the sides of a right triangle, or the fact that certain series of numbers add in a certain
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way, was known in antiquity as geometry and arithmetic long before Euclid axiomatized geometry. Such was the high regard in which Euclid's axiomatization came to be held, that over time the word 'mathematical' has come to have as one of its meanings 'axiomatical'. But in fact mathematics is a subject of much greater antiquity; Euclid's axiomatization of geometry was a comparative latecomer to the scene. The axiomatization of arithmetic was still later accomplished, by Dedekind and also by Peano, not so many years prior to this century. For these reasons I would like to distinguish between mathematical fact and mathematical theorem. For the sake of this discussion let us call a theorem a derivation in an axiomatic system which mayor may not be mathematical and mayor may not be factual, whereas what I call mathematics will be certain facts of geometry, arithmetic, and certain other new subjects such as the differential calculus or the calculus of probability, whether or not they come in an axiomatic fonn, but which are algorithmically related to the earlier mathematical subjects. What is characteristic of mathematical facts is not a nature that they possess, but that they originate in the intellectual traditions of geometry and arithmetic. I will leave the task of determining the true nature of mathematics to those of you who insist that our subjects have natures.26 If we glance at the mathematical sciences in antiquity, we find that they are both closely related to practical action. Land mensuration and keeping accounts are two examples of their use. Looked at thus, they are not much different from our knowledge of the properties of medicinal roots for use in alleviating suffering. Such lists, when truthful, may also be described as knowledge. They are equally closely related to practical action. But if we compare the two kinds of knowledge or purported knowledge, there is a striking difference between them. Knowledge of trees and roots seems to be relatively discrete or atomic in structure, whereas the knowledge of mathematics is holistic, in the sense that its facts turn out to be interconnected in a very remarkable way. This interconnection must not be confused with the logical connection of statements. Any knowledge which we possess in an explicit form is expressed in statements. Statements can be related to each other by the relation of entailment, or of contradiction. In this respect, any statement about the world is interrelated with a denumerable number of other statements in a trivial way. If facts about trees and roots and their uses are taken as an axiomatic basis, for example, we do not think that it is surprising if from them we could derive, by the use of rules of inference, a wide variety of complex statements. While all knowledge can be axiomatic in this sense, there is another sense in which our knowledge of trees and roots in classical systems of medicine is not like mathematics: if we study our knowledge of roots and plants we would be most surprised to fmd that the knowledge of one kind of plant and that of another were interrelated in such a way that if we had the first we could work out the second by an algorithm.
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We have a great many skills but all of them are different from each other, and where we know explicitly what must be the case for some skill to be appropriate to a situation, this knowledge in tum is usually a discrete piece of knowledge. Mathematics, it turns out, is unlike that What is surprising about apparently discrete mathematical statements presupposed by discrete mathematical skills is the way in which they are nevertheless interrelated, without any axiomatic regimentation. The relation of number to space is algorithmic, and not axiomatic. Because theoretical mathematics is stated in language, it can be axiomatized, of course, but this might only serve to teach us even more about the algorithms. Logical derivations themselves may be studied mathematically. Logic has its own algorithm, but that does not take away my point. From a logicist's point of view it is only to be expected that mathematical truths are so beautifully interrelated, because all mathematical truths are regarded as empty, and therefore trivially interrelated. 27 But if GOdel is correct in that the truth of a mathematical statement is not the same as its provability, then the interrelatedness of mathematical truth as opposed to any other kind of truth is one that deserves more study. The fll'St recorded intimation of the unity of all mathematics was the Pythagorean doctrine, according to which all is number. However wild his doctrine may seem when applied to ethics and the advisability of eating beans, it gives an acceptable account of the workings of geometry. It is precisely because counting, and the objects presupposed by our skills governing counting, give us an insight into shapes that the reduction of geometry to arithmetic was such an important event in the history of ideas. Were it not for this success, the discovery of the irrationality of the square root of the number two would not have excited remark in antiquity. It is the interrelation of mathematical techniques which gives rise to the study of pure mathematics. Pure mathematics is the study of pure technique, where every technique is grounded eventually in an established skill. The knowledge of mathematical theory which results from the study of pure mathematics is not, however, the basis on which our mathematical skills are founded, but quite the contrary. Because our abstract mathematical knowledge is holistic, we are tempted to think that we understand how to do what we do with number or figure only because we have that knowledge. But a look at the history of mathematics tells us that this is not so. Pythagoms had quite an elaborate theory of number, which was known as the knowledge of the odd and the even. But in retrospect it surprises us that Pythagoras did not have the concept of zero. If we look at any modem definitions of the operation of addition or multiplication we will find that those operations are considered indefinable unless we are able to say that there is a number M such that any number N added to M gives the number N, and such that any number P multiplied by M gives us the number M. Since Pythagoras did not have the concept of zero we might conclude that he did not know how to perform the basic operations of addition, subtraction, multiplication, and division. But to do so
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would be a mistake. The ability shown by ancient Greek mathematicians with number series or Diophantine equations leaves no doubt of their ability to add and multiply. It is just that mathematical theory was not as well developed. A similar case can be made about the discovery of the differential calculus by Newton and Leibniz and its relation to the theory that came to be adopted later, called 'analysis'. As a general rule it seems to be the case that our skills at manipulating number and figure far exceeds our theory. In order of richness, therefore, we have the following: knowledge implicit in mathematical skills > explicit knowledge of mathematical truths > mathematical theorems. (Or: Techniques > theories > theorems.) Although this is true at any given time, there is a certain relationship between explicit knowledge and skills that is important We are organisms that are adapted to our niches as well or as poorly as other life forms. We are remarkably similar physiologically to our nearest species, the chimpanzee. We may ask ourselves what value our relatively untrustworthy explicit knowledge can be to us if a chimp gets by without it. If we are adapted to the world in the fIrst place, what is the advantage that we reap from the search for truth? What is the practical value of uncertain knowledge which can only be founded on practice, when we have the practice all along? The answer is this. Our skills work well only in our niches. Our adaptation is only a little bit better than that of our competitors. It is not perfect. These facts of Darwinian theory tell us that any form of life that experiments considerably with changing habitats must change its skills in order to survive. Among human beings, the use of explicit knowledge from a biological perspective lies simply in its potential as a modifier of our skills. An example outside of mathematics will be revealing. The clearest example of 'the relationship between explicit knowledge and natuml ability is to be found in the relationship of coaching to sport. If Ben Johnson is by far the fastest sprinter in the world, why would he need a coach? If a coach knows more about running than Ben Johnson, why is the latter the fastest sprinter? And if not, how can the coach have anything of use to offer? IT we study an athlete in training, however, we find that to remain on top of his fonn or to train for a major event, the natural ability of the athlete must be modified in little ways for improvement Starting out of the block, for example, is a learned technique, and not entirely natuml. Small pointers from a coach can often lead to significant improvements in the competitive ability of a sportsman. If this were not so, the world's fastest sprinter could not learn from anybody. That he can learn shows that a theoritician, who is a poor sprinter, may yet, as a theoritician, teach another to sprint better than he otherwise could. Explicit knowledge may not be able to tell us why Ben Johnson does what he does so well, at least not completely, but it may nevertheless help him to do what he does better.The role of explicit knowledge lies in the improvement of skills. In mathematics, this is most evident in learning new techniques to do old tricks more easily, or more reliably, or even just differently. Thus, in
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mathematics, there is this odd relationship between manipulative skills with symbols and the theories of mathematics: the theories help give us more and better skills, while, as a direct result the skills, becoming richer, afford more scope for the study of theory. An example will illustrate this. Multiplication is an old technique that is well known. We can easily understand what a square or a cube of a number is in terms of multiplication, and thus also the general concept of a number to the power n. We can equally learn, using our old notion of division, that if a raised to the power n is divided by a, the result will be a to the power n-l. Generally, if we divide a to the power n by a to the power m, then we get a to the power n-m. From this we can conclude that a to the power negative m is nothing more than dividing one by the number a to the power m. As a consequence we can derive that a to the power zero (or n-n) is 1. All of a sudden we have a new operation called exponentiation, which we can practice, and fmd 'that it gives us all sorts of wonderful new techniques. Logarithms, for example, cannot be understood until we have a clear gmsp of the technique of handling exponents. These in tum give us a new way to calculate what are otherwise very tedious results. (Here, in fact, lies the clue to the importance of good notation in ma'thematics-- it supports good mathematical habits. But once we have a technique of this kind we can investigate it as an interesting object in its own right. What would happen, if, for example, we were to raise two to aleph zero? Such questions can be asked and answered only because in our old domain of natural numbers, in our well established niche, as it were, we can handle exponents with great facility. We are able to ask if, for example, we called the nUlllber obtained by raising two to the aleph zero by the name 'aleph one', and two raised to that number 'aleph two' and so on, whether there are cardinals which are strictly more than one such number and strictly less than the next higher cardinal in the series defined by exponentiation. If we were unsure of our operations of set theory, or of exponents, or of our ability to check whether one of Cantor's claims are true or not, then we would be unable to ask such a question, nor would we have the slightest clue as to how it may be answered, or how we may determine that the question is not answerable. As we increase our mathematical skills, our mathematical theory becomes that much less descriptive of the knowledge that we implicitly possess in the perfonnance. In general, then, our mathematical theory is always much less infonnative than necessary to understand our mathematical skills, but it is nevertheless good enough to improve our skills here and there. When we come finally to deductive methods, we have a new dimension in interrelating theories. But the fact that pure mathematics can be axiomatized does not make it unique in this regard. Spinoza's ethics was also axiomatic in its fonn, as was Newton's physics.2I It is interesting that logic has its own algorithm, which may be generated out of set theory by the metamathematical techniques devised by Tarski, for example. This does not show that mathematics is specially related to logic, but only that
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mathematical logic is a kind of mathematics. That is, to use a phrase beloved of logicists, merely a tautology. The astonishing interrelatedness of mathematical facts did suggest that there is a close relationship between mathematics and axiomatics, which is basically Leibniz's hunch. The development of proof procedures in the nineteenth century makes this point of view even more attractive. It is not at all swprising that with the development of rigor and of axiomatic technique in the nineteenth century it became the next step at the turn of 'the century to derive mathematics from logic. Once we accept the implication of GOdel's theorem for the incompleteness of the axioms of arithmetic, however, we can no longer accept logicism. We need not give up our appreciation of proof procedures as algorithm, merely as foundations. The success of Russell and Whitehead, such as it was, in deriving as much as they did from as little as they started with deserves a remark. It seems to me that their success must be attributed to the fact that they took mathematics to be its axiomatics, and derived the axiomatics from logic (including a theory of classes, of course). 29 It is revealing, though, that Russell remarked that mathematics only began, properly speaking, with George Boole. Of course it is only about then that axiomatics and mathematical rigor came into its own. It is not swprising that Russell thought that mathematics began about then, because rigorous axiomatics only begins about then.. For a logicist there is no more to mathematics than its axiomatization. We must recognize that the remarkable unity of mathematical knowledge arises only from the fact that Pythagoms and Galileo accidentally hit upon about space, time, and motion. Because we reflect a mathematical universe, its knowledge is implicit in so many of our skills, in different ways. Therefore, we find remarkable correlations between mathematical knowledge in different fields. Our physiology manifests the mathematics of the universe as surely as a crystal of common salt exhibits symmetries which reflect the geometry of the space in which we live. Our physiology exhibits 'the dynamics even more explicitly in our skills.. So completely do we exhibit the dynamics of the world, that every skill we possess, including even the very specialized linguistic ones, exhibit the mathematical structures which physicists and molecular biologists are groping to find On this construal of mathematics, we must assume that we are basically able to do any mathematics at all because we have the skills necessary to survive in our niche. It follows that the relationship between pure and applied mathematics is not what it is ordinarily assumed to be. If I am right, it is applied mathematics which is basic, and forms the testing ground for theories in the domain of so-called 'pure mathemabcs'. Pure mathematics is the science of the pure technique of manipulating symbols, whereas the mathematical reality that we know in our basic skills foons the experimental laboratory in which the theories of pure mathematics must eventually either work or fail. For this reason I would count myself also as an empiricist where mathematics is concerned, because all the sciences use
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well established routines to test hypotheses, and mathematics is no exception to this rule.
I should add that logical truth, unlike mathematics, seems to me be empty. The skills on which logic relies are our skills with our explicit language, and not those skills which we need in our general dealings with the world. Logical truth yields us a device to handle our own statements better. but in the end it tells us nothing about what is the case. It seems that logical truth does depend on the logical or grammatical particles of our language. Against recent tradition in the philosophy of mathematics. therefore, I must endorse the judgment of Galileo, Descartes, Huygens, Newton, and Locke. One concludes that the logic beloved of scholastics, on the one hand, and mathematics as envisioned by Galileo to describe motion itself, on the other, must fall on opposite sides of the great seventeenth century divide: logic is either subjective in the sense of being a human product, or uninformative about the world, whereas mathematics is neither. Mathematics has given us an insight into the nature of the universe, which distinguishes the rise of modern science, and for better or worse, gives us the possibility of modem technology.30
388 ENDNOTES 1. See: David Hmne, Treatise on Human Natwe, ed. Selby-Bigge (Oxford: Oxford University, 1968). 2. See: Nicola Abbagnano, "Psychologism," trans. Nino Langiulli, in The Encyclopedia of Philosophy, ed. Paul Edwards (London: Collier-Macmillan, 1967), Vol. 5-6, pp. 520-1. 3. The expression 'sociologism' is rarely used to describe one's own philosophy, but has a certain vogue today to describe a widespread hypothesis, to the effect that every feature of human knowledge has its origin in some feature of hwnan society- be it a social category of thought, as in Durkheim's school, a politico-economic factor as in one of the schools following Marx, a 'structure' as in another school, or in a nondescript sociology as in the school from Edinburgh which calls itself the 'strong programme'. I do not know who coined the phrase, though I first came across it in: Karl R. Popper, The Poverty of Historicism (London: Routledge and Kegan Paul, 1957). 4. As Mark Notturno has identified, the two classic sources which discuss psychologism critically are Frege's (and, derivatively, Husserl's) writings concerning the nature of logical and arithmetical truth, and Popper's investigations of the empirical basis. See: MA. Notturno, Objectivity, Rationality and the Third Realm: Justification and the Grounds of Psychologism (Boston: Martinus Nijhoff, 1985). 5. Mr. Avshalom Adam, who studies conventionalism in astronomy and in philosophy with me accused me in a heated argwnent of being a Pythagorean, for which I am grateful. I had always imagined that point of view to be ridiculous, perhaps due to the influence of Bertrand Russell's views on mathematics, but in my defense against Adam's spirited attack I discovered that in all these years my excitement in discussing Galileo, Descartes, and Newton stemmed very often from my agreement with their 'Pythagoreanism' as I interpret it, which, because I subconsciously believed it to be indefensible today, I did not maintain. This experience has led me to wonder whether many historians of science who passionately expound and defend a certain philosopher or scientist might benefit from asking whether in fact their love of history is sometimes only another aspect of their unwillingness to defend a point of view which they secretly share with their hero. Along these lines I suspect that something like my view is implicit in the writings of Alexandre Koyre, who must therefore be credited with it, if not Edmund Husserl. See: Alexandre Koyre, From the Closed World to the In{miJe Universe (Baltimore: Johns Hopkins, 1957) which is a more accessible account than his classic Galileo Studies, trans. S. Drake from fro of 1939 (Atlantic Highlands: Humanities Press, 1978). As for Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology, trans. David Carr from german orig. of 1937 (Evanston: Northwestern University, 1970), it seems to prepare the way for the work of Husserl's student Koyre though Husserl himself is writing this as an introduction to his phenomenology, with its obvious Kantian overtones. Koyre therefore deserves much of the credit for such a courageous stand on mathematics in the heyday of Russell's logicism. 6. See: "Empiricism from a Biological Perspective" in: J.N. Hattiangadi, How is Language Possible? (La Salle: Open Court, 1987), in which I propose the central thesis of the second sort in this paper. It may also be found in: IN. Hattiangadi, "Knowing That, and How," METHODOLCXJY AND SCIENCE, Vol. 17, no. 3, (1984).
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7. Newton's claim is to be f01.Dld in the "General Scholium" at the end of Book ill of Isaac Newton, Mathematical Principles of Natural Philosophy, ed. F. Cajori, trans. A. Motte from Latin orig. of 1687 (Berkeley: Berkeley, 1968). 8. Locke was closely allied with Newton's point of view in the eighteenth century, though it is something of a guess that Newton agreed with Locke regarding the importance of percepts as the source of knowledge. Newton does not write much about these matters, but it seems to me that had he not agreed with Locke, this would have been noted in the Leibni7lClarke Correspondence. See: H.G. Alexander, 00., The LeibnizlClarlce Corresp~nce, from the dispute dating from about 1705 (Manchestel': Manchester University, 1956). 9. See: Bertrand Russell, An Essay on the Foundations of Geometry (New York: Simon and Schuster, 1959). originally, 1897. 10. See: Bertrand Russell, My Philosophical Development (New York: Simon and Schuster, 1959), in which Russell describes his earlier work as false in every respect except on matters of detail. It is the abandonment of Kant's philosophy which leads Russell to reexamine the arguments of Berkeley and Hurne in: Bertrand Russell, The Problems of Philosophy, Home University of Modem Knowledge Series (London: Thornton Butterworth, 1936), originally 1912, in which are laid down the central issues which were to exercise his followers, who dominated philosophy in the years following, sometimes in agreement with him and sometimes qualifying his point of view. 11. See: Bertrand Russell, Principles of Mathematics (London: Allen and Unwin, 1956), originally 1903. 12. The derivation is accomplished in: Bertrand Russell and Alfred North Whitehead, Principia Mathematica (Cambridge: Cambridge University, 1910-13), in 3 vols. 13. See: L.EJ. Brouwer, ''Inaugural Lecture, 14 Oct. 1912," trans. A. Dresden, BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 20, 1914. A satisfying interpretation of modem intuitionism is to be found in: Karl R. Popper, Objective Knowledge (Oxford: Oxford University, 1972), pp. 128-140. Popper shows the interesting relationship between Brouwer's thought and that of Kant See also: L.E.J. Brouwer, "Philosophy and Mathematics," PROCEEDINGS OF THE TENTH INTERNATIONAL CONGRESS OF PHll.OSOPHY, Vol. 1; and Bertrand Russell,
My Philosophical Development. 14. See: Alfred Tarski, "Concept of Truth in Formalized Languages," in Alfred Tarski, Logic, Semantics, MetQ11&Qthematics, trans. Woodger (Oxford: Oxford University, 1956), orig. 1931. Tarski showed that any metalanguage rich enough to define the semantics of an object language satisfactorily is richer than the object language. 15. For an excellent survey of the weaknesses of logicism, see: Alan Musgrave, "Logicism Revisited,.. in THE BRITISH JOURNAL FOR THE PIDLOSOPHY OF SCIENCE, Vol. 28 (2), 1977. 16. Most mathematicians have adopted this view, and so, too, it seems did Kurt G&lel. See: Hao Wang, From Mathematics to Philosophy (London: Routledge and Kegan Paul, 1974). 17. On this point, I confess, I depart from the views of Koyre and Husserl, who seem to regard the scientific revolution as a fulfillment of a Platonic
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if taken 100 far it has the consequence that nothing new is ever said, which no longer explains why we choose who we do to study influences. (Preswnably Galileo is important because something that he said was not said by Plato, or anyone else.) I tend to look for the origin of ideas in problems, as I have described them in: J.N. Hattiangadi, ''The Structure of Problems," PIllLOSOPHY OF THE SOCIAL SCIENCES, Vols. 8,9, (1978-79), md in: I.N. Hattiangadi, "A Methodology Without Methodological Rules" in Langu.age, Logic and Method, 00. R. Cohen and M. Wartowski (Dordrecht: D. Reidel, 1983). Since problems are difficulties in existing viable theories, and solving them involves modifying old theories, all new theories are bound to resemble old theories in many respects. But since the 'theories are proposed to solve problems, it is they which determine criteria for satisfactory solutions. Hence, the origins of Galilee's thought are to be fO\Dld in the intellectual situation of Copernican thought, which defines Galileo's problems. 18. For an excellent discussion of this, see: Paul Benacerraf, "Mathematical Truth," THE JOURNAL OF PIDLOSOPHY, Vol. LXX (19), 1973. See also: Philip Kitcher, The Nature of Mathematical Knowledge (Oxford: Oxford University, 1983); Michael Hallett, Cantor ian Set Theory and Limitations of Size (Oxford: Clarendo~ 1984); and Penelope Maddy, "Mathematical Epistemology: What is the Question?" THE MONIST, Vol. 67, (1), 1984. 19. The failure results from the fact that for Mill's induction to be the fOWldation of all knowledge, we need another principle of induction to establish it. This leads either to an infmite regress, a vicious circle, or the arbitrary assumption of the principle. The last alternative is consistent, but not much better than adopting the various theories to be tested arbitrarily. 20. See my forthcoming review of The Philosophy of W.V.Quine, in the Library of Living Philosophers series, ed. Schilpp and Hahn, La Salle TIl: Open Court, 1987, the review to be published in Philosophy of the Social Sciences. 21. See: Hattiangadi, "Empiricism from a Biological Perspective," in How is
Language Possible? 22. Michael Ruse, who begins his Taking Darwin Seriously (Oxford: Basil Blackwell, 1986) by taking Darwin seriously, takes others to task for neglecting this. But when he comes to his own views, at the end of the book, which he calls 'Darwinian' theories of knowledge and ethics, he forgets that the sort of mechanisms that he proposes are not empirically established. Nor is it reasonable to imagine mammals developing out of what they bring to the world into epistemic creatures described by Ruse. However, Ruse's injunction to us to take Darwin seriously is worth taking seriously, even if Ruse cannot find the magic potion that converts human beings from Hyde to Jekyll. 23. This aspect of human action is beautifully described by Erwin Schroedinger. See: Erwin Schroedinger, Mind and Matter (Cambridge: Cambridge University, 1959), p. 105. 24. It seems that much of the so-called 'territoriality' of certain species may be understood in tenns of the confidence born of familiarity. 25. I suppose that the central point of Lorenz's paper, "Kant's Doctrine of the A Priori in the Light of Contemporary Biology," trans. C. Ghurye, from German original of 1941, in General Systems, Yearbook of the Society of General Systems Research, vol. 8, 1962, is just this, but Lorenz also recognizes the importance of the relation of actions to perception here and elsewhere. 26. Having listened recently to Brian Baigrie take Popper, Ruse, and Campbell to task for their analogical description of epistemology in evolutionary or Darwinian, I am now inclined to think that if there is an analogy between the origin of species
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and hwnan knowledge, then it is has to do with subjects (like physics, chemistry, psychology, or sociology.) It seems that they develop out of certain 'theories which at one time are part of earlier subjects, in much the same way that species arise out of varieties. To carry. this thought further, a't the risk of losing plausibility, the problems as I account for them in 'The Structure of Problems" and in "A Methodology Without Methodological Rules" may be described as the relatively stable heritable characters that are transmitted from theory to theory in the subject. Baigrle is right Such analogies do not lead us far. For what it is wo~ I believe that subjects, or disciplines, no less than species, evolve in time, and therefore do not have timeless natures. 27. A serious difficulty regarding the very possibility of applying a rule has been noticed by Kripke in: Saul A. Kripke, Wittgenstein on Rules and Private Language (Cambridge: Harvard University, 1982)" If we take an elementary rule (such as the rule for addition) we cannot distinguish between it and another rule which is identical with it in the domain in which the first has been applied, but differs elsewhere within the domain of application (such as in the addition of two sufficiently large numbers, which we have not so far tried, where our rule of addition and the new rule may give divergent answers). In such cases it seems that the very possibility of applying the rule in some unique way, on the basis of the rule itself, is ruled out Kripke suggests that Wittgenstein's solution to the problem is that the correct rule is the one which we as a group apply. But this does not help either, since we as a group may not converge in the next case. The difficulty here is strictly one for logicists, because mathematics has been understood as generated by a weak basis (logic). If 'the fOlDldation of mathematics lies in a multiplicity of skills at a logically 'lower' level, then each rule can act as a check on the next application of one of the other rules, giving mathematical rules a condition of uniqueness to the extent that we have it at all. This sheer abundance of rules, each with a limited range of applicability, creates redundancy, which has been shown in information theory to reduce ambiguity. The logicist eschews redundancy for Occam's razor, and so has to live for every with ambiguity at every tum. I am indebted to Leslie Tripp for an interesting comment on Kripke's discussion of Wittgenstein. 28. See: Baruch SpinOlA, Ethics, trans. S. Shirley, 00. S. Feldman, Indianapolis, Indiana: Hackett P.C., 1982 and I. Newton, Mathematical Prin£iples of Natural Philosophy, see note 7. 29. See Alan Musgrave's description of 'if-thenism', which I have in mind, note
15. 30. I am grateful to the History and Philosophy of Mathematics Seminar, York University, for comments, and to Professor Israel Kleiner and Professor A. Shenitzer for inviting me to read my paper there. Also to Professor 1. Brown for arranging to let me try out my paper at the Department of Philosophy, University of Toronto, to Mr. Avshalom Adam for assistance with the references and notes, and to Professor Ian Jarvie, Andrew Irvine, Peter Danielson, Fraser Cowley, Kathy Miller, and John Metcalfe who have helped me to improve the paper and make it clearer than it was.
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L The Problem and a Proposal (in brief) A: Should philosophy of science be interested in the question of truth? I think philosophy of science should be interested in the question of truth, but 'this should not be construed as implying that all philosophers of science should be. Science itself is a complex task. Not everybody need do all the parts of it to be legitimately a scientist This explains why a number of radically different characterizations of science could all be valid, provided they were taken to be partial descriptions. Philosophers interested in solving problems science poses need not attempt all the problems to be legitimate philosophers of science. The question of truth could be left alone, legitimately. One could go further and say that if a scientist did not construe her or his task within science as (a part of) the search for truth, but, rather, for example, as an attempt to classify data in some domain in a neat and parsimonious manner, science's task would (in part) be furthered by that, and a philosopher studying that part of the enterprise might not be overly harmed by not raising the question of truth. Nonetheless, for a complete picture, the question must be raised. Because of science's origins, both in the social context of an expectation of improvements on commonsense and in the religious context of an expectation of thinking God's thoughts after him (or her), and because of a continuing public expectation upon science to deliver the truth, or some reasonable facsimile, a fully adequate account of science cannot be given without the question of truth being discussed, even if only for truth to be put aside and the common expectations to be declared improper. But I do not think a proper analysis of truth will lead to its being set aside, even though I do not think a satisfactory account of truth, as it concerns science as well as ordinary life, has yet been given.
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B: Should students of psychologism and of anti-psychologism be concerned with the question of truth? Yes. I say this, oot only because students of psychologism, etc., should be to some extent philosophers of science - that would oot suffice, since not all philosophers of science need concern themselves with truth - but, principally, because the attack upon psychologism is motivated, as far as I can tell, as a defense of the possibility of objective truth. I am not quite sure how to characterize the outcome of the study of the notion of truth undertaken here in tenns of the debate about psychologism, though I suspect that fervent Fregeians or Popperians will not find themselves immediately drawn to my conclusions. Let that fallout as it may. My proposal, here, is not presented as a result of grinding any axes, except perhaps this one: philosophy proceeds by attempting to improve upon extant attempts to solve interesting problems.
C: Why am I putting forward a complex theory of truth? I am putting forward a complex theory of truth because none of the standard simple theories - coherence, conventional, correspondence, perfonnative, pragmatic, redundancy, semantic - seems completely adequate. Some deficiencies are specific to individual theories, some are shared by all. Let me mention some of the general problems frrst, and then say, briefly, how I propose to overcome them. After that, I want to go over the standard theories one by one, as a means of developing my own proposal and of arguing for it In the first place, standard theories, as usually represented, give us no way of thinking about animals' beliefs as true, because they all focus on linguistic objects, such as statements or sentences, as bearers of truth.' We need something much more general as a basic truth bearer, with linguistic objects as secondary or derivative. My second criticism assumes that there is a rough general usage that any adequate theory of truth must somehow save. Roughly, people think that whether something is true depends upon how it matches up to something external to itself. The correspondence theory as usually presented - there are various versions, of course - aims to say what it is that matches what, but fails. The other theories do not even try. Some of them even imply that the general usage is, on this point, in error. Thirdly, all the theories mentioned presuppose what I think is a problematic construal of what an utterance means: they all presuppose that what an utterance or a sentence or a statement means is unproblematic. I don't share this view because of some implications of studies concerning how language is learnt It seems to me that the language each person uses, however public she or he aims it to be - for example, by close attention to
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criticism and to other people's usage - is irredeemably private to some extent. Often, this does not matter. And often again, we have great confidence that what has just been said is thoroughly understood, though these later cases are usually cases where we are talking with someone we know well. It is rare that a public speaker has much confidence that everyone has understood all that has been said. This may be why public speaking degenerates so easily into demagoguery, where it matters more that people share roughly the same feelings about some ill-defmed object than that they have understood what has been said.
D: What I propose, in a nutshell First, the primary truth-bearers are beliefs. As it stands this is not unusual. What is unusual is that I mean to include several categories of belief that are usually excluded, principally, unarticulated and even unarticulatable beliefs, and beliefs that are more like unstated expectations. And I mean not to emphasize, as primary truth-bearers, the kind of beliefs philosophers usually like to focus on: the ones that conveniently have a readily disclosable or imaginable linguistic form. The principle virtues of the kinds of beliefs which I take to be primary are, that animals other than human beings can reasonably be supposed to have them, and that they are much more the kind of thing that could correspond to the natural world, which is the object of so much belief, in the sense of being homomorphic with it, than are linguistic objects. Secondly, what it is about one of these beliefs that makes it true, in the respect and to the extent that it is, is its correspondence to its objectmost often some aspect of the inhabited environment. Thus, I put correspondence at the heart of the matter. Of course, we do not expect beliefs to correspond exactly and in every detail to their objects, at least because our beliefs about objects in our environment are commonly fonned from our sense perceptions, which are notoriously restricted in the information they supply us with, not only because our senses pick up only a minute fraction of the infonnation around us but also because of the various selecting and suppressing devices our nervous system employs. Thus it will only be a qualified correspondence our beliefs achieve, a correspondence in some respects and to some extent. This does not mean that all our truths will be merely approximate, though many will be. It will be quite possible for us to be absolutely correct about some things-- for instance, that Canada is larger than England, or that a person with three children has more children than a person with only one, or that there is nothing I can do to alter yesterday (though there may be much I can do to alter how yesterday is remembered). But while correspondence confers truth on a belief, even if only approximate truth, truth in some respects or to some extent, it is not fully what truth consists of. In my view, truth is also a special case of
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trustworthiness. Pragmatism had its fmger on a worthwhile point, but it missed the complexity of truth's connection with the virtue of not letting you down, of not disappointing your expectations. Sometimes it may be a happy accident that acting on our beliefs brings us something like our expected reward, because what we believed was simply false, but the truth was kind in some quite unexpected way. Statements or sentences can acquire the virtue of not letting us down, but only through conventions which link strings of words to the objects of beliefs, to which, in themselves, words or verbal strings could hardly correspond. The truth of statements or sentences is, thus, derivative and somewhat precarious. I take the primary meaning of any utterance - this is my third item - to be tied to the unarticulated belief of the utterer, which he or she aims to articulate in this particular utterance. This third, frankly psychologistic, point has important repercussions for theories of language and for theories of a third realm (World 3). I think it can help some solve some problems in these domains, though it poses a challenge to champions of the usual kinds of objectivity, since it appears that it might plunge us straight into a pernicious subjectivism. I shall hope to show that appearances are here deceptive. I am perfectly content to borrow from the coherence theory its most conspicuous contribution, the implication that true things will cohere. There will be several layers to this, however. If the universe is coherent or harmonious, as we tend to think or hope it is, we shall look for true beliefs to be compatible with one another. And we shall expect this compatibility to be reflected in the logical compatibility of statements or utterances which express these beliefs. Thus, in my theory, truth is not a simple property that one kind of entity may bear, though the correspondence of a belief to its object is. Truth is a complex of properties various connected entities might bear, depending on their connections, with the simple notion of correspondence at the heart of the complex. And whether something is true will often, perhaps even usually, be a matter of respects and degrees; many things which we are happy to call true would have to be called false, if we wanted to be more strict I shall say more on this point later.
II. Six of the Seven Standard Theories Briefly Discussed A: Coherence Strictly speaking, this is not so much a theory of truth as a family of theories whose main distinguishing common characteristic is the requirement that all statements held to be true agree with each other, and that any new candidates cohere with the body of already accepted statements. Some coherence theories are scrupulous, and insist that the body of accepted
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statements be interrelated by deductively valid logical links. Euclid's geometry is the exemplar. Others, acknowledging some measure of human fallibility, are more lenient, allowing some inconsistencies in the system temporarily, and taking them as a task for elimination. These more lenient theories have it that a statement is true to the extent it coheres with the system. It is a little misleading to say, as is usually said by the theory's detractors, that bUth is s:'mply a matter of coherence. Most often in the Western philosophical tradition, the truth at stake has been secured by some one or more leading statements being regarded as self-evident or absolutely indubitable (perhaps because its or their falsity seems to lead to a contmdiction), all other statements being true by implication. This leaves unanswered the question what it is for the leading statement or statements to be true and answers only the question what relational properties true statements will have to each other. To that question, coherence theories give unquestionably the correct answer: true statements will cohere together logically, more or less well. But this can only be a necessary, not a sufficient, condition for truth. As countless anthropologists have taught us, none perhaps better than Evans-Pritchard did with his study of magic and witchcraft among the Azande,2 there are many internally consistent systems of belief irredeemably inconsistent with each other. Where coherence theory does not acquire plausibility from the seeming incontestability of some leading statement or statements, it might acquire it from the coupling of the expectation that the set of all true statements would form a coherent system with the conjecture that, pending our coming to know all true statements, limited sets of beliefs that are better approximations to the whole truth will show increased coherence. But this air of plausibility would be misleading. Any inconsistent set of beliefs can be rendered consistent by dropping a sub-set of them. And, indeed, it is a good idea for a person whose set of beliefs is inconsistent to consider which ones to drop, since some of them must be false. Without any particular statements to bank upon, thought, and absent the correspondence component to suggest trusting statements that stand up to empirical enquiry, a coherentist might be at something of a loss to know which to drop. Nicholas Rescher has suggeste(p that people select according to their epistemic values- he both says that they do and recommends it. But he may be wrong. I suspect that some overt coherentists are covert correspondentists, especially recent ones influenced by science, and that, in selecting what to retain and what to drop, they make use of experience's testimony as to how things are, retreating into coherence theory only when pressed to vindicate their criteria. The point here is that there are not any infallible criteria for beliefs corresponding to how things are, which disappoints people. My recommendation is to acknowledge truth's complexity, rather than drop (covert) correspondentism. Let me digress for a moment to say that this paper intends to discuss only what it is for something to be true and not to take up the very
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interesting but different questions of how one tells when something is true or of how one decides what to think true when there does not seem any way of telling, though I may indulge in stray remarks on these topics from time to time, in passing. The original and sustaining rationale for the coherence theory of truth in the Western philosophical tradition - leave aside pragmatists like Rescher has three assumptions: that our senses do not deliver reality to our minds however hard we concentrate on what they do deliver; that reality is orderly; and that the order is graspable by the mind and describable in language- though it may be the language of mathematics. Thus the coherence theory is linked, in our tradition, with a rationalist approach to philosophy. This link does not exist among the Azande, who seem to be quite confident that they are describing an external reality with their true statements, and who might, thus, usefully be classed as adherents of a correspondence theory. Some of their beliefs, about everyday matters, say, are made to stand up to quite ordinary empirical tests. They do not have any other way than we do to tell whether the chicken that dies in the poison oracle is dead. But other beliefs, such as what it is the poison oracle has the power to tell us, are not made to satisfy such tests. These matters are more remote from test, as are some theories in science and most theories in philosophy. Unlike our traditions of science and philosophy, Azande tradition appears to lack a critical component with respect to these remoter beliefs. For the Azande, therefore, the coherence of their beliefs has the function of rendering them all more or less impervious to criticism. This kind of system has been called, rather graphically, a reinforced dogmatism, with each belief reinforcing all the others by virtue of their coherence. The point is that their use of the correspondence element in truth is only half-hearted. They do not use the widest available experience to test their systems as a whole, but use elements of the system to exclude adverse evidence from counting against their system. It is hard to see how any system of beliefs about which it is claimed that their coherence warrants their truth could escape the charge of being a reinforced dogmatism. But any reinforced dogmatism is probably false. The argument goes this way. There are many internally coherent systems incompatible with each other. Only one at most can be true. If all depend upon coherence as their defense, this cannot pick out which is superior. To the uncommitted bystander, who, in her or his ignorance must see all candidates as equally probable, all appear (equally) improbable. Only the committed see it otherwise. Could a system, probably false on this kind of evidence, actually be true? Of course. In a lottery, each of the ticket holders will probably not win the prize, but one of them actually will. The evidence we have before the draw, however, never tells us which ticket will win (except in the case of fixed draws, when there might be evidence as to the result of the fixing). The main point against coherence theories, however, is this: coherence is not
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enough. Given that there are so many systems to choose from (or even given only that there are two), all (both) more or less coherent, the poor, innocent, inquiring bystander needs fwther help to make a choice. Some consideration other than coherence will be crucial. IT one were brought up within one of these systems, not exposed to alternatives, not given to thinking up any for oneself, then one would not be a poor, innocent, inquiring bystander and one probably would not want help, even if one needed it for one's own good! But the philosophical ttadition in the West has never been so monolithic, even though, from time to time, religious or political leaders have tried to suppress other systems than their own. Even during the period in Europe when Christianity dominated the intellectual scene, Christianity itself was not monolithic, to the chagrin of its leaders. So we need to ask of any coherent system of beliefs, why it is to be preferred to its rivals. Of course, this point is well taken within the rationalist tradition, as well as more recent pragmatic coherentists. Each rationalist offers us arguments why his (it always has been 'his'- is there a lesson here?) system should be endorsed, and the argument usually is, as I have remarked already, that some one or more fundamental beliefs are self-evident, or in some other wise indubitable. Each pragmatist usually argues that more value of the most desirable kind is realized or conserved by her or his system than by rivals'. I recommend not endorsing any system of beliefs which is unable to offer any ground why its fundamental beliefs should be regarded as true, unless the system offers, alternatively, some method or strategy for detecting error in these beliefs, should they be mistaken. Seeming to enhance life is not enough, unless one wants to risk a fool's paradise. Iris Murdoch has wonderful warnings against being deluded by beliefs that console us- 'the fat, relentless ego' is not to be trusted.4 So far as our search for an acceptable theory of truth is concerned, the coherence theory leaves us still searching, though I recommend that we can still borrow from it the constraint that any bundle of particular true statements we feel inclined to endorse should hang together more or less well. At fIrst glance, this might appear to be too strong a constraint upon truth, because it looks as though such a restraint requires the universe to be thoroughly orderly and intelligible, as, I think, people in the rationalist ttadition commonly suppose it to be. But this would be a mistake. It does not require this. Of course, the universe must be orderly to some extent for us to be, in some sense, enduring objects, posing this question to ourselves. And it must be orderly in other ways for us to learn a language in which to discuss this question with each other. But just how orderly it actually is, is something we can leave to be found out by inquiry. We have no need to decide it in advance. We should not, in any case, expect true statements to contradict each other.
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B: Conventional We should distinguish right away between two different kinds of conventionalism. The fIrst, which will not concern us here at all, says that some seeming statements are neither true nor false. Some thinkers say this of scientifIc theories. They mean to leave scientists free to adopt and use the theory that is most attractive to them or that is most convenient for the purposes at hand. This kind of conventionalism is not a theory of truth at all, but a theory about scientific theories, to the effect that they should not be regarded as falling under the purview of any theory of truth. The second kind of conventionalism is quite different from the fIrst kind, though it may be closely allied to it in some ways. It endorses the fIrst kind's view that sentences that seem true or false are conventions, but it goes on to say that it is their being conventionally agreed upon that makes them true or is the same thing as their being true. Peirce's view seems, to some readers, to have amounted to this. For instance, Erorsky5 reads Peirce' this way: "if belief 'were to tend indefmitely toward fIxity' we would have the truth.'" More recently, Ziman seems to espouse this view,' emphasizing science as consensus and as reliable knowledge, though in his later book he claims that science keeps in touch with reality.' He rarely mentions truth. His view seems to owe something to Polanyi's, for whom what is true is what is passionately asseverated by the connoisseur. 1o Zirnan avoids the obvious objection connected with experts' idiosyncrasies. It has always puzzled me why anyone - especially anyone as clear thinking as Peirce - would want to believe the conventionalist theory: it seems such an obvious muddle. Perhaps it is an over-emphasis upon how we fmd out what is true coupled with a kind of pragmatism that downplays any speculative difference between what is true and what we think is true if there is no difference we can detect in practice. I do not know. I shall return to this point about downplaying speculative differences when I discuss the pragmatic theory. I do not have any doubt that language is conventional. Thus, any statement of truth must have an irreducible conventional component But whether or not there is cream on my porridge or butter on my toast does not seem to depend upon people's agreement A conventionalist might reply that it is not simply people's actually agreeing with me that my breakfast is correctly described by saying that there is cream on my porridge but that my toast is not yet buttered that makes the description true. Rather, it is their potential to do so. If I were to invite the neighborhood in, which heaven forfend, to check out my hypothesis that I already added the cream to one part but not the butter to another part of my breakfast, they would agree with me. But, I want to know, could I not tell already for myself by looking at the porridge and the toast and going by how they looked? And is not that just how my neighbors would tell? Would not it be our common experience of how the breakfast looked that would underwrite our judgment as to whether the correct description had been given? And would not, then,
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something more like a correspondence theory (leaving undecided for the moment what exactly was to correspond to what, and how) be more fundamental than agreement? I have another objection. If I am to reserve 'truth' for matters on which there is agreement among members of some appropriate group, what shall I call the property those sentences have which describe correctly, according to some linguistic conventions, the state of my breakfast? Some people do not think it is important to haggle over how words are to be used, so that my complaint that I am being robbed of a term's more common usage would be thought trivial. But I do not agree. I do not at all object to a word's being given a special narrow sense for some technical purposes; nor to a word's being given a new stretched sense, as in poetry or metaphor, in an effort to get us to see the world differently; nor, again, to proposals for not using words in certain ways because it leads to confusion. But I do object to effort to take a word over and to shift its meaning without either a really good excuse, or common consent. What is commonly meant by truth is very close to what Aristotle meant when he said that someone speaks truly if what he says is how things are. Conventionalists have got to come up with a very good excuse to have us drop that sense. So far they have not. A conventionalist could point out that truth, in this common sense, was not demonstrable (and he or she would be right), so that nobody can ever make a truth-claim it was not legitimate to challenge. Right, again. It might thus seem that the term should fall into disuse, if people were scrupulous, since no one could ever be fully warranted in saying of anything that it was true, in the common sense. Therefore, the term was ripe for a takeover. Not right! The tenn is invaluable, in the common sense, for expressing or appraising people's opinions. Or a conventionalist could say how untrustworthy individual opinions commonly are and invite us to put our trust only in what is agreed by some trustworthy group- in contemporary versions of conventionalism, the group proposed is often the scientific community, or the experts in a field. Now, I am just as ready as the next person to say that scientists or other experts are more knowledgeable about matters in their disciplines than I am. But if they too are fallible, then their expertise does not imply that they should be trusted. Their fallibility implies that acting on their advice is risky. Some aspects of that risk are calculable, perhaps. But usually there are some aspects that are not. What is risked, calculably or not, is some ill outcome of the distance between what the convention says and how things are. Conventionalism tends to blur over the possibility of that distance and is, therefore, dangerous. But, a conventionalist - let's say a defender of the thesis that our best knowledge, what we can most mtionally believe and act upon, is science could retort, that I have already conceded that the scientist knows more than I do and, thus, to follow my own opinion instead of the expert's would be even more dangerous. Sometimes that would be so. But quite often this way of putting things distorts them. To refrain from acting on the expert's
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advice, or even to forbid the expert from acting on his own advice, is sometimes to block the introduction of some novel technology or the undertaking of some specific research, where the alternatives are all safer. These days, when our power to wreak possible havoc has run far ahead of our power to foretell accurately the consequences of our actions on sensitive, complex systems, we have some responsibility to be cautious,! I and this tells against conventionalism.
c: Redundancy Here I can be brief. The idea that the notion of truth is redundant l2 has some initial plausibility when attention is directed at the informative content of assertions. What is added, one might wonder, to the assertion 'This teacup is empty', by saying that it is true? But the idea, that what is involved in saying that that assertion is true is the same as reasserting it, is false. A person may wish to achieve some other purpose by his or her utterance, as Strawson suggested. 13 In any case, hanging on to the redundancy idea rather robs one of the facility of talking about how statements seem to connect with reality without asserting or denying them.
D: Semantic The semantic theory thinks something different is being said with "'This teacup is empty" is true' from what is being said with the bare assertion 'This teacup is empty'. It claims that while the assertion about the teacup is an assertion about a physical object, the assertion '"This teacup is empty" is true' is about a linguistic object and not about that physical object. We are invited to notice that languages have different levels, or even that there are languages within languages. The simplest language is a physical object language. To discuss utterances in that simplest language one nee9s a meta-language rich enough to permit reference to sentences as objects. Ordinary languages of the familiar kind are all rich enough to do this. What am I calling the semantic theory, when Tarski carefully called what he discussed the semantic concept of truth,!4 is the theory that Tarski's elucidation of the concept works for ordinary languages. In the 1931 paper, Tarski set himself the task of constructing "a materially adequate and formally correct definition of the term 'true sentence'," 15 and expressed little hope that he could illuminate ordinary languages with his defmition. But he plainly shared the positivists' hope that science's language could be thoroughly formalized and thus that scientific truth could be defmed by his method. It is more common now to think that hope forlorn. So we can sensibly ask, whatever success Tarski achieved with respect to formalized languages, whether his work advances our understanding of 'true', as it
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applies to ordinary languages and to science, much beyond Aristotle's dictum which he quotes with approval. I think it does nol I even think that Tarski may have been wrong about how badly ordinary language needed help. Let me explain. Tarski asks US 16 to consider the sentence 'e is not a true sentence', where 'e' is the name of the very sentence 'e is not a true sentence'. Since, seemingly, 'e is not a true sentence' is a true sentence if and only if e is not a true sentence, we look as though we are landed in a contradiction. One is tempted to wonder right away whether e could be a true sentence in the sense of a genuine sentence, for it is hard to tell what c is saying, since spelling out the full sentence instead of using its name never gets rid of the name. It is difficult to know how one would form the belief that would underlie uttering such a sentence, and just as difficult to comprehend what would have to be the case for c to be true. It looks very much as if the contmdiction follows from abusing the language, as White suggests,17 and could be overcome by ceasing to abuse it. I do not suppose all forms of the liar paradox can be so easily disposed of. My sense of the inadequacy of the semantic concept for illuminating the ordinary sense of truth comes primarily from its not dealing well with the most interesting part of the question of truth: the mysterious connection between an utterance (say, 'This teacup is empty') and anything else that would make it that 'This teacup is empty' was true, if it was. Tarski's proposal, by which he defines truth, is in terms of the concept of satisfaction. He says, "a sentence is true if it is satisfied by all objects, and false otherwise." II Satisfaction is to be defmed recursively for sentential functions, such as 'x is greater than y', and then conditions can be stated under which given objects satisfy a compound function. Sentences tum out to be satisfied automatically by all objects or by none. All this seems completely unsatisfactory to me. For one thing it too closely resembles the absurdities Hempel drew our attention to concerning confrrmation. 'All ravens are black' turned out to be confrrmed by 'This is a red herring'. Commonsense rightly asks that what is to be taken to confmn an hypothesis or make it true should be relevant to il If truth is to lie in correspondence, as Tarski seemed to want it to, the truth of the sentence 'my horse is eating alfalfa hay' should lie in its correspondence to what animals I own and to how their nutritional needs are being mel What is going on in your home or for that matter what is going on on the other side of my bam - should not need to count. Some thinkers, for instance Popper,19 say that Tarski's work rescued the correspondence theory of truth. This seems to me deeply implausible. Satisfaction, at least as far as ordinary languages go, is the much more elusive notion. I shall say more about another source of dissatisfaction with Tarski's contribution, the use of sentences as paradigm truth-bearers, when I discuss the correspondence theory, shortly.
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E: Performative When Strawson introduced the performative (quasi-)theory to correct and complement the redundancy (non-)theory, he intended it to answer the semantic theory as well.20 The view advanced was that 'true' is not a descriptive predicate at all, but a performative one. Descriptive predicates say something about what they qualify, that they are green, say, or large, or, as with some unfortunate people's teacups, empty. By contrast, Strawson suggested, 'true' is used to effect a performance of some kind: to re-assert what has just been asserted, or what· might be asserted, or to endorse it or to admit it or what not. In consequence, the phrase 'is true' can always be paraphrased out of the language, for example, responding to Arthur's assertion with 'Things are as Arthur asserts'. The semantic theory becomes itself redundant on this view, for '''p'' is true if and only if p' can be pamphrased as 'What a person says in uttering Up" is how things are, if and only if p', which comes down to 'What a person says in uttering "p" is how things are, if and only if things are as he says', which does not say much. This quasi-theory is unsatisfactory at least for leaving undiscussed what it is for things to be as someone says they are, but it challenges us to show whether there is any ground for the common sense idea that truth can be descriptively predicated of anything. To be fair to Strawson, he never pretended to be delivering us a theory of truth, but rather to be bringing into the open the way 'is true' functions in the language.
F: Pragmatic There is not only one pragmatic theory of truth, of course, any more than there is simply one coherence theory or one correspondence theory. The views of Peirce and James and Dewey, to name only the most famous, differ quite significantly on a number of essentials in their theories. In fact, the view of Peirce, as I have suggested, seems much more like what I have called the conventionalist view, since in his philosophy what is true is what competent experimenters or inquirers eventually agree upon. Nonetheless, there is enough that is common for us to pick out a plausible theory worth the label 'pragmatic'. The essential point is that an hypothesis is to be regarded as true that has worked, in some sense. James introduced some ambiguities into this idea by discussing how one could make what one believed come true by acting on it He had in mind the effects one can have upon people by trusting them, for instance.21 But we can leave such matters aside, and concentrate simply upon the notion, which I have already introduced, of an hypothesis' not letting us down. This notion has a quite straightforward common sense significance and needs only some amendment of purpose to emerge as
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confrrmation, of the sort scientists might be interested in. It is our not being let down, or 'things turning out as the hypothesis said they would or implied they would, which underlies Dewey's criterion of warranted assertabilty.22 The word 'verify' is both accurate and tell-tale: for Dewey, hypotheses are made true, become true, by their consequence being in line with experience. There is a definite advantage to this view when considering the matter of, to take Aristotle's example, the sea-battle there mayor not be tomorrow. If one does not want to be committed to a determinism in which the future is already fIXed - and 1 certainly do oot23 - then one wants to be able to deny a truth value to straightforward indicative statements concerning the future. One wants to be able to say that it is at the moment neither true nor false that there will be a sea-battle tomorrow. But nothing like this indecision attends logically universal hypotheses of the kind it is science's business to propose to us. These may be true or false now (of course, in this or that respect and to this or that extent), even though they have implications for the future. The point is that their implications are conditional statements of the kind 'If x is the case tomorrow, then y will also be the case' or of the kind 'If x were to be the case tomorrow, y would also be the case.' A pragmatism that denied the possibility of such universal statements being true (more or less) today would effectively be denying the reality of regularities in nature. Now this might be a motive for adopting pragmatism, that it saved one from too strenuous a realism. But there are gentler ways of avoiding a commitment to too strong a realism than by denying it One could simply refrain from asserting it. What Van Fraassen calls constructive empiricism,24 which he offers as an alternative to the currently more popular scientific realism,25 does not deny that scientific theories may be true in what they assert that goes beyond experience, but disdains saying that they are, absent the warrant he thinks that would need. It seems to me to be a desideratum for any theory of truth that it not be tied too strongly to particular metaphysical commitments. So I would count it against the pragmatic theory of truth if it did not leave room for scientific realists to make sense when talking about the current truth of scientific laws. (I do not know whether all versions of the pragmatic theory have this fault.) Numerous critics have pointed out how the pragmatic concept collapses together two ideas which common sense thought we could separate: the idea of a thing's being true and the idea of our being able to tell that it was or of our being entitled to affmn it I think this is perfectly appropriate as a criticism, but it does not seem to me quite as telling as the one I offer in a moment The pragmatist can always reply that the distinction which common sense here adverts to lacks any practical significance and should be shaved off Occam-wise. In short, pragmatism can be presented as reformist, as proposing that what we have been accustomed to should make way for a neater, more economical view. No such reply can be made to the challenge that the pragmatic view either implies a vicious regress or is parasitic upon a quite different theory of what it is for an hypotheses to be true. I am not here alluding to the
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problem of induction, the problem, say, of verifying general hypotheses by the repeated confrrmation of instances of them, though the pragmatic view certainly must face this problem and must do so in its theory of truth, nOl only in its theory of knowledge. I have in mind the problem caused by the contingent nature of the claim that a particular hypothesis has worked. Take, for example, the hypothesis that this object which I have just thrown up will shortly come down. I suppose that we should say that the hypothesis works, and is therefore true, if we experience the object in question actually coming down shortly after I threw it up. But the claim that the hypothesis works is a different claim from the one the hypothesis itself makes. Call the hypothesis 'h/. Call the claim 'hi works' 'h z'. The problem I am here proposing for the pragmatic theory is to say what it amounts to for hz to be true. If it is both a necessary and sufficient criterion of something's being true that it works, then hz's truth depends upon its working. The belief that hz works, let us call it 11" will in turn have to work to be true. And we are plunged into a regress. But it is more likely that there will either be an appeal to immediate experience, showing pragmatism to be parasitic upon a theory of the veridicalness of immediate experience, or an appeal to a correspondence between hz and reality. In any case, the pragmatic theory of truth breaks down. Some defenders of the pragmatic theory might want to say that the theory is actually a complex theory- and who am I to say that one should nOl have a complex theory? They might want to incorporate an element of correspondence into their theory, and I should not cavil at that. After all, I want to incorporate a pragmatic element into mine. I want to say that pragmatism is very near the mark. I think it is an essential constituent of truth that true statements or beliefs do not let one down. But I do not think it is a sufficient constituent The characteristic is shared by some false statements and beliefs, also, just in case the difference between what is true and what is false cannot be detected yet, or even is never detectable, the actual differences being too subtle or minute for detection, or belonging to some characteristic we have no senses or apparatus to detect Here I want to return to an earlier point about some people's downplaying or ignoring any difference between what they believe and what is so in cases where they are unable to detect it Take the example of a stroke victim or a person otherwise paralyzed, unable to tell us what she is thinking, but quite able to understand what we say and do, though we do not know this. And suppose she dies without recovering. Then we never are able to detect the difference between the belief that she could not hear us and the truth that she could The difference is surely there, though it escapes our detection. How she should be treated while alive is perhaps a question on which morally sensitive pragmatism (James's kind) departs from neutralist or even cynical varieties. But there is no pragmatic test we can perform using the consequences of our belief, though the difference between treating her as if she did understand and treating, her as if she did not are detectable by her.
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A similar argument applies in philosophical theology in cases where the theory of god at issue can answer to no immediate practical test of its truth or falsity. But the stroke victim example is more telling because most of us know people who have recovered and who have reported to us their frustration over being unable to respond adequately. Theories of what truth amounts to have to leave room for a beliefs being false even when all available tests cannot show it up. I recommend rejecting any version of the pragmatic theory that makes the error of supposing that its necessary condition of truth is also sufficient
III. The Correspondence Theory, in more detail A: What can it be that does the corresponding? Any version of what could reasonably be called a correspondence theory of truth has to say, first, what sort of thing it is that corresponds to what other sort of thing, such that the correspondence makes a thing of the first sort true, and also, in case it is not obvious, what it is for things of the first sort to correspond to things of the second sort. Common sense, following Aristotle, makes pretty light of this. A person speaks truly if what he or she says is how things are. Philosophers have made heavier weather, and not without some reason. What makes a correspondence theory plausible is acquaintance with competent use of a language. But what makes it unconvincing in its usual forms is a series of difficulties which beset every effort to be specific as to what sort of thing it is that is true, as well as difficulties with how what is true can correspond to what it is that makes it true. Let us look fmt at some of the candidates for what it is that can be true. An obvious candidate is utterances. But this can be quickly disposed of, if by utterances we mean crudely the physical object which results from speech or writing. If we mean something more abstract, something independent of the medium of utterance, it might seem that we had better make sentences our candidate. But sentences won't do either, since we should hardly want to say of sentences themselves that they were true, outside the spatio-temporal circumstances of their utterance, or, at least, their consideration. Take the sentence, 'There is a fig on the plate beside me'. Since there is no longer a plate beside me, though earlier there was, and earlier still there was a fig on it, along with dates and raisins and nuts, I am unwilling to say that the sentence is a candidate for either truth or falsity. Earlier, that there was a fig on the plate beside me was false. Earlier still, just before I ate the last fig, it was true. Of course, not all sentences depend upon a spatio-temporal context for their meaning or for their prospects of being true. Sentences which specify spatial and temporal coordinates for the events they purport to describe look
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as though they have a better chance. But the difficulty mentioned above is not the only one sentences have. We should hardly want to say of a sentence which was merely being mentioned or put forward as an exercise in translation or was being repeated uncomprehendingly by a parrot that it was true or false, though we certainly could sensibly ask whether it was well-formed or grammatical or, perhaps, colloquial. More fundamentally, I do not for a moment believe that the meaning of sentences, no matter how well-formed, etc., can in general be known outside the context of their use. Let us explore this point more fully. Let us suppose, for the moment, that we have no difficulty understanding people when they speak: to us in ordinary life, nor in understanding the letters of people we know when they write to us. I do not think this is completely true, though it may be true enough for some practical purposes. What, however, are we to make of the text of a good play? (Leave aside bad ones, since they introduce difficulties of their own that are not relevant here.) The supposition that it is a good play imposes upon the actors and the director the task of making coherent sense of the text and the stage directions. It is an important part of my argument that this is a task. It is not straightforwardly obvious how each line is to be delivered. Yet how it is delivered - tone of voice, variations of pitch or volume, implicit emotional engagement, the way the head is held, and the hands and the shoulders, the way the actor is moving or standing or whatever, all this and more - affects what the audience understands the character to have meant by the sentences uttered. In the light of such considerations as these, perhaps we should rather say that it is not sentences that are true or false when someone speaks or writes sentences, it is what the utterance conveys. But even this will not do, since an utterance may convey different things to different auditors or readers. As any writer knows who wants a certain point to be taken, it is a very difficult task to write in such a manner that no competent reader of the language could mistake what is being said There is a very strong tradition in philosophy that holds that there is a single correct meaning for any well-formed and properly used sentence. Let me call this meaning (if there is such a thing) the conventional meaning. What does it amount to for there to be a conventional meaning to a sentence? It plainly cannot mean that for every sentence in a language there is just one meaning fIXed for all time, because of the plain historical fact that words change their meanings through time, sometimes even reversing them, and sentences cannot remain immune to changes in the meanings of their constituent words. Does it then mean that for every sentence at every instant there is a precise meaning, though this may vary at the next instant? This seems absurd if we pay the slightest attention to how the meanings of words change. They change through use, slowly. More importantly, they change through use, locally. It is only since the advent of culture-wide communications media that we can nowadays witness a sudden, widespread change in the meaning of a word, usually as a result of its misuse by some
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more or less incompetent public figure. The changes brought about by misuse by less well-known people will be slow and local. (It will emerge in a moment what I mean by misuse.) What follows from this theory of the dynamics of word meaning change is that there never is a fully stable correct meaning for any sentence across the whole culture that uses the language, even if we fully accept that language is conventional. What is there, then? Could there be a central meaning for a word, which, when you want to be clearly understood, is what you intend the word to convey and hope it will actually convey to your audience? I am not sure even of this, because I have no direct access to what anyone takes me to have said, when I have spoken, nor to what anyone intends me to understand, when I am spoken to. I am on my own, to a considerable extent, inventing possible meanings for words I hear and words I use. There is, of course, feedback. There is positive feedback when people behave in the way I think they would have behaved if we had understood each other completely. And there is negative feedback when they don't. And this feedback is adequate for many practical purposes, though it often is not precise and it may leave me wondering if comprehension has been complete. Any teacher knows from the work of her or his students that comprehension may often be only partial, at best I am led, by considerations such as these, to propose a cluster theory of the meaning of words and sentences. I take as primary what it is I want to convey by a word or what I usually take a word to mean, and I conjecture that everybody with whom I converse does the same. I also conjecture that other people share with me the wish for adequate understanding and aim, as I do, to get their meanings as closely matched as they can to what they take me and the other people they talk to to mean. Our intended meanings will tend to cluster. (I am leaving aside, here, the way language is used by artists - say, poets - who, rather, often aim for new meanings, and thus set tasks of invention or conjecture for their readers. In this way, they leave their work open to interpretation. What they utter may convey, quite legitimately, different things to different readers.. And what the author meant by what he or she wrote may legitimately be ignored when people gather to see what can be got from a literary work.) On this theory, what we call the conventional meaning of a word can be nothing other than the meaning we take people usually to have in mind It is obvious that there are as many candidates for that as there are people caring about the matter. It is also obvious that these many meanings will tend to cluster, and that where 'they cluster will move, over time. Roughly, what I mean by the misuse of a word is a use that departs confusingly rather than illuminatingly from what people usually seem (to me) to take each other to mean by it. A much more important implication of this theory is that what people have often meant as candidates for bearer of truth within a correspondence theory become somewhat incoherent There are three standard candidates when sentences are ruled out: propositions, statements, and 'what is said'. I
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take all three of these to be attempts to identify some mind-independent and context-independent entity which can be said to be the bearer of truth. Let us glance flfSl at propositions. I have failed to find any even half-convincing argument for supposing that propositions, as usually understood, exist, unless a proposition is just what a person intends to say in an ulU7ance or what a person would usually take people to intend to convey or what a person believes. But these senses do not give propositions the objectivity their promoters would like them to have.:16 A similar, but not exactly the same, fate as that of propositions attends statements. No doubt people do make statements, but what statement it is a person has actually made in some utterance is never, on my theory, available to us: what is available is what I or you take her or him to have stated. And we can only compare notes by making further statements via further utterances, which must be similarly open to interpretation. The same is true for 'what is said', as a candidate. Neither what is stated nor what is said is a public object. In this sense, neither is objective, neither is a World 3 object, in Popper's sense. I really do not mind a theory that holds that either what is stated or what is said is an entity distinct from the states of mind of the utterer and the auditor, and therefore not a World 2 object, in Popper's sense. But this does not imply that they are World 3 objects. There are more kinds of things than the three that it suited Popper's purposes to distinguish in his 1967 and 1968 lectures,Z7 as Popper himself readily admits (private communication). I shall return to this question shortly. This leads me to propose that a more fundamental truth bearer is what a person (or, more generally, an animal) intends to convey. But what a person intends to convey is not itself a linguistic object. Linguistic objects are the modes of conveyance, not the cargo. But perhaps the transport metaphor is not right When I am conversing with a person, or when, as now, I am writing with the hope that there will be readers, What I aim for is not actually the transport of anything. I am aiming to achieve certain states of mind, certain occurrent belief-states, as the jargon has it, in my audience, or certain attitudes or certain emotions. Or am I aiming to have people do certain things. Let us stick for the moment to what beliefs I want to achieve. I should like two or three things. I should primarily like it if the people who hear or read what I say would understand what I say and thus hold correct beliefs as to what my beliefs are. Secondly, I should like it if people think that I am right, and thus believe that what I say is so. But perhaps I am not right In that case, I should like to stimulate thought and the articulation of criticisms and of better hypotheses or theories. If there is any transport at all, and I am not convinced there is - except, for example, for the transport of an utterance through the air, for speech, or the mail, for writing - it is a means to an end. Dropping the transport metaphor pushes me to the view that what it is that primarily bears truth is the (non-linguistic) content of people's (animals') beliefs.
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B: What can beliefs correspond to? The most obvious candidate is facts, but I reject this candidate. In fact, if we were to have a redundancy theory of anything, it should be of facts. I have no objection whatever to the word 'fact' nor to most of the uses to which people put it I simply object to the notion that there are any such things. Talking about facts is a way of talking about some other things that there actually are, and often it is a convenient or useful way of doing so. Sometimes, though, it is confusing. The main source of confusion lies in the tension over whether facts (on the supposition that there are any) are more like events than they are like statements. Some thinkers say that facts are events; some, that they are true statements. This is a troubling question since many people are used to the idea that facts stand for reality. No doubt this is fed by the usualness of the locution 'It is a fact that.. ' followed by a description of an event. They do not, however, stand for uninterpreted reality. Facts can hardly be identified with the relevant events, if only because events have locations and dates and the facts do not The closest that could be plausible is to take facts as events under a certain description. Something would not then be a fact if the description was awry, even though the misdescription would leave the event undisturbed. It does nor quite work to identify facts with true descriptions of events, however, if only because the grammar or logic of facts and descriptions are not identical. But for our purposes here, on the lookout for an acceptable theory of truth, anything like an identification of facts with statements would give beliefs nothing to correspond to except the conventional mode for expressing them, which would be rather fatuous. Those thinkers who most strongly tend to run facts and true statements together wisely drop correspondence as a mark of truth. A close examination of the (ambiguous) way the word 'fact' is used by competent speakers of the language does not support either interpretation, however, as White correctly says in his defense of facts as what what is said correSl>'OOds to. 2I But White mistakes what facts could be and what they could achieve. At one point he says, "It was the fact, not the true statement, that the train was diverted which made me late for my lecture...29 Of course, he is right to deny causal power to a statement in this case, but what made him late was the train's being diverted, not the fact that it was diverted. White suggests that fact is a notion which 'applies', as he rather unhelpfully puts it, to how things are or to what the world is like. But how things are includes their being colored or near each other or in reaction with each other. All these are relations in which things stand to each other. Certainly there are such relations. But nothing exists over and above these relations to act as the facts that something is colored, or that some one thing is near some other thing. Facts are empty reifications from noun clauses. They do not have enough substance to be what gives truth to our beliefs.
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Unfortunately, language has another trap for us. It is quite certain that we are aided in our grasp of how things are by the language we use to sort things and quantities. I should say it is just as certain that what we believe things to be like has been conditioned or distorted by the language used for their description. But it is not only language which stands in the way of direct apprehension here. Animals have, as far as we can tell, their own ways to sort things out, their own view of what the world is like, which must be different from ours since their senses differ from OUl'S.. Thus, even if we were to suppose that in some respects the world is as it seems to us to be, we should have to allow that it need not be so in all respects. If not facts, then what? Does a correspondence theory that eschews propositions and facts commit a person to realism? I'd say not, unless 'realism' is the proper name for the denial of solipsism. As long as a person thinks there is something other than his or her beliefs for those beliefs to correspond to, there is some applicability for the theory. And there are many varieties of non-solipsism that satisfy this, whether or not they want to be called realism.. Let me give a few examples. At the end of his discussion of correspondence theories, O'Connor suggests that we distinguish what he calls 'status rerwn' from what everybody calls things, their properties, situations, events, and so on. These latter entities, known to us in sensory experience, are what commonsense counts as real. But our perception of them is significantly mediated by language. O'Connor sees them as a processed and edited version of status rerum, which he describes as "the raw unexperienced welter of objects and events. tl30 With O'Connor's welter, there is something for beliefs to correspond to more or less well. How is it with commonsense realism? This is a little more complicated, because, to the extent commonsense realism is naive, perception is a direct apprehension of reality, leaving no gap betw~n belief and reality for correspondence to bridge. The only parts of reality about which there is room for mere belief are the currently unperceived parts. In respect of these, belief will be thought correct if anticipation corresponds to subsequent perceptions. Where commonsense is more sophisticated, people will try to get their personal models of the world in line with those of others whom they respect. This leads to a cluster theory of commonsense views of the world, similar to my cluster theory of conventional meanings for words. But here there could be an independent reality for the cluster to try to match. Someone who did not want to be a realist would have to deny that there was anything external to the various believers trying to align their various views. But what about their beliefs about each other? Would not there need to be at least as much reality as permitted the existence of the other believers? Similarly, some rudimentary realism is needed to give an account of empirical science. There needs to be a classical world of middle-sized apparatus, housed in laboratories, where colleagues read off the results of experiments, even if one wants to deny reality to putative submicroscopic phenomena which stay unrecorded by any apparatus. Today's followers of
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Bohr's interpretation of quantum theory do not speak with one voice on the matter, but they do all repudiate realistic talk about quanta between readings, as was shown in a series of interviews on BBC radio, subsequently published.31 Paul Davies interviewed a number of leading physicists on the question of the theoretical impact of some recent experiments, notably Aspect'S.32 This experiment confrrmed quantum theory's predictions just at a point where those predictions would not have been expected if one adopted both of the following assumptions: no signal can travel faster than light; physical objects have definite position, momentum, energy, and so on, even where these are not measured or even measurable. Some physicists do not want to give up defmiteness for the values mentioned, for example Bohm and Hiley." They then are placed in the position of hoping to work out how an influence can travel faster than light without being a signal. But our interest is in the followers of Bohr. Davies himself thinks that the sole purpose of the models physics is concerned to make 'of the world about us' is "to help us relate one type of observation to another." He says, "And there is no such thing as a 'real world' in the sense of something which exists 'out there' to which our models are mere approximations. "34 Others share his view with variations. Peierls says, "I don't know what reality is."35 Wheeler says, "...we have no right to talk about what that photon is doing during its long travel from the point of entry...to the point of registration."" And we could contrast the realism of those who claim that what is real is what science says is real with Whitehead's objection that science abstracts from the concrete, and makes space and time external relations, giving us at best a partial picture of reality." But enough has been said to show that, far from the correspondence theory picking out a realism for you, the version of non-solipsism you espouse will pick out for you what kind of thing there is for your beliefs to correspond to.
c: How could beliefs correspond to what makes them true? Let us consider first what I take to be the primary kind of belief, perception. At the level of bacteria or amoeba, perception is very crude and probably does not involve representation. External objects are encountered, some features of them are discriminated, and some response appropriate to the life of the creature is undertaken. At the level of the higher mammals, whose more developed brains can interpret quite complex input from a variety of senses, especially sight, there is almost certainly representation of external objects and some thought as to what to do about them. I shall not discuss the bacterial level any farther, but restrict the discussion to mammalian beliefs. It is important to distinguish between occurent beliefs and dispositional beliefs, although I do not introduce the distinction, as O'Connor did, in order to drop dispositional beliefs from the reckoning. He claimed that
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occurent beliefs must be prior to and basic to dispositions, and that "our dispositions to believe are not innate."31 In both these claims he is mistaken, though some of our occurent beliefs are, of course, prior to and basic to some of our dispositions. But it is quite plain from observation of the behavior of mammalian neonates, that they do not come into the world with clean mental slates. They are disposed to seek food and shelter in quite specific ways, to mention only the most immediately obvious predispositions. Innate dispositional beliefs perhaps function in some of the ways memory does, since memory may influence our actions without becoming occurrences of remembering. Probably all mammals are born with a rough and ready dispositional, four-dimensional, world-view. They know up from down, they immediately attempt three dimensional movement, and they are equipped with quite sophisticated body-clocks of differing rhythms. Just like scientists, animals are apt to perform inductions concerning interesting items of their environment, the results of which it would be silly to deny form part of their belief system. For animals, their entire belief system is probably made up of perceptual information, either occurring to them at a particular time or remembered by them, and thus partially constituting acquired dispositional beliefs, or prefigured for them in whatever manner their innate dispositions arrive. Human beings, and any other animals capable of descriptive language (in case there are any: I am not sme about that), expand their belief network using language and abstractions. Philosophers have concentrated upon beliefs cast in language, or capable of being cast in language, and I think this has been a mistake, since it has blocked them from making the fundamental connection, for the purposes of a theory of truth, between how we picture the world and how it is. For any theory that would pennit us to include animal beliefs as true, this is fatal. It might be that we think of the world in sentences, though I doubt it Certainly, animals don't No doubt sentences are the most convenient way of conveying some information from one person to another, since sentences encapsulate experience and may provoke rich images. No doubt, too, sentences may organize experience and make some vague intuitions sharp. On the other hand, the service performed by sentences may be vicious, as when important idiosyncratic details available to eye-witnesses drop out under the stereotyping summarizing of ordinary speech. And some scenes beggar description, but can still be taken in. In my view, very many of our beliefs are what we might call right-brain domiciled. Ah, but, says the linguophile, everything we believe is capable of description, in principle. I do not believe that, though I shall not argue the point here. It suffices that no beliefs of animals and not all beliefs of human beings present themselves as propositional. We need a theory that lets us talk about the truth of non-propositional beliefs. Sticking to some kind of realism, I should say that beliefs of the kind we are considering are true if how they represent the world to us is how it is. In view of my reservations about the accuracy and completeness of our sensory representations, I judge ttuth, here, to be a matter of degree. All
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claims to truth of this kind will be claims to approximate truth. I do not think that the kinds of correspondence I need to invoke here is troublesome, even though settling the degrees to which rival truth-claims have approximated their relata will be very difficult, if not impossible. We can readily form a sense of what it is for one thing to model another more or less well, since we have many examples of things modeling other things, including things of quite different kinds--- for example, we have two-dimensional models (portraits, photographs) of four-dimensional things (people); mathematical models of music; stick-and-ball models of molecules. In these examples, and many more like them, which fill out our sense of what it is for one thing to model another, we have independent access to both relata of the modeling relation. That we sometimes have no independent access to the thing modeled does not affect the conceptual validity of the idea of modeling, though it does get in the way of measuring our success. What we say to express our beliefs, to the extent that we can be successful at that, can be true, on the proposed theory, only derivativelyand only Conventionally, since it is conventions which settle (as far as anything does) the appropriateness of what we say to what we believe. The correspondence of what we say to how things are is mediated by linguistic conventions and by the correspondence of what we believe to how things are.
IV. The Proposed Complex Theory A: Truth as (in part) trustworthiness It should be clear by now that I greatly favour the correspondence of beliefs to their objects as fundamental to truth. I think it is quite sufficient to bestow truth upon a belief for it so to correspond. But I do not think correspondence is the whole story because there are kinds of beliefs that I want to say may be true but which do not correspond in this way. I shall say more about that in the next section. Here I want to introduce what, in my view, is a constant constituent of truth: trustworthiness. I do not mean to say that what is trustworthy is true. That would be a crude pragmatic blunder, though some people make it. But I do mean to say that what is true is trustworthy. The connection between 'true' and trustworthiness is a thousand years old in the English language, and it is no accident. This is a rather practical way to understand truth, but not, I hope, unacceptably so. I do not think there are any cases where we want to talk of something's being true where the notion of its being trustworthy would be out of place. The most obvious challenges would come from mathematics or from logic, either concerning the axioms of a branch of mathematics or concerning the rules for the derivation of theorems. But in
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both these cases I think trustworthiness makes sense. As regards rules, it is fairly obvious. The logical truths that rules of inference metamorphose into are plainly hoped to be trustworthy in the function they are designed to serve, and are quickly dropped if they are not As for axioms, they go to define a model of a possible world. The question whether they are true arises only in case one wants a mathematical model of the world to be taken to represent it accurately, as people ask of some geometries. In those cases, trustworthiness is not an inappropriate demand. I take trustworthiness to be more or less the quality a thing has of not letting us down when relied upon. But this is not a straightforward matter. When our beliefs correspond to reality (and thus are true) they usually do so only in certain respects and to a certain extent or only to within a certain degree of accuracy, though some simple beliefs, such as that I am the only person in my library at the moment, may be absolutely correct. Thus, usually the truth of our beliefs will only be partial. They can be relied upon only when the respects in which our beliefs match reality are relevant to the circumstances and to our purposes, and when the extent to which they do so is adequate. Fortune may smile and we may not be let down even where this does not hold. But this only means trustworthiness is not a sufficient condition for truth. On the other hand, it may ironically be the case, on some occasions we are let down, that had we been ignorant of some things we correctly believed, we might not have been let down. This should not be read to mean that truth lets us down, since plainly it was the conjunction of our knowledge with some false beliefs that let us down, and this by itself tells us nothing about which beliefs were the culprits. To find that out, if we can, we have to examine our relevant beliefs one by one. The point is that when our relevant beliefs are all true in all relevant respects, etc., we shall not be let down, so that it is appropriate to blame the false ones and to acknowledge trustworthiness as a constituent of truth. Since trustworthiness is obviously dependent upon context and purpose, the connection between it and truth alerts us to a feature of truth which is somewhat neglected by philosophers who emphasize two-valued logic and the search for stable, objective truth, and perhaps not properly interpreted by those who promote relativism. Truth, on my analysis should be treated as partial, rather than as relative. What is adequately thought true in some contexts may prove inadequate in others, as Newton's dynamics proves inadequate for computations involving relative speeds close to that of light, but the inadequacy has nothing to do with who believes it It is inadequate for the quite objective reason that Newton's theory only corresponds to reality in certain respects, etc., and this is so whoever the believer is. Of course, opinions are always relative to the holder, but truth is not. How about justification? Here I want to express my disagreement with Notturno, who, after an excellent discussion of the anti-psychologism of Frege and Popper, adverts to what he calls a "psychologism without tearS."39 Having abandoned justificationism - roughly, the idea that there can be
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absolute certainty as a result of the proper use of reason - Nottumo thinks that all attempts to justify theories as true or false are in the same boat40 But this presumes that justifying is an all or nothing affair and I am not willing to give up the word 'justify' to the absolutists, any more than I was willing to give up the word 'true' to the conventionalists. There is an ancient history to the notion of justifying as showing to some appropriate court that someone is innocent of some charge. I think this is a good cue for us. Justification, in my view, can best be seen as the act of satisfying an appropriate body of people that some belief or action is what a person should hold or do, or may hold or do. Life is full of it, though which body of people we are trying to satisfy, and what the standards are that we have to meet to do so, vary enormously. Philosophers have tended to regard rational justification as the task of providing such reasons as would compel the consent of all rational people. More recently, since it became common to think that there were no truths which could be proved absolutely conclusively, philosophers retreated to the weaker, but still arrogant and authoritarian position, advocated by Hume, that rational people apportion the strength of their beliefs to the evidence. But we can no more tell definitively what the weight of the evidence is, in order to have the strength of our beliefs match it, than we can tell, infallibly, what is true. So this does not help, either as a strategy of inquiry or as a standard of reasonableness. The best bet as to strategy is to avoid, if we can, errors which will cost us, or others who matter to us, dearly. And the best standard of reasonableness matches this. But it is not an authoritarian standard It does not prove the reliability of our hypotheses, their trustworthiness. This must continue to be at once a matter of conjecture and of risk. Although there do exist in each epoch or culture or subculture types of arguments or kinds of evidence commonly taken to be compelling, there does not seem to exist a standard which has the right to compel. But this does not mean that there is no detectable difference between standards, that none are any better than others. Nor does it mean, as Notturno claims, that rational judgments of rationality "are possible onjy given the acceptance of foundational principles (goals, values, etc.,) and are made only with reference to the foundational principles accepted. "41 If this were so, radical changes of mind when faced by preferable systems of metaphysics or preferable styles of reasoning would be the height of unreasonableness. Yet those who make such switches often see themselves to have been eminently reasonable at the time. They see themselves as having exercised powerful critical acumen in performing the non-foundational feat of comparing two different sets of foundations. Thus, trustworthiness, as a property constituent of truth, is not to be confused with the quality called 'reliability' which some philosophers have claimed inductive arguments may endow our beliefs with. In our effort to hold only trustworthy beliefs, we can never be relieved of the risk attendant upon our own judgment. But our judgments are arbitrary only to the extent
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we refmin from gIvIng attention to pertinent arguments which suggest specific errors we may have made. Notice, though, that the bare possibility that we might be in error is never a reason for thinking that we are. The caricature sceptic, or beginning philosopher, who has spotted the truth that apodictic certainty is not available, provides me with no reason to doubt my beliefs by informing me that I shall not be able to convince him (or her).
B: Trustworthiness as rooted in correspondence Perceptions are more or less trustworthy. If we ask how this comes to be so, the scientific answer would be in terms of the evolution of sensory appamtus. According to this story, some comparative advantage, both in survival and in mating, would be conferred upon those members of a population whose senses more accurately represent their environment to them, at least in the details relevant to survival and to mating. Those with the superior senses would pass on their genes in larger nUlTlbers, so that to the extent those genes promoted those superior senses (not forgetting that natural selection bites on the phenotype, not the genotype) the genes would increase proportionately, as would the phenotypes they supported, in subsequent generations, other things being equal. A measure of trustworthiness rooted in accumcy of representation is what one would expect, on 'this story, of animal - and therefore human - perception. Theories in science probe structures 100 small to yield sensory infonnation without considerable magnification, and thus cannot use the excuse that evolution has taught us to make trustworthy inductions in such cases. We have been given too many instances in recent decades of the failure of things which our best science told us would not fail for us to want to drop public caution, even in the face of scientists' confidence. This need not stop us from thinking that scientific theories model reality very well. But what they miss out is another - very interesting - story. It is sufficient for the truth of a belief that it corresponds to how things are. If it does so, then it will not let us down. But correspondence is a matter of degree, since it is a matter of modeling in suspect media- I mean media suspected of getting the match between belief and reality only as good as is needed for survival and mating. This is a new thought. Traditionally, when truth has been a matter of matching words to perceptions, as it was for Aristotle (and for many thinkers since), one could expect a perfect match. After all, the match hung on getting a linguistic convention right, and this could be got exactly right This, aided by the simplification logic demands, led to the view that there were exactly two truth values: true and false. But on the theory I am proposing, there are indefinitely many degrees of resemblance between beliefs and reality. And the matter is not linear; there are indefinitely many dimensions in anyone
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of which a model may err. I think this makes better sense of the nature of our beliefs than does the earlier, more naive view. I have said 'that not all truths correspond and I want to give some examples here. If people do not agree, and would rather go for a thorough correspondence theory, simplifying matters somewhat in this respect, that is all right by me. I do not want to press the point But my preference is defInitely for a more complex theory of truth to avoid the other difficulties. First, I do not think negative beliefs such as 'There are no unicorns' or 'My wife is not at home today' or 'The battle of Waterloo did not take place in 1817' correspond to reality, though they are true. Some people have thought it a difficulty for correspondence theories that there does not obviously seem to be anything to which the absence of animals or people from certain places at certain times corresponds. And I agree that this is a difficulty. I have not been convinced by those who sought to dismiss it. It seems rather that it is the failure of reality to correspond to those creatures' presence that makes belief in their absence true. The tranquility of the countryside around Waterloo all year was inconsistent with their having been a battle there in 1817. The engagement of my wife in some important matters away from home is inconsistent with her being here. All creatures we know of have descriptions that fail to match the description people give in story and fable of unicorns. It is better to construe these negative beliefs as true by virtue of being logical consequences of other beliefs true by correspondence. Secondly, I should like my theory of truth to leave it open as to whether there are any abstract entities to which beliefs in mathematical truths correspond. There might be, and I should not mind. Or there might not be, and that would be all right. It is convenient not to have to take sides on this controversy in order to say what truth in general is. The constituent of trustworthiness gives me this option, as I have already suggested. We can test rules of inference as to trustworthiness using cases where we independently think premises and conclusions true by correspondence. We can thus obtain some mathematical and logical truths by transmuting the rules into statements. (The usual inductive inference patterns in science fail this test, though mathematical induction does not.) We can obtain other truths by defmition or stipulation and let implication take care of the rest Thirdly, statements or sentences, where they are true, will not be true by correspondence. They will be true by virtue of being correct expressions, according to linguistic conventions, of beliefs which correspond, or by being logical implications of such correct expressions. Of course, where true they are trustworthy.
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C: The transmission of truth The chief function of validity in argument is to ensme the transmission of truth from premises, in case they are true, to conclusion. What, on my theory, is being transmitted? Of course, truth! By which I mean a measure of trustworthiness. A significant advantage of the complex theory over the more traditional simple ones is that I do not have to wrestle with the difficulty of pretending that correspondence is transmissible by logical deduction. Of course, some conclusions of arguments with premises which express beliefs which correspond to reality may themselves express beliefs of the same kind. But whether a conclusion expresses such a belief will be a matter of whether reality includes a counterpart to the belief the conclusion expresses, not a matter of the validity of the argument.
D: Truth in science I confess to having more or less refused, for a very long time, to allow that any deliverance of science, especially any scientific theory, could be true. I used to say, instead, that the theories of science were all, strictly speaking, false. The development of the theory being proposed here permits me now to say that science may furnish us with truths, though I shall have to say this with caution before audiences which still retain traditional theories of truth, which imply that what is true is strictly and accmately true, and so trustworthy in all circumstances. There is nothing new in the implication that what science has to say is approximately how things are. Many thinkers advert to the view that scientific theories involve simplifications or idealizations of natural processes and, thus, cannot be absolutely accurate. Scientific theories, on ,this view, furnish us with models of the world rather than with facsimiles. Others, who do not share such a realistic approach to scientific knowledge, may nonetheless endorse the notion of scientific theories as models, without committing themselves to there being anything to model. But I do have something which might be new to suggest regarding verisimilitude, though I am not at all sure how fruitful the idea might be. Discussions of verisimilitude usually treat it as a logical matter; perhaps a matter of the closeness of match between the implications of a theory and the class of all true statements or sentences;42 perhaps a matter of the logical relation of a theory to its evidence.43 I think this is a mistake. The usual notion, something like Popper's, is at odds with the correspondence theory, which students of verisimilitude usually espouse. Assume truth is a matter of correspondence between what is believed and reality, and reckon that the correspondence is usually only partial or approximate. Assume x is an agreed way of expressing what scientists severally believe. Then 'x is
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true' should be glossed as 'x expresses beliefs which are quite like how things are' or 'the beliefs x expresses are homomorphic with some elements or features of reality' or, better, 'x says how, in some respects and to some extent, things are'. These glosses suggest that if scientists wanted to be strict they should say 'x is verisimilar' rather than 'x is true'. This would save confusion when more stringency leads people to prefer to say that x is false. 'Verisimilitude' might not be the right word, here, since its etymology suggests that it is a theory's resembling the whole truth about the world that is meant, rather than its property of correctly expressing beliefs which correspond more or less well to reality. And this could send thought off on the wrong track. Unger has suggested that there is no such thing as the whole truth about the world,44 and I incline to agree with him. But if one is committed to truth's being carried primarily by linguistic objects, rather than by beliefs arising from experience, the set of all true objects (sentences or propositions or statements, according to taste) might seem a relevant and not incoherent notion. Perhaps we need a new word, something like 'res-similitude', to suggest we look in the other direction for an analysis of that desirable quality by which we rank our preferred theories, the direction of the ways in which and the extent to which our beliefs, expressed in our theories, match how things are. It does seem to me that scientific activity is more bent towards correcting elements of mismatch of scientists' theories with the world, than it is concerned with matching the set of all true sentences, or some such. There is an important difference between verisimilitude (res-similitude) and empirical success or adequacy. (Bunge's characterization in the work cited seems to confuse these.) The frrst is an ontological notion, having reference to how things are, while the second is a purely logical notion measuring the match between the implications of a theory and relevant reports of experience. It is perfectly possible that theories which point to grossly dissimilar ontologies may be indistinguishable as to empirical success. It was a positivist fashion, now mercifully on the wane, to disclaim any interest in theoretical distinctions which could not sport detectably different empirical consequences. On the other hand, it is an inductivist conceit to take empirical success as a mark of verisimilitude. I have no faith in this, though I do think empirical failure points to dissimilarities between beliefs and nature.
E: The irreducible subjectivity of objective knowledge The main difficulty for theories of a third realm or of World 3 is that many of the abstract objects which promoters of these worlds like to think of as their best citizens are arguably incurably subjective. Their objective counterparts simply do not exist. Perhaps this is not the case for such clean straight forward objects as numbers, which are so very well defmed and so
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easy to grasp that it does seem as though you and I are both believing very much in the same thing when we talk of numbers. But then, when we start doing philosophy of mathematics seriously, it becomes quickly apparent that there are at least seveml, possibly many, radically different notions as to what numbers are (leave aside mathematical objects of any great complexity or subtleness), if 'are' is the right word. One loses confidence that numbers are independently existing real entities waiting for each of us to make their discovery freshly for ourselves, in each generation. Perhaps each of us is really inventing numbers afresh, aided by teachers who seem to know more with each generation, though how teachers view numbers and how they try to get their pupils to conceive of them is subject to change. We are all of us constrained in our inventions by the need to get the same answers as each other to the problems the teachers set us, though this seems beyond some poor students. I have no doubt that there is some abstract content to my numerical thoughts and to yours, but then the denizens of World 3, say, fission into myriads of subjectively rooted objects, clustering together because of the constraints, but not clustering around anything in particular. I am by no means sure that there are no such things as Frege and Popper postulate for their third worlds. If we were to introduce some sort of god into the picture, for example Whitehead's,45 God's thought might guarantee what Frege wanted, but hardly what Popper wants, since he wants World 3 objects to be man-made. But absent God arbitrating what numbers and the like are, I strongly doubt man's propensity to create the objective objects needed. Where it seems quite clear that we do not agree on concepts is in science, despite the consensus scientists reach upon the fonnulae to use for computational or, sometimes, explanatory purposes. Take quanta. Everybody agrees that quantum theory is the best confmned scientific theory ever, but there is widespread disagreement on how to understand it. On the surface, the dispute is about the defmiteness of the values of some properties of whatever is there. Opinions range from the classical defmiteness of properties Einstein seems to have believed in,'" through the 'smeared' values Bunge proposed,·7 and the influence of the observers' actions on the past of the observed particles,48 to the full involvement of the observers' minds!' Or the dispute is superficially about the propriety or meaningfulness of talk about any submicroscopic reality between observations. Hacking argues for what he calls entity realism rather than theory realism, because, as he says, all working scientists in the field agree that electrons are real because they can manipulate them: "if you can spray them, they are real," he saYS.5O But there is no disagreement among scientists, even those working in the same team, as to what electrons are. Now, if we do not all see quanta and electrons the same way, we can hardly be supposed to agree in our beliefs about the larger objects they comprise (atoms, molecules). And if not them, what we envisage grosser material objects to be will hardly coincide, especially when scientific models
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are admittedly idealizations and we are left on our own how we jump from them to the objects of ordinary experience. The problem for objective, independent denizens of World 3 comes in spades when we consider art objects, whether these depend upon performance, as with music or drama, or not, as with poetry, novels, paintings and the like. With the fIXed type of art object, there is the question of what its abstract counterpart could possibly be, given that no two people appreciate a work of art identically, and the creator is not allowed a privileged position on what the work. really says. I have already commented upon the difficulty inherent in staging a good play. It is even more difficult when the playwright, as in the case even with geniuses, was unable to solve some problems of coherence himself or herself. The director and the actors have to bring their own views as to how this is to be done to the job on hand But even with a definitive text acknowledged as completely coherent, there is not enough specificity to rule out quite significantly and creatively different, completely faithful, presentations. The same is true, it seems to me in music. No doubt Mozart heard his music as he wrote, and no doubt conductors and many musicians hear the music as they read the scores. Lesser mortals need it performing for them. And no two performances are the same in every respect Wha4 with all this, is the real piece? What is in World 3? On my view, all the hearings are hearings of similar but not identical abstract ideas, and there probably is not a definitive something or other about which they all cluster. It is another question all together, and a very interesting one, whether any of these abstract objects endures, and if so in what sense? But I shall not take up this metaphysically deeper topic here. Suffice it for now that my attempt to say what it is for something to be objectively true has driven me to dispute the existence of just those objects that seem to be needed by some of the opponents of psychologism to underwrite what they want to call objective knowledge. But the subjectivism I have displayed is not pernicious since it is not authoritarian. It leaves you with the responsibility, and the risk, of your own inquiry at the same time as it advertises my need of your cooperation in mine.
423 ENDNOTES 1. Bertrand Russell's theory is an exception. See: Bertrand Russell, Human Knowledge (London: George Allen and Unwin, 1948). 2. See: E.E. Evans-Pritchard, Witchcraft, Oracles and Magic among the Azande (Oxford: Oxford University, 1937). 3. See: Nicholas Rescher, The Strife of Systems (Pittsburgh: University of Pittsburgh, 1985). 4. See: Iris Murdoch. The Sovereignty of Good (London: Routledge & Kegan Paul, 1970). 5. See: Gertrude Ezorsky, "Pragmatic Theory of Truth," in The Encyclopedia of Philosophy, 00. Paul Edwards (London: Collier-Macmillan, 1967), Vol. 6, pp. 427-430. 6. See: Charles S. Peirce, ''What Pragmatism Is," THE MONIST (1905); cited in: Ezorsky, "Pragmatic Theory of Truth," p. 427. 7. Ezorsky, "Pragmatic Theory of Truth," p. 427. 8. See: John Ziman, Public Knowledge (Cambridge: Cambridge University, 1968). See also: John Ziman, Reliable Knowledge (Cambridge: Cambridge University, 1978). 9. Ziman, Reliable Knowledge, pp. 132-137. 10. See: Michael Polany~ PersoNJl Knowledge (London: Routledge & Kegan Paul, 1958). 11. See Hans Jonas's excellent discussion of this issue in: Hans Jonas, The Imperative of Responsibility (Chicago: University of Chicago, 1984). 12. See: F.P. Ramsay, "Facts and Propositions," PRCX:EEDINGS OF THE ARISTOTELIAN SOCIETY (1927); excerpted in: George Pitcher, 00., Truth (Englewood Cliffs, N.J.: Prentice-Hall, 1964), pp. 16-17. 13. See: Peter Strawson, "Truth," ANALYSIS, Vol. 9, no. 6 (1949), pp. 83-97. See also: Peter Strawson, ''Truth,'' PROCEEDINGS OF THE ARISTOTELIAN SOCIETY, Supp. Vol. XXIV (1950); reprinted in: Pitcher, Truth, pp. 32-53. 14. See: Alfred Tarski, "On the notion of truth in reference to fonnalized deductive sciences," RUCH FILOZOFICZNY, Vol. XU, (1931); reprinted under the title 'The Concept of Truth in Formalized Languages' in: Alfred Tarski, Logic, Semantics, Metamathematics (Oxford: Oxford University, 1956), Ch. VITI. See also: Alfred Tarski, ''The Semantic Concept of Truth and the Foundations of Semantics," PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH, Vol. 4 (1944); reprinted in H. Feigl and W. Sellars, eds., Readings in Philosophical Analysis (New York: Appleton-Century-Crofts, 1949). 15. Tarski, Logic, Semantics, Metamathematics, p. 152. 16. See: Ibid., p. 158. 17. See: Alan R. White, Truth (London: Macmillan, 1970), pp. 97-98. 18. Tarski, ''The Semantic Concept of Truth and the Foundations of Semantics," p. 63. 19. See: Karl R. Popper, The Logic of Scientific Discovery (London: Hutchinson, 1959), p. 274n. 20. See: Peter Strawson, ''Truth,'' (1949); see also: Peter Strawson, ''Truth,'' (1950). 21. See: William James, The Will to Believe and Other Essays (New York: Longmans, Green & Co., 1897). 22. See: John Dewey, Essays in Experimental Logic (Chicago: University of Chicago, 1916). >
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23. Cf., Tom Settle, "Human Freedom and 1568 Versions of Determinism and Indetenninism," in M. Bunge, ed, The Methodological Unity of Science (Dordrecht: D. Reidel, 1973), pp. 245-264; Tom Settle, "Indeterminism Undermines Science," FUNDAMENTA SCIENTIAE, Vol. 3, no. 1 (1982), pp. 103-112; and Tom Settle, "Self-defeat is not so Frequent," DI.ALCKJUE (Forthcoming). 24. See: Bas van Fraassen, The ScientifIC Imo.ge (Oxford: Oxford University, 1980). See also: Bas C. van Fraassen, "Empiricism in the Philosophy of Science," in Paul Churchland and C. Hooker, eds., Images of Science (Chicago: University of Chicago Press, 1985), pp. 245-308. 25. See: Jarrett Leplin. ScientifiC Realism (Berkeley: University of California, 1984). See also: Churchland and Hooker, Imo.ges of Science. 26. Whitehead's sense of what a proposition is - "the abstract possibility of some specified nexus of actualities realizing some eternal object" - is quite different from what is usual, and nothing I say rules out what he meant See: Alfred North Whitehead, Adventures of Ideas (Cambridge: Cambridge University, 1933), p. 312. See also: Alfred North Whitehead, Process and Reality (London= Macmillan, 1929), Part II, ch. IX. 27. See: Karl R. Popper, Objective Knowledge (Oxford: Oxford University, 1972), cbs. 3,4. 28. See: White, Truth. 29. Ibid., p. 83. 30. D.I. Q'Cormor, The Correspondence Theory of Truth (London: Hutchinson, 1975), p. 130. 31. See: P.C.W. Davies and IR. Brown, cds., The Ghost of the Atom (Cambridge: Carrlbridge University, 1986). 32. See: A. Aspect, 1. Dalibard, and G. Rodger, "Experimental Test of Bell's Inequalities Using Time-Varying Analyzers," PHYSICAL REVIEW LEITERS, Vol. 49, no. 25 (1982), pp. 1804-1807. 33. See: Davies and Brown, The Ghost of the Atom. 34. Ibid., p. 124. 35. Ibid., p. 74. 36. Ibid., p. 66. 37. See: Alfred North Whitehe~ The Concepts of Nature (Cambridge: Cambridge University, 1920). 38. O'Connor, The Correspondence Theory of Truth; p. 30. 39. See: Mark Amadeus Notturno, Objectivity, Rationality, and the Third Realm (Dordrecht: Martinm Nijhoff, 1985), ch. 12. 40. Ibid., p. 214. 41. Ibid., p. 215. 42. See: Karl R. Popper, Conjectures and Refutations (London: Routledge & Kegan Paul, 1962); Popper, Objective Knowledge; and Newton-Smith, The Rationality of Science (London: Routledge & Kegan Paul, 1981). 43. See: Mario Bunge, ScientifIC Research I & II (New York: Springer-Verlag, 1967). 44. See: Peter Unger, Ignorance (Oxford: Oxford University, 1975). 45. See: Whitehead, Process and Reality. 46. See: A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" PHYSICAL REVIEW, Vol. 47 (1935), pp. 777-780. 47. See: Mario Bunge, ''The Interpretation of Heisenberg's Inequalities," in H. Pfeiffer, ed., Denken u.nd Undenken (Miinchen: R. Piper &, Co., 1977).
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48. See: Davies and Brown, The Ghost in, the Atom. 49. See: Wigner, SY11l1Mtries and Reflections. SO. Ian Hacking, Representing Q1II/. Intervening (Cambridge: Cambridge University,
1983).
FEDERIGO ENRIQUES: A PSYCHOLOGISTIC APPROACH FOR THE WORKING MATHEMATICIAN GIORGIO ISRAEL
I. The Influence of Axiomatic Thought on Contemporary Mathematics and the Historiography of Mathematics The influence of the axiomatic approach on mathematical research and the historiography of mathematics has clearly been in decline for some time now. Many years have past since Nicolas Bourbaki's Elements de mathematique were the standard texts for mathematicians. These volumes are now gathering dust on library shelves, replaced by a plethora of manuals using an informal approach to the subject. And in the field of the history of mathematics too, the range of textbooks and manuals is widening all the time, as is the variety of historiographical methodologies. Some have taken this to indicate that a criticism of the axiomatic approach is now outmoded, overtaken by events, and probably a waste of time. But in our view, the historiography of mathematics, in order to develop fully, must be 'cleansed' of every vestige of axiomatic stereotypes: the case study examined here would be quite unthinkable in terms of those stereotypes. Cultural fashions do not offer a reliable image of the concepts that actually occupy the minds and dominate the work of scientific researchers. And the fact that axiomatic ideology has gone out of fashion does not mean that it has not left lasting effects on the thinking of mathematicians (and historians of mathematics) or that it is not still at work, albeit subconsciously. These effects are due to the greatest boon that the axiomatic approach can rightly claim to have brought to the world of research: the articulation of a paradigm and research method that enabled the mathematical community to recover its faith in research after the dramatic loss of confidence that was triggered by the so-called 'crisis in foundations' that occurred between the end of the nineteenth century and the beginning of the twentieth. The axiomatic movement managed to do this by suggesting that all the issues that had previously been at the focus of attention in the great philosophical debate on the foundations of mathematics should be ignored, and that mathematics should be severed from the rest of science, particularly applied
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science. We feel that it would be useful to rapidly examine how this occurred. In a paper published in 1951; Jean Dieudonne used already traditional examples and concepts to describe the axiomatic method. In so doing, he not only rejected any intuitionist, empiricist, or psychologistic approach out of hand, but declared that any philosophical debate on the foundations of mathematics is futile. Dieudonne found the non-axiomatic mathematicians' approach unacceptable because it privileged certain classical notions (the concept of integer numbers, and the basic notions of elementary geometry, for example) on the grounds that they have a special link with the sensible world from which they are derived by abstraction.2 And that was not all: Dieudonne believed that the spread of the axiomatic method had radically changed the mentality of mathematicians. Whereas the 'classical' mathematician was psychologically predisposed to privilege notions which he considered to be closer to tangible reality, the mentality of the axiomatic mathematician in the Fifties led him to entirely reject debate on this issue, or to even fail to understand what it was all about Hence, Dieudonne wrote that "when mathematicians of my generation read the controversy of the century between the 'empiricists' and the 'idealists', they find it hard to understand the attitude of most of the antagonists."3 Axiomatic theory placed all mathematical theories on the same plane, and banished every 'philosophical' problem with a stroke: The modem mathematician has a perfectly clear conscience, caring little for the pseudo-problems that haunted his predecessors. The logic and theory of classical sets, that form the base of his language, have long since been systematized in order to respond to all his needs, exorcizing completely the 'paradoxes' that terrorized the contemporaries of Cantor.... TIle monster of Contradiction itself, brandished with such persistence by Poincare against axiomatics, has lost its scariness: to ascertain that a theory whose axioms are A, B, and C is contradictory is, for us, only to prove the proposition 'not C' in the theory whose axioms are A and B; from this point of view one can without paradox maintain that, for the mathematician, it is more interesting to prove mathematically that a theory is contradictory (which is a theorem), than to prove metamath£matically that it is not (which simply means that there is no chance that one will ever prove mathematically that the theory is contradictory). All questions such as the non-contradiction of theories, the 'EnJsch£idungsproblem', and in general all that relates to proof theory, are responsible now to a science that is completely separate from mathematics, 'Metamathematics'; this new discipline is constantly developing and has already provided many interesting new results, but it is perfectly permissible for the mathematician to ignore it completely without being at all hindered in his research.4
In many respects, emptying mathematics of its content reduced it to a "gigantic combinatorial game'" and made mathematicians "wholly independent of philosophy. "6 Hence, Dieudonne wrote that:
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... it is always possible for the philosopher to be in disagreement with all or part of our system, in the name of the possible relations between this system and the other thought processes or reality; ... as mathematicians, this affects us very little. What justly bothered our predecessors was that philosophers could fmd fault with their reasoning from within, so to speak; by that, I mean finding obscurities, incoherences, and contradictions in their reasoning. The great critical revision that followed the crisis of 1900 gave us solid enough bases so that we now feel completely immune to that d3l1ger.'
This is not the appropriate place to examine the benefits and risks of this view, particularly in the light of the forty years of mathematical history that separate us from the time it was formulated. We will merely note that Dieudonne spoke not only of the benefits but also of the risk: (which he considered to be of secondary importance) that the conception of mathematics as a 'huge combinatorial game' might make research sterile. His main point, however, was that the debate which resulted from the crisis in the foundations of mathematics already seemed ancient and was fading to incomprehensibility. The other writings of the 'Bourbaki group' similarly attempted to 'protect' the mathematician against infection from philosophical doubt.8 In an article on "Foundations of Mathematics for the working mathematician," Bourbaki dealt with the problem of the relationship between mathematics and logic, emphasizing logic's subordinate role to mathematics. Its task is merely to 'prepare' the mathematician's working tools. No result obtained autonomously in the field of mathematical logic can change the empirical attitude which the mathematician now assumes toward his problems.' That same article spells out quite clearly the minimal set of logical rules and 'recipes' which the mathematician needs in order to proceed without the fear of being hampered by conttadictions or paradoxes, and they are discussed even more explicitly in two articles written by Dieudonne and Henri Cartan. 10 Contrary to the intuitionists, they claim that mathematics can be based on logic. But which logic? The mathematician "does not need metaphysical defmitions,"u and only wants to know the rules governing the use of the concepts with which he is familiar. Fortunately for him, these rules are ones which the mathematician has been applying for centuries- the rules of classical Aristotelian logic, "tertium non datur," appropriately completed and brought up to date. 12 The establishment of a code containing only 'the logical rules to be used by the mathematician, as a kind of 'recipe' imposed on him by the standard practice of research, was accompanied by a strategic move of crucial importance. Mathematics was emptied of content, reduced to a formal system (founded solely on logic), and thereby made into a colossal game of chess in which the rules of the game alone are of interest, and not the shape or color of the pieces. This strategic move banished at a stroke all the contradictions which had caused so many headaches for mathematicians around the tum of the century:
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...with this concept, the famous 'paradoxes' disappear by themselves, for the simple reason that their statement has not yet been able to be [ormaJized. 13
Henri Cartan, rather more soberly, put it in this way: The goal that Hilbert proposed - to assure once and for all the fO\D1dations of mathematics - seems to us well attained, if we give up trying to resolve the fundamental questions of logic (Entscheidungsproblem) and if we fix with precision the true goal to be reached: to biUld malhemalics solely on Iogic. H
So the problems had not been solved, but swept away by a decision. Emptying mathematics of its substance was tantamount to the 'official expulsion' of the 'bogeymen' who had caused our ancestors so many sleepless nights. It was the 'official expulsion' of any philosophical problem from the field of mathematics. What a paradox the axiomatic school of thought led to! On the one hand, it could not, in wanting to base mathematics on formal logic, avoid referring to the achievements of Cantor, Frege, Peano, and Russell. But at the same time, it was obliged to maintain that the philosophical issues that those men deemed so important are, wholly irrelevant- even though these arguments had been their main source of fire against their opponents' stances, such as Brouwer's intuitionist position, or Poincare's semi-intuitionist stance. While Bourbaki had to stand with Frege against psychologism, with Cantor against the many French opponents of set theory, and with Hilbert against the intuitionists, he was simultaneously forced to declare that most of the topics of their work are irrelevant For the axiomatic school, Cantor's set theory (to quote Hilbert) was the 'paradise' from which no one would ever be able to chase the mathematician. But Cantor, as we know very well, was wholly opposed to an axiomatic approach. IS Cantor's philosophical ideas must therefore be ignored by the mathematician who wants to peacefully enjoy the fruits of that 'Cantorian paradise'. But without saying so. The most that axiomatic thought could permit itself was a purely accumulative historiographic view. All those who had helped to develop the symbolic logic which would henceforth become the mathematician's working tool (perhaps even subconsciously, like Moliere's 'bourgeois gentilhomme' who spoke prose without realizing it) had to be characterized as the forerunners ofaxiomatics. All that was left of Cantor's work was the formal framework of set theory, and the assumption that the essence of mathematics lies in its freedom. The axiomatic approach not only robbed mathematics of its content, it belittled the ideas of those whom it was forced to consider as its forerunners, presenting us with a boring portrait gallery of individuals whose greatest or least merit is merely that of having helped to build up the final edifice. The crucial point is that in the classical debate on foundations, everything held together. For the protagonists in that debate, the intention was not to
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reassure the mathematician from the practical point of view. If it had only been a question of deciding between an intuitionist type and an axiomatic type discovery 'technique', the debate would never have reached the history books. No advocate ofaxiomalics ever dreamed of denying the fundamental, indeed the primary, role of intuition in mathematical discovery. 16 All he demands is an axiomatic presentation of theories, a presentation which he deems an "absolute necessity imposed on any mathematician who cares for intellectual integrity." 17 But his most serious demand is that such a presentation requires that there be no debate aoout the nature of mathematical entities. He declares that debate about whether the concept of number is logical, psychological, or empirical, and about whether the concepts of geometry are empirical or physical, or 'axioms' or 'conventions' is insignificanl All of this was put over - with a slightly mischievous and compliant glance at the researchers who are only interested in the 'crude' production of theorems - as a learned, but futile, diatribe. For the main protagonists, such as Frege, Poincare, Brouwer, and to a certain extent Hilbert, this debate was supposed to establish the place of mathematics in the context of human knowledge, its role as a tool for analyzing, describing, and interpreting physical phenomena, and its relationship to philosophical thoughl The radical axiomatic approach did not have its own answers to these issues: it decided not to answer, declaring them irrelevant, separating mathematics from philosophy, separating mathematics from the other sciences, and declaring the relationship between mathematics and the empirical or experimental sciences to be a matter of pure chance. 18 The problem of the nature of mathematical concepts was not solved, it was eliminated: "Whether mathematical thought is logical in its essence is a partly psychological and partly metaphysical question which I am quite incompetent to discuss," declared Nicolas Bourbaki. 19 See, for example, how Frege's work is presented in Dieudonne's Abrege d' Histore des MatMmatiques. 20 In one chapter, revealingly entitled "Les progres vers la formalisation et ]a comprehension de son role," the author mentions only his technical contributions to formal logic, and therefore to founding mathematics on rules of logic. Only a fleeting, non-committal mention is made of Frege's ideas about the nature of the concept of number, and nothing at all is said about Frege's attack on psychologism. This, however, is hardly surprising: everything is acceptable to the axiomatic school provided that they are not put out by philosophical or epistemological problems. Even an irrationalist view of mathematical discovery is acceptable, such as that weird and woolly mixture of Platonism and drawing-room gossip psychologism offered up by Bourbaki: ...one cannot insist enough on the fundamental role played, in [the] research [of the mathematician], by a particular intuition...that is not the vulgar sensible intuition but rather a kind of direct divination (anterior to all reasoning) of the normal behavior that he has the right to expect from mathematical entities that
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long acquaintance has rendered almost as familiar to him as the beings of the real world 21
In the Forties and Fifties, the situation was eventually settled: the axiomatic point of view become the 'general ideology' of the mathematical researcher. The mathematician had gained a reasswing psychological peace of mind, feeling 'free' to busy himself with his theorems without having to be accountable to the physicist or the philosopher. This is not the place to debate the way in which the axiomatic ideology became established, or who were mainly responsible for these developments. 22 We would, however, like to draw attention to the general framework, which had acquired standard features by the end of the Thirties, and which was particularly prominent in the two leading European schools of mathematics. German mathematics seemed to be wholly on the side of the axiomatic stance, and the emigration of so many leading protagonists of the school to the United States led to a transfer not only of scientist but also of scientific methods, and this was to leave a lasting impression on America's approach to research in general. French mathematics, after a long period of decline - which had, due to the lack of development in axiomatic mathematics' twin, theoretical physics, gone hand-in-hand with a decline in physics - showed signs of a recovery WIder the impetus of the Bourbaki school. By the Forties - as Dieudonne rightly pointed out - the arguments of a few decades earlier seemed to belong to some remote age. The new school had become established practice, perhaps subconsciously, so much so that even today the return to a more 'concrete' mathematics, a return which seems determined not only by the spread of mathematical modelling, but also by the spread of infonnation theory and numerical analysis, is occurring in the context of a practicist approach- indeed, a blatantly practicist approach. It is not, in any event, occurring as a result of the need to create a carefully considered relationship in which even philosophy could reestablish the contact with mathematical research which it lost so long ago. While axiomatic thought has had a pretty strong influence on mathematical research methods, its influence on the historiography of mathematics has, perhaps, been even stronger. The historiography of mathematics has always suffered from a sharp weakness in the context of the historiography of science. There are a great many reasons for this weakness. One major reason is the technical difficulty of the subject. But even more serious is the problem of the relationships between mathematics and the other fields: because of the close relationship between mathematics and physics, whole chapters of its history have been lost to the history of physics. The history of ordinary differential equations and partial differential equations, for example, has been almost systematically taken over by the histories of mechanics and mathematical physics, respectively. On the other hand, the historical analysis of disciplines, not viewed in terms of their applications, has suffered from a spontaneously accumulative-oriented teehnicist approach. Looking through
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the best known history of mathematics manuals, which are few and far between, one can detect a Jack of any thorough historiographic methodology and a widespread reluctance to discuss matters of conceptual orientation in the history of the discipline. It is almost as if their authors had a fear of 'soiling their hands' by getting involved in pointless chatter and thereby giving the impression of wanting to avoid the real issue: the technical problems. The spread of the axiomatic movement only helped to reinforce this tendency by proposing a dogmatic approach that views the whole history of the discipline as a monotonous tendency towards the final 'triumph' of the axiomatization of mathematics, thereby following a historiographic stereotype which is a perfect example of what Thomas Kuhn called 'the concept of development-by-accumulation'.23 Most members of the community of mathematical historians have adapted to this stereotype, intimidated by theses that were presented not so much as the result of historical research, but as the 'last word' of some leading researchers in the scientific community, almost as if they were the 'official' spokesmen of this community.:M This historiography has sifted through most of the history of mathematics, judging crudely in terms of the degree of adherence to the 'fmal' stage of mathematics. Like Dante Alighieri's Minos, the axiomatic historian "examines their offences at the entrance, judges and despatches them according as he girds himself. ,,25 The result is that even though axiomatic thought has lost its hold today, the historiography of mathematics has been strongly influenced by an accumulation of hasty and superficial judgments about periods and crucial aspects of the history of the discipline, and hesitates when faced with the task of critically reappraising the axiomatics' Divine Comedy. We cannot provide even a very rough list of these historiographical distortions in this paper. That would require a long essay on that subject alone. Here, all we wish to do is to show the serious degree to which the contribution of modern Italian mathematics has been penalized by axiomatic historiography, despite the fact that Italian mathematics - at least between 1870 and 1930 - ranked in importance immediately after the great Gennan and French schools.'" The reason for this is probably that Italian mathematics was 'guilty' of never having taken axiomatic thought on board. For example, everyone knows that Vito Volterra was the fIrst mathematician to introduce the concept of 'functional', but that he deliberately relegated the problem of founding general functional calculus to a secondary plane because he was mostly interested in applied mathematics. His 'punishment' was to be virtually expunged from the list of the founders of functional analysis.'r1 No less brutal treatment was meted out to Italian algebraic geometry: despite 'the fact that the contemporary American and Soviet schools explicitly drew on the research begun by the Italian school and acknowledged its great importance, the axiomatics schools devoted only a few derogatory words to it.
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We shall later turn to the substance of this historical appraisal. For the moment. suffice it to say that it was dictated by the hostility to the Italian geometers' quasi-empirical approach, an approach which was deemed to be lacking in rigor. Yet it is precisely the 'negative' features of this approach which link up with a fascinating historical event that puts the lie to the commonplace that there was no room in the mathematical community after the end of the nineteenth century for any apJX08Ch but intuitionism (or semi-intuitionism) or axiomatics. The Italian geometric school seemed to be inspired (due to its leading 'theoretical' exponent. Federigo Enriques), by an openly psychologistic approach, albeit sui generis. As a result, a school of philosophy of mathematics which seemed to have been not only beaten but wholly expunged from the field of mathematics, reemerged in the work of a scientific school of great vitality and prestige. We shall see how Enriques' psychologism, which the whole of the Italian geometric school more or less explicitly and unanimously endorsed, was not merely a 'philosophical ornament' or generic ideological framework, but a research method that was consistently applied. The relevance of this intellectual development therefore lies in the fact that something occurred that was perhaps unique: a psychologistic conception directly applying to mathematical discovery, and not limited to playing the part of a general philosophical conception of the foundations of mathematics. Let us see how Enriques' ideas took shape in the context of Italian science at the close of the last century.
ll. The Emergence of Enriques' Ideas in Italian Scientific Thought at the Turn of the Century Anyone wishing to study the history of modern Italian mathematics must inevitably take account of the influence of the very weak state of Italian science as a whole before Italian Unification. Physics was particularly weak, and almost exclusively experimental. Mathematical physics was as poorly developed, and was almost exclusively influenced by the work of Lagrange who was popular in northern Italian scientific circles, especially in Turin. Lagrange's influence (and ignorance of Cauchy's work) led to a predominantly algebraic approach to mathematical analysis. Geometry was considered solely as a technical tool for research in mechanics and for the study of analytical problems. Much of the research was concerned with questions of elementary algebra and analytical geometry of the simplest plane curves. It was such an unsatisfactory situation that one of the first steps taken by many scientists in the period immediately after Unification was to go abroad to find out what was happening there, and if possible to import the tradition of the leading European schools. 28 One of the features of post-Unification Italian mathematics was, therefore, the feverish interest in foreign contacts, an interest which reached such a pitch that Italian
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mathematics became rapidly involved in the mainstream of international scientific relations. While this was all to the good. it nevertheless had one drawback: these scientists' ideas, personal inclinations, and preferences for one school of research rather than another were, as a result of their international inquiries, to have a great influence on the development of the new Italian mathematics. Italian mathematics was therefore not only indebted to imported ideas, even though these were soon developed autonomously at home, but these ideas were selectively chosen because of the preferences and interests of influential scientists such as Enrico Betti or Luigi Cremona. We cannot give a thorough account of these choices or of the most marked foreign influences in this paper.29 We will merely list very briefly (and very roughly) the main trends. First, a much closer relationship was established with the French mathematical physics tradition (as a natural result of the great prestige of Lagrange's work). Secondly - and this is certainly the most important point - there was explicit acceptance of Riemann's ideas, and his work had an enormous influence. What so fascinated the Italians about Riemann and his school was his synthesis of geometric and analytical thought, his view of analysis inspired by intuitive geometric and even physical ideas. The third aspect was the acceptance of the concept of 'rigor' of the Cauchy and Weierstrass school, a concept which was enthusiastically taken up in particular by Ulisse Dini. Simply by mentioning these three aspects one can immediately see the source of some of the main concepts of Italian mathematics at the tum of the century. On the one hand, it explains the focus on French style mathematical physics inaugurated by Betti, of which Volterra was one of the main exponents. And on the other, the influence of Riemann explains the apparently odd emergence of a great deal of valuable research in the field of differential geometry, research which culminated in the work of Bianchi, Ricci-Curbastro and Levi-Civita, and in that unusual synthesis of differential geometry and mathematical analysis which is absolute differential calculus. Levi-Civita, in particular, produced an extraordinary synthesis between mathematical physics and differential geometry. But interest in research into geometry also developed in another direction which combined Riemann's intuitive approach with a tendency towards geometrical research freed from the constraints of the algebraic approach and no longer limited to the study of the analytical properties of elementary curves (a limitation that was responsible for the paltry nature of some aspects of pre-Unification Italian mathematics). This geometry referred back to the synthetic method of the Greeks, and its main exponents were Chasles and de Jonquieres in France, MObius, PlUcker, and Steiner in Germany, and Salmon, Cayley, and Sylvester in Britain. The Italian school was led by Luigi Cremona. There was absolutely no interest whatsoever in those schools of mathematics that we might call 'pre-axiomatic', and which developed mainly in Germany around early research into abstract algebra. Perhaps
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'new' Italian mathematics felt 100 strong an aversion towards algebraic methods for any Italian mathematician to be willing to follow this trend. But there is no doubt that it was this lack of interest which paved the way for the failure of axiomatic mathematics to catch on in Italy.30 There can be no doubt that the rediscovery of the synthetic method and the role of geometric intuition was the result of a reaction to certain excesses of Weierstrassian analysis. In an article published in 1920, Enriques described these excesses in the following terms: The analysts, looking at the Weierstrassian star, were pleased to say that the moment had come to free Analysis from the jallaciOlU or at least the extraneous intuitions of space; the aim of Analysis, for whomever considers the logical dignity of science, seems to consist in transforming the whole structure of modem mathematics into a rigidly formalistic theory, discormected from the external world, and in suppressing any conceptual dynamism, by substituting the 'pseudopassages' into infinity with chains of inequalities.'l
And so the criticism of the 19th century idea of 'rigor' became a criticism of every formalist approach, accusing it of tending towards abstraction, and rejecting the 'old' dynamic approach in favor of a static mathematics based on pure logic. These attitudes also explain why axiomatics failed to make much headway in Italy: it was seen as the daughter of abstract rigorism in mathematical analysis. Synthetic geometers seemed to share a common deep hostility to the oppressive domination of the analysts. 32 The ideal of purism, while not being an exclusively Italian product, reached truly great extremes in Italy: To perfect the synthetic method up to the point of making any help from algebra useless was the more or less explicit intention of every geometer: some even went so far as to proclaim rigidly that Geometry ends when you start to talk about nwnber. "33
It is quite true that analysis was adamantly rejected. Synthetic geometers nonetheless based their reasonings on classical algebra, but following a kind of geometric 'insight': ...[an algebra] so happily guided by geometrical intuition as to appear almost transfigured, the algebra of which not the algorithmic development appears, but the qualitative content..., which, if effectively interpreted, leads in a simple and incredible way to fimdamental and instrinsic results.34
We should not underestimate the power of the new method, which seemed to open up prospects for development to a hitherto unexpected degree. More than for its 'purity of methods', the geometrical approach was fascinating on account of its originality:
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The geometrical vision of algebraic entities was atlractve for its novelty and for the fact that easier and more abundant objects of study lXesented themselves. It appeared as if a new world opened itself to the geometer, a world in which one had only to open a hand in order to harvest plenty of discoveries, and in which the imagination, triwnphantly advancing, would always open new magic doors, as in a palace built by fairies."
Enriques goes on to describe very effectively the triumphant success of the purest geometric method in the Italian mathematical world: As soon as the geometers saw this enchanted world, the announcement of the promised land attracted those astonished men. Everywhere geometers multiplied themselves....that was a time in which, as a colleague and teacher of mine used to wittily say, it sufficed to sow a bean to see a geometer bom.16
Yet the negative consequences of this 'purist' avalanche soon made themselves felt. On the one hand. they were due to the fairly fanatical hostility to analysis, which very soon led - as Volterra was to later complain - to a split in Italian mathematics, with two schools at loggerheads with each other. On the other hand, the fascination with the new methods led to an inordinate passion for the demonstrative technique as an end in itself. And this led to the subordination of the problems to the methods. Research was no longer directed by clusters of large problems whose objective importance was acknowledged by the scientific community, but by individual free choice. As Corrado Segre said in a very important article that paved the way for a new phase in Italian geometry, an artificial geometry had been created in which imagination was allowed free rein, and the problem was often conceived simply to be able to use the method. 37 Corrado Segre was an unusual man in many respects: although he was not a brilliant mathematician, he did have an extraordinary intuitive ability to suggest the best ways of revitalizing geometric research. Above all else, he was a 'master': and this is how he was considered by all his colleagues from the age of thirty. From 1880 to 1890, thanks to Corrado Segre, as well as Giuseppe Veronese and Eugenio Bertini, the foundations were laid for a new, highly productive phase in Italian geometry which culminated in the work of Enriques and Castelnuovo. Segre's contribution was not limited to merely criticizing purist excesses. He also indicated a number of fundamental issues and avenues. As far as method is concerned, he remained a staunch advocate of the need to maintain the vitality of synthetic methods, but stressed the need to avoid separating analysis from geometry and to find new forms of synthesis focusing on problems rather than methods. It was necessary to refer back again to the German school of Riemann and Klein, and exploit the great possibilities offered by linking analytical problems to the geometric-intuitive approach which inspired that school. In the specific field of algebraic geometry, Segre took up the study of geometry on an algebraic curve following Riemann, which had been developed along algebraic lines by Brill and Noether. The brilliant idea that
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enabled him to work on the methods of projective and synthetic geometry, in a new context that was not stifled by tight purist constraints, referred back to the ideas of Noether and Klein: he reconsbUcted Brill and Noether's results in the field of hyperspatial projective geometry, translating the invariant properties of a curve under birational transformations into projective properties of a model of the curve. His brilliant fmdings opened up the path to similar research in the field of the theory of surfaces. And it is here that the contribution of Castelnuovo and Enriques comes in. Federigo Enriques was born in Livorno in 1871 and studied at the University and the Scuola Normale Superiore di Pisa, graduating in mathematics in 1891. His academic background included two decisive periods: a specialization year in Rome in 1892-3, and a short stay in Turin working with Corrado Segre. Although he was certainly influenced by Segre's opinions during the second period, he had earlier had the chance to study under Cremona during the year spent in Rome. But Cremona was a source of deep disappointment to him, and it was his meeting with Guido Castelnuovo (who was six years his senior and was later to become his colleague and brother-in-law) that had a far-reaching effect on him. Castelnuovo, who was already a professor at the time, and to whom Enriques - disappointed with Cremona's 'purism' - had turned to understand Serge's new approach, described the character of Enriques in an address in his honor: I was going to suggest to him the reading of books and memoirs, but I soon realized that this would not have been the most appropriate way. Federigo Enriques was a mediocre reader. He did not see what was written on the page in front of him, but rather what his mind was casting upon it. I therefore adopted another method: conversation. Not the conversation in front of a table with paper and pen, but the peripatetic conversation. It was then that began those endless walks through the streets of Rome, during which algebraic geometry was the favorite themes of our discussions. After having in a short time assimilated all the conquests of the Italian school in the field of algebraic curves, Enriques resolutely set about treating geometry on an algebraic surface. He kept me daily informed on the progress of his researches, which I subjected to severe criticisms. It is not an exaggeration to say that in those conversations the theory of algebraic surfaces according to the Italian way was constructed. 31
This description mentions a number of key points. Firstly, Enriques' personal propensity to tackle problems intuitively and even with rough approximation, and his irritation with methodical, pedantic methods of study.» Secondly, the influence of geometric thought on his academic background, to which he was urged by his own inclinations and which, in turn, gave those inclinations a scientific method and an epistemological system. But one other basic element is missing to which Enriques himself referred on many an occasion, recalling how his interest in mathematics began as the result of a 'philosophical infection ('infezione filosojica') while at high school. Enriques' interest in scientific problems (and geometry in
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particular) was never a mere technical interest, but stemmed from his interest in problems of 'general culture' and from his keen interest in the role of scientific thought in culture and human activities. His mathematical research overlaps with his investigations into the major philosophical issues related to the foundations of science. It is impossible to draw a line between Enriques the philosopher and Enriques the researcher, without running the risk of never understanding anything about either. It is an arduous task trying to reconstruct an organic overview of Enriques' ideas. We are not dealing with an organized system of thought, but with the representation of certain fundamental ideas in more or less the same form within a context of comments, judgments, and examples in which it is easy to identify contradictions and changes of attitude. The definitions and philosophical categories which Enriques uses are often sketchy.40 One example of this is the name he gave to his system of thought - critical positivism - even though Positivism was one of his pet targets (at most he might have called it a critique of Positivism).41 He therefore approached philosophy with what we might call an uncluttered mind, which is simultaneously a strength and a weakness. It is a weakness in that one can clearly see the conceptual errors and approximations that abound in the syntheses that Enriques made of other people's philosophical ideas. But it is also a strength, in that Enriques expresses his ideas stripped of any of the traditional prejudices. And so he was quite ready to take on the role of metaphysics, without succumbing to the climate of shame in which Positivism had managed to shroud it. Equally open-minded was the way he reexamined the psychogenesis of scientific concepts-- one of the central themes of his thought The complex and eclectic nature of Enriques' thought makes it impossible to provide a satisfactory summary of it in a few pages. We will therefore take a more direct approach that may prove more interesting since it has not yet been explored. We will draw a direct analogy between Enriques' method of geometric research and his view of the psychological nature of scientific concepts, and mathematical concepts in particular, and from there attempt to define some of the fundamental features of his ideas. This will not only show us the underlying motivations that run throughout the whole of Enriques' thought, it will also help us to see an unusual double movement- a conception of the philosophy of mathematics directly related to research practice, and vice-versa, a research practice that is transfonned into a philosophical concept of the nature of mathematical entities.
IlL The 'Psychological Logic' of Scientific Discovery In the previous section, we alluded to the starting-point of Castelnuovo and Enriques' ideas about the theory of algebraic swfaces: they intended to pursue, in the framework of the ideas laid down by Corrado Segre, the frrst
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attempts by Noether to build up a geometry of algebraic surfaces in terms of the model of Brill and Noether's theory of algebraic surfaces. We cannot go into the very complex technical details in this paper.42 All we will say here is that the biggest difficulties arise when trying to extend to surfaces the methods of geometry on a curve, and more specifically, when trying to characterize surfaces which behave 'irregularly' with respect to the notion of 'genus'.43 Castelnuovo delivered a lecture in 1928 in which he gave a very vivid account of the method used by himself and Enriques in their research: We had constructed (in an abstract sense of COlUse) a great number of models of surfaces of our space and of superior spaces; and we had distributed these models, so to speak, in two windows. The one contained the regular surfaces for which everything proceeded as in the best of all possible worlds; the analogy allowed to transpose to them the most important properties of plane curves. But when we tried to verify those properties on the surfaces belonging to the other 'window', namely the irregular ones, the troubles began and exceptions of all sorts appeared. In the end, the assiduous study of our models had led us to predict some properties which should hold good, with suitable modifications, for the surfaces of both windows; we then tested those properties by constructing new models. As a last phase, if they resisted the test, we looked for their logical justification. With this procedure, which resembles that used in the experimental science, we succeeded in establishing some distinguishing characters among the families of surfaces.44
It would be a mistake to imagine that this is the description of a method used completely accidentally and in a particular context. And it is equally clear that Enriques' mentality had a great part to play in defining this research method, which was fashioned - at least in part - on the experimental sciences. There is a good deal of other evidence to confirm this. We will refer briefly to some of this evidence in a few other writings. In another paper, written in 1947, in which he described the origin of this research, Castelnuovo said that it was Enriques who had perceived the importance of the notion of 'genus' , and went on to describe the "systematic research plan" which Enriques had designed and which he implemented "until his fmal years": The plan consists in characterizing the properties of surfaces in relation to the values of the genus, starting from the surfaces with the lowest genus. The analogy would recall the classification of animals and plants made by the naturalists, starting from the simplest organisms. But in order for the analogy to be exact, we should imagine a naturalist who, being shut in his study, investigated from a theoretical point of view which kinds of organisms are compatible with the laws of morphology and physiology, and then enquired which among these can be actually found in nature.4S
Castelnuovo also stressed one of the outstanding qualities of Enriques in the following words:
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...the gift of intuition, which had led him several times to establish a result long before he had a satisfactory demonstration for it. Intuition intervenes above all when he appeals, as he often does, to the principle of continuity, which leads him to transfer the properties of an entity to other entities close to the first, and then to all those entities which stand to the first as in the same continuous system.46
The continuity principle occupied a central place in Enriques' ideas, almost as if it were the reflex of a metaphysical concept of the world of algebra-geometrical entities, as if this world were ordered into a sort of 'Great Chain of Being' .47 F. ConfOrto wrote that he viewed this world "as self-existent., independent and out of our mind, a world regulated by a supreme rule, the law of continuity, which reflects the analyticity of the entities under consideration," and then went on to add significantly: In order to understand such a world one ought not to fIx an ideal of logical perfection; even less ought one to proceed axiomatically, starting from postulates established somewhat arbitrarily.... The algebraic world exists in itself, and it is impossible to exclude from it certain entities, as for example those which constitute conceptions, because this would contradict the law of continuity. On the contrary, exceptions must be received and explained in the light of continuity itself. Understanding the algebraic world is not so much a question of correct deduction, as before and above all a question of 'seeing'.·
Actually, the impression that these quotations create is not wholly accurate- the impression of a mixture of Platonism (quite common among professional mathematicians) and a sort of experimental method applied to this world of ideal beings, creating, like Galileo, abstract models and putting them to the test of 'reality' (the Galilean 'cimerno'). The fact is that insofar as the nature of the objects studied by mathematics is concerned, Enriques denied that they had any purely objective character. This was in the year 1894-5, when he devoted himself to the study of the foundations of geometry, and concluded that in this study the logical and psychological approaches had to be taken in conjunction; in other words, the researcher had to investigate the sensations and experiences that led to the fonnulation of the postulates of geometry. The problem of the psychogenesis of scientific concepts had excited Enriques from his earliest years of activity, and as early as 1896 he had set about studying physiological psychology. That year he wrote to Castelnuovo: For my part, I approach this research with an enthusiasm which you will consider worthy of a better cause, but which is certainly greater than what I have ever felt for any other question.49
It was this research that led him to write a famous thesis in an article published in 1901, and subsequently refonnulated in Problemi della Scienza,50 reinterpreting Klein's Erlangen Program, classifying fundamental geometries in tenns of the criterion of the psychological acquisition of their
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fundamental concepts. Topology, metric geometry, and projective geometry, would, according to this classification, be linked respectively to general muscular tactile sensations, the special sense of touch, and sight But, before examining in greater detail the general aspects of Enriques' philosophy of mathematics and science, let us return briefly to the issues mentioned at the beginning of this essay, and particularly to the research methodology set out in the quotations. Let us also consider the explanation of this methodology in its rather rough and ready fonn. Even in this fonn, it cannot be likened to any concept of the 'bourbakist' axiomatic conception as described in the fIrst paragraph. According to this conception, Castelnuovo's account might be viewed as a kind of 'diary' describing one of the 'irrational' phases in which the mathematician is inspired by "a sort of direct divination, "51 a phase preceding the rigorous arrangement of the discovered result in a logical-deductive fonn. Seen from this point of view, the specific intuitive approach to discovery is irrelevant: it was the approach used, but it could equally have been another. The 'diary' of the scientist's emotions is irrelevant for the axiomatic scientist: knowing how a theorem fllSt came to mind does not affect the validity of the theorem, which is guaranteed by the instruments of formal logic. But for Enriques, Imowledge of the forms of psychological acquisition of scientifIc concepts is at least as important as their verifIcation in the fIeld of formal logic. The argument that Enriques supplies for his point of view is that scientifIc concepts are determined by the psychological process through which they are acquired. This means that the application of the formal logic method is only one aspect - and not the most important one at that - of the process through which a mathematical theory, or a scientifIc theory in general, is formed. It is not the most important aspect because it is limited solely to the aspect of verification which, apart from everything else, is 'optional', referring as it does to a particular way of looking at the scientifIc result. Just think if Enriques could have accepted the idea that the fonns of intuition and reasoning through which the mathematician makes his discoveries are secondary! On the contrary, the analysis of these fonns - that is to say, the psychogenesis of scientifIc concepts - is of fundamental importance. One can also understand how this approach places so much importance on the history of science, because it is more useful than any other discipline in reconstructing the genesis, and hence the deepest meaning, of scientifIc concepts and theories. This viewpoint, which turns the axiomatic approach on its head, is set out in its clearest fonn in a crucial passage from Problemi della Scienza. Enriques points out that formal logic offers two possibilities: [on the one hand, as] deductive theory modeled upon Arithmetic or Geometry... offers computations, abbreviates and controls certain developments, [on the other hand, as] study of the process of thought, directly reconstructed through its scientific products, apart from any particular expression through words or signs.52
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And he continues observing: ...with the traditional concept of grammatical, or more generally, symbolic Logic, we contrast that of a Psychological logic, which in its schemas and signs does not so much concern the written formulas as the conventions and the noons not stated on the paper (and unintelligible outside the psychological considerations) which guide its modes of COD"lbination.
It is only if understood in this way that logic does not play second fiddle to science: Logic, thus understood, does not constitute anymore a deductive theory subsidiary to scientific developments, but a science of observation and comparison having as its own object the critique of the elementary processes of thought, such as are reflected in the fundamental principles of reasoning; which processes it aims at explaining as a psychological reality.53
Having said that, he hastens to reject the objection that Logic has 'a normative value with respect to truth' whereas Psychology is 'a pure description of mental procedures whether false or true' (which is a decisive point of view in the context of what we said earlier): According to our own point of view (rigorously formal) it is above all necessary to correct the opinion that logical norms have an a priori value with respect to truth.... Logic can be considered as a set of noons, which must be observed, if one wants the consistency of reasoning. But this can also be expressed by saying that: among the various mental processes, some can be selected in which certain conditions of consistency are voluntarily satisfied. Those are precisely called logical processes. In this sense Logic can be considered as a part of psychology.54
Nothing could be further from Enriques' position than the idea that the role of intuition is as important to discovery as it is irrelevant to the theory, which is only legitimatized by verifying the logical consistency of the reasoning. The process of the psychological acquisition of the result is not only fundamental to the constitution of the theory, it identifies the features and defines the nature of its concepts as well. Verification using formal logic is useful, even though it is not essential, and it is certainly not the only way to legitimatize the theory. We have seen how Castelnuovo himself only spoke of resorting, in the final stage, to 'the logical justification of the results. An 'experimental' type procedure, albeit sui generis,55 of the kind described by Castelnuovo is therefore not a secondary aspect, but is central to the constitution of the theory. The use of 'models', 'windows', and 'trial' ('cimento'), according to Enriques, is justified by the idea that swfaces can be classified in terms of the genus, and that this classification is justified by the continuity principle. And so just as abstract mathematical 'models' of Galileo's physics are the 'lenses' through which the scientist observes and interprets reality, which is never presented to him directly and immediately,
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the mathematician analyzes the objects of his theory through the lens of the psychological construction which is built up out of it, and which becomes an inseparable part of the structure of the theory itself. For example, the purely logical fonn of the axioms of metric geometry explains nothing: yet the origin of this geometry is the consequence of a psychological process, namely, of the isolation of the metric (or mechanical) properties which depend on the concepts of measure, the equality of figures, and the possibility of superimposing one upon the other through motion. For the Italian school of geometry inspired by Enriques' ideas, the acquisition of the results through intuition is not a flawed, illegitimate, or provisional procedure awaiting the 'healing hand' of fonnal logic: it is the very feature of geometric, and more generally of mathematical and scientific, thought" This is of considerable importance, and we shall return to it at the end of the paper. It was through this unusual avenue that the Italian school of algebraic geometry chalked up a number of considerable successes, even though they could not be easily accepted by the scientific community because of the unusual nature of the procedures used, which were alien to the common verification criteria For this reason, and also because of a certain difficulty in understanding the school's philosophical reasoning, this school, which produced so many 'non-proven discoveries', was explained away in research circles and in the few historiographic writings on the subject, using the most obvious arguments (such as the 'particular mentality' of its exponents), which were so obvious that they explained nothing.
IV. The Place of Enriques' Ideas in European Philosophical and Scientific Thought We spoke earlier of the original and unusual nature of Enriques' ideas and their independence from the philosophical ideas of his age, an independence heightened by the fact that Enriques was not very well infonned about them and based his system on the vague impressions he had of them. For these reasons, his ideas did not fit into a well-defmed slot, and are a strange mixture of 'ancient' and 'modem' points of view. For example, his distance from the axiomatic approach and any abstract approach was decidedly 19th century, and was not only dictated by a methodological rejection of them, but caused him to misunderstand various technical achievements of the mathematics of his age. Yet his sensitivity to aspects of new theoretical physics appears to be very modem: Enriques was one of the main advocates and proponents of relativity theory in Italy, in contrast to the physicists and physico-mathematicians who were not only hesitant, but openly hostile to it. It is possible to understand how this occurred, and how this strange mixture of backwardness and modernity was constructed. only by isolating a number of constants in Enriques' ideas.
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In our view, the most important of these constants is his reference to a synthetic and unitary type of approach and his resultant rejection of every form of dualism. Here, Enriques' own interpretation of the meaning of the name he gave his system - 'critical positivism' - is revealing. Enriques did not conceal "the deep-seated differences" which separated his ideas "from those that go under the name of critical positivism, "57 but he called the system 'positive' and 'critical' at the same time, because he wanted to reinterpret the speculative approach on which he had based his early ideas (namely, the positivist and critical approach) "in a more scientific and clear way" and - let us emphasize this crucial point - "to reconciliate them without eclectic compromises."58 In other words, 'reconciliation', 'synthesis', even though this was alien to any eclectic compromise. This is one of the keys to understanding Enriques' system: his attempt to synthesize opposites and to overcome every form of dualistic alternative runs throughout his writings. He therefore rejected the idea of setting off Positivism against Kantianism in the philosophy of science, but he also rejected any attempt to set off subjectivism against objectivism. The Positivism vs. Kantianism dualism is found also in what he called the contrast between empiricism and innatism: this is a fundamental aspect of his theory because he thought that this contrast might be resolved by using his psychologistic approach. Enriques also thought that the materialism vs. idealism dualism could be resolved by a more mature synthesis of the subjectivist and objectivist approaches. However, it must not be forgotten that Enriques' synthetic point of view was not perfectly balanced and that he tended to come down on the subjectivist side. This is evidently the result of his opinion that the objectivist approach had been far too prevalent and needed to be cut down to size. In this regard. his stance in the dispute symbolized by Fourier and Jacobi in mathematics is quite revealing. Everyone knows what Jacobi wrote in a letter to Legendre in 1830: "It is true that Fourier is of the opinion that the principal object of mathematics is the public utility and the explanation of natural phenomena; but a scientist like him ought to know that the unique object of science is the honor of the human spirit and on this basis a question of [the theory of] numbers is worth as much as a question about the planetary system."59 In this dispute, Enriques was not on Jacobi's side, because he repeatedly warned against the risk of leaving scientific research "at the mercy of individual free choice."60 But he was even less on Fourier's side61 • Not just because he was worried about the risk that mathematics could become subservient to applications, but also because of the hostility that he felt for the 'anti-historical' ideal of classical physico-mathematical reductionism- for its extreme objectivism which dogmatically denied any place for the 'activity of spirit': such as "Laplace's mathematical ideal, which aims at representing the whole reality sub specie aeternitatis by the equations of Universe, from which, overcoming the difficulties of mathematical integration, it would be possible to obtain the
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prevision of any particular event."62 His criticism of reductionism, and the strictly qualitative objectivist approach of classical mathematical physics is certainly one of the most original and modern aspects of Enriques' ideas, and we shall return to it shortly. In addition to this criticism, which we might characterize as being as anomalous as it was 'courageous' in the context of the scientific thought of his day, he also reappraised the role of metaphysics, closely linked to the theme of the psychological representation of the objects of scientific knowledge. This is another fundamental point to which we shall return. To sum up, the fundamental features of Enriques' thought were the adoption of a synthetic and qualitative point of view, accompanied by an attack on the 'dogmatism' of the analytical, quantitative, and objectivist approach, and his advocacy of the psychological analysis of the genesis of scientific concepts as a way of revitalizing empiricism after its defeat by Kantian criticism. We said earlier that one of Enriques' main objectives was to criticize Kantianism and Positivism, and to attempt to combine them in a higher synthesis; he accompanied this with a radical criticism of what he curiously called the 'French nominalism' of Henri Poincare (the thesis that the axioms of geometry are of the nature of 'conventions', a thesis that is more correctly called 'conventionalism'). One of the main grounds on which Enriques criticized 19th century science was its open rejection of the problems raised by metaphysics, mainly under the influence of Positivism, which had led to an all-out form of pusillanimity in scientific thought. He maintained that there was no such thing as an insoluble problem, but merely problems which had not yet been properly formulated; and that there was no such thing as a necessarily 'unknowable' reality (a criticism which was also aimed at Kant), but only an infinite series of objects, all of which are accessible to scientific thought. The infinite character of this series, and the fact that knowledge cannot be exhausted in finite time, creates the false illusion of the unknowable nature of the world. It should be noted that this idea of an infinite series is closely linked to a concept of the infmite as potential, with the resultant rejection of any idea of the infinite as actual. On this question, Enriques supported the more traditional point of view of classical analysis, and went so far as to deny that the transcendental procedures of analysis were of any value at all. Indeed, his criticism of transcendental procedures in Problemi della Scienza led him to reject the concept of set as 'actually given', and therefore implicitely to reject the heart of Cantorian thought and the Cantorian construction of real numbers." Yet this is one of the central issues in Enriques' thought and links up with other 'syntheses' (or attempts to overcome dualism): namely, the criticism of the distinctions between absolute and relative, and between subjective and objective. For Enriques, the absolute is a limit that we attempt to reach unsuccessfully. Like mathematical infinity, it is only
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potential or genetic and cannot therefore be distinguished from the relative acquisition of knowledge. He applied the same idea to the relationship that exists between subjective and objective, if viewed 'positively'. For example, if we examine the way children acquire the notion of nwnber, we can easily see that there is not only an objective element, but that there is also a psychological form which confers subjective features on it. For this reason, "a purely objective knowledge is not possible" and "the subjective way of representation affects prevision itself..., so one must admit that it includes something objective."M He concludes that, "subjectivity and objectivity are not two irreducible aspects of knowledge,,:65 subjective representation (which is resolved in psychological acquisition) is a condition for the expansion of objective knowledge. Science aims at this (and therefore at an 'absolute'); but aiming at "ever-increasing objectivity" can only be successful by pushing ever higher the subjectivity of the representations, namely by perfecting the system of images and mental associations which are "the way by which science moves ahead. tt66 One of Enriques' main complaints against Kantianism was that it attributed transcendental significance to the distinction between subjectivity and objectivity. "Is there something valid in the old Metaphysics?" asked Enriques. 67 His answer to this question is very interesting. What Positivism did wrong was to condemn metaphysics on the ground that it had taken as its object of knowledge the absolute, something which Positivism held to be unknowable. But according to Enriques, the absolute is not unknowable: it is merely a meaningless symbol, and Positivism had rated metaphysics 100 highly. On the other hand it underrated metaphysics when it claimed that it only combined meaningless symbols and did not represent its object through images with a concrete value. Ontological systems generated entities which, although "different from concrete objects" are "images of real things":68 In the [mal analysis, an ontology is a subjective representation of reality, a model formed by the hwnan mind, the elements of which, drawn from real objects, are combined so as to account for a certain order in the items of knowledge, according to a particular point of view, which is arbitrarily chosen to be universal.fIJ
So even though it is easy, too easy perhaps, to criticize the metaphysical systems, they do contain a system of images, a model which can foster associations that are useful to the development of science. These systems are rightly and justifiably to be condemned for claiming to provide objective knowledge, "but we cannot accept, without a more careful and critical analysis, the thesis that these theories (which we will call metaphysical theories) are devoid of any value, with respect to the genetic progress of science, if we consider them as psychological representations...."70 Closely connected with this reappraisal of metaphysics, Enriques sketched out a critique of the attempt to extend a mechanistic approach to areas of science outside physics, such as biology, physiology, and psychology. His
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criticism of a crude kind of materialistic reductionism is highly topical and relevant today: it provides an unusual argument against certain forms of mechanistic reductionism that are still rife today. But we shall not, for the sake of brevity, dwell on this in the present paper. More closely related to our topic is what Enriques said about the role of psychological representations, which he attributed to metaphysical constructions. Not only did he propose a broader approach to the ways in which scientific knowledge is acquired, which includes certain forms of modelling that are typical of so-called 'metaphysical' thought, and hence a broader conception of knowledge, but he placed the analysis of the psychogenesis of scientific concepts at the center of the theory of knowledge. Psychological representations have a central importance because they fonn the core of the new positive Gnoseology that he set out to give scientific epistemology, and which consists of a study of the psychological origin of scientific concepts. A core theme in Enriques' gnoseology was the redefinition of the concept of fact, which he linked to the mathematical notion of invariant. Enriques' concept of 'reality' was different from Mach's, because it did not belong to the realm of 'sensations' but to realm of "sensations associated to some voluntary actions. "71 Sensations can be associated with new sensations, modified by the effect of our will. If invariable aspects are manifested in all the associations between our acts of the. will and their corresponding sensations, these invariant aspects make up the 'real' fact This means that reality is defmed as an "invariant in the correspondence between volitions and sensations."72 Consequently, there is no difference in principle between a 'real fact' and a 'scientific fact', just as scientific knowledge is only a more elaborate form of ordinary knowledge, in that it uses processes of abstraction which transform raw facts into concepts.73 We have already spoken of the role of logic in the process of scientific knowledge and of the broader defmition of Logic through which Enriques subordinated formal logic to psychological logic. The legitimacy of formal logic is once again linked to the psychological analysis of knowledge. If concepts are an abstraction, it means that the logician, by an act of will, isolates a number of invariants upon which he operates the deductive procedure. But if logic is to have an objective value, nature has to offer similar invariants, and this can only be ascertained through a psychological analysis of the genesis of scientific concepts. We can now understand why Enriques not only considered the axiomatic approach to be meaningless, but, paradoxically, why he was highly critical of the approach which attempts to defend an intuitionistic view of geometry namely, Poincare's against the attack of Hilbertian formalism: conventionalism.74 It is true, Enriques observed, that the axioms of geometry have an arbitrary aspect, but it is equally true that when intuition selects them, it "makes a choice, constructing the representation of a space defined through a psychological approach."7s Here again, we have to avoid any exclusive distinction between innatism (which, according to Kantian theses, links intuition of spatial relations to man's anatomic-physical-psychological
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structure) and emplnclsm (which reduces them to a swn of items of perceived knowledge). They are reconciled in the attempt to "explain spatial intuition as a psychological development from some sensations, in which we take account of the structure of the subject. "76 We can therefore see that nluch of Enriques' effort was devoted to explaining the genesis of the basic concepts of geometry and mechanics through an analysis of physiological psychology. We will not go into details here, mainly for reasons of space, but also because it would lead us into a more specific sphere that lies outside the scope of the present paper. We will conclude with a number of remarks about the consequences of Enriques' point of view for the specific field of mathematical research. We have seen how Enriques countered 'purism' with the need for a synthesis between geometry and analysis. We should not, however, allow this to deceive us: he was advocating an iniquitous 'accord' in which geometry has the lion's share. 'Purism', meaning the separateness of geometry from analysis, is out; but he would save the core of the program, namely, the synthetic and qualitative method, which he wanted to become the method of all mathematics. The lesson that Enriques drew from the historical analysis of the trends in mathematics and from the great lesson of Riemann, not without stretching the facts to their limits at times, was that a major change in direction had occurred, towards a qualitative approach, the main idea being to replace calculations with thought. This tendency, according to Enriques, had been confmned by the revolutionary developments in physics, which was by now getting over the old quantitative reductionism of Fourier and Poincare. Einstein's relativity theory, now wholly based on 'global' and 'synthetic' concepts and on the Riemannian geometric approach, was demonstrating the need for a new mathematics, a mathematics no longer based on the centrality of differential equations (and therefore on the quantitative approach). And Enriques believed that he was able to perceive a trend in the developments in analysis which (as a consequence of Lie's research) would include the whole theory of integration of differential equations in the field of geometry. He was therefore proposing a new and more sophisticated form of the hegemony of geometry over analysis: a hegemony which was to be put into practice and which was to have considerable repercussions in the development of Italian mathematics. What the benefits and drawbacks were to be as a result of this will be examined in our concluding remarks.
v. Concluding Remarks How to sum up Enriques' philosophical-scientific experience? This is certainly a highly complex issue and we will therefore restrict our comments to a few very general remarks.
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The ftrst set of problems relates to the role that Enriques played in the development in Italy of philosophy and history of science, on the one hand, and of scientiftc research, on the other.77 Let us ftrst examine the former. It is very easy to imagine the enormous influence of the work of such an extraordinary personality as Enriques and the way it affected the work of many other scholars. Despite this, however, the overall judgment is rather negative. One cannot examine this question without reference to the famous controversy at the beginning of the century between Enriques and the neo-idealistic philosopher, Benedetto Croce, which eventually became an all-out clash between scientific culture and philosophical culture. What was at stake was the cognitive value of science, which Croce had challenged by likening it to practical knowledge. And Enriques became the spokesman for a scientiftc world which, after managing to become established as a specialty, was set on acquiring a cultural dignity. The defeat which Enriques suffered (with quasi-offtcial backing) was a cultural defeat for the whole of the Italian scientiftc world. It was relegated to dealing with technical-practical knowledge, and 'pure' philosophy was given pride of place over 'real' knowledge. The defeat of Enriques was the direct result of the limitations of his thoughL Not only the limitations of his incomplete philosophical culture which became clear in the debate - but also of the contradictions which emerged in his stance. He was forced to put up a positive image of modem science in his controversy with Croce, while he was subjecting the same scientiftc developments to a severe criticism which revealed its difftculties and inconsistencies. Furthermore, he did it from a point of view that was alien to the dominant scientiftc culture, namely, from positions that were rather close to idealism! So much so that later on, the other great Italian neo-idealist philosopher, Giovanni Gentile., noticed thin kinship with the stance of Enriques, and successfully attempted to reconcile it with his approach, although the scientiftc community was no longer interested. Although Italian science had been up to European standards in technical terms, it still needed to absorb scientiftc culture, even if only passively, and the epistemological debate that was going on abroad. Enriques tried to introduce a 'critical' scientiftc culture that was still too fragile: having to ftght on too many fronts, his battle was completely lost and this defeat weighed on the development of the philosophy of science and the history of science in Italy, which marked time for several decades. On the other hand the international impact of Enriques' thought was quite differenL One only needs to thumb through the year's volumes of RIVISTA DI SCIENZA (later renamed SCIENTIA) during the period in which Enriques' influence was at his peak, to see the large number of his international collaborators, and the breadth and interdisciplinary nature of the subjects discussed: very few journals anywhere in the world offered such a wide-ranging wealth of cultural contributions. The situation was more complex in the fteld of mathematical research. Here, the huge and surprising number of ftndings produced by the Italian
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school are the best evidence of the effectiveness of the method. Naturally, Enriques' intuitive method had aristocratic overtones, in contrast to the axiomatic method which, in its methodical unifonnity, seems more 'democratic'. But this is only apparent, because the axiomatic method also delegates the discovery procedure to pure intuition. It is true that the intuitive method's refusal to systematically endorse the logical verification procedure prevented a uniform recognition of the validity of its results: in this regard, the homogeneous nature of the axiomatic procedure is more reliable as far as the working mathematician is concerned. Italian geometers had 'demonstrated' (more or less acceptably in the light of the criteria of fonnal logic) an astonishingly large number of results, and for a long time it was hard to know whether many of these were 'true' or 'false'. But it is hard to maintain that this could have been the main reason for the crisis. It was not mainly a crisis of method (and does anyone know of any scientific method that has retained an indestructible validity throughout the course of history?): it was a crisis of substance. What was in question was the claim to be able to unify mathematics by applying the synthetic-qualitative approach, and subordinate analysis to geometry. The followers of Enriques and Castelnuovo, and later of Seven, were defeated in their endeavors as a result of painstaking research, developed with synthetical and geometrical methods, to obtain results which could have been much more simply and effectively obtained using the classical tools of the theory of differential equations. We must therefore draw a distinction between Enriques' method in the context of geometry, and his extrapolation for a program for the whole of mathematics. It was this latter which failed, contaminating geometric research as the crisis deepened. Confirmation of this comes from an analysis of the influence of the work carried out by the Italian school in the context of international research. The spread of the axiomatic approach in algebraic geometry pushed the results of the Italian school into the background, aided by the irritation that most people felt at the obsessive dogmatism of the members of the school, particularly Francesco Severi. However, in some instances the disregard for the contribution of the Italian school verged on gratuitous arrogance.78 The historiography ofaxiomatics eventually buried the entire Italian school. In an article on the historical development of algebraic geometry, Dieudonne took a sly swipe at the Italian geometric school in a section significantly entitled "Development and Chaos." This is what he said: Around 1890, the Italian school of algebraic geometry, lDlder the leadership of a trio of great geometers: Castelnuovo, Enriques and (slightly later) Severi, embarked upon a program of study of algebraic surfaces (and later higher dimensional varieties) generalizing the Brill-Noether approach via linear systems: they chiefly worked with purely geometric methods, such as projections or intersections of curves and surfaces in projective space, with as little use as possible of methods belonging either to analysis and topology, or to 'abstract' algebra. These limitations implied serious difficulties in the definitions of the main concepts and the use of geometric methods.... Working under such considerable
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handicaps, it is amazing to see how many new and deep results were discovered by the Italian geometers."
In our view, there was nothing whatsoever 'amazing' about this success. It was due to the power and flexibility of the method, at least in this phase of research. What is really 'amazing' is the speed with which the axiomatic treatises, which had been heralded as the New Testament of algebraic geometry, fell into oblivion, without the authors even feeling the need to complete them. Far from being useless, their technical contribution was a fundamental reorganizational phase, but it was reabsorbed in a context that was no longer stifled by the general program of a global and '[mal' axiomatic reorganization of the theory. In the end, what had been designed as a monument, able to weather the passage of time, found its way into 'development and chaos', and just as the program of the old Italian algebraic geometry withered and died, so did the axiomatic program, whose text turned out to be more outdated than the old Italian manuals that are now almost a century old, and which are still being read and reread today by contemporary researchers. The abstract algebraic methods have proven their worth thanks to their contact with the old problems and methods set out in those texts. Modern American and Soviet schools of algebraic geometry explicitly acknowledge their debt to the crucial role played by the rereading of Italian geometers - and of Enriques and Castelnuovo in particular - in the fresh boost that they have given to research. so The story of the Italian school of algebraic geometry - the story of a psychologistic approach directly related to mathematical research - is an episode that cannot be repeated, and it would be grotesque to hold it up as an example, in any form whatsoever. But it does offer a most important lesson for us: even the history of a discipline like mathematics can take a different path from what one would expect from the commonly held image of a rigorously formal science. Mathematics is indeed one of the bulwarks of the accumulative view of the history of science, and the axiomatic approach is the most obstinate guardian of this bulwark. Case studies of this kind help to free us from the stifling straitjacket into which axiomatic-accumulative theory has forced the history of mathematics, namely, the straitjacket of the "bleak alternative between the rationalism of a machine and the irrationalism of blind guessing"" which Lakatos rightly decried.
452 ENDNOTES 1. See: Jean Dieudonne, "L'axiomatique dans les mathematiques modemes," in Congres International de Philosophie des Sciences (Paris, 1949) (Paris: Hermann, 1951), pp. 47-53. 2. Hence, Dieudorme writes: A typical exaJl1ple of this illusion is the privileged role accorded by Poincare and the intuitionists to natural integers; there is, no dou~ at the bottom of this concept a psychological confusion between the particularly clear and immediate intuition we have of the properties of small nwnbers and the extension of these properties to all the integers, which, in my opinion, is based on purely arbitrary axioms.... (Ibid., pp. 50-51) Classical structures, as integer numbers, have a particular feature: they are 'univalent', i.e., they are completely determined, but for an isomorphism, by a set of axioms. This is the deep reason, following Dieudonne, for the privileged role that they play in classical mathematics: ...a circwnstance which could serve only to reinforce the belief in the character of necessity of these notions and to connect them to notions of sensible experience. (Ibid., p. 50) This psychological explanation seems to us somewhat over-simplified. But Dieudonne's distinction between univalent and non-univalent structures is very important and allows us to understand the difference between the classical Hilbertian axiomatics (which still privileged univalent structures) and Bourbaki's 'structuralist' axiomatics. 3. Ibid., p. 51. 4. Ibid., pp. 51-2. 5. Ibid., p. 52. 6. Ibid. Our italics. 7. Ibid. 8. We shall shortly show how it was, on the contrary, a philosophical 'infection' that led Enriques to mathematics. 9. Explicitly: ...if logic (as grammar), is to acquire a normative value, it must, with proper caution, allow the mathematician to say what he really wants to say, and not try to make him conform to some elaborate and useless ritual. After the logician has properly discharged such duties, and helped the mathematician to lay suitable foundations for his science, he may then set himself further objectives.... (Nicolas Bourbaki, "Foundations of Mathematics for the Working Mathematician," THE JOURNAL OF SYMBOUC LOGIC, Vol. 14, No.1 (March, 1949), p. 2) And again:
What will be the working mathematician's attitude when confronted with such dilemmas? It need not, I believe, be other than strictly empirical. We cannot hope to prove that every defmition, every symbol, every abbreviation that we introduce is free from potential ambiguities, that it does not bring about the possibility of a contradiction that might not otherwise have been present Let the rules be so formulated, the definitions so laid out, that every contradiction may most easily be traced back to its cause, and the latter either removed or so surrounded by warning signs as to prevent serious trouble. This to the mathematician, ought to be sufficient; and it is with this comparatively modest and limited objective in mind that I have sought to lay the fOWldations for my mathematical treatise. (Ibid., p.3)
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10. See: lean Dieudonne, "Les methodes axiomatiques modemes et les fondements des mathematiques," REVUE SClENTIFIQUE, LXXVII, (1939), pp. 224-232; and Henri Cartan. "Sur Ie fondement logique des mathematiques," REVUE SClENTIFIQUE, LXXXI, (1943), pp. 3-11. 11. Caftan. "Sur Ie fondement logique des mathematiques," p. 1. 12. Cartan refers to the two fundamental branches: first or
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25. Dante Alighieri, La Divina Commedia, Inferno, V, 5-6. We agree with Lakatos' observation: None of the creative periods and hardly any of the 'critical' periods of the mathematical theories would be admitted into the formalist heaven, where mathematical theories dwell like the seraphim, purged of all the impurities of earthly uncertainty. (Imre Lakatos, Proofs and RefilloJions: The Logic of MaJhemalical Discovery, ed. by J. Worrall and E. Zahar (Cambridge: Cambridge University, 1976), p. 2) 26. Let us recall the names of Enrico Betti, Eugenio Beltrami, Luigi Cremona, Ulisse Dini, Luigi Bianchi, Giuseppe Peano, Vito Volterra, Tullio Levi-Civita, Gregorio Ricci-Curbastro, Federigo Enrlques, Guido Castelnuovo, Guido Fubini, Francesco Severi, and many others besides. One only has to think of the major international role of Italy's scientific institutions in those days, and the importance of such initiatives as the Circolo Matematico di Palermo. For a discussion of the Mathematical Circle of Palermo, see: A. Brigaglia, and G. Masotto, eds., II Circolo MaJemalico di Palemw (Bari: Dedalo, 1982). 27. On this topic, see: Jean Dieudonne, History of Functional Analysis (New York: North-Holland, 1981). 28. Outstanding names include Betti, Brioschi, Casorati, and Cremona. 29. For a more detailed account, see: L. Nurzia, "Relazioni tra Ie concezioni geometriche di Federigo Enriques e la matematica intuizionista tedesca," PHYSIS, XXI (1979), pp. 157-193; and Georgio Israel, "Le due vie della matematica italiana contemporanea," in La ristrulturazione delle scienze fra Ie due gue"e mondiali, 2 vols., ed. G. Battimeli, M. De Maria, and A. Rossi (Rome: Universitaria di Roma 'La Goliardica', 1984), Vol. I, pp. 253-287. 30. Later attempts by G. Scorza and others to develop abstract algebraic research in Italy were a complete failure. On this topic, see: A. Brigaglia, "La teoria generale delle algebre in Italia dal 1919 al 1937," RIVlSTA DI STORIA DELLA SOENZA, Vol. I, no. 2 (1984), pp. 199-237. 31. Federigo Enriques, "La evolucion del concepto de la Geometria y la Escuela Italiana durante los ultimos cincuenta anos," REVlSTA MATEMATICA HISPANO-AMERICANA, n, 1-2 (1920), p. 2. 32. Cremona's correspondence suggests that there was a very broad consensus in the international community of geometers to establish a 'new' approach in mathematical research. See: Georgio Israel and L. Nurzia, "Correspondence and manuscripts recovered at the Istituto Matematico 'G. Castelnuovo' of the University of Rome," HISTORIA MATHEMATICA, Vol. 10, no. 1, (February 1983), pp. 93-97. 33. Enriques, "La evolucion del concepto de la Geometria y la Escuela Italiana durante los ultimos cincuenta anos," p. 2. 34. Guido Castelnuovo, "La Geometria algebrica e la Scuola italiana," in Atti del Congresso Internazionale dei MaJemalici, Bologna 3-10 Settemhre 1928 (Bologna: Nicola Zanichelli, 1929), p. 192. Our italics. 35. Enriques, "La evolucion del concepto de la Geometria y la Escuela Italiana durante los uItimos cincuenta anos," p. 3. 36. Ibid. The colleague and mentor to whom Enriques alludes is probably Castelnuovo. 37. See: Corrado Segre, "Su alcuni indirizzi nelle investigazioni geometriche," RIVISTA A MATEMATICA, I, (1891), pp. 42-66. See also: M. Menghini, "SuI ruolo di Corrado Segre nella geometria algebrica italiana," RIVlSTA DI STORIA DELLA SOENZA, Vol. 3, no. 3 (1986), pp. 303-322.
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38. Guido Castelnuovo, "Commemorazione di Federigo Enriques," PERIODICO DI MATEMATICHE, Vol. 25, no. 4 (1947), pp. 81-2. 39. It is well known that Enriques claimed to be able to grasp the contents of a book by reading its foreword and conclusions, and thwnbing through the rest. As far as his preference for the 'intuitive demonstration' of the results of mathematics is concerned, what Conforto has to say is quite revealing: Having once declared to him that I could not see the truth of an assertion which he considered evident, he suddenly stopped (it was during one of our customary walks) and, instead of attempting an ultimate demonstration, he whirled his stick, pointed it at a dog sitting on a windowsill and said to me: "Don't you see? For me it is as if you told me that I don't see that dog!" Nevertheless, that particular property, which we found a way of including in a volume on rational surfaces, awaits perhaps still today a satisfactory demonstration. (F. Conforto, "Federigo Enriques," RENDICONTI DI MATEMATICA, Vol. 6, no. 5 (1947), p. 232) 40. Enriques himself said, in his introduction to Problemi della Scienza, "the general theory of the treatise can hardly be explained in relation to the philosophical distinctions of the schools." (Federigo Enriques, Problemi della Scienza (Bologna: Nicola Zanichelli, 1906), p. v) 41. This caused some WlusUal misunderstandings among quite a few historians of philosophy. Some, for example, considered the controversy between Croce and Enriques to be a clash between Idealism and Positivism, whereas, as we shall show, Enriques was certainly much closer to Idealism than to Positivism. 42. On this topic, see: Castelnuovo, "La Geometria algebrica e la Seuola italiana"; Castelnuov0, "Commemorazione di Federigo Enriques"; Conforto, "Federigo Enriques"; and B. Segre, "Riflessi vicini e lontani del pensiero e dell'opera di Federigo Enriques," in Aui del Convegno Intemazionale di Geometria (a celebrazione del centenario della nascita di F. Enriques), Milano, 31/5-3/6/1971, (1973), pp. 11-25. 43. In other words, there was a divergence between the geometric genus and the arithemetic genus. 44. Castelnuovo, "La Geometria algebrica e la Scuola italiana," p. 194. Our italics. 45. Castelnuovo, "Commemorazione di Federigo Enriques," pp. 82-3
46. Ibid. 47. See: A.D. Lovejoy, The Great Chain of Being: A Study of History of an Idea (Cambridge: Harvard University, 1936). 48. Conforto, "Federigo Enriques," p. 231. 49. Quoted in: Castelnuovo, "Commemorazione di Federigo Enriques," p. 88.
50. See: Federigo Enriques, "Sulla spiegazione psicologica dei postulati della geometria," RIVISTA FILOSOFICA, Vol. 4 (1901), pp. 171-195. See also: Eniiques, Problemi della Scienza. 51. Quoted in note 21. 52. Enriques, Problemi della Scienza, p. 93. 53. Ibid., p. 94. 54. Ibid.
55. This experimental procedure is conducted on 'abstract' objects. See the quotation from Castelnuovo at the beginning of the paragraph. 56. Wholly consistent with this general attitude, Enriques suggested a new way of writing the treatises and conflIDled very clearly that the intuitive approaeh possessed the status of a fully-flegged method. Read 'the very interesting introduction to: Federigo Enriques and O. Chisini, Lezioni suJla teoria geometrica delle equazioni e delle jimzioni algebriche (Bologna: Nicola Zanichelli, 1915):
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...the ancient classical model of the treatise. which goes back to the venerable tradition of Euclid [founded upon the idea] of a rational science, logically constructed as a deductive theory...• appears to conform badly to the particular subject of our lectures [and] is contrary...to the general philosophy of science born from modem critique. In fact, the logical and gnoseological critique succeeds in defining the field of logic and in recognizing in each theory those elements of different kind which provide it with meaning and value. [This critique] goes beyond the opposition between the deductive and inductive methods, and considers deduction itself as a phase of a single process, leading from the particular to the general and back to the particular. According to Enriques, then, it was necessary to devise a new kind of treatise "closer to the reality of scientific progress." (Ibid., p. ix) See also: Federigo Enriques, "Reflexions sur l'art d'ecrire un traiti. A propos d'un traiti de mathematiques." SCIENTIA, xvm (1915). pp. 152-155. 57. Enriques, Problemi della scienza. p. v. 58. Ibid. 59. C.GJ. Jacobi, Ges. Werke, I, pp. 454-455, Letter of 2 July. 1830. 60. Enriques, "La evolucion del concepto de la Geometria y la Escuela Italiana durante los ultimos cincuenta anos," p. 4. 61. 'The mathematical science could not adjust itself to serve the needs of its practical applications, without being wounded to death in its development" Ibid. 62. Federigo Enriques, La theorie de la connaissance scientijique de Kant Ii nos jours (paris: Hermann. 1938). 63. The fact that in several later works. using some dialectical balancing tricks, Enriques managed to reappropriate the concept of the actual infinite confirms the eclecticism and approximation of his system of ideas. See, for example: Federigo Enriques. "I numeri e l'infmito," SCIENTIA, IX (1911). pp. 1-24. 64. Enriques. Problemi della scienza. p. 21. Note how Enriques' point of view shares many points in common with Mill's, confIrming the close link between his ideas and traditional psychologism. In several places, Enriques actually quotes Mill. revealing his interest in Mill's philosophy. despite a certain caution. For example, Enriques believed that Mill had spelled out more clearly than Kant the distinction between quality and quantity. And he judged Mill's Positivism to be "superior" to Comte's. (Ibid., p. 46.) 65. Ibid. 66. Ibid., p. 26. 67. Ibid., p. 27. 68. Ibid., p. 28. 69. Ibid. 70. Ibid., p. 29. This 'reappraisal' of metaphysics is of great contemporary relevance. The difficulties encountered when building mathematical models which are rigorously predictive in fields other than physics have led to a reappraisal of a 'hermeneutic' approach, in which the role of imagination is fundamental. It would be interesting to study the similarities between the points of view expressed by Enriques and Rene Thorn. 71. Ibid., p. 50. 72 Ibid., p. 58. 73. Once again we see here the tendency towards a unitary view of the process of knowledge acquisition which is typical of Enriques' ideas. 74. But this is only strange up to a point, because Enriques rightly perceived that Poincare was also attempting to save what was salvageable in Kantianism.
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75. Ibid., p. 174. 76. Ibid. 77. These problems are examined in: Georgio Israel, "Le due vie della matematica italiana contemporanea." 78. In his major axiomatic treatise, A. Grothendieck wrote: Fonnally at least. the subjects treated in our work are rather new, which will explain the rarity of references made to the Fathers of Algebraic Geometry of the 19th century and the beginning of the 20th century, whose work we know only by hearsay. (A. Grothendiec~ Elements de Geontetrie Algebriqu.e (rediges avec La collaboration de Jean DieudonnJ), Vol. I (paris: Institut des Hautes Etudes Scientifiques, Publications Mathematiques, 1960), p. 7.) 79. Jean Dieudonne, "The Historical Development of Algebraic geometry," THE AMERICAN MATHEMATICAL MONTHLY, Vol. 79 (1972), p. 845. A similar point of view is expressed in: Dieudonne, COUTS de Geontetrie Algebrique; and Jean Dieudonne, History of Algebraic Geometry (Monterey: Wordsworth, 1985) (which is an up-to-date translation of COUTS de Geontetrie Algebrique). 80. "A great help in the understanding of algebraic geometry is familiarity with the work of dle classical, above all the Italian geometers." I.R. Shafarevich, Basic Algebraic Geometry (Berlin: Springer, 1977). Shafarevich mentions above all the Enriques-Chisini treatise which is the most complete example of Enriques' demonstrative and explanatory method (see: note 56). 81. Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, p. 4.
PSYCHOLOGISM IN LINGUISTICS TAKASHI YAGISAWA Psychologisrn in linguistics is the thesis, championed by Chomsky, that linguistics is a branch of psychology. I The purpose of this paper is to cast doubt on that thesis.
I. Actual Human Natural Languages It seems utterly uncontroversial that linguistics is about actual human natural languages. Linguists may talk about various other things (e.g., history, sociology, psychology, formal logic, computers, etc.) in the course of their investigations, and different branches of linguistics may be concerned with diversely different aspects of actual human natural languages. But it seems undeniably correct to say that the basic, core subject matter of linguistics is actual human natural languages. Thus, it seems undeniably correct to say that if actual human natural languages are (identical with) X, then linguistics is about X. Suppose this is so. The question then is: What are actual human natural languages? Actual human natural languages include Swahili, Russian, Mandarin, etc. Take English as an example. What is English? English consists of English expressions which are written and pronounced in certain ways and which have certain meanings. English expressions include 'divine' meaning divine, 'dog' meaning dog, and 'Dogs are divine' meaning dogs are divine. I propose that we forget about meanings for our purposes (except in chapter XIV). Many people think that meanings are a funny kind of entities if they are entities. If they are not entities, what are they? There is no agreement among philosophers and linguists as to what meanings are and what relation it is that must hold between an expression and a meaning in order for that expression to have that meaning. I do not want to presuppose any particular theory on any of theses issues. So let us stay away from the swamp of meanings. 2 The rest of the ground is muddy enough. Let us start by asking ourselves, 'What are the English expressions, which are written and pronounced in certain ways and which (as associated with certain meanings) comprise English?' It should be obvious that those English expressions which have been actually produced up to the present moment do not exhaust all English expressions. Some English expressions will be written or pronounced for the first time in the next thirty seconds, some in the next five minutes, some in the next two years, and some in the
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next millenium. Some English expressions will never be produced at all. So, it is a mistake to identify the totality of English expressions with the totality of English expressions which are (that is, were, are being, or will be) uttered. What then is the totality of English expressions? A natural suggestion is that the totality of English expressions is the totality of English expressions which could possibly be uttered. But, 'could possibly be uttered' by whom? By humans, one should imagine, for we are talking about a human language. But which humans? Actual humans, one should imagine, for we are talking about an actual human language. 3 Some English expressions which could possibly be uttered are actually uttered. But what exactly are those English expressions which could possibly be uttered and are never actually uttered? Two options are open at this stage. The fIrst option is to identify such expressions with certain nonactual possibilia, viz.• nonactual possibly utterable English expressions. There are two questions to be asked. Nonactual possibilia do not actually exist. Then how can English, an actual language, partially consist of entities which do not actually exist? What is the metaphysical status of nonactual possibilia, in any case? I am not sure whether these questions are suffIciently troublesome to make the fIrst option unattractive. I suspect, however, that many philosophers are inclined to think so. The second option is to identify unuttered possibly utterable English expressions, as well as actually uttered English expressions, with English expression types. Types actually exist even if they are not 'betokened'. So this option avoids positing nonactual possibilia. Some types are actually 'betokened', some not We can identify the totality of English expressions with the totality of English expression types. Does this answer our question, 'What are English expressions?' No, not until we are told what English expression types are. Expression types cannot be physical, for any expression that is physical must be a written or pronounced particular and any such particular is a token. Expression types must therefore be nonphysical. But what are they'r To be told that they are nonphysical is not to be told much. Sets are presumably nonphysical, too. Are expression types sets? If so, what are their members? Expression tokens? If so, which tokens? They should include more than actual tokens; otherwise, why should we not have stopped after introducing actually uttered expressions? But what more? Possibilia? We would then be back to the first option, plus the complication of the type-token distinction. Types seem mysterious. We seem to have to say that they are nonphysical nonsets. Numbers also seem to be nonphysical nonsets. 5 But we do not stop talking about numbers simply because of that Mysterious as they may be, we should perhaps not refrain from talking about types. The conclusion of our brief discussion in this section is this: Accept either nonactual (as well as actual) physical possibilia or else nonphysical types, as comprising the totality of the expressions of each of the actual human natural languages. Either way, linguistics seems to be about something nonpsychological, if it is about actual human natural languages. Some who are sympathetic with psychologism might think that this is too
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quick or irrelevant or both. I do not think so, but let us pretend that it is, for the sake of discussion, and reorient our approach. Let us then start again with a new question, 'What do linguists do?' instead of 'What is linguistics about?'
II. What Psychologism Exactly Is Linguists are people and therefore do a variety of things. But what do they do qua linguists? English is our example again. Linguists specify English expressions phonologically, authographically, and semantically, note and explain their grammatical (i.e., phonological, syntactic, and semantic) properties and relations, and perhaps also search for grammatical universals English shares with all other actual human natural languages; all this is linguistics proper. They also describe how the English expressions are recognized. processed, and associated with their meanings by English speakers (psycholinguistics), and report how the English expressions are used in communication and other social interactions (sociolinguistics). Linguists are also interested in how all this changes over time (dyachronic studies). It is analytically trivial that psycholinguistics is a branch of psychology, as well as a branch of linguistics. Psychologism in linguistics is far from being analytically trivial. Therefore, psychologism in linguistics is not the thesis that psycholinguistics is a branch of psychology. Also, the thesis that linguistics as a whole is a branch(es) of psychology is false to the extent that sociolinguistics is not a branch of psychology, for linguistics as a whole includes sociolinguistics. We cannot expect to be able to do a comprehensive sociolinguistic study without relying on the rest of sociology; the rest of sociology is an integral part of sociolinguistics. The claim that sociology is a branch of psychology would misleadingly obscure the nature of sociology, to say the least; that sociology is a branch of psychology seems as unlikely as that it is a branch of physics. In any case, Chomsky and his followers certainly do not wish to defend psychologism by relying on the reduction of sociolinguistics to psychology. So, the most charitable interpretaion of psychologism in linguistics is that linguistics proper is a branch of psychology, that is to say, that it is a task in psychology to specify the expressions of actual human natural languages, note and explain their grammatical properties and relations, and perhaps search for grammatical universals. I shall assume this interpretaion of psychologism for the rest of the paper. Chomsky says that "language is a derivative and perhaps not very interesting concept'16 By this he does not mean to deny that linguistics proper is concerned with matters of syntax, phonology, and semantics; for him, linguistics proper is about grammatical competence, and he says, "I am assuming grammatical competence to be a system of rules that generate certain mental representations, including in particular representations of form and meaning."7 The 'form and meaning' that he
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speaks of belong to what we may call the 'idiolect' of the speaker. Chomsky's opposition to the concept 'language' (he sometimes uses the word 'superlanguage'') is directed at shared languages like English, Tagalog, etc., and not idiolects. I will return to this point in section X. Since nothing crucial in our discussion hinges on the distinction between shared language and idiolect, we shall continue to speak of English as our example.
ill. Psychologism Against Enumeration Against psychologism it is sufficient to argue that some part of linguistics proper is nonpsychological. I think in fact it can be argued that every part of linguistics proper is nonpsychological, that is, that it is not a task in psychology: (i) to specify the expressions of actual human natural languages; or (ii) to note and explain their grammatical properties and relations; or (iii) to search for grammatical universals. JJ. Katz, an ardent proponent of Platonistic nonpsychologism, argues against psychologism mainly by arguing in effect that (ii) and (iii) are not psychology.' I have little to add to the arguments Katz skillfully presents. Instead, I want to offer a somewhat different line of argument against psychologism. I want to argue that (i) is not psychology. Linguists agree that simple enumeration will not do for the purpose of (i). They agree that (i) calls for something more structured than a mere list of expressions. Moreover, they agree that the method should be at least recursive. Why should enumeration be inadequate for (i)? Why should (i) call for recursion? Psychologism appears to offer the only available satisfactory answer. I will argue that this is only an appearance and that nonpsychologism can account for the inadequacy of enumeration equally well. There are two accounts from psychologism for the inadequacy of enumeration. I claim that the fIrst account is unsatisfactory. The second account is better; we will turn to it in section VI. The fIrst account says that the following four theses are such that (a) they jointly entail that we cannot adequately enumerate all and only English expressions, and (b) they are all true:
TM Infinity TMsisTM Finiteness Th£sisTM Decidability TMsisTM Mimicry TMsis-
There are infinitely many English expressions. English speakers' cognitive capacities are finite. English expressions are decidable by English speakers. Any adequate specification of English expressions should mimic the decision procedure(s) used (unconsciously) by English speakers.
Almost everyone seems to accept the Infinity Thesis. It, of course, does not assert the existence of infrnitely many useful English expressions, so the
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fmiteness of useful English expressions does not refute it. As for the Finiteness Thesis, the cognitive capacities in question are not just linguistic capacities, which· are specific to the language module. They include all those cognitive capacities which participate in the mental process of deciding whether a given expression is English or not. The language module does not make the decision. The speaker does. In doing so, the speaker obviously uses the language module but also uses other modules (e.g., those pertaining to perception) and the central system. It is therefore already plain that this first account is not one that a Chomskian grammarian can give qua grammarian; Chomsky has repeatedly claimed that the grammarian qua grammarian is concerned exclusively with the language module. More on this in section V. In any case, the Finiteness Thesis seems undeniably true. The Decidability Thesis says that for any expressions, a sufficiently competent English speaker could tell (that is, correctly decide after a finite amount of time) whether that expression is a (well-formed) English expression or not. The Mimicry Thesis assumes the Decidability Thesis and is a natural consequence of psychologism. The Finiteness and the Decidability Theses yield the claim that English speakers' decision procedure(s) is(are) finitely based. This claim, when combined with the Infinity Thesis, gives us the further claim that the decision procedure(s) can decide an infinite set on a finite basis. From this claim and the Mimicry Thesis we obtain the claim that any adequate specification of English expressions should be able to decide an infmite set (of English expressions) on a finite basis. But, a simple enumeration of the members of an infinite set is not fmitely based. So, enumeration is not an adequate specification of English expressions. The above four theses entail that no specification that is not finitely based or not infinite in scope is adequate. Does this mean that psychologism succeeds in accounting for the inadequacy of enumeration for (i)? I think noL I think there is room for skepticism in connection with two of the four theses in question. I shall discuss them in the next two sections.
IV. The Infinity Thesis How do we know that the Infmity Thesis is true? It should be uncontroversial that whether a given expression is English is ultimately to be decided by reference to the verdicts given by native English speakers. For short expressions, to be English is to be accepted as English by native English speakers. For long and complicated expressions, however, the matter is less straightforward. Some expressions are too long and complicated for most English speakers to classify as English (or not). Given the finiteness of English vocabulary, it is plain that there are only finitely many expressions which are short and simple enough for actual speakers to accept as English. Three options become available at this point.
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The frrst option is to identify being English with being possibly directly accepted as English by actual native English speakers. Some expressions are never actually directly accepted as English; but some of those expressions would be directly so accepted, should the actual native English speakers face the choice of accepting or rejecting them. However, since every actual speaker is fmite, there is a finite upper bound to the length and complexity of expressions actual speakers could classify one way or the other. So, given the fmiteness of English vocabulary, there is a fmite upper bound to the number of expressions actual speakers could classify as English. Thus, the frrst option commits us to the denial of the Infmity Thesis. The second option is to identify being English with being possibly directly accepted as English by an ideally competent English speaker. An ideally competent English s~~er is just like an actual native English speaker except in two respects. First, her competence is maximal, that is, she knows all English vocabulary and can correctly classify as English or not any expression comprehensible within the limitations of her overall cognitive capacities (including attention span, memory power, etc.). Second, her competence is unbounded, that is, there are no limitations to her cognitive capacities. Thus, if, as it is, the fmiteness of actual speakers is the obstacle blocking the Infmity Thesis, the second option clears the way. It, however, must posit an ideally competent speaker, with whom no actual speaker is identical. The third option avoids both (a) identifying being English with being possibly directly accepted as English by actual English speakers and (b) positing an ideally competent speaker. It avoids (a) while retaining the idea that whether a given expression is English is ultimately decided on the basis of actual English speakers' verdicts. It also saves the Infmity Thesis. The idea is to use so-called coordinate constructions to generate infinitely many English expressions from a finite stock of English expressions directly so accepted by actual English speakers. Consider, for example, the following claim: (*) For any English sentences s and s', s and s' is an English sentence. (Similar claims can be obtained by using other coordinate constructions, such as 'or', 'if...then', etc.)
There is at least one English sentence directly accepted as English by actual English speakers. So, if (*) is true, there are infmitely many English sentences. However, there is a problem. Where does (*) come from? Certainly some instances of s and s' are too long for actual speakers even to keep track of. So (*) cannot be justified by possible direct acceptance by actual speakers of all instances of sands'. The third option is not to invoke an ideally competent speaker. How is (*) justified, then? The third option bmnches off to two sub-options at this point. The frrst sub-option is to directly query actual native English speakers about (*) itself. If responses to a query about a quantified metalinguistic claim like
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(*) are taken to be legitimate data, the linguist can use them to justify (*). One problem with this sub-option is that actual speakers might not fully grasp the import of (*). They might not realize that (*) has an infinite generative potential. If they do not, their responses to the query about (*) are not clean data and therefore are of dubious acceptability to the linguist. If they do fully grasp the import of (*), then they might not accept it They might think that there is some, perhaps very vague, upper bound to the length of English expressions. Or they might accept (*) for all that.. The matter is empirical and rather unpredictable in advance. Thus, the support for the Infinity Thesis by the first sub-option is philosophically unstable. The second sub-option is suggested by, among others, Langendoen and Postal. 10 Compare (*) to the following claim: (**) For any English sentence sands' in C, sands' is an English sentence (where C is some set of English sentences of a fixed cardinality).
(*) imposes no restriction on the cardinality of the totality of English expressions, while (**) does. So (*) is simpler than (**), hence by Occam's razor, it is theoretically preferable to (**), according to Langendoen and Postal. Note that if the native speakers' responses to the query about (*) are acceptable data, then it is not so clear that the simplicity gives (*) a sufficient edge over (**); for such data might tip the scale in favor of (**) after all. Langendoen and Postal offer another justification for (*): One can regard grammars and grammatical theory as concerned with projecting
from the properties of attested NL [natural language] sentences, the basic data of grammatical investigation, to the maximal lawfully characterized collections of which these attested sentences are accidental examples. One wants, given a sample of English sentences, to characterize the collection of all English sentences, and, given a sample of NL sentences, the collection of NL sentences per se. General scientific principles demand that the projections from the small fmite samples to the desired characterizations involve the maximally general laws (principles) projecting the regularities found in observed cases to the collections as wholes. l1
The same qualification concerning the data obtained by the query about (*) should be noted here also, as the following passage by Langendoen and Postal reminds us: ... one can never justifiably replace a more general projection by a less general one unless this is factually motivated, in particular, by the excess generality leading to some false entailment, e.g. a false claim about attested examples, some contradiction, etc. 12
We have seen three options, with the third option branching off to two sub-options.
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Which of those three options is (are) a good option(s) for psychologism? The fU'St option is not very good, for it blocks the argument in question against enumeration (given at the beginning of this section) by denying the Infinity Thesis. Few supporters of psychologism take this option, anyway. The second option saves the Infmity Thesis, but at the expense of introducing an ideally competent speaker. The introduction of an ideally competent speaker turns out to have unfortunate repurcussions for psychologism. I will discuss this matter in the next section in connection with the Decidability Thesis. The third option saves the Infinity Thesis without introducing anything like an ideally competent speaker- except for the first sub-option conjoined with the empirical possiblity of actual English speakers rejecting (*), in which case the Infinity Thesis is not saved and the argument against enumeration is blocked; not a happy result for psychologism. It does oot need the qualification on legitimate data noted above. The most serious problem with the third option for psychologism, however, is that it leads to a vastly nonpsychological picture of natural languages. IT (*) is secured by the third option, via the first or second sub-option, then nothing can prevent (ole) and other principles concerning coordinate constructions (call them, including (ole), 'coordinate construction principles') from generating enormously many English expressions, so enormous that the totality of English expressions will not have a fixed cardinality. Langendoen and Postal prove a general version of this result (which they call 'the NL Vastness Theorem') by applying Cantor's powerset theorem to linguistic expressions." The NL Vastness Theorem clearly places English expressions well beyond the reach of psychology. As if this were not enough, Langendoen and Postal also prove what they call 'the No Upper Bound Theorem' from the coordinate construction principles. 14 The No Upper Bound Theorem in effect says that there is no upper bound to the length of an English expression. Notice that the theorem says, 'no upper bound', not '00 fmite upper bound'. Thus, the coordinate construction principles entail that some English expressions are enormously long, so long that their lengths exceed the cardinality of the powerset of the powerset of the powerset oLof the powerset of all the space-time points in the entire history of the universe. They are obviously not psychological objects. Langendoen and Postal's work contains a number of enlightening discussions surrounding the two theorems. Let us remind ourselves that in order to refute psychologism it is sufficient to show that the subject matter of linguistics proper is nonpsychological. The subject matter of linguistics proper consists of actual human natural languages, which in turn consist of expressions, with phonological, syntactic, and semantic properties. The Vastness and the No Upper Bound Theorems say that those expressions are hugely many in number and include hugely long expressions; so huge that the entire universe contains far less space-time points in comparison. So, actual human natural languages are nonpsychological. Therefore, linguistics proper is not psychology. Notice that the fact, if it is a fact, that native speakers have internalized
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grammatical rules which could in principle 'generate' all and only those expressions independently of whether the speakers can comprehend them or not does not make the totality of the expressions psychological, any more than the fact that we have internalized a rule (the successor operation) which could in principle 'generate' all and only natural numbers makes the totality of natural numbers psychological. The Finiteness Thesis entails that the speaker is limited to finitude in applying the grammatical rules she has internalized, so that the set of expressions she is capable of 'generating' by correct applications of the rules falls far short of the totality of English expressions. This is sufficient to refute the claim that the totality of English expressions is psychological. Since linguistics proper is about the totality of English expressions, it follows that linguistics proper is about something nonpsychological.
V. The Decidability Thesis The Decidability Thesis is clearly false if it asserts decidability of the totality of English expressions by actual English speakers. Clearly, there are English expressions which, due to their lengths and/or structural complexities, cannot be recognized as English by most actual English speakers, and there are non-English expressions which are so similar to some English expressions that most actual English speakers would mistake them for the English expressions. Actual English speakers are not perfect detectors of English well-formedness or ill-formedness; because they, like anyone else, are limited in their cognitive capacities (attention span, memory power, etc.). If we idealize actual speakers' cognitive capacities (cf., the second option in the preceeding discussion on the Infinity Thesis), we may have a perfect detector of well-formedness or ill-formedness. But any idealization must be made with uUllost caution in any science. Idealization should be useful and faithful at the same time. To be useful, it needs to simplify the features of the actual entities in question, trimming accidental frills. To be faithful, it must not idealize away important features of those entities. The art of idealization consists in hitting the right balance in this tradeoff. Consider the following argument against idealization of English speakers: Actual English speakers are humans. Any human is essentially a human!' All humans have a limited brain size, and no human could possibly have an unlimited brain size. So, given physicalism, actual English speakers are essenJially limited in their cognitive capacities.
Is this a good objection to the idealization of actual English speakers' cognitive capacities to be unlimited? No. If any idealization is useful and faithful, Newton's idealization of actual physical mass into point mass was. Every macro physical object is essentially extended, i.e., no macro physical
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object could possibly be a point mass. This fact does not constitute a good objection to Newton's idealization. Essenlial features of the actual entities in question may not be important features to be preserved in a faithful idealization. Then, what are the important features of actual English speakers which should not be idealized away? Importance of a feature is relative to the theory in which the idealization is made. In Newtonian physics, we can include, among idealized objects, an absolutely reliable measuring rod which retains exactly the unit length irrespective of the speed of its lengthwise motion, or a very long perfectly rigid stick which does not bend at all when swung. In Einsteinian physics, we cannot include such items among idealized items, for the existence of such items is inconsistent with the rest of the theory. Unlimited cognitive capacities of English speakers is inconsistent with the Finiteness Thesis. Thus, if we want this idealization, we must abandon the Finiteness Thesis; but then we will lose the argument. On the other hand, if we want to retain the Finiteness Thesis, we must abandon the idealization; but then we cannot support the Decidability Thesis and therefore will lose the argument. Either way, the argument is lost. Notice that the idealization which is necessary to support the Decidability Thesis is stronger than positing that the rules which are actually internalized in the language module of English speakers provide an algorithm for classifying any arbitrary expression as English or not. Such a posit does not support the Decidability Thesis unless the following claim is also accepted: English speakers have cognitive capacities to use the algorithm in question to classify any arbitrary expression as English or not. This claim is the force of the idealization, and is plainly incompatible with the Finiteness Thesis. The idealization discussed so far was not made in the Chomskian spirit. Perhaps, then, if it is made in the Chomskian spirit, it may not be problematic after all. However, it is not clear what it is to make the idealization in the Chomskian spirit. According to Chomsky, the subject matter of linguistics proper is the language module, considered in separation from other parts of the mind. Language use is not a proper subject for the grammarian, for it involves other parts of the mind beyond the language module. Of course, grammatical data collection, which involves the entire speaker, cannot bypass the other parts of the mind, but the grammarian should separate the language module in theoretical abstraction and construct a theory exclusively about it. There is nothing outlandish about such practice in science; physical scientists make similar theoretical abstractions routinely. Now, if this is Chomsky's position - and it is - then why does he say, "Linguistic theory is concerned primarily with an ideal speaker-listener in a completely homogenious speech-community, who knows its language perfectly and is unaffected by memory limitations, distractions, etc."?16 Why does he have to idealize the speaker to obtain the subject matter of linguistic theory? Why is it not enough to say that linguistic theory is concerned primarily with the language module of an actual speaker? If the mind is modular, as Chomsky believes it is, then any
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part of the mind outside the language module will be automatically
excluded from the primary domain of linguistic theory. Idealization is not necessary for the correct statement of the subject matter of Chomskian linguistic theory. It is also misleading. By saying that linguistic theory is about the language faculty of an ideal speaker, Chomsky gives the false impression that he means to deny that linguistic theory is about the language faculty of an actual, non-idealized, speaker. What is idealized is not the language module, but other surrounding parts of the mind, such as those pertaining to memory, attention, etc. So the idealization leaves the language module untouched; that is the very point of emphasizing the modularity of the mind. Thus, if the ideal speaker's language faculty is the subject matter of linguistic theory, so is the actual, non-idealized, speaker's language faculty; for their faculties are one and the same. Idealization certainly serves no methodological purposes, either, for no actual speaker is an ideal speaker and the grammarian can query only actual speakers. What, then, is the point of Chomsky's making the idealization? I see none. Why does he make it? My conjecture is that it is a hangover from the nineteen-sixties, when he did not yet embrace the modularity thesis. Without the modularity thesis, Chomsky needed to make the idealization in order to purge theoretically irrelevant limitations of the mind for a clear statement of the subject matter of linguistic theory. What was not changed by the idealization remained as the focus of linguistic theory.17 Once the modularity of the mind is fully acknowledged, the idealization is no longer needed. However, since it played such an important role in his early exposition of his theory, Chomsky fails to see its uselessness and sticks to it Or else, perhaps more charitably, we might conclude that Chomsky does not really believe in the modularity of the mind in its fullest sense. If so, he cannot demarcate the language faculty as a separate module, so he is tempted to highlight it by idealizing away all irrelevant limitations of the mind. Is the introduction of an ideally competent speaker a good move for psychologism, independently of its coherence with the other theses in the argument against enumeration? I think not. Very few defenders of psychologism reject the coordinate construction principles. But those principles entail the Vastness Theorem and the No Upper Bound Theorem. So, in order to make an ideally competent speaker do the work required by psychologism, namely, to have the capacity to decide the set of all and only English expressions, we must stipulate her cognitive capacities to be enormous, so enormous that she will bear little resemblance to actual humans. Such an ideally competent speaker would be cognitively as remote from us as we are from amoebae. The idealization will completely rob linguistics proper of all relevance to human psychology. Note that my use of the phrase, 'have the capacity', is perfectly consonant with Chomsky's. He says: When I say that a person has the capacity to do so-and-so at a particular time, I mean that as physically and mentally constituted at that time, he needs no further
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instruction, training, physical development, etc., to do so-and-so if placed under appropriate external conditions...the Olympic swimming champion lacks the capacity to swim if his arms and legs are amputated or broken, but not if he is tied to a chair or asleep or absorbed in a book.1I
It is clear that, given the Vastness and the No Upper Bound Theorems, unless she has enormous cognitive capacities, the speaker would defmitely need far more than 'further instruction, training, physical development, etc.' to classify any arbitrary expression as English or not 'under appropriate external conditions'. I doubt that a creature with such enormous cognitive capacities is even humanly imaginable. It might be objected that the preceding discussion is not fair to Chomsky. Chomsky could use the following theses instead of the Finiteness, the Decidability, and the Mimicry Theses to account for the inadequacy of enumeration: The Modular Finiteness Thesir.The Modular Generation Thesis-
The Modular Mimicry Thesir.-
The language module of an English speaker is finite. English expressions are generatable by the language module of an English speaker; that is, the language module contains a mechanism for generating all and only English expressions. Any adequate specification of English expressions should mimic the generative mechanism of the language module.
The Modular Finiteness and Modular Generation Theses yield the claim that the language module's generative mechanism is fmitely based. This claim, when combined with the Infinity Thesis, gives us the further claim that the mechanism can generate an infinite set on a finite basis. From this claim and the Modular Mimicry Thesis we obtain the claim that any adequate specification of English expressions should be able to generate an infinite set on a finite basis. But a simple enumeration of all members of an infinite set is not fmitely based. What is wrong with this version of the argument? What is wrong is that essentially the same difficulty plagues the Modular Generation Thesis as it did the Decidability Thesis. Since the generative mechanism is physically fmite - it lasts only for a fmite length of time, for example - there is a finite upper bound to the number and the length of English expressions it can generate, but there is no such upper bound to the number and the length of English expressions. To save the Modular Generation Thesis, one needs idealization. The language module has to be idealized so as to be able to generate all English expressions. But that will contradict the Modular Finiteness Thesis. The Vastness and the No Upper Bound Theorems again help dramatize the enormity of the required idealization. The idealization will flatly contradict the Modular Finiteness Thesis and
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completely rob linguistics proper of all relevance to human psychology by blowing up the language module totally out of human psychological (and biological) reality, and perhaps even out of human imaginability. Thus the switch to the 'Modular' versions of the three theses will not help psychologism.
VI. Psychologism Against Enumeration Again However, there is a different argument from psychologism for the claim that no adequate specification of English expressions can be given by enumeration. This argument does not depend on the Infinity Thesis or the Decidability Thesis, but uses the following celebrnted Chomskian thesis 19 instead: The Projectibility Thesis- English speakers can correcty recognize as English novel English expressions they have never encountered before.
By the Finiteness and the Projectibility Theses, the decision procedure{s) used (unconsciously) by English speakers to recognize English expressisons must be fmitely based and 'projectible' to novel cases. So by the Mimicry Thesis, any adequate sepcification of English expressions should be fmitely based and 'projectible'. But even if the set of all English expressions is [mite, hence its enumeration [mite, the enumeration will not be 'projectible'; no enumeration is. (The corresponding 'Modular' version of this argument is easy to construct) This argument escapes the difficulties associated with the Infmity and the Decidability Theses, and still uses the Mimicry Thesis (as well as the Finiteness and the Projectibility Theses). Thus, it is an argument from psychologism against enumeration which escapes all the objections raised in sections IV and V. Does this mean that a strong point is scored for psychologism after all?
VIL Nonpsychologism Against Enumeration No. There is an equally good argument against enumeration without reliance on psychologism at all. If English expressions are infinite in number, an enumeration of all English expressions is an impossible task for the linguist, who is finite. So, if we require that any adequate specification be possible for the linguist to carry out (call this requirement 'the attainability requirement'), then, given the Infmity Thesis, no enumeration of any sort is adequate. The attainability requirement is certainly reasonable. What does 'adequate' mean if not
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adequate to the linguist, or more generally, humanly adequate? Now, this might make it appear that inadequacy of enumeration hinges on the Infmity Thesis. But suppose the Infinity Thesis is false. Does it then follow that some enumeration of the expressions is adequate? No. The set of English expressions may be so large, though finite, that no human linguist(s) can enumerate them all before the end of the universe. Any enumeration that takes the linguist(s) longer than the life span of the universe is surely inadequate. Given the nature of our linguist(s), we might even be able to show that any adequate specification must be recursive. Thus inadequacy of enumeration does not hinge on the Infinity Thesis. Clearly, all this is independent of the Decidability, the Projectibility, or the Mimicry Thesis. Therefore, the demand for a specification which is more structured than enumeration can be argued for without a hint of motivation for psychologism.
VIII. Psychologism on Linguistic Data Collection Linguistics is a controlled discipline. Linguists are engaged in rational investigations of whatever they investigate. This means at least that linguists collect data and construct theories from those data in a certain controlled manner. We are thus led to an important question: What are the data the linguist collects? For any behavioristically oriented linguist, the answer would be something like, 'The native speakers' utterances as described purely physically'. Behaviorism, however, is both implausible and out of fashion in linguistics and psychology.20 Thus let us safely ignore behaviorism. Linguists rely on native informants. As a frrst approximation we can say that native speakers' judgments on the grammatical (i.e., phonological, syntactic, semantic) features of sample utterances provide the linguist with raw data. Native speakers' testimony is the starting point of and the last tribunal for linguistic theories. At this point we face an extremely important question: How do native speakers know about the grammatical features of sample utterances? Any satisfactory answer to this question must account for the priviledged access, granted only to native speakers, to the grammatical features of utterances. A most readily given answer is that native speakers' grammatical knowledge is based on their grammatical intuition. There is no consensus as to the nature of such intuition. Psychologism appears to provide a satisfactory picture of the nature of grammatical intuition. According to psychologism, the grammar of a language is nothing more than its native speakers' grammatical knowledge, and the native speakers' grammatical knowledge is nothing more than their grammatical beliefs21 naturally acquired in the process of learning the (first) language. It is easy to see how psychologism accounts for the priviledged status of the native speakers' testimony. The native speakers' sincere
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testimony is the direct expression of their grammatical beliefs; but their grammatical beliefs, as having been acquired the way they have been, constitute their grammatical knowledge, which constitutes the grammar of the language; so their sincere testimony is in effect the direct expression of the grammar of the language. The native speakers' intuiting the grammatical features of expressions consists in their intuiting their own grammatical beliefs and therefore is a particular case of their intuiting their own beliefs. The native speakers themselves need not understand the mechanism of the acquisition and justification of their own grammatical beliefs any more than they need to understand the mechanism and justification of their own directly perceptual beliefs. According to psychologism, grammatical questions the linguist poses to the native informant are nothing more or less than a probe into that part of the human mind which deals with grammatical matters. A psychologist studying vision asks the subject to push the botton whenever she sees a dot on the screen. The subject's response to the appearance of a dot on the screen provides raw data for the psychologist to work with. Using those and other similarly collected results as data revealing that part of the human mind which deals with visual perception, the psychologist constructs and tests a theory about that part of the mind. Analogously, according to psychologism, the linguist constructs a theory about the linguistic part of the mind, using the native informant's testimony as data revealing the mechanism of that part of the mind. The native informant's response to a grammatical query is regarded on a par with the subject's response to a stimulus in a psychological experiment; the speaker's response gives a clue to the inner mechanism of her linguistic competence, just as the subject's response gives a clue to the inner mechanism of her visual perception. This appears to be a compelling picture of linguistic data collection. Thus, a valuable point is scored for psychologism.
IX. Linguistic Data Collection Against Psychologism Psychologism appears to present a compelling picture of linguistic data collection after the model of experimental psychological research. In this section I argue that the very analogy between linguistic and experimental psychological data collection undermines psychologism. Consider the psychologist conducting the experiment on visual perception. From the data collected as a result of the subject's button-pushing performance, the psychologist reaches a certain theoretical claim. In doing so, she assumes a number of things as her background information, without which her theoretical claim could not have been reached. First of all, she assumes that the experimental setup she has built is under control, that is, that she understands the physical mechanism of the setup so as to be able to control important physical parameters affecting the outcome of the
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experiment From physics she borrows the knowledge concerning the physical aspects of the setup. Those aspects are the controlled aspects of the experiment and, as such, are not under investigation. The subject is exposed to physical stimuli and emits physical responses as a result It is important to note that the subject is supposed to respond, and does respond, to physical phenomena (flashing dots on the screen). The objects of her visual perception are external physical phenomena occurring independently of her perception, and not any psychological or internal phenomena. This is the reason why the physical aspects of the setup should be controlled. The subject's response is the result of the combined effect of the physical and the psychological parameters. The objective of the experiment is to learn about the psychological parameters. Therefore the physical parameters must be carefully controlled. The researcher cannot do psychology and physics at the same time. She needs to have her physics under her belt even before designing the experimental setup.22 The subject's response comes as a result of her perception of the flashing dots on the screen. Now, as a result of what does the native informant's response to a grammatical query come? What corresponds to the subject's perception of the dots, in the linguistic case? What parallels perceptual capacities? The capacity to intuitively grasp the grammatical features seems to parallel perceptual capacities. Intuitive grasp of the grammatical features of the presented expressions corresponds to the perception of the dots. The native informant's response to the grammatical query comes as the result of her grasping the grammatical features of the expressions. The objects of the native speaker's intuitive grasp are the grammatical features of the expressions. We observed that the psychologist of vision must assume (relevant portions of) physics as the controlled background Likewise, the linguist must assume (relevant portions of) the discipline which studies the expressions in their grammatical aspects. The subject in the vision experiment perceives the physical features of the screen (the dots on it), and that is why physics is the assumed discipline. The native informant grasps the grammatical features of the expressions, and therefore the discipline assumed must be one that studies the grammatical features of the expressions. What I have called 'linguistic proper' is exactly such a discipline. Thus, if the practice of linguists in their data collection - that is, asking native informants grammatical questions - is to be understood after the model of the practice of psychologists in their data collection such as the visual experiment above, then we must conclude that there is a separate discipline, i.e., linguistics proper, which is assumed to be providing the controlled background. Therefore, those linguists of whom the analogy with psychologists is supposed to hold are not practitioners of linguistics proper. So the analogy does not help the thesis that linguitics proper is psychology. On the contrary, the analogy encourages a picture according to which that part of linguistics of which the analogy holds is psycholinguistics and psycholinguistics presupposes linguistics proper. Thus, either psychologism in linguistics is false or the analogy in question is untenable. If the analogy
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is untenable, a strong basis for psychologism collapses and psychologism leaves us in the dark as to the data-collecting method of linguistics proper. There is an independent reason why the analogy is unsatisfactory in any case. The issue here is the status of the linguist's access to the grammatical facts. When the linguist collects her data by asking native speakers of an alien language, her access to the grammatical facts relies on things other than herself, namely the native speakers. This is mirrored by the psychologist's access to the working of the subject's visual center; the psychologist relies on the subject and the experimental setup for her data. However, there has been a concensus among generative grammarians (typical defenders of psychologism) that when the linguist herself is a native speaker of the language under investigation, she need not query other native speakers, except in cases of dialectical variations. She can rely on her own intuitive grasp of the grammatical features of the expressions of her own native language. She needs no help from anyone else or any data-collecting machinery. She is an autonomous source of data in that sense. No corresponding autonomy is to be found in psychology, even if the psychologist is the subject of her own experiment. She cannot simply 'intuit' her own reaction time, for example. She needs to rely on some measuring device for such data. It might be suggested that some data-collecting methods in psychology essentially involve the subject's introspection of her own psychological states and that when the subject in such a case is the psychologist herself, she is an autonomous source of data. Consider, for example, collecting data on the presence and the quality of pain, feeling, emotion, or color perception, or on the intensity of pain, feeling, or emotion. To such a suggestion I would say that the psychologist is not really autonomous in those suggested cases. She would need a pin or a fmgemail (for pain), a sample sheet of color (for color perception), a physical, pictorial, or verbal depiction of a sample situation (for a feeling or emotion). In contrast, the self-querying linguist does not even need a piece of paper. She needs a piece of paper or something to record the collected data. but recording collected data is different from collecting data. In any event, it is unlikely that the defenders of psychologism wish to assimilate linguistics to introspective psychology. The defenders of psychologism might object that the analogy with experimental psychology is not quite fair to linguistics proper after all. They might say that although experimental psychology like psychology of vision relies on a separately controlled discipline (physics), linguistics proper does not rely on a separately controlled discipline. When the linguist tests a certain hypothesis - they might say - the controlled background of the investigation is nothing but some other portion of linguistics proper. Some portion of linguistics proper is fixed for the current concern and regarded as providing the background setup against which a certain hypothesis in linguistics proper is to be tested. Linguistics proper might be said to be self-regulating in that sense. The distinction between the fixed background portion of linguistics proper and the tested portion is, of course, by no means absolutely rigid. Surprisingly
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unexpected results might upset the distinction, forcing a revIsion of the fIXed portion. But there is nothing problematic about that. Physics is a self-regulating discipline; in testing a physical hypothesis, a certain portion of physics is fIXed and used to provide a controlled background. It is well known from the history of physics that the distinction between the supposedly fixed background physics and the tested hypothesis is sometimes upset. Thus, the defenders of psychologism might claim, linguistics proper is rather like physics than experimental psychology in this regard. It sounds peculair 10 say that psychologism assimilates linguistics to physics rather than 10 psychology, and the peculiarity may well be an indication of something seriously wrong with psychologism. However, I would like 10 pursue a different line of rejoinder here. If linguistics is psychology and is self-regulating the way physics is, then data collected to test linguistic hypotheses must be purely psychological data, i.e., data concerning the psychological and nothing else. (Data collected to test physical hypotheses are purely physical, Le., data concerning the physical and nothing else, and that makes physics self-regulating.) Data collected to test linguistic hypotheses include such data as, '''John goes to school" is well-formed' and '''John goed to school" is not well-formed'. Those data are data concerning expressions, such as 'John goes to school' and 'John goed to school', but these expressions are not psychological objects (cf., sec. 1). So those data are not purely psychological data. Therefore, linguistics proper is not self-regulating the way suggested by the above defense of psychologism after alL
x. Shared Language versus Idiolect Thus far we have assumed that linguistics proper is a study of actual human natural languages like English. It might appear to some that psychologism will be given support if we deny that assumption. Since it would be bizarre and extremely hard to deny the assumption once the existence of actual human natural languages like English is granted, the least implausible way to deny the assumption is to deny the existence of actual human natural languages like English. This way is least implausible, but drastic nonetheless. Chomsky explicitly makes this move. 23 His argument parallels Quine's argument against nonactual possibilia by means of the celebrated doctrine, 'No entity without identity'.24 Quine argues that since there is no clear identity criterion for nonactual possibilia, we should not seriously talk about them. Chomsky similarly argues that since there is no clear identity criterion for languages like English, we should not seriously talk about them. Quine's argument is suspect for two reasons. First, it is not evident that there is no clear identity criterion for nonactual possibilia. 2S Secondly, it is not evident that Quine's doctrine, 'No entity without identity', should be accepted. 26 Chomsky's argument suffers similarly. It is not evident that there
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is no clear identity criterion for languages like English. The problem of providing such a criterion is easier to handle than the probelm of providing a clear identity criterion for nonactual possibilia, because unlike possibilia, of which there are so many diverse kinds (including possible languages), actual human natuml languages like English are fairly uniform identity-wise. Also, we need not worry a~t coming up with an identity criterion which is applicable to nonactual possible hwnan natuml languages; linguistics is not a study of nonactual possible human natuml languages. Even if it turns out to be 'the case that Quine's doctrine forces us to purge English, Tagalog, Swahili, etc., out of the set of actual human natural languages, that will not mean that there are no actual human natuml languages not purged by Quine's doctrine. Quine's doctrine may well leave us with equally actual equally natural languages whose delineations cut across the boundaries of English, Tagalog, etc. But suppose there are no actual human natuml languages that are shared. What is left? Idiolects. Chomsky does not deny that there are actual human natuml idiolects. There may be as many idiolects as there are human speakers. If so, that will be a significant fact and may possibly give rise to some problems in some areas of philosophy of language/linguistics/ communication. But not for us. The situation remains the same with respect to the controversy between psychologism and nonpsychologism. Instead of talking about shared languages and expressions, talk about idiolects and their expressions, and we will be able to go through all the arguments presented against psychologism just as before.
XI. Fodor's Right View An attempt to defend psychologism recently came from Jerry A. Fodor. XI Fodor contrasts the view he defends, which he calls 'the Right View', with what he calls 'the Wrong View'. (1be two terms are supposedly proper names, without descriptive contents.) Nonpsychologism can be defended independently of defending the Wrong View.18 So Fodor's contrast is misleading if his aim is to defend psychologism. We need not go into Fodor's discussion of the Wrong View. It is sufficiently instructive to examine his Right View separately. The Right View consists of the following four theses: (a) (b)
(c) (d)
Linguistic theories are descriptions of grammars. It is nomologically necessary that learning one's native language involves learning its grammar, so a theory of how grammars are learned is de facto a (partial [1]) theory of how languages are learned. It is nomologically necessary that the grammar of a language is internally represented by speakerlhearers of that language. It is nomologically necessary that the internal representation of the grammar is causally implicated in communication exchanges between speakers and
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hearers insofar as these exchanges are mediated by their use of the language that they share.:l.9
F<Xb'says: ...according to the Right View, linguistics is embedded in psychology (it offers a partial theory of the capacities and behaviors of speakerlhearers)....30
and: Linguistics is certainly part of human psychology, according to the Right View.... ]1
It is obvious that Fodor thinks he is fonnulating psychologism, or a view that entails psychologism, by formulating the Right View. But the Right View, which Fodor so explicitly formulates in terms of (a)-(d), is clearly weaker than psychologism. Indeed, it is so much weaker than psychologism as to be compatible even with Katz's Platonism.32 (c) and (d) only assert nomological necessities concerning grammar, internal representation, and communication exchange, and therefore have nothing to say directly about the subject matter of linguistics proper. So, if the Right View is or entails psychologism, it is (a) and/or (b) that say or entail psychologism. But neither (a) nor (b) nor their combination says or entails psychologism. (a) says that linguistic theories are descriptions of grammars. Even Katz would agree that linguistic theories are descriptions of grammars. (b) says that a theory of grammar learning is a theory of language learning. Again, there is no reason why even Platonists like Katz could not agree. (a) and (b) jointly do not entail that linguistic theories are theories of language learning or grammar learning. Nor do they entail anything psychological about linguistic theories. Peculiarly enough, (a), on the straightforward reading of it, even supports nonpsychologism. If linguistic theories are descriptions of grammars, correct descriptions of grammars are all that linguistic theories are required to provide. And grammars, straightforwardly understood, are not psychological entities, or at least, it would take substantial argumentation to show that they are. The internal representations of grammars may be psychological entities, but Fodor himself is careful enough to distinguish grammars from their internal representations. 33 If the Right View is to count as a thesis of psychologism, it needs to include the claim that lingustic theories are theories of language learning or the claim that linguistic theories are theories of the internal representations of grammars. No such claim is entailed by (a)-(d). Thus, if the word 'grammar' is understood straightforwardly to mean principles of grammatical (phonological, syntactic, and semantic) features of expressions, the Right View does not characterize psychologism at all. However, there is good evidence that Fodor is using the word 'grammar' in a certain psychologically loaded manner. He says that "grammars per se are theories about Ideal Speaker/Hearers."34 If grammars are theories about
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Ideal Speaker/Hearers, it will be less strange that Fodor thinks that the Right View characterizes psychologism. But the trouble is that Fooor's fonnulation of the Right View will then become a fonnulation of an absurdly implausible view: (a') Linguistic theories are descriptions of theories about Ideal Speaker/Hearers. (b') It is nomologically necessary that learning one's native language involves learning a [correct?] theory about Ideal Speaker/Hearers of that language, so a theory of how theories about Ideal SpeakerlHearers are learned is de facto a (partial [?]) theory of how languages are learned. (c') It is nomologica11y necessary that a [correct?] theory about Ideal Speak.erlHearers of a language is internally represented by speaker/hearers of that language. (d') It is nomologically necessary that the internal representation of a [correct?] theory about Ideal SpeakerlHearers is causally implicated in communication exchanges between speakers and hearers insofar as these exchanges are mediated by their use of the language that they share.
Even the defenders of psychologism would not accept (a'). Linguistic theories do not describe theories about Ideal Speaker/Hearers on anyone's view. It would perhaps be acceptable to the defenders of psychologism to say that linguistic theories are descriptions of, or theories about, Ideal Speaker/Hearers. But that is not what (a') says. As for (b'), learning one's native language does not involve learning a (correct) theory about Ideal Speaker/Hearers, on anyone's view. It involves learning the expressions of that language and how they behave phonologically, syntactically, and semantically. But it certainly does not involve learning anything like a (correct) theory about Ideal Speaker/Hearers. If it did, every native speaker would have mastered a (correct) theory about Ideal Speaker/Hearers, but even the defenders of psychologism would not go so far as to say that any native speaker possesses a (correct) theory about Ideal Speaker/Hearers. Similarly for (c'). No theory about Ideal Speaker/Hearers is internally represented by speaker/hearers per se; at most, a theory about the phonological, syntactic, and semantic features of the expressions of the language is. (d') is even more extravagant. Even if a (correct) theory about Ideal Speaker/Hearers were intemally represented, it would have little relevance to communication exchanges between actual language users, who are known to be far from being Ideal Speaker/Hearers. Thus, Fodor's fonnulation of the Right View is mther confused and confusing.
XII. Fodor's Argument Fodor offers an argument for the Right View, somewhat reminiscent of the argument examined in sec. VIII, as follows:
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...an adequate linguistics should explain why it is thai the intuitions of speaker/hearers constitute data relevant to the confirmation of gramml.lT. The Right View meets this condition. It says, ''We can use intuitions to confinn grammars because grammars are internally represented and lICtually contribute to the etiology of the speaker/hearer's intuitive judgments."lS
In view of the foregoing discussion, we need to be charitable and ignore Fodor's charcterization of a grammar as a theory about Ideal Speaker/Hearers. We should instead understand 'grammar' in an unloaded and more standard way, to mean principles (or theory) of grammatical (that is, phonological, syntactic, and semantic) features of expressions. Now, under this standard reading of 'grammar', the Right View does appear to meet the adequacy condition Fodor mentions, as we in effect saw in sec. VIII. But the important question here is whether nonpyschologism fails to meet the condition. If it does not, Fodor's argument fails. I said that the Right View is compatible with nonpsychologism. Here I say that nonpsychologism can meet the condition if the Right View does. To see this, fIrst note that the Right View's resort, in meeting the condition, to the internal representations of grammars is otiose. The condition is met equally well if one says, (#) 'We can use intuitions to confIrm grammars because grammars are known by the speaker/hearers and that knowledge actually contributes to the etiology of their intuitive judgments'. But this is something the defenders of nonpsychologism have no trouble saying at all. They need not deny that the actual users of a language know its grammar (partially and implicitly) or that their intuitive grammatical judgments come from that knowledge. Perhaps, Fodor's charge is really that the defenders of nonpsychologism cannot say (#) within linguistics proper, i.e., that a nonpsychologistic conception of linguistics proper does not allow the students of linguistics proper per se to say (#), for (#) talks about the psychology of speaker/hearers. But this understanding of the adequacy condition is implausible. Mathematicians take their intuitions that 0+0=0, 0+1=1, 0+2=2, .... 1+0=1. 1+1=2. 1+2=3..... 2+0=2. 2+1=3. 2+2=4.... and so on. as data relevant to any satisfactory theory of integers. Why is it not good enough for them to say. 'We can use those intuitions to confIrm theories about integers because we know facts about integers and that knowledge actually contributes to the etiology of those intuitive judgments'? Do they have to be committed to psychologism in mathematics in order for such a remark to satisfy the adequacy condition? No. Indeed. even in the case of physics. which is Fodor's favorite stock exarnple,36 the condition need not be met within the discipline. Physicists use perception to confIrm their theories about the physical world. Why does perception (perceptual judgments) 'constitute data relevant to the confIrmation of physical theories? Physicists would say something like, 'We can use perception to confrrm physical theories because physical theories are about the physical world, perception gives us access to the physical world, and our perceptual judgments come as a result of that access'. Such a reply involves some
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psychological element; it mentions psychology of perception. Does this mean that physicists are committed to psychologism in physics in order to meet the adequacy condition in question? Certainly not. I conclude that Fodor's argument is useless as an argument for psychologism.
XIll. Katz' Platonism The main tenet of Katz' Platonism is that linguistics proper is a study of abstract entities and that it is an a priori study of abstract entities. Katz draws a heavy analogy between linguistics and mathematics; linguistics is as a priori as mathematics and its subject matter is as abstract as the subject matter of mathematics. I agree that linguistics is about abstract entities, but do not agree that it is a priori. This might sound like an untenable position, but it is not I will discuss this issue in the next section. Here let me focus on Katz' analogy with mathematics. The fast thing that immediately strikes us when we read Katz is the fact that he boldly assumes Platonism in mathematics. But of course, Platonism is by no means the philosophy of mathematics or a very popular philosophy of mathematics. If Platonism in mathematics is false one way or another, Katz' analogy will automatically destroy Platonism in linguistics. If mathematics is not a priori, to say that linguistics is as a priori as mathematics is to say that linguistics is not a priori. If the subject matter of mathematics is not abstract, to say that the subject matter of linguistics is as abstract as the subject matter of mathematics is to say that the subject matter of linguistics is not abstract. So, those parts of Katz' discussion which rely on the analogy with mathematics are not convincing to disbelievers of Platonism in mathematics. To complicate the matter, it is not crystal clear how far Katz should really want the analogy to hold. For example, consider the following two passages: Linguistic theory, on the Platonist view, is a theory of the invariances in the grammatical structures of all natural languages.... A 'correct linguistic theory' states all invariances and essential properties of natural language in the simplest way.Y7 ...Platonists constrain the choice of what can be studied in linguistics only in the minimal way that they constrain the choice of what can be studied in mathematics, any possible language mo.y be taken as an object of study in linguistics, just as any possible system of numbers mo.y be taken as an object of study in mathematics.:II
So, linguists study (the invariances and essential properties of) natural languages, but they may study 'any possible language' just as mathematicians may study any possible system of numbers. This is not very clear. What is the force of 'may' here? Is it a 'may' of permission? But if linguistics is about natural languages, as the frrst quotation says, then
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linguists per se are not pennitted to study other possible languages, except when doing so is part of their study of natural languages. On the other hand, mathematicians per se are permitted to smdy any possible system of numbers independently of their smdy of natural numbers. So, if 'may' here is a 'may' of permission, the analogy breaks down. Perhaps, 'may' here should be read as a counterfactual 'might'. On that reading, linguistics is acb1ally a smdy of nothing other than natural languages but might possibly be a smdy of any possible language. However, mathematics not only might possibly be, but is actually, about any possible number system. Again, the analogy breaks down. I am not aware of any reading of 'may' here that supports the analogy. In any event, Katz cannot ignore the fact that linguists are particularly interested in natural languages, rather than any possible language whatever. Thus, consider what he says: [Platonism] does not preclude the linguist from emphasizing the study of natural languages any more than it has precluded mathematicians from emphasizing the study of natural numbers."
First of all, I am not at all sure if it is correct to say that mathematicians 'emphasize the smdy of nablral numbers'. Many mathematicians are interested in all possible systems of numbers alike. Secondly, even those who are interested in numbers which have manifestations, so to speak, in the natural world around us rarely focus only on natural numbers, for other numbers, e.g., real numbers, have manifestations in the natural world also. In this sense natural numbers are a poor analogue for natural languages. Thirdly, it is certainly an understatement to say that linguists 'emphasize' the study of natural languages. Linguists per se do not much care about anything else but natural languages. They investigate whatever they investigate only insofar as they think it helps them understand natural languages better. Again, the same is not true of mathematicians per se; their investigations of nonnatural numbers are often independent of their smdy of natural numbers. Fourthly, linguists are interested in actual natural languages, not any old possible natural language. Nothing analogous can be said of mathematicians.
XIV. A posteriority of Linguistics Proper I shall now argue that linguistics proper is a posteriori even though it is about abstract entities.40 I have four arguments. Argument I Katz' claim of a priority of linguistics proper derives from the fact that linguists rely on native informants' inblitive judgments on grammatical features in their data collection. Facts concerning the speaker's actual use, either inside her head or in relation to other speakers in her linguistic community, are empirical and therefore knowledge of them is a
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posteriori. So it is essential to Katz' Platonism that those facts are excluded from the relevant data base for the linguist The native speakers' intuitions are presumably an a priori means of grammatical knowledge, just as our mathematical intuitions are presumably an a priori means of mathematical knowledge. So, Katz must, and does, insist 'that the native speakers' intuitions are the only legitimate source of grammatical data. The pool of the native speakers' intuitions is where grammatical theory construction begins and theory confmnation and comparison end. Thus Katz does not agree with Stich, who says the following: Perhaps the most important sort of evidence for the grammarian besides intuitions of acceptability is the actual unreflective speech of his subject. An informant's protest that a given sequence is \Dlacceptable may be ignored if he is caught in the act, regularly uttering unpremeditatedly wh~ on meditati~ he alleges he doesn't say. In addition to actual speech, there is a host of further clues for the grammarian. Stress patterns, facts about how sentences are heard and data on short-term verbal recall are among them.41
This passage would not convince any serious Katzian, who could say something like the following in response: When catching the informant in the act, ask him immediately for his intuition about the acceptability of the utterance he has just made. If he is a reliable source of grammatical data, he will withdraw either his utterance or his testimony. IT he does not, we should suspect that there is something wrong with him as a source of grammatical data and stop using his testimony as clean data. Relevance of the other kinds of data Stich mentions simply presupposes psychologism.
Now, I claim that, given a highly plausible assumption, Katz' thesis that the native speakers' intuitions are the only and ultimate source of grammatical data entails a posteriority of linguistics. The assumption in question is this: It is not the case that the linguist per se should study only her own native language to the exclusion of any other. Some linguists may choose to concentrate on their own mother tongue exclusively, but they do not have to. Indeed, few linguists, if at all, are in fact so mdically egocentric. Thus the assumption is a highly plausible one. Imagine the linguist studying a language of which she is not a native speaker. Assume Katz' thesis that native speakers' intuitions are the only and ultimate source of data. Then since she is not a native speaker of the language under study, the linguist has to draw on the intuitions of someone else, viz., some native speaker. Any such informant is nonidentical with the linguist, so the linguist has to ask for the informant's intuition and receive it from that informant empirically. Such an interaction is certainly a posteriori. Thus the linguist's study of any language other than her own has to be a posteriori. A defender of Katz' position might suggest that this shows that there are portions of linguistics proper which are a posteriori, but does not show that there is no portion of linguistics proper which is a priori; the linguist's
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study of her own native language is such a portion. Such a suggestion would save the a priority of linguistics only by reducing a priori linguistics to a bizarre enterprise. According to the suggestion, linguistics is not a posteriori everywhere; only that type of linguistic research which is done by the linguist who exclusively studies her own native language, exclusively drawing on her own intuitions, is a priori. But that type of linguistic research cannot extend beyond 'the linguist's own idiolect So, unless we assume that all native English (or Swahili or Russian or ...) speakers share one and the same idiolect (which is an extremely implausible assumption), that type of research is not about English (or Swahili or ...). English (or Swahili or ...) is actually a shared language (whether it could possibly be unshared is irrelevant), and idiolects most plausibly are not So any study which cannot go beyond a particular idiolect is not about English (or Swahili or ...). Therefore, according to the suggestion above, the a priori portion of linguistics proper is not about English (or Swahili or ...). This makes that portion a bizarre enterprise. Argument II: This argument is a variation of the previous argument. It argues, for the purpose of reductio, that given a highly plausible assumption, Katz' thesis that native speakers' intuitions are the only and ultimate source of grammatical data excludes a certain kind of actual human natuml languages from the subject matter of linguistics proper. The assumption in question is this: Linguistics proper should be blind to the spatio-temporal location of the linguistic community of any given natural language, that is, no actual human natural language is to be excluded from linguistics proper merely because of the spatio-temporal location of its host community. This assumption is independently plausible, but is even more plausible from the Platonistic point of view. If linguistics proper is study of abstract entities per se, their empirical manifestations - which include all the sociological, psychological, and other empirical facts concerning the host linguistic community and its members - should be irrelevant to linguistics proper. Thus, linguistics proper includes past natural languages which are no longer spoken. Take any human natural language that was used in the past but no longer, say Linear B or Aymara. Since there is no native informant available to the linguist concerning such a language, there is no ultimate source of data for the linguist; records of inscriptions made by native speakers are records of mere actual utterances and cannot take the place of native infonnants' linguistic intuitions. Therefore, the subject matter of linguistics proper includes no such language. An absurdity. Why should native intuitions be the only source of data in any case? Why should the linguist not use other sources concerning the language under investigation as ultimate sources? It seems impossible to answer this question in favor of Katz' view on neutral grounds. Argument //1: The a priori-a posteriori distinction is a distinction in point of the justification of the knowledge claim. When a native speaker is asked for a justification of her claim that some expressions of her language have certain grammatical features, she should not reply, 'I just intuit it', but say
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instead, 'That's the way we talk (grammatically)'. The way they use the expressions in question as expressions in their language is the source of justification for her claim, and that is certainly a posteriori. Note that this is compatible with the claim that the native speakers' intuitions are the only and ultimate source of data. Justification can point beyond the only and ultimate source of data. Suppose that an astronomer observes certain types of radiation in the sky and examines them. As a result she makes the claim that there was a stellar explosion in a certain region of the universe at a certain time. When asked for a justification of her claim based on the observation, she should at least cite a theoretically posited general connection between a stellar explosion and emission of certain types of radiation. Such a posit goes beyond the astronomical data base, for it is theoretical. Similarly, a satisfactory justification of the native informant's grammatical claim based on inwition should cite a theoretically posited general connection between the way they talk and the informant's intuitive grammatical judgments. Someone might ask, 'Why should the linguist not directly observe the way they talk, sidestepping their intuitions?' The answer is that direct observation of how they actually produce utterances gives the linguist only actual linguistic performance, which is a mixed bag including many extralinguistic factors. The fact that a certain sound sequence is often uttered by them does not entail that it is a grammatical sequence. The way they actually produce utterances justifies a grammatical claim not directly but via a systematic and coherent grammatical theory We should distinguish our knowledge that any walking person is moving, from our knowledge concerning the meanings of 'walk' and 'move'. The frrst is a priori but is not semantic knowledge, whereas the second is semantic knowledge but is not a priori. We are justified in believing that the meanings of 'walk' and 'move' are such and such, by the way we use these words in English (which way we intuit as native speakers), and that is an a posteriori justification. Someone who believes that our knowledge that the meanings of 'walk' and 'move' are such that any walking person is moving is a priori might object that if, as I say, our knowledge that the meanings of 'walk' and 'move' are such that any walking person is moving is a posteriori, our knowledge that any walking person is moving must also be a posteriori,42 but that the latter knowledge is a priori. In response I would say that the justification for the latter knowledge netC
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F<x any human being H, it is an empirical matter how many siblings H
has. So, for a certain given number, the knowledge that the number of H's siblings is that number is a posteriori. Let us assume that every number of siblings is identical with an abstract object Call that abstract object which
is identical with the number of H's siblings 'N'. Then, the knowledge that the number of H's siblings is N is a posteriori. If H had m<Xe, or less, siblings than H actually does, a counting of the number of H's siblings would not be a counting of N. So, the fact that a counting of the number of H's siblings is a counting of N is an empirical fact. Suppose that counting the number of H's siblings results in the claim that the number in question is F. 'F' may be 'odd', 'even', 'prime', or any numerical predicate. It is an empirical fact that the above claim, resulting from the counting, that the number in question is F is a claim about N. So, the knowledge that the claim is about N is a posteriori. But such knowledge is essential to the task of anyone who relies on a counting of H's siblings in making a claim about a number, which happens to be identical with N. Theref<Xe, such a person's claim is known a posteriori, despite the fact that it is actually about a certain particular abstract object, N. In a parallel manner I argue as follows: For any native speaker S of a natural language, it is an empirical matter which particular natural language is S's mother tongue. So, f<x a certain given natural language, the knowledge that S is a native speaker of that language is a posteriori. Let us agree with Katz and assume that every natural language is identical with an abstract object Call the abstract object which is identical with S's native language 'L'. Then, the knowledge that S is a native speaker of L is a posteriori. If S were a native speaker of a different language, S's native linguistic intuitions would not be about L. So, the fact that S's native linguistic intuitions are about L is an empirical fact Suppose that S has a native linguistic intuition that P. 'P' may be 'This and that expressions sound alike', 'This expression is not grammatical', 'That expression is ambiguous' or any sentence expressing a native linguitic observation concerning grammatical matters. The fact that S's intuition that P is about L is an empirical fact. So, the knowledge that S's intuition that P is about L is a posteriori. But such knowledge is essential to the task of any grammarian, possibly including S, who relies on S's intuitions in constructing a grammatical theory about a language, which happens to be identical with L. Therefore, the grammarian's grammatical theory is known a posteriori, despite the fact that it is actually about a certain particular abstract object, L. Since English is identical with an abstract entity, a priori study of the entity with which English is identical is possible. But linguistics proper is not such study. Linguists study the entity with which English is identical insofar as English, or some other natural language, is identical with it. Economists study numbers insofar as they are the numbers with which, say, the Dow-Jones industrial average and other leading economic indicators are identical. What they study are abstract entities (assuming that numbers are
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abstract entities). So what they study can be studied a priori. But such a priori study would not be economics. Economists study numbers under certain proprietary descriptions, i.e., under economic descriptions. Abandon economic descriptions, and you abandon economics. Similarly, linguists study absttact entities under their proprietary descriptions, such as 'the language spoken in England in 1987', 'the language spoken by that group of people in 1587', etc. They have shorthand terms for these descriptions, e.g., ,Contemporary British English', 'Elizabethan English', etc. These and other even shorter, and vaguer, tenns like 'English', 'Swahili', etc., are non-rigid designators of abstract entities.·3 That is, they actually refer to certain particular abstract objects but could have referred to other particular abstract objects. If certain things had not happened the way they actually did during the development of the language in England, British English today would have been different, that is, British English would have been identical with an abstract entity with which British English is not actually identical. It is plain!y false to say that had things gone slightly different!y in the linguistic development in England, there would have been no British English at all. The correct thing to say is that British English would have been a different language than the one we actually have. Since the proprietary descriptions linguists use are contingent descriptions of their referents, linguistics proper is a posteriori.
xv. Epilogue The falsity of psychologism does not undermine the importance of Chomsky's revolution in linguistics. Chomsky's reorientation of linguistic research should not be understood to be an attempt to turn linguistics proper into psychology. It should instead be understood to be an enshrinement of psycholinguistics as a centrally important branch of linguistics. At the same time we should be careful to distinguish linguistics proper from psycholinguistics as a sepamte and nonreducible branch of linguistics.
487 ENDNOTES I thank Robezt C. Richardson for substantive conunents on an earlier version, which improved the paper. 1. Chomsky starts with the psychologistic conception of linguistics; for him, a linguistic theory has explanatory adequacy only if it explains first-language acquisition by humans. At the inception of his psychologism Chomsky was reacting against the structuralist linguistics of the day and therefore argued for his psychologism against the structuralist conception of linguistics. But he did not and does not argue for psychologism against any other nonpsychologistic conception of linguistics. He subsumes linguistics under a general study of the human cognitive capacities and pursues the former as a special case of the latter. Psychologism is the given for Chomsky's methodology, its starting point This, of course, does not mean that Chomsky's work is unimportant. Nor does it mean that psychologism is true. 2. 1.1. Katz battles against psychologism on that muddy ground in: 1.1. Katz, Language and Oth£r Abstract Objects (Totowa: Roman and Littlefield, 1981). See also: S. Soames, "Semantics and Psychology," in 1.1. Katz, ed., The Philosophy of Linguistics (New York: Oxford University, 1985), pp. 172-203. 3. Suppose, plausibly, that there are infinitely many English expressions. Then, actual humans could not possibly finish uttering all English expressions. But this poses no problem, as far as each English expression is such that an actual human speaker could possibly finish uttering it 4. Katz expresses skepticism about the possibility of a psychologistically adequate answer. See: Katz, Language and Other Abstract Objects, pp. 56, 74n 16. 5. See: Paul Benacerraf, "What Numbers Could Not Be," THE PHILOSOPHICAL REVIEW, 74 (1965), pp. 47-73. 6. Noam Chomsky, Rules and Representations (New York: Columbia University, 1980), p. 90. 7. Ibid., emphasis mine. 8. See: Ibid., pp. 118-119. See also: Soames, 9. See: Katz, Language and Other Abstract Objects. "Semantics and Psychology." 10. See: D.T. Langendoen and P.M. Postal, The Vastness of Natural Languages (Oxford: Basil Blackwell, 1984), ch. 4. 11. Ibid., p. 63. 12. Ibid. 13. See: Ibid., pp. 58-59. 14. See: Ibid., pp. 65-66. 15. I am uncritically following Saul A. Kripke, Naming and Necessity (Cambridge: Harvard University, 1980), pp. 46, 125-126, 138. 16. Noam Chomsky, Aspects of the Theory of Syntax (Cambridge: MIT, 1965), p. 3, and Chomsky, Rules and Representations, pp. 24-25. 17. Absence of the modularity thesis also seems to have been responsible for blurring his own distinction between competence and performance in connection with the subject matter of linguistic theory: "...languages have in conunon...their 'creative' aspect. Thus an essential property of language is that it provides the means for expressing indefinitely many thoughts and for reacting appropriately in an indefinite range of new situations.... The grammar of a particular language, then, is to be supplemented by a universal grammar that acconunodates the creative aspect of language use and expresses the deep-seated regularities.... It is only when supplemented by a universal grammar that the grammar of a language provides a
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full account of the speaker-hearer's competence." Chomsky, Aspects of the Theory of Syntax, p. 6. The 'creative aspect' pertains to language use, hence performance, and as such it is not supposed to be accounted for by a universal grammar or any part of linguistics proper. Chomsky is free from this confusion in: Chomsky, Rules and Representations, pp. 76-79, 222-223. 18. Ibid., p. 4. 19. This is a purer version of Chomsky's thesis asserting the 'creative aspect'. See: Chomsky, Aspects of the Theory of Syntax, p. 6. Unlike Chomsky's thesis, it is primarily syntactic- it avoids mentioning 'thoughts' - and scarcely pragmatic - it avoids talk of 'reacting appropriately in an indefmite range of new situations'. 20. See: Noam Chomsky, 'The Case Against B.F. Skinner," NEW YORK REVIEW OF BOOKS, December 30, 1971; and Daniel C. Dennett, "Skinner Skinn~" in Daniel C. Dennett, Brain Storms (Montgomery: Bradford, 1978), pp. 53-70. 21. I follow Chomsky in suggesting that if 'belief' and 'knowledge' are inappropriate notions here, stipulate 'cognate' to be the appropriate notion and substitute it for 'belief and 'knowledge'. See: Chomsky, Rules and Representations, pp. 69-73, 92-102. 22. Unless the psychology in question is a kind which requires no experiment, e.g., purely introspective psychology. 23. See: Ibid., pp. 217-219, also pp. 117-127. 24. See: W.V. Quine, "On What There is," in W.V. Quine, From a Logical Point of View (New York: Harper and Row, 1953), pp. 1-19. See also: W.V. Quine, Word and Object (Cambridge: MIT, 1960), pp. 200-206, 211, 244. 25. See: David Lewis, COlU1lerfactuals (Cambridge: Harvard University, 1973), p. 87. 26. See: Terrance Parsons, "Entities Without Identity," in IE. Tomberlin, 00., Philosophical Perspectives, 1, (Ridgeview, 1987), pp. 1-19. See also: J.1. Katz, "An Outline of Platonist Grammar," in Katz, ed., The Philosophy of Linguistics, p. 180, for his criticism of Chomsky on this point 27. See: Jerry A. Fodor, "Some Notes on What Linguistics is About," in Ned Block, 00., Readings in Philosophy of Psychology, VoL 2 (Cambridge: Harvard University, 1981), pp. 197-207. 28. The Wrong View says, "(a) that there is a specifiable data base for linguistic theories; (b) that this data base can be specified antecedent to theory construction; (c) that the empirical content of linguistic theories consists of what they say about the data base; and...(d) that the data base for linguistics consists of the intuitions (about grammaticality, ambiguity, and so on) that informants produce (or would produce....)" Ibid., p. 198. 29. Ibid., p. 199. 30. Ibid. 31. Ibid., p. 207n 2. 32. The Right View is also stronger than psychologism in its commitment to internal representations. But this is not relevant to our concerns. 33. However, Fodor does slip into saying, "...the internal representation of the grammar (or, equivalently for these purposes, the internally represented grammar)..., talking and understanding the language normally involve exploiting the internally represented grammar," Ibid., p. 199, thus obliterating the distinction between grammar and its internal representation, which is crucial to the controversy at issue. 34. Ibid., p. 203.
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35. Ibid., p. 200-201. 36. See: Ibid., p. 200. 37. Katz, The Philosophy of Lingwistics, pp. 201-202. 38. Ibid., p. 177. 39. Ibid., pp. 177-178. 40. James Higgenbotham attempts such an argument in: James Higgenbo~ "Is Grammar Psychological'!" in Leigh Cauman, et al., eds., How Many Questions? (Cambridge: Hackett, 1983), pp. 170-179. As Katz observes in: Katz, Language and Other Abstract Objects, pp. 179-18011 18, it is not convincing. 41. Stephen Stich, "Grammar, Psychology, and Indeterminacy," THE JOURNAL OF PHILOSOPHY, 79 (1972), pp. 799-818. 42 There is an argwneDt which is being assumed here: The meanings of 'walk' and 'move' are such that for any x, if 'walk' is true of x, 'move' is true of x. But for any x, 'walk' is true of x if and only if x walks, and 'move' is we of x if and only if x moves. Therefore, The meanings of 'walk' and 'move' are such that for any x, if x walks, x moves, that is, any walking person is moving. 43. See: Kripke, Naming and Necessity, for the notion of nomigid designator.
POEMS, PAINTINGS, AND INTENTIONS GREGORY CURRIE II. Psychologism Revived 'Psychologism' has turned out to be a confusingly adaptive tenn. But one kind of mistake that commonly goes by that name is the running together of questions about the origin of some intellectual, or more generally cultural product with questions about its appraisal. Thus Frege, the great opponent of psychologism in logic, insists that we "distinguish between the grounds that justify a conviction and the causes that actually produce it." I When William Wimsatt and Monroe Beardsley identified what they famously called the 'intentional fallacy' they did not describe it as a species of psychologism, but they well might have. Early on they illustrate the fallacy by imagining a critic who says: "In order to judge the poet's performance, we must know what he intended." And they reply: "to insist on the designing intellect as a cause is not to grant the design or intention as a standard by which to judge the worth of the poet's perfonnance.. "2 Wimsatt and Beardsley's paper had the emotional attractions, and the intellectual drawbacks, of a radical manifesto. While it portrayed the opposition as (at best) confused by a woolly minded attachment to 'the spirit of poetry', its sweeping denunciation and urgent message disguised the gaps and ambiguities in the argument To consider just one obvious defect: their reply to the intentionalist that I quoted above illustrates their own commiunent to a fallacy. For we may hold that intentions (of certain kinds) are relevant to a decision about the value of the work without holding that these or any other intentions dictate the nonns of criticism. But Wimsatt and Beardsley have been roughly handled by their critics already, and I don't wish to explore the details of their argument any further. 3 Anyway, by the standards of today, their essay seems impeccably conservative in its defense of objective criticism. If the idea of 'the text' has taken a beating in recent critical writing, it may in part be in reaction to some of the implausibilities in the critical objectivism that Wimsatt and Beardsley defended. Not that currently fashionable schools of criticism have gone back to the author; it is the reader whose mental states now take center stage. In this essay I want to defend the critical importance of authorial (and more generally artistic) intention. I want to enumerate a number of ways in which the artist's intention is an intrinsic feature of the work. Intrinsic in the sense that in the absence of that intention, the work would be different
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in some aesthetically important way. And this relation between intention and work is not to be thought of as causal, but logical. It is not possible for the work to have these aesthetic features in the absence of these intentions. What I should like to present is a general theory which maps and explains the exact nature of the relation between work, intention, and critical judgment Unfortunately, I do not have such a theory (though I've tried make a start on it elsewhere4). There are those, of course, who think that there can be no systematic theorizing in this area. Frank Cioffi for example, in rejecting the intentional fallacy, pr~nts a budget of examples where authorial intention seems pretty clearly" to play a legitimate role in judgments about the work. But his aim is to undermine a general thesis, not to put another in its place. 5 I think Cioffi's examples are telling, and that we can hope to take the matter further. Science has sometimes been thought of as a three level activity, comprised of particular observations, inductive generalizations, and unifying theoretical laws. Without taking this picture too seriously, I think we can use it to illustrate the present strategy. Here I want to do some work at level two; to formulate a set of relatively disconnected hypotheses about the ways in which the artist's intentions bear upon our understanding and evaluation of the work. If we can achieve generality at this level, there doesn't seem to be any reason in principle why we should not eventually achieve a deep theoretical unification of these generalizations. Art may not be quite the motley that Cioffi, in Wittgensteinian mode, supposes it to be. But there is no straight rule of induction at work here; the generalities I want to offer cannot be obtained by asceptic inference from uncontroversial data. Perhaps one needs to see a number of issues in aesthetic theory in the way I see them in order to find my generalizations convincing. I put them forward as a double challenge: to integrate them into some deeper theoretical framework, or to show that they are not true to the data culled from our experience of particular works. My theses are psychologistic - nol, I hope, in the sense that they conflate psychological causes with evaluative standards - but in that they affirm the inseparability of work and intention. Here I must sharply distinguish my position from one sometimes adopted in order to defuse the issue raised by Wimsatt and Beardsley: that an author's intentions can be regarded as fully public objects, embodied in the text. I can make no sense of this idea of 'embodied intentions' unless it is a misleading way of saying that the text contains evidence for some hypothesis about what the author's intentions are. Behavior and the results of behavior, like a text or a painted canvas, do not embody intentions. Intentions bear to the artist's product the same kind of relation as that of the theoretical entities of science to the observable world- belief in them is warranted by inference to the best explanation rather than by direct acquaintance. So when I argue, as I shall, that intentions of various kinds are constitutive of the art work, I shall be arguing that there are things constitutive of a work of art that do not belong to the public domain. So my position is psychologistic in a further sense; it is based on the idea that the mental is essentially interior. Frege himself
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would not have recognized this as a species of psychologism, since this is exactly his own view of the mental.' But I note a modern tendency to use the term in exactly this sense. Thus, Ned Block defends a view, which he calls 'psychologism', that two systems could be identical in actual and potential behavior, while only one of them is intelligent; for intelligence is a function, not of behavioral dispositions, but of 'internal information processing'.' And John McDowell has characterized psychologism as the view that "the significance of others' utterances is a subject for guesswork and speculation as to how things are in a private sphere concealed behind their behavior."' The doctrine that McDowell characterizes - with a view to refuting it, of course - seems to me roughly correct.
ll. Intentions and Text One of the things that Wimsatt and Beardsley argued for in their original essay is that the object of critical scrutiny is not the artist's intentions, but the text of the work. I want to argue ftrst that there is no dichotomy between text and intention, for the text of the work is the text the author in/ended it to have. In saying this, I do not commit myself to the proposition that if the artist merely intended the text to be better than it turned out to be, then there is a non-visible text that is the real text of the work, better than the written text. What determines the text of the work is the author's lexically specific intentions. The author has a lexically specific intention when he intends to write a certain word or sequence of words, spelt in a certain way. When the author has such an intention, his act of writing may fail to embody that intention; he may, through oversight or because he is a bad speller, write something that does not correctly mirror his intentions. If he does, the text he inscribes will deviate in some way from the text of the work. Our practice in the treatment of texts seems to conform to this line of thought Editors routinely correct the misspellings of authors; sometimes, no doubt, referring their corrections back to him for authorization. But where the author is not available for comment such corrections are still frequently made. What principles govern the alteration of such misspellings? One might suppose that a change is judged allowable simply if it amounts to a correction of spelling- bringing the text into line with correct spelling conventions. Corrections beyond this minimum may be made, but they would be regarded as a dubious practice. But we see, on reflection, that a spelling change is allowable only if there is reason to think the change brought the spelling of the text into line with the spelling the author intended, and not allowable merely on the grounds that the change amounts to a correction in the above sense. A copy editor who 'corrected' the spelling in an anthology of poems by e.e. cummings would not keep his job long. Clearly, the reason we would deplore such a change is that we have
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reason to believe that cummings intended his poems to be spelt in a non-standard way. Faced with a text that shows no signs of having been produced with such an intention, we correct the occasional misspelling with a good conscience. But when doubts about the author's intentions creep in, we hesitate. It might be argued that whatever our unreflective practices may be, the principle I offer as a rationalization of them has an unacceptable result: that where the author has false beliefs about how a word is spell, those beliefs will feed into intentions that will set his mistakes in concrete, so to speak. If the author intends to spell 'cat' 'c-a-t-t' because he thinks that is how it is correctly spelt, then the intentionally determined text will have all occurrences of 'cat' misspell. And this would be a gratuitous multiplication of error. But in these cases of error based on ignorance the author has conflicting intentions. He intends to spell 'cat' correctly, and because he believes that it is spelt 'catt' he intends to spell :t like that. Clearly, the intention to spell the word correctly dominates the intention to spell it any particular way. If the error was pointed out to the author, he would abandon the intention to spell it that way. So we let the dominant intention be the determinant of the text This shows that we cannot understand the phrase 'lexically sPecific intentions' to apply narrowly to intentions to write a certain series of letters in a certain order; to do so would be to rob ourselves of the opportunity to solve the kind of problem we are considering here by allowing the intention to spell the world correctly to dominate. Lexically specific intentions are intentions to write words spelt in way F, where 'way F' might be a rigid or a non-rigid designator of letter sequences. 'c-a-t-t' rigidly designates a letter sequence, while 'the correct sequence of letters for spelling "cat"' designates different letter sequences in different worlds. On the other hand, merely intending to spell the word the way it would be spelt by someone who was a bad speller would not count as a lexically specific intention; there is no unique way that a bad speller would spell 'cat', and 'the way a bad speller would spell "cat"' is an improper description. Notice that we are not inclined to say anything comparable about painting. We do sometimes alter the appearance of a painting in order to restore it to its original state (though it is often questionable as to whether that is actually the effect of the alteration), but it would be regarded as indefensible to alter a painting because you thought that you were bringing it into line with the painter's intentions about how it was to look (rather than, as in the case of successful restoration, bringing it into line with how it did previously look). The only legitimate revision of a painting is that done by the artist, when the revision will count as a stage in the production of a yet to be completed work. If our intuitions about what practices are legitimate are based on anything more than prejudice (and a widespread but wholly ungrounded prejudice in this area would certainly need some explaining), it seems there must be a fundamental asymmetry between the
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aesthetic' condition of painting and the aesthetic condition of writing. In what does this asymmetry consist? One rather superficial difference (superficial in this context anyway) between literature and painting is 'that there is nothing comparable to a misspelling in painting, because there is nothing comparable to an alphabet in painting.' There can be artistic mistakes, but they are of the same kind as the choice of an infelicitous metaphor. This has the effect of making it extremely difficult for anyone to attribute to the painter an intention that is specific enough for us to be able to say with certainty what alteration to the painting would count as bringing the picture into line with that intention. We might be able to say that the painter intended that shade of blue to be darker, or that figure a bit further to the left. But who can say exactly how much darker or further to the left he intended it to be? Indeed, we would strongly suspect that there simply are no answers to these questions. Since colors are continuously variable in hue and shapes continuously variable in position, it is very hard to imagine a painter intending to produce exactly that hue and no other, or exactly that positioning of the figure and no other. But nothing is easier than to intend to write this letter rather than some other. But suppose the artist was capable of a purely mental detennination of the exact pictorial structure of his projected work (exact down to the threshold of discriminable difference), yet failed to produce that exact pictorial structure on his canvas. Would the mentally conceived structure constitute the real pictorial structure of the work, to which the appearance of the canvas was but a poor approximation? I suppose Croce and Collingwood would have said so. But they would have been wrong. For the painting stands in relation to the artist's intention in a quite different way from the way the misspelling stands to the author's intentions. The painting itself is not just a register of the author's choices about the visual pattern he wants to select; the artistic performance that we judge does not consist just in choosing a structure of lines and colors- it consists in presenting such a structure using those means that the medium of painting allows. The act of painting is part of the artist's performance that we judge when we judge the quality of the work, for the artist must employ artistic skills in embodying his plan for the work on canvas. But the writer's act of inscribing words is no part of what we judge when we judge the work. The act of inscription is achievable without the employment of artistic skills, and if the writer uses such skills - say, by employing the skills of a calligrapher - they are skills irrelevant to the kind of work he is producing. Tom Jones would not be a better novel if Fielding had had more beautiful handwriting. The endpoint of the author's artistic activity is the point at which his indexically specific intentions are determinate. This explains why we might correct an author's manuscript, but never a painter's canvas. In correcting the author's manuscript, we try to make clear some aspect of his perfonnance that the manuscript obscures; we try to set the record straight. But to 'correct' the painter's canvas by overpainting, or
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whatever, would be to obscure some aspect of the painter's performance that the canvas previously made clear; it would be to falsify the record. To sum up. In literature, the execution of the work consists in deciding what words to use. Whether this is done antecedently to writing or in the very act of writing, it is the decision that counts towards the performance, not the transcription of the words. But in the visual arts, there is no such thing as a set of decisions that determine the geometrical structure of the work. That is determined in the act of painting, and that is the stage of execution.
III. Intention and Fiction One very important class of literary works is the class of fictional works. But what, exactly, distinguishes fiction from non-fiction? Again, the answer is to be found in a certain constitutive intention of the author- constitutive because fictional status is constitutive of the work. Imagine a possible world in which Henry Fielding wrote a book called 'Tom Jones' in which he detailed, with truthful intent, the life of someone he was acquainted with. Would that be a world in which Fielding wrote Tom Jones, the work with which we are familiar- a world in which that very work just happened not to be fiction? Hardly. The non-fictional story called 'Tom Jones' would, even if word for word identical with the text of Tom Jones, be different from it in aesthetically significant respects. 'Tom Jones' might be good or bad biography, but the relevant criteria with which to judge it would be different from those we would use to judge Tom Jones. Sameness of text might be necessary for trans-world identification of works, but it is certainly not sufficient. 10 To see the text alone as constitutive of the work is a New-Critical dogma we shall have to abandon. If works can share the same text while only one of them is fiction (as I have just supposed), it is plain that the fictional status of a work cannot supervene on any or all of its textual properties. It must then be something external to the text that determines fictionality, and here there are but two plausible candidates: audience practices of regarding the work in a certain way, and authorial intentions. But the fIrst is unsatisfactory; audience practices can vary over time, but a fictional work surely does not cease to be fiction if audience reaction to it changes. Elsewhere I have argued that fiction is constituted by a certain kind of communicative intention on the part of the author- a (Gricean) intention to get the audience to take the attitude of make-believe towards the story that is told. ll On this view, the act of producing fiction ('fiction-making', as Kendall Walton calls itl~ is a communicative act of the same kind as those acts, sometimes called 'illocutionary acts', amongst which are asserting and requesting. These are acts which have in common the familiar reflexive intention; 'the intention to achieve a certain effect via the recognition of that very intention, and which are differentiated one from another in terms of
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the specific effect that it is intended that they will achieve. This view stands in sharp contrast to the view that fiction-making involves some kind of pretence on the part of the author. Thus, it is said that the author of fiction pretends to be asserting what he says, that he pretends to have knowledge of the events he describes. 13 This seems to me a highly implausible view. That is, it is implausible to say that an author who types out his story and sends it off to the press is pretending to do anything. Perhaps camp fife story tellers can be said to take on a pretended persona for the duration of their tale- the persona of one who knows the truth of which he speaks. But these days, acts of authorship are rarely undertaken in so picturesque a setting. This implausible theory may be the product of a confused perception of something closer to the truth: that readers of fiction pretend that the story is related to them by someone who knows the facts of which he speaks, and they perceive that this is intended by the author to be their pretence. I" But, of course, to encourage pretence in an audience one need not engage in pretence oneself.
IV. Intention and the Story I have said that the text of the work depends upon the author's lexically specific intentions, and that the question of whether the work is fiction or not depends upon the author's communicative intentions. But to show that the traffic is not all one way along this street, I want now to argue that the story that is told by a fictional work is not a function of the author's intentions. This will seem paradoxical only if we assume that the structure of the story - what is, as we say, 'true in the story' - depends wholly on the text; for then, by the transitivity of 'detennines' we would get the result that the author's lexically specific intentions determine the story. But clearly elements of a fictional story are left undetermined by the text There are things true in the stories about Sherlock Holmes that are not explicit in the text, and not entailed by anything that is explicit in the text It is possible to fmd quite bizarre interpretations of these stories that are formally consistent with the text One might suppose that Watson is a lunatic or a liar who never met anyone called 'Holmes' and that the story is his mvings or invention. One might explain Holmes' superior powers of inference and observation on the hypothesis that he is a supernatural being in disguise. IS But it is intuitively obvious that these things are not true in the stories; Watson is by and large a reliable reporter of the facts of Holmes' cases, and Holmes himself is a human being, if an unusual one. Clearly, what is true in the stories is not just a matter of what is said in the text, but of what can be inferred on the basis of the text together with certain collateral information. Exactly what this collateral information is and how these inferences are to be made is a matter of some controversy. 16 But one thing seems clear: we cannot say that what is true in the story is what the author intended to be true in the story. Conan Doyle might have had quite strange
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intentions concerning what is to be taken as true in his story, he might have had strange beliefs about, f(»" instance, extraterrestrial beings who visit us, and he might have believed that these beliefs were widely shared by members of his community. He might have thought that it would be as obvious to most people as it was to him that the likely explanation of Holmes' superi(»" mental powers was that he was an alien being, and for this reason he did not make this part of the story explicit. But if we discovered that all this was indeed true of Conan Doyle's beliefs and intentions, I do not think it would give us any reason to revise our views about what is true in his stories. Whatever is legitimate collateral information about what is true in a story, extra-textual revelations about the author's intentions in this area are not relevant information. The reason has something to do with a point already made: that a judgment of the work is a judgment of the author's achievement. Merely for the author to intend that the story be interpreted in a certain way constitutes no achievement on his part. But it is part of his artistic achievement to write in such a way that his intentions in this area be put into effect- that readers, if they are well provided with relevant collateral information and are attentive to the text, will be likely to interpret the story in the way intended.
V. Intention and Representation I want to turn finally to an example of constitutive intention in painting. (What I say here would apply, I think, equally well to sculpture and other forms of visual representation.) My claim is that it is a necessary condition for a painting to depict something that the artist intended it to depict that thing. I am not claiming, on the other hand. that it is a sufficient condition; an artist may intend to depict something and fail, for various reasons, to be successful in carrying out his intention. Nor am I claiming that we can go any way towards explaining what it is for a picture to depict in terms of what it is for an artist to intend to depict. On the contrary, it seems likely that we shall have to explain intending to depict in terms of depicting. My claim is just that in order for there to be depiction, there must be a depictive intention. Why does depiction presuppose intention? Because only intention has the fmely tuned capacity to connect marks on canvas with the objects in the world that we regard those marks as depicting, and only intention has the kind of logical structure that will allow us to depict the non-existent (as we are inclined to say; more on this in a moment). This might be doubted on the grounds that language has the same discriminatory/intentionalistic features, without being subject to the same intentionalistic constraints that I claim for pictures. In order for a word-token to refer to a, it is not required that the speaker intend to refer to a by means of that word. Of course, this is not to deny that linguistic reference depends ultimately on, and in
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complex ways on, speakers' intentions; rather, it is to say that the conventionality of language loosens its ties with intention. But it is this element of conventionality that distinguishes the linguistic case from the pictorial one. Pictorial representation is not conventional in the way that linguistic representation is. What a linguistic expression refers to is a matter of there being a convention in the relevant community to the effect that the word has that reference. Pictures, at least as we commonly use them, are not governed by any similar convention. There are no conventions to the effect that certain patterns of shape and color depict certain objects or kinds of objects. It makes nonsense of the history of art to suppose that a regular practice of depicting a certain object by means of a certain kind of picture entrenches to the point where a picture of the kind depicts that object whatever the artist intends it to depict Pictorial depiction is more like the kind of pre-linguistic communication imagined by Bennett and other Gricean-minded philosophers, where an 'on-off' gesture or sound can be counted on to get across the speaker's intentions, because of its iconic relation to the state of affairs represented. 17 There are, of course, regularities of practice in painting that we tend to call conventions, and there may be some temptation to suppose that these 'conventions' can fall sufficiently hard on an artist's activity to tip the balance against his intentions. Imagine an artist who has seen plenty of Pietas, but does not know what they represent If he makes a work in the same form, surely it represents the Virgin and the dead Christ regardless of his intentions. Two different cases need to be distinguished here. In one, the artist has no ideas one way or the other about what is represented, but he intends to represent whoever is usually represented in works of this kind. His action is like the reference borrowing action of one who uses the name 'Napoleon', not knowing to whom it refers, but intending to refer to whoever is referred to by users back along the reference borrowing chain. Such a claim is no counterexample to the thesis that representation depends upon the artist's intentions. In the other case, the artist has intentions about who is represented, but his intentions are deviant with respect to the community; he intends to represent someone other than the person normally represented in such works. It seems clear that such a work can represent what the artist intends it to represenL Imagine a tasteless representation in Pieta style entitled 'Jackie and J.F.K., Dallas, 1963'. We may object to the high-jacking of a sacred imagine, but the reason we do is surely that a work which ought to represent one thing is being used to represent another. Without a title or some other authoritative indication of the artist's intention we would probably take the work as orthodox in its representational properties. But that just shows we can be wrong about what is represented. We are familiar in the philosophy of language with the distinction between what a speaker means and what a speaker says, or - what is more to the point here - between speaker's reference and semantic reference. Thus, philosophers have wondered how and in exactly what sense a speaker
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can say 'The man drinking champagne is happy tonight' and refer to someone who is not, in fact, drinking champagne. II But examples of the Pieta variety show, I think, that there is no comparable distinction to be made for pictorial depiction. There is no sense in which the Pieta-like representation itself depicts (or, in 'the tendentious language of semiotics, 'denotes') Mary and Christ, while the artist depicts something else. The difference between language and painting is that language is essentially conventional while painting is nOl The use of signs on an ad hoc basis, each chosen for the needs of the moment, is not the use of a language. A language involves signs recmrently used to signify a given state of affairs, where there is common knowledge between language users of the use to which a sign is to be put. Nothing precludes pictures being used in this way, but a regular practice of pictorial depiction can emerge without there being such conventions for the use of signs. Words and sentences cannot mean things without there being conventions of meaning, but pictures can depict without conventions of depiction. And that is, by and large, the condition of pictures in our artistic culture. There are no conventions that determine that a given picture depicts a given thing. Since depicting might have been conventional, we can sensibly ask why it is not. To see the answer, we need to take a closer look at the notion of a convention. According to David Lewis, conventions are regularities of behavior which are conformed to because they are solutions to co-ordination problems. I' For example, the speaker and his audience want to co-ordinate their actions; the speaker has to choose some means of expressing his thought (a sign) and the audience has to associate the sign with the thought expressed. It does not matter very much what sign is used; what matters is that speaker and audience associate the same sign with the same thought. Once communication has been achieved with the use of a given sign, it is likely that the same sign will be used again for the same purpose. For speaker and audience will expect each to use the strategy that succeeded before, and this expectation gives them both a reason for so using it themselves. A convention is born. Now something similar can be said about the situation of painter and audience. The painter wants to represent something and the public wants to know what is represented. But several things militate against ta'le development of conventions to solve this problem. First, with high probability, painter and public can co-ordinate their actions without convention. For the development of a realistic style of pictorial depiction has enabled painters to count on the ability of the audience to know what is represented simply on the basis of their perception of visual properties of the picture. Of course, this will work only some times and for some audiences. But the artist can also exploit pre-existent conventions of language in order to give his work a title and thereby indicate what it represents. Secondly, conventions here would in many cases be pointless, because painters often work without any background of regularity in depicting that thing, and without any expectation that such a regularity will
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develop. Thirdly, conventions would be costly in their imposition of constraints on the artist who wants to be free to depict in whatever manner he chooses. I have remarked that in our culture regularities do sometimes emerge in connection with the depiction of particular things or kinds of things, but these regularities are not happily described as conventions in the present sense. Thus, The Saints are regularly depicted as having halos, but this is not a convention. They are thus depicted because of certain views about the nature and/or appearance of saints that people hold or did hold. Thus, there were (what were taken to be) good reasons for so depicting The Saints, and hence, so depicting them was not an arbitrary choice. But a convention proper is arbitrary. In some periods, the Virgin is regularly depicted in clothes of a certain color. But again, this is not a convention; it is regularly adhered to because it was judged to have certain aesthetic or devotional effects, not because it solved a co-ordination problem. Pictorial style is often described by art critics and historians as conventional. Cubist painters depict objects in a way systematically different from the way, say, Impressionist painters depict objects. But the elements of Cubist style are not conventional in our sense, for they are non-arbitrary; Cubist painters paint objects that way because they prefer, for aesthetic reasons, painting that way to any other. Neither are the elements of style solutions to co-ordination problems. Once a painter paints that way, his or her audience have the problem of interpreting the work, and they may do this partly by assimilating the elements of the style. The style creates a communicative problem rather than solving one. Perhaps what sounds like a bold thesis - that there are no conventions in painting - is merely a restrictive stipulation about the meaning of 'convention'. But we must remember what is at stake here. I don't claim that what art historians have called 'conventions' in painting don't exist, and I don't dispute their right to so call them. But I do insist that we distinguish conventions in this weak sense from conventions of a kind sufficient to generate a language. Since the question before is whether depiction in painting is in any sense linguistic, it is proper to concentrate our attention on conventions of the kind that Lewis has analyzed. Turning away from conventions as an alternative to intentions, it might be said that what is represented is determined ultimately by causal facts of a brute kind; that, for instance, it was the Duke of Wellington who sat before Goya; that light reflected from the surface of the Duke and impinged upon Goya's eyes as he painted. And this is what makes it the case that the Duke is represented. We need not assume that Goya' s actions as he painted were those of an automaton, that his act of painting was not controlled by intentions. It is just that no intention he had was relevant to determining the identity of what is represented. Goya might have thought that it was Napoleon sitting in front of him, intending that it be Napoleon represented. But as long as the object in his line of sight was Wellington and not Napoleon, it is Wellington and not Napoleon that is represented.
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Such uncompromising causalism can hardly explain the representation of non-existents (since one cannot be causally related to a non-existent), nor the fact that a picture may represent St. John even though it was an artist's model that stood before the painter. These cases are much better handled in tenns of the artist's intention. What about cases involving the kind of mistake just alluded to- when an artist thinks he is painting one person or scene, but is in fact painting another? These too can be explained in terms of the artist's intention. For the artist might be mistaken about the identity of the man before him, or about the location in which he paints, but he still intends to represent that man (the one in front of him) or the scene here abouts. In these cases, the artist has conflicting intentions. He intends to represent that man, and to represent the Duke, but that man is not the Duke. I suggest that the former intention, a demonstrative intention as we may call it, has priority in determining what is represented. For the having of a demonstrative intention signifies a peculiarly close relation between the artist and his subject; it is the kind of intention that he can have only when he is in close proximity to the subject. 211 In order to represent something, the artist need not have a demonstrative intention to represent that thing- he need not have a de re intention at all. The artist can depict Smith's murderer without knowing who Smith's murderer is, carrying out his work on the basis of the police evidence alone. 21 But where there is a demonstrative intention it will be decisive for representation. Where there is no demonstrative intention, representation can, in unfavorable circumstances, become ambiguous or indeterminate. Imagine an artist whose knowledge of the Bible is hazy. He intends to paint Joseph, the man who was both the father of Jesus and the owner of the tomb in which Jesus was laid. He is confused as between Joseph of Nazareth and Joseph of Arimethea, and nothing else he knows tells in favor of the one over the other. The picture itself does not unambiguously depict an incident in the life of either man. Here there is no reason for saying it is one Joseph rather than the other that is depicted. An intentional account of representation does not dispense with causation. Causation plays its part in determining representation because it plays a part in constraining representational intention. Whatever the causal constraints on depiction are (and what they are is controversial), they are just the causal constraints on intending. Thus, the object of the artist's demonstrative intention (and hence the very identity of that intention) will be determined by his causal proximity to that object. Similarly, if there cannot be a depiction of anything that is not causally connected with the picture, the reason will be that no one can intend anything concerning an entity from which they are causally disconnected.
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VI. Conclusions I have argued that the very identity of a work of art depends upon certain quite specific intentions that the artist or author must have.. These intentions are interior states of the artist that can at best be inferred from the public object that the artist has left us - text or canvas - together with whatever relevant historical and psychological knowledge we may have. These inferences can vary from the near trivial (in which case they will be made by almost everyone under almost all circumstances of information) to the highly complex (in which case they will require a great deal of art historical knowledge and are likely to be controversial). If I am right about this, we shall have to rethink some of our assumptions about the 'public' nature of artworks.
503 ENDNOTES 1. Gottlob Frege, Nachgelassene Schriften, ed H. Hermes, F. Kambartel, and F. Kaulbach (Hambmg: Felix Meiner, 1969), p. 159. On Frege and psychologism, see: Gregory Currie, "Frege and Popper: Two enemies of Psychologism," in K. Gavroglu, ed, Proceedings of the Thessaloniki Conference (Dordrecht: Reidel, 1988). It is interesting to note that Frege, who did so much to rid logic and mathematics of unwanted psychologism, was sceptical about the possibility of objective criticism in the arts. He thought that a work of art is nothing but 'a structme of ideas within us'; that the beautiful is just what seems to individual persons to be beautiful. See: Gottlob Frege, Nachgelassene Schriften, p. 144. Here, Frege is close to endorsing another 'fallacy' announced by Wimsatt and Beardsley: the affective fallacy. 2. William Wimsatt and Monroe Beardsley, 'The Intentional Fallacy," SEWANEE REVIEW, 54 (1946), pp. 468-88; reprinted in D. Newton-de Molina, ed, On Literary Intentions (Edinbmgh: Edinburgh University, 1976), p. 1. The first quotation above appears in quotation marks in the original text, but is unattributed. Italics in the original. 3. The volume cited in note 2 is a good somce of critical reactions to Wimsatt and Beardsley's original statement 4. See: Gregory Currie, An Ontology of Art (London: Macmillan, 1988). 5. See: Frank Cioffi, "Intention and Interpretation in Criticism," PROCEEDINGS OF THE ARISTOTEUAN SOCIETY, LXIV (1963-4), pp. 85-106; reprinted in Newton-de Molina, ed, On Literary Intentions. 6. See, for example, Frege's notorious discussion of mental images in: Gottlob Frege, "On Sense and Reference"; reprinted as "On Sense and Meaning" in Gottlob Frege, Collected Papers on Mathematics, Logic and Philosophy, ed. B.F. McGuiness (Oxford: Basil Blackwell, 1984), especially p. 160. 7. See: Ned Block, "Psychologism and Behaviourism," PHILOSOPHICAL REVIEW, 60 (1981), pp. 5-43. 8. John McDowell, 'The Epistemology of Understanding," in 1. Bouveresse and H. Parret, eds., Meaning and Understanding (Berlin: de Grayter, 1981) p. 225. 9. See: Nelson Goodman, Languages of Art (Indianapolis: Hackett, 1976), cbs. 3-5. 10. See: Currie, An Ontology of Art, sec. 39. 11. See: Gregory Currie, The Nature of Fiction (Forthcoming), ch. 1. 12. See: Kendall Walton, "Fiction, Fiction-Making and Styles of Fictionality," PHILOSOPHY AND UTERATURE, 7 (1983), pp. 78-88. But the argument of Walton's paper is deeply at odds with my own conclusions; see: Currie, The Nature of Fiction, ch. I, sec. 4. 13. This view is an extremely popular one. See, for example: John Searle, 'The Logical Structme of Fictional Discomse," in John Searle, Expression and Meaning (Cambridge: Cambridge University, 1979) for a version of it 14. Closer to the truth but not true, I think. For pretence and make-believe are not the same. See: Currie, The Nature of Fiction, ch. I, sec. 7. 15. One rather dreary modem day Holmes patische takes this line. 16. For competing views, see: David Lewis, ''Truth in Fiction," AMERICAN PHILOSOPHICAL QUARTERLY, 15 (1978), pp. 37-46; see also: Currie, The Nature of Fiction, ch. 2. 17. See: Jonathan Bennett, Linguistic Behaviour (Cambridge: Cambridge University, 1976). For the reasons given above and further on, I reject all 'semiotic' theories of pictorial depiction as based on a quite fallacious assimilation of depiction
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to linguistic representation. The best known semiotic theory is, of course, contained in: Goodman, Languages of Art. 18. See: Keith Donnellan, "Reference and Definite Descriptions," PIDLOSOPIDCAL REVIEW, LXXV, pp. 183-205; see also: Saul Kripke, "Speaker's Reference and Semantic Reference," MIDWEST STUDIES IN PIDLOSOPHY, Vol. 2, (1977). 19. See: David K. Lewis, Convention (Cambridge: Harvard University, 1969). 20. Compare this with the case of conflicting lexicographic intentions discussed in section II of this paper. 21. Thus, for a picture to depict a, the artist must have the intention to depict the CI», for some CI» where the CI» is an a, or he must have a singular intention- to depict Wellington, or thai man.
