Synthese (2011) 181:1–2 DOI 10.1007/s11229-009-9596-7
Introduction to the Synthese special issue on Hans Reichenbach, Istanbul, and Experience and Prediction Gürol Irzık · Elliott Sober
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 4 July 2009 © Springer Science+Business Media B.V. 2009
Fleeing from the Nazi rise to power in 1933, Hans Reichenbach resigned his post at the University of Berlin and accepted a five-year position at the University of Istanbul. It was there that he wrote his first book in English, Experience and Prediction, which the University of Chicago Press published in 1938. Reichenbach left Istanbul in 1938 to take up a position at University of California, Los Angeles, where he taught until his death in 1953. The papers collected in this Synthese special issue are the result of a conference that one of us (ES) casually suggested and the other (GI) organized, which took place at Bo˘gaziçi University in Istanbul, in May 2008, to commemorate the seventieth anniversary of the publication of Experience and Prediction. The lectures presented at that conference are all represented here, with the exception of Alan Richardson’s, and one of the paper included here, that of Frederick Eberhardt, was not presented at the conference. These papers are historical and philosophical in varying degrees. Some seek to situate Reichenbach in the political upheavals that drove him from Germany and the social transformations that led him to be welcomed to Turkey. Others connect Reichenbach’s work to the historical development of scientific philosophy, linking Reichenbach’s ideas to those of other scientists and philosophers who worked on induction, probability, and scientific realism. And still other essays are not historical in their fundamental orientation at all, in that they seek to draw from Reichenbach ideas that are of enduring importance in the attempt to solve philosophical problems in a scientific spirit.
G. Irzık (B) Philosophy Department, Bo˘gaziçi University, 34342 Bebek, Istanbul, Turkey e-mail:
[email protected] E. Sober Philosophy Department, 5185 Helen White C. Hall, University of Wisconsin-Madison, Madison, WI 53706, USA
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Reichenbach is now often lumped together with the logical positivists of the Vienna Circle, but his ideas, especially those in Experience and Prediction, were often developed in opposition to positivism. Reichenbach frequently sought to save concepts and problems from the many positivists who sought to discredit them. For example, he thought that causality has a place in science and that the problem of the external world is not a pseudo-problem. Indeed, Reichenbach always defended realism against positivism, and his defense was truly ingenious. It has been standard for decades to refer complacently to “the demise of logical positivism,” but the so-called positivists were more various than the standard stereotype would suggest. In addition, Reichenbach’s independent outlook connects in substantive ways with research agendas that now thrive in post-positivist philosophy of science. We hope that the essays collected here will be a resource for philosophers who work on the problems that Reichenbach addressed, and also that these essays will be useful to historians who want to develop a deeper understanding of Reichenbach in his historical context. We are grateful to Joshua Filler, Omca Korugan, Zeynep Savas, Tugba Sevinc, and Erturk Demirel for their help in organizing the Istanbul conference and in helping prepare these papers for publication.
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Synthese (2011) 181:3–21 DOI 10.1007/s11229-009-9593-x
Reichenbach’s cubical universe and the problem of the external world Elliott Sober
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 2 July 2009 © Springer Science+Business Media B.V. 2009
Abstract This paper is a sympathetic critique of the argument that Reichenbach develops in Chap. 2 of Experience and Prediction for the thesis that sense experience justifies belief in the existence of an external world. After discussing his attack on the positivist theory of meaning, I describe the probability ideas that Reichenbach presents. I argue that Reichenbach begins with an argument grounded in the Law of Likelihood but that he then endorses a different argument that involves prior probabilities. I try to show how this second step in Reichenbach’s approach can be strengthened by using ideas that have been developed recently for understanding causation in terms of the idea of intervention. Keywords Common cause · Correlation · External world · Likelihood · Realism · Reichenbach · Solipsism 1 Chapter 2 of Reichenbach’s Experience and Prediction has two big themes, one negative and one positive. The negative theme is Reichenbach’s attack on the positivist theory of meaning. The positive theme is Reichenbach’s attempt to show why your sense experience justifies your believing that material objects exist independent of experience. The two themes are connected, in that the negative is a necessary prole-
All citations, unless otherwise noted, are from Hans Reichenbach. (1938). Experience and Prediction—An Analysis of the Foundations and Structure of Knowledge. University of Chicago Press. E. Sober (B) Department of Philosophy, University of Wisconsin-Madison, 5185 Helen C White Hall, Madison, WI 53706, USA e-mail:
[email protected]
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gomenon to the positive. This is because the positivist theory of meaning entails that solipsism and realism about material objects are equivalent rather than incompatible. If the positivists were right about this, the problem of the external world would be a pseudo-problem—something to dissolve, not solve. My subject here is Reichenbach’s epistemology, but I do have a few comments on what he says about meaning. In Chap. 1, Reichenbach (pp. 30–31) formulates the positivist theory of meaning as having two parts: (1) A sentence has meaning if and only if it is verifiable as true or false. (2) Two sentences have the same meaning if and only if they obtain the same determination as true or false by every possible observation. By “verifiable,” Reichenbach means deducible from a finite set of jointly consistent observation statements. He points out that many of the statements that are taken seriously in science and in ordinary life are not verifiable in this sense. This leads him to liberalize the positivist theory: (1 ) A sentence has meaning if and only if it has a degree of probability. (2 ) Two sentences have the same meaning if and only if they obtain the same degree of probability from every possible observation (p. 54). Reichenbach’s (1 ) is intended to parallel the positivist’s (1), in that Reichenbach thinks it is sense experience that makes sentences meaningful by conferring degrees of probability on them. This is Reichenbach’s probability theory of meaning.1 Reichenbach’s proposal is an improvement over positivism, but problems remain. First, there is the question of what “probability” should be taken to mean. Reichenbach refers the reader to his earlier (Reichenbach 1935) treatise where he defends a frequency interpretation of the concept (p. 304). This raises the question of how scientific theories like Einstein’s theory of general relativity or Darwin’s theory of evolution can be said to have a probability in this sense. If there were finitely many universes, we could think of the prior probability of a theory’s being true in our universe in terms of the frequency of universes in which the theory is true.2 Unfortunately, this suggestion comes to nothing if there is no such set of universes. If we abandon Reichenbach’s commitment to a frequency interpretation and follow subjective Bayesians by interpreting probability as an agent’s degree of belief, this problem disappears but another pops up in its stead—a single theory will have as many different probabilities as there are agents who have different degrees of certainty about it. And a sentence can be meaningful for me though it is meaningless to you, because I assign it a degree of belief and you do not. Shifting to a third interpretation is problematic as well. If we 1 It is interesting that Reichenbach identifies a sentence’s being meaningful with its having a probability,
not with its confirmability. Bayesians say that a sentence is confirmable if the sentence’s probability can be changed by new observations; Skyrms (1984) suggests that this provides an account of testability, which I discuss in Sober (2008, pp. 148–154). 2 This is not how Reichenbach, in the second edition of his 1935 book (pp. 434–442), proposes to understand “the probability of hypotheses.” He discusses Newton’s law of gravitation by considering a data set that describes how frequently various measurements on planets conform to the law; Reichenbach applies the straight rule of induction to the data to infer a probability for the law. Notice that this is an exercise in the epistemology of probability, not in its semantics. For an argument that the straight rule is nonBayesian, see Sober (2008, pp. 20–24).
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think of probability as normative—as the degree of belief that an agent ought to have in a sentence, given some body of observations—it again becomes difficult to see what values those probabilities actually have (since their posterior probabilities will depend on choices of values for prior probabilities). Another problem for Reichenbach’s theory stems from the fact that a sentence can be meaningful even if we have no clue as to how probable it is. Consider the sentence “undetectable angels exist.” If this really were meaningless gibberish, we could not discuss its epistemic status or its logical relationships to other sentences. But we can.3 And surely “undetectable angels exist” and “undetectable unicorns exist” differ in meaning, though they seem to have the same epistemic status. Reichenbach’s theory, like the positivism he sought to supersede, draws too close a connection between semantics and epistemology, as Putnam (1975) argued so cogently. Reichenbach says that it is a virtue of his theory that it explains why the following two sentences differ in meaning: (3) The material world will continue to exist after I am dead. (4) The material world will cease to exist when I do (p. 133). In contrast, the positivist theory says they are synonymous—there is no experience I can ever have that will discriminate between them. Reichenbach asks why positivists bother to buy life insurance policies if they believe that the two sentences are equivalent. He says that he does “not doubt the seriousness of the positivists” when they do so; however, “they cannot justify this carefulness” (p. 135). These good points encourage the reader to expect Reichenbach to conclude that the positivist theory of meaning is false while his own theory is true, but this is not what he says. Rather, his view is that it is a matter of choice, not fact, which theory of meaning we adopt—“we cannot forbid anyone to choose the definition of meaning he prefers (p. 149).” To a postpositivist ear, this sounds like backsliding. If the theory of meaning is a theory about the languages and language users we see around us, then it is answerable to empirical considerations. A theory of meaning is false if it says that (3) and (4) are synonymous sentences of English (Carnap 1953; Sober 2000). Of course, the word “synonymous” can be redefined, but that isn’t relevant, since any term can be redefined, trivially.
2 It is one thing to say that (3) and (4) differ in meaning, another to show that (3) is more probable than (4), given the evidence I have. In just the same way, the epistemological task of comparing the probabilities of the following two sentences remains even after we grant that they are incompatible: (5) The only things that exist are my mind and my experiences. (6) In addition to my mind and my experiences, material objects also exist. 3 As Glymour (1977, p. 228) says, “it is only because we can understand something of hypotheses and
make rough judgments of their implications that we can test them. Not the other way round.”
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Fig. 1 The observer in the cubical universe sees shadows on the walls that are produced, with the help of mirrors, by the birds outside; from Reichenbach (1938, p. 117)
Proposition (5) expresses the thesis of solipsism, while (6) expresses the thesis of realism about material objects.4 Reichenbach’s question is how my sense experiences justify my postulating entities that are distinct from my mind and the experiences I have. He addresses the difference between (5) and (6) by describing a thought experiment; the picture he uses to explain the example is reproduced here in Fig. 1. We are asked to imagine a world in which the whole of mankind is imprisoned in a huge cube, the walls of which are made of sheets of white cloth, translucent as the screen of a cinema but not permeable by direct light rays. Outside this cube there live birds, the shadows of which are projected on the ceiling of the cube by the sun rays; on account of the translucent character of this screen, the shadow-figures of the birds can be seen by the men within the cube. The birds themselves cannot be seen, and their singing cannot be heard. To introduce the second set of shadow-figures on the vertical plane, we image a system of mirrors outside the cube which a friendly ghost has constructed in such a way that a second system of light rays running horizontally projects shadow-figures of the birds on one of the vertical walls of the cube … As a genuine ghost this invisible friend of mankind does not betray anything of his construction, or of the world outside the cube, to the people within; he leaves them entirely to their own observations and waits to see whether they will discover the birds outside. He even constructs a system of repulsive forces so that any near approach toward the walls of the cube is impossible for the men; any penetration through the walls, therefore, is excluded, and 4 I take it that solipsism leaves open whether my mind reduces to the experiences I have, or is a distinct entity, and that both (5) and (6) leave open whether phenomenalism is right in its claim that the truth conditions for sentences like “there is a table here now” can be given in a sense datum language.
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men are dependent on the observation of the shadows for all statements they make about the “external” world, the world outside the cube (pp. 115–116). As is standard, Reichenbach (p. 154) takes the epistemological relationship of objects observed (shadows on the sides of the cube) to objects merely inferred (the birds outside) to be the same as the relationship of your sensations to the physical objects that cause them. He relates these problems to each other by a striking image: Our situation with regard to external things is not essentially different from that of the inhabitants of the cubical world with respect to the birds outside; imagine the surface surrounding that world to contract until it surrounds only our own body, until it finally, with some geometrical deformations, becomes identical with the surface of our body—we arrive, then, at the actual conditions for the construction of human knowledge, all our information about the world being bound to the traces which causal processes project from external things to the surface of our body. Reichenbach (163 ff.) is right that the point of this analogy is not subverted by the fact that we observe physical objects though we rarely, if ever, observe our own experiences. He also is right that the problem of the external world does not require the assumption that our knowledge of our own sensations is absolutely certain; this is inessential, just as the problem of the cubical world does not require that we be absolutely certain about the properties that the shadow-figures have. Reichenbach concludes his description of the cubical world and its inhabitants with a question: “Will these men discover that there are things outside their cube different from the shadow-figures?” He tells us that, initially, they do not. But after a while, a gifted individual (“a Copernicus”) …will direct telescopes to the walls and will discover that the dark spots have the shape of animals; and what is more important still, that there are corresponding pairs of black dots, consisting of one dot on the ceiling and one dot on the side wall, which show a very similar shape. If a1 , a dot on the ceiling, is small and shows a short neck, there is a corresponding dot a2 on the side wall which is also small and shows a short neck; if b1 on the ceiling shows long legs (like a stork), then b2 on the side wall shows on most occasions long legs also. It cannot be maintained that there is always a corresponding dot on the other screen but this is generally the case (pp. 117–118). What interests Reichenbach about these figures on the walls of the cube is the “correspondence” that obtains between the “internal motions” of pairs: If the shade a1 wags its tail, then the shade a2 also wags its tail at the same moment. Sometimes there are fights among the shades; then, if a1 is in a fight with b1 , a2 is always simultaneously in a fight with b2 (p. 118). Reichenbach says that the hero of his story, Copernicus, will surprise mankind by the exposition of a very suggestive theory. He will maintain that the strange correspondence between the two shades of one pair
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cannot be a matter of chance but that these two shades are nothing but effects caused by one individual thing situated outside the cube within free space. He calls these things “birds” and says that these are animals flying outside the cube, different from the shadow-figures, having an existence of their own, and that the black spots are nothing but shadows (p. 118). 3 Here I will interrupt Reichenbach’s story to characterize the two hypotheses he has so far introduced and the bearing of the observations on them. Though my interpretation is close to some of what Reichenbach says, it does not coincide with his in all particulars. The observations are sample frequencies. What we observe, for a given pair of shadow figures i and j, is that (Obs) freq(i has F & j has F) > freq(i has F)freq( j has F), for some range of properties F. I will describe this inequality by saying that we observe that the traits of i and j are associated with each other. There are two hypotheses that Reichenbach has so far considered: (Common Cause) i’s having F and j’s having F are joint effects of a common cause. (Coincidence) i’s having F and j’s having F are causally unconnected. The point of interest is that, (7) Pr(Obs|Common Cause) > Pr(Obs|Coincidence). The reason (7) is true is that the common cause model that Reichenbach is considering entails that there will be a correlation between i’s having F and j’s having F, where correlation is a fact about probabilities, not sample frequencies: (Correlation)
Pr(i has F & j has F) > Pr(i has F)Pr( j has F).
In contrast, the Coincidence model he is considering entails that the two events are probabilistically independent: (Independence)
Pr(i has F & j has F) = Pr(i has F)Pr( j has F).
In formulating the argument in this way, I am distinguishing observed association from probabilistic correlation. The former involves frequencies in a sample; the latter involves probabilities whose application is not limited to that sample. The hypotheses are, by construction, related deductively to propositions about correlations; they do not have deductive connections to propositions about sample frequencies. If the Common Cause hypothesis makes the data more probable than the Coincidence hypothesis does, what is the epistemological significance of this fact? The Law of Likelihood (Hacking 1965; Edwards 1972; Royall 1997; Sober 2008) provides an answer: Observation O favors hypothesis H1 over hypothesis H2 precisely when Pr(O|H1 ) > Pr(O|H2 ).
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The observed association of the shapes of two shadow-figures favors Common Cause over Coincidence in just the way that the matching of two student essays favors the hypothesis that the students plagiarized from a common source over the hypothesis that they produced their essays independently (Salmon 1984). One virtue of this likelihood formulation of Reichenbach’s argument is that it undercuts the following objection. It is alleged that inferring the existence of external objects is problematic because external objects are objects of a different “kind” from the sensory experiences that provide your evidence. This point about kinds might be relevant if the argument concluded that we are justified in believing that external objects exist. But the Law of Likelihood is not a rule for acceptance. The Law cares nothing for “kinds.” The only thing that matters is how different competing hypotheses probabilify the data. The likelihood reconstruction of Reichenbach’s reasoning captures some of what he is getting at when he says that … it seems highly improbable that the strange coincidences observed for one pair of dots are an effect of pure chance. It is, of course, not impossible that, when one shade has its shade-tail plucked off, at the same moment the same thing happens to another shade on another plane; it is not even impossible that the same coincidence is sometimes repeated. But it is improbable; and any physicist who sees this will not believe in a matter of chance but will look for a causal connection (pp. 120–121). However, this passage also suggests that Reichenbach may be venturing beyond what the Law of Likelihood sanctions. Inequality (7) does not show that Common Cause is more probable than Coincidence. It does not follow from (7) that (8) Pr(Common Cause|Obs) > Pr(Coincidence|Obs) unless assumptions are made about the prior probabilities of the two hypotheses. 4 The plot then thickens because Reichenbach sees that his adversary, the positivist, has a reply. The positivist grants that Common Cause and Coincidence “furnish different consequences within the domain of our observable facts” (p. 122) and that the two hypotheses thereby obtain different probabilities. But the positivist then claims that there is a third hypothesis that is predictively equivalent to the hypothesis of Common Cause. This is the hypothesis that the elements within a pair are related as cause to effect: (Cause/Effect)
i’s being F causes j’s being F, or vice versa.
This hypothesis does not postulate the existence of entities outside. Yet, it predicts that there will be a positive association between i’s and j’s properties, just as the Common Cause hypothesis does. Reichenbach then argues that the Common Cause hypothesis nonetheless is superior to the hypothesis of Cause/Effect. He puts his point in the mouth of “the physicist”, who
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… simply states that, wherever he observed simultaneous changes in dark spots like these, there was a third body different from the spots; the changes happened, then, in the third body and were projected by light rays to the dark spots which he used to call shadow-figures … Whenever there were corresponding shadow-figures like the spots on the screen, there was in addition, a third body with independent existence; it is therefore highly probable that there is also such a third body in the case in question (p. 123). Reichenbach is arguing that there are associated events that occur inside the cube that resemble the shadow-images on the cube’s surfaces and which have the additional feature that the cube’s inhabitants can observe what makes the events in a pair similar. The cubists observe that such pairs are usually associated because they trace back to common causes and only rarely are they associated because they are related to each other as cause to effect.5 I see no way to defend this part of Reichenbach’s argument. Event types are associated in our world because they are produced by common causes and also because they are related to each other as cause to effect. Both arrangements occur in abundance. For example, consider pairs of birds inside our universe; sometimes we see two flying birds change direction in unison because a predator approaches them both and sometimes we see them do so because one bird is chasing the other. Each may look like a “dark spot” that we see against the sky. In general, when we observe that event types e1 and e2 are associated because they have a common cause c, we also observe that c and e1 are associated with each other because they are related to each other as cause to effect, and the same is true of the association of c to e2 . For each Common Cause pattern that we observe, there are two Cause/Effect patterns that we also observe. How, then, could the former arrangement be more frequent? I take it that the same is true of what goes on in the cubical universe. Furthermore, even if Reichenbach were right about what is common and what is rare in the observations that the cubists make inside their universe, it is hard to see how this point would carry over to the problem of the external world. Cubists who see the shadow-images on the cube’s surfaces also can observe what is happening in the cube’s interior. But when we notice associations between our sensations, we cannot drop back to another sort of association whose causal origins are plain to us. Reichenbach has a footnote on the next page (p. 124) that makes it clear that we are not here mistaking what his argument is. He says that the Common Cause hypothesis has a higher posterior probability than the Cause/Effect hypothesis because the former has the higher prior and in spite of the fact that the two hypotheses confer on the observed association the same probability (they have identical likelihoods). It isn’t the observed association of the shadows that makes it more probable that birds exist outside the cube than that the shadows cause each other; rather, what does the work, according to Reichenbach, is the fact that the existence of birds outside has the higher prior probability. 5 It is interesting that Reichenbach does not argue that the shadow-images in a pair cannot be related as cause to effect on the grounds that they occur simultaneously (and via appeal to the principle that cause must precede effect). He does say a few times that the events are simultaneous, but his diagram of the cubical world suggests that this would not be exactly true.
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5 Reichenbach’s epistemology of the cubical universe calls to mind his now-famous Principle of the Common Cause, which he states as follows in his posthumously published book, The Direction of Time: If an improbable coincidence has occurred, there must exist a common cause … Chance coincidences, of course, are not impossible … The existence of a common cause is therefore … not absolutely certain, but only probable (Reichenbach 1956, pp. 157–158). Reichenbach does not cite this general principle in Experience and Prediction. If it were correct, it would provide a simple rationale for concluding that the correlated shadow-images have a common cause (Salmon 1999). However, a further argument would be needed to show that this common cause is outside the cube, let alone a bird outside. In any event, the common cause principle has problems, so it is good that Reichenbach does not appeal to it in his 1938 book. First, notice that Reichenbach gives two formulations of the principle in the passage quoted above; the first says that a common cause must exist while the second says that it probably does. The first is an overstatement, since, as Reichenbach notes, improbable coincidences without a common cause are not impossible.6 The probabilistic formulation, on the other hand, requires that you have prior probabilities for common cause hypotheses, and, as we have seen, these are sometimes difficult to justify. In addition, the principle takes you from correlations to (probable) common causes without pausing to consider, as Reichenbach does in his discussion of the cubical universe, that a correlation might be due to the correlates being related as cause to effect. It therefore is better to formulate Reichenbach’s principle as saying that correlated events must be (or probably are) causally connected, where this means that the events either have a common cause or are related as cause to effect. But it is even better to formulate the principle as an instance of the Law of Likelihood.7 Unfortunately, this fails to settle why the hypothesis of Common Cause is better than the hypothesis of Cause-Effect. 6 In 1936, two years before the publication of Experience and Prediction, Einstein noted that the general theory of relativity predicts that an astronomical object can act as a “gravitational lens” and produce a “gravitational mirage,” as shown in Fig. 2. If a massive object lies between the observer and a distant object, light from the distant object will bend around the intervening object, leading the observer to see two (or more) images, not one. This possibility was described qualitatively by the St. Petersburg 6 Abandoning the “must” in stating the principle of the common cause suffices to ensure that the Bell inequality results are not a counterexample. 7 Even when modified in this way, the principle still encounters a problem first described by Yule (1926);
the mechanisms behind two causally unconnected time series sometimes entail cross-process correlations. See Sober (2001, 2008) for discussion.
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I1
I2
O Observer
Galaxy
Quasar
Fig. 2 When light from a quasar bends around a lensing galaxy, an observer will see two images (I1 and I2 ) of the quasar
physicist Orest Chwolson in 1924. In 1936 Einstein considered the example of a single star serving as a lens and concluded that the effect would be too small for current instrumentation to detect. In 1937, Fritz Zwicky realized that a whole galaxy could act as a lens and that the more pronounced image doubling should be easy to detect. The first real example was discovered in 1979 by Dennis Walsh, Bob Carswell, and Ray Weymann using the Kitt Peak National Observatory 2.1 meter telescope. It was called the “Twin Quasar” because it initially looked like two identical quasars; its official name is Q0957 + 561.8 Did Reichenbach know about Chwolson’s, Einstein’s, and Zwicky’s ideas? If so, did he consider using the idea of gravitational lensing in Experience and Prediction as a real-world example that makes the same point as the shadow images on the walls of his fanciful cubical universe? And even if Reichenbach did not consider this way of telling his story, would real science have served his purpose better than science fiction? I will not try to answer the biographical questions, but I do want to say a little about how gravitational lensing is related to the problem that Reichenbach describes. We see what appear to be two astronomical objects in different parts of the sky. Our measurements show that they are identical in numerous respects. We consider and reject the possibility that this is just an elaborate coincidence. There must be a causal connection. Either one object causes the other, or the two are effects of a common cause. Both these hypotheses predict the similarities we observe. A difference between the hypotheses may be found in the fact that we have an independently confirmed theory (the General Theory of Relativity) that says that the Common Cause pattern should be exemplified; on the other hand, no current theory describes a process in which one huge astronomical object can cause a carbon copy of itself to exist someplace else. This provides a justification for assigning Common Cause a higher prior probability than Cause/Effect. The prior does not come from a priori reasoning, but is grounded by an empirical theory. This appeal to prior probabilities to deal with astronomical twins seems much less artificial than Reichenbach’s appeal to prior probabilities when he discusses twin shadows in his cubical universe. Even so, there is something missing 8 See the Wikipedia article at http://en.wikipedia.org/wiki/Gravitational_lensing.
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in this example from physics. Granted, a background theory can furnish us with defensible priors, but what if we have no such theory? This is where the example of the cubical universe has a utility that gravitational lensing does not. 7 Let us return to Reichenbach’s claim that Common Cause and Cause/Effect confer the same probability on the observations that Copernicus makes in his cubical universe. Do you really need to appeal to prior probabilities to find an epistemic difference between the two hypotheses? Present-day causal modelers have thought about this problem (Hausman 1998; Woodward 2003). We can take our cue from them. Here is a simple and shopworn example. Why do we think that barometer readings and storms are joint effects of a common cause (the barometric pressure) rather than being related to each other as cause to effect? The readings and the rain are associated in our data, in that freq(storm at t2 | low barometer reading at t1 ) > freq(storm at t2 | high barometer reading at t1 ). This association is evidence that there is an underlying probabilistic correlation: (9) Pr(storm at t2 | low barometer reading at t1 ) > Pr(storm at t2 | high barometer reading at t1 ). If the two events were joint effects of a common cause, that would explain the observed association, but the association also would be explained if barometer readings caused storms. To discriminate between these two hypotheses, there is no need to appeal to prior probabilities; rather, a different type of fact can be brought to bear. Manipulating the barometer reading does not change the probability of a storm: (10) Pr(storm at t2 | low barometer reading at t0 & I make the barometer read low at t1 ) = Pr(storm at t2 | low barometer reading at t0 & I make the barometer read high at t1 ). The manipulation at t1 takes place shortly after t0 , but before t2 . Manipulating the barometer reading just after the barometer reads high exhibits the same pattern: Pr(storm at t2 | high barometer reading at t0 & I make the barometer read low at t1 ) = Pr(storm at t2 | high barometer reading at t0 & I make the barometer read high at t1 ). Although Common Cause and Cause/Effect both predict that low barometer readings and storms will be associated, the two hypotheses make different predictions about what will happen when we perform manipulations. The concept of manipulation (or intervention) needs to be specified carefully. It is a causal process (not necessarily one initiated by a conscious agent), but not just any way of causing the barometer to read low counts as an intervention. Interventions must be surgical, not ham-fisted. The concept is defined relationally; we need to define what it takes for I to be an intervention on the barometer reading (R) relative to the
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storm (S). The key idea is that any effect that I has on S must pass through R; there can be no second pathway by which this influence is transmitted (nor can I be correlated with a factor Z that influences S by a separate pathway). For example, if you perform an action that simultaneously makes the barometer read low and also raises the barometric pressure, your action is not an intervention.9 In this circumstance, your act of ham-fistedly changing the barometer reading is associated with an increase in the frequency of storms, but that isn’t evidence that barometer readings cause storms. If barometer readings cause storms, then interventions on the readings can be expected to be associated with storms. If the two are joint effects of a common cause, then interventions on the barometer readings can be expected to not be associated with storms. If no such association is observed, this is evidence favoring Common Cause over Cause/Effect. I say that interventions provide data that favor one hypothesis over another, not that they provide data that definitively refutes either. As noted earlier, the hypotheses under discussion do not have deductively entailments as to whether there will be associations in the data; rather, they have entailments about whether there will be probabilistic correlations. These correlations are not what we observe; what we observe are associations. Reichenbach’s thought experiment about the cubical world includes the detail that the people in the cube cannot manipulate the shadow-images that appear on the cube’s surfaces. As quoted above, he stipulates that powerful force fields prevent them from doing so. This makes the puzzle harder to solve. Had Copernicus or his successors sent rockets to alter or remove one of the shadow-images in a pair (perhaps by smearing whitewash on it), these manipulations would have yielded evidence that favors Common Cause over Cause/Effect.10 How does this point about manipulations bear on the problem of the external world? Each of us can manipulate sensations that we find correlated. In my experience, the visual impression (V ) that there are waves breaking on a beach is associated with the auditory impression (A) of the crashing of waves. Are these two types of experience related as cause to effect or do they trace back to a common cause? The answer can be found by manipulating each. When I have both experiences, I can easily shut down the one but not the other, and shut down the other but not the one. When I open and close my eyes, my visual impressions flip in perfect synchrony though I continue to have the same auditory impression. When I hold my ears and release them, my auditory impressions stop and start though I continue to have the same visual impressions.11 The visual (V ) and auditory (A) impressions are probabilistically correlated, but manipulating the one does not change the probability of the other. That is, it is true both that 9 See Woodward (2003, pp. 98–103) for further details on how the concept of intervention should be
defined. 10 Reichenbach (1925, pp. 101–102) anticipates this point about manipulations; he says that “if Ais the
cause of C and a slight alteration is induced in A, a slight alteration will also appear in C. But if C is altered slightly, no change will arise in A.” Perhaps he does not use this idea in Experience and Prediction because he thought it was not needed to solve the problem at hand. 11 I am not advancing the strong thesis that there is no manipulation of visual experience that affects audition. My claim is more modest. See McGurk and McDonald (1976) for discussion of a case in which vision influences what we hear.
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Fig. 3 Even though X causes Y , manipulating X by changing its value from X = a to X = b is not associated with an expected change in the state of Y
Y
a
b X
(11) Pr(I have A at t2 | I have V at t1 ) > Pr(I have A at t2 | I don’t have V at t1 ) and (12) Pr(I have A at t2 | I have V at t0 and I cause V to occur at t1 by keeping my eyes open) = Pr(I have A at t2 | I have V at t0 and I cause V to not occur at t1 by closing my eyes). The Common Cause and Cause/Effect hypotheses agree that (11) should be true, but they disagree about whether (12) is.12 The operative principle, both with respect to the barometer and with respect to the beach, is: X causes Y if and only if there is a possible intervention on X that entails an expected change in the state of Y . This is what distinguishes X ’s causing Y from Y ’s causing X and from X and Y ’s being joint effects of a common cause. There is an existential quantifier in this criterion, not a universal quantifier, because some interventions on a cause can fail to be associated with an expected change in its effect. Consider, for example, the relationship of a cause X to its effect Y that is depicted in Fig. 3. If X is manipulated by changing its value from X = a to X = b, the expected value of Y remains the same. But notice that intervening on X by changing its value from X = a to X = c (where c = b) entails that the expected value of Y will be different. In general, when X is manipulated and no change in the state of Y occurs, this is evidence, not proof, that favors the hypothesis that X and Y have a common cause over the hypothesis that they are related to each other as cause to effect. It is only evidence for two reasons. First, as already noted, what you observe is a fact about frequencies, not a probabilistic equality. Second, even if a probabilistic equality is true for the particular manipulation you have performed, it may fail to be true for others. When 12 Consider Locke’s comment in Book 4, Chap. 11 of his Essay Concerning Human Understanding: “our senses assist one another’s testimony of the existence of outward things, and enable us to predict. Our senses in many cases bear witness to the truth of each other’s report, concerning the existence of sensible things without us. He that sees a fire, may, if he doubts whether it be anything more than a bare fancy, feel it too; and be convinced, by putting his hand in it.”
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a manipulation fails to produce a difference in observed frequencies, this is evidence that favors Common Cause over Cause/Effect in the sense described by the Law of Likelihood. The observations are less probable if X is a cause of Y than they would be if X were not. Fiddling with the barometer fails to be associated with a change in the frequency of storms. And my fiddling with my visual impressions of waves by fluttering my eyes fails to be associated with a change in the frequency of my auditory impressions of waves. The observations discriminate between Common Cause and Cause/Effect; you do not need prior probabilities to find a difference between the two hypotheses. 8 Does this successfully complete Reichenbach’s argument for the external world? I hope it is clear that the pattern pertaining to my auditory and visual impressions of waves has wide applicability. I do not claim that the argument I have described establishes that there probably is a common cause. The more modest thesis to consider is that the associated sensations and the results of my manipulation experiments are evidence for this conclusion in the sense described by the Law of Likelihood. But even with this caveat, this evidential argument for the external world13 is not yet complete. How do I know that my shutting my eyes and my holding my ears are manipulations in the required sense? And why must the common cause for which I claim to have evidence be something outside my own mind? The worry represented by the first question is depicted in Fig. 4. Perhaps my opening and closing my eyes (E) is not a manipulation of my visual impressions V with respect to my auditory impressions A in the required technical sense. My eye fluttering (E) will be a ham-fisted nonintervention if it affects my seeming to hear the waves (A) by some pathway other than the one that goes through my visual impressions (V ), or if E is associated with a causal factor (Z ) that affects my auditory impressions by some other pathway. Let’s focus on the first of these options, as the issues raised are the same. The problem is that it is possible for V to cause A even though E and A are uncorrelated. This will happen if E raises the probability of A along one pathway and lowers it along the other, where the magnitudes of these two components exactly cancel each other, so that the net effect of E on A is zero. Some causal modelers (Spirtes et al. 2001) adopt an assumption (the “faithfulness” condition) that rules this out. But even without this assumption, the observations still favor Common Cause over Cause/Effect if there is some chance that my fluttering my eyes is an intervention on V with respect to A. The second question does not contest the thesis that E is an intervention on V with respect to A nor does it deny that the result of this experiment favors the hypothesis that V and A have a common cause. Rather, the question is why I should think that this common cause of my visual and auditory impressions of waves is something outside 13 I call this the evidential argument for the external world to parallel the evidential argument from evil, which claims, not that the evil we observe proves that there is no God, but that it is evidence against the existence of God; see the articles collected in Howard-Snyder (1996) and the brief discussion in Chap. 2 of Sober (2008, pp. 164–167).
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Fig. 4 Suppose E (my closing my eyes) is not an intervention on V (my visual impressions) with respect to A (my auditory impressions) because I not only affects V , but also affects A via a distinct pathway. I is therefore hamfisted Fig. 5 My intending to go to the beach is a common cause of the visual (V ) and auditory (A) experiences of waves that I have. If the intending does not screen off V from A , this is evidence for there being an intervening common cause (an I CC)
E
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A
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my own mind.14 For example, why cannot the common cause just be the intention I form to go to the beach? The answer is that the intention is a common cause, but that this does not mark a victory for solipsism. The first thing to note is that, in fact, the intention does not screen-off the two types of experience from each other (i.e., it does not render them conditionally independent of each other), since Pr(V at t2 and A at t2 | I intend to go to the beach at t1 ) > Pr(V at t2 | I intend to go to the beach at t1 )Pr(A at t2 | I intend to go to the beach at t1 ). This probabilistic inequality is sanctioned by frequency data. For example, suppose that I do not always have wavy visual and auditory experiences after I form the intention to go to the beach, but that when I have one of these experiences I always have the other. If V and A are correlated even after I take account of my intending to go to the beach, how is this failure of screening-off to be explained? One possibility is depicted in Fig. 5; perhaps there is an intervening common cause, one that comes between my intending to go to the beach at t1 and my having wavy auditory and visual sensations at t2 .15 But what is the nature of this intervening common cause? The realist will say that it is a state of the world external to my own mind—perhaps it is the state of my actually being at the beach. Solipsists will reply that there is a state of my own mind that screens off V from A. 14 This question recapitulates the one I asked earlier about the cubical universe: if the shadow images in a pair have a common cause, why must that common cause be outside the cube, let alone a bird? 15 In a causal chain from the more distal common cause C to the more proximal common cause C to p d the two effects V and A, Cd will fail to screen off V from A if (i) C p screens off V from A, (ii) C p screens off V from Cd , (iii) C p screens of A from Cd , and (iv) all the probabilities involved are between 0 and 1
noninclusive (Sober 1988).
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18 Fig. 6 If my intending to go to the beach fails to screen off my wavy visual (V ) and auditory (A) sensations from each other, one possible explanation is that there is a second common cause at work
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I intend to go to
V
the beach
SCC
A
A second explanation for why my intending to go to the beach does not screen off my wavy auditory and visual experiences from each other is that there is a second common cause (not caused by the first), as depicted in Fig. 6.16 Here again, the question arises of what kind of state this second common cause is. The solipsist will say that it must be a state of my own mind; the realist will deny this. I take it that the solipsist must concede that there is evidence that something is going on in the production of my wavy visual and auditory sensations besides my intending to go to the beach. The challenge for the solipsist is to point to some other mental state that I occupy that plays the role of this something else. I suggest that often there is nothing of the sort to which the solipsist can point. Suppose, for example, that right after I form the intention to go to the beach that I am rendered unconscious; the next thing I know, I am either experiencing wavy visual and auditory experiences, or I am experiencing neither. When I introspect, I find no further experiences that I can cite to explain this uncanny correlation of V and A. Realists will maintain that I not only have evidence for a common cause, but also have evidence that this common cause is not one of my mental states. “It’s the external world that is doing the work, stupid,” they will impatiently insist. Can the solipsist reply that there is a mental state that screens off V and A from each other, but that this is something to which I have no introspective access? I concede that this reply is possible. However, it undermines the epistemological idea that is supposed to motivate solipsism in the first place. The solipsist thinks it is clear that his own mind and his experiences exist, but then he questions whether there is anything else. This clarity and query are supposed to reflect the fact that I am immediately aware of my own mind and mental states—I can have no doubt about their existence—but the physical world is something more iffy. If the solipsist is driven to countenance introspectively inaccessible mental states, what is the basis for his doubting the existence of an external physical world?
16 If there are two common causes of V and A where each makes a difference in the probability of the two effects, and their joint states screen off V from A, then neither common cause screens-off V from A by itself (Sober 1988).
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9 Does the inference from associated sensations to an extra-mental common cause beg the question against solipsism? Empiricists have objected to defenses of scientific realism that appeal to “inference to the best explanation” on this ground (Fine 1984). One difference is that the argument for the external world presented here is evidential and rests just on the Law of Likelihood, whereas the realist’s inference to the best explanation involves acceptance. Even so, it is open to the solipsist to reject the Law of Likelihood and therefore to reject Bayesianism. The question then arises of which probabilistic principles for interpreting evidence solipsists are prepared to embrace. If solipsists say “none at all”—that the only inference principles they countenance are deductive—that is reason enough to reject their epistemology, since it prevents them from holding that present and past experiences provide evidence concerning which experiences will occur in the future.17
10 The positivists thought that the problem of the external world is a pseudo-problem mired in metaphysical muck. Believing as he did that solipsism and realism about material objects are predictively equivalent, Carnap (1956) concluded that the choice between them is a matter of convenience, not fact; this is what he meant by classifying this philosophical issue as an external question, not an internal question. Although Reichenbach’s probability theory of meaning allows the problem of the external world to be resuscitated, we now have the option of regarding that theory as a ladder that we can kick away once we have climbed it. Solipsism and realism about material objects are not synonymous; we can recognize this without needing to have a fully adequate theory of meaning at our fingertips. Reichenbach was right that probabilistic tools can be brought to bear on the epistemological problem of evaluating solipsism and realism as competing hypotheses.18 We are no more cut off from solving this problem than scientists are cut off from reasoning about the existence of unobservable entities.19 However, the hypothesis that there is something outside need not be assessed by invoking prior probabilities. These priors are difficult to justify, and placing the entire burden of the argument on the assignment of prior probabilities has the implication that our experiences provide no evidence, one way or the other, for an external world. 17 I argue that the realism/empiricism debate should be understood as a debate about evidence, rather than as a debate about acceptance, in Sober (2007). 18 It is curious that Reichenbach’s animus against positivism occasionally manifests itself as ad hominem slams against positivists. For example, in Chap. 2, he says that “the preachers of positivism” remind him of “the fanaticism of a religious sect” (p. 103); he also comments that positivists “usually become offended when they are told that they do not believe that the physical world will continue to exist after their death” (p. 134). Who are these dogmatic and prickly positivists whom Reichenbach found so irritating? Presumably not the gentle Carnap; maybe the testy Neurath or the messianic Ayer or the recently murdered Schlick? 19 An analog for the problem of the external world that includes a role for manipulations can be extracted from Hacking (1985) discussion of how microscopists distinguish properties of a specimen from artifacts of the apparatus.
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Reichenbach’s cube is a beautiful analogy for the problem of the external world. And his focus on the correlations that exist between shadow images on the walls of the cube directs our attention to a key issue—the correlations that exist between the different experiences that we have. But there is a disanalogy that needs to be corrected. Because of powerful force fields, the cubists are passive observers of the images on the walls of their cube, just as the chained prisoners in Plato’s cave are passive observers of the shadows cast there. In contrast, each of us is related to his or her experiences actively, not passively. We influence which experiences we have by acts of will. This provides us with experimental opportunities that the cubists cannot exploit. Perhaps this is enough to show that I have evidence, not just that some of my experiences have common causes, but that those common causes are not states of my consciousness. Acknowledgements I thank Martin Barrett, David Chavez, Juan Comesaña, Richard Creath, Joshua Filler, Clark Glymour, Guven Guzeldere, Daniel Hausman, Gurol Irzik, John Koolage, Flavia Padovani, Maria Reichenbach, Alan Richardson, Carolina Sartorio, Friedrich Stadler, Michael Stoelzner, Michael Strevens, Steve Swartzer, and James Woodward for useful comments. I also have benefitted from discussing this paper at the 2008 Reichenbach conference at Bogazici University in Istanbul and at the University of Nebraska, Lincoln.
References Carnap, R. (1953). Meaning and synonymy in natural languages. Philosophical Studies, 6, 33–47. Carnap, R. (1956). Empiricism, semantics, and ontology. In Meaning and necessity. Chicago: University of Chicago Press. Edwards, A. (1972). Likelihood. Cambridge: Cambridge University Press. Fine, A. (1984). The natural ontological attitude. In J. Leplin (Ed.), Scientific realism (pp. 83–107). Berkeley: University of California Press. (Reprinted in The shaky game, pp. 112–135. Chicago: University of Chicago Press). Glymour, C. (1977). Reichenbach’s entanglements. Synthese, 34, 219–235. Hacking, I. (1965). The logic of statistical inference. Cambridge: Cambridge University Press. Hacking, I. (1985). Do we see through the microscope?. In P. Churchland & C. Hooker (Eds.), Images of science: Essays on realism and empiricism. Chicago: University of Chicago Press. Hausman, D. (1998). , Churchland, P., Hooker, C. (Eds.), Causal asymmetries. Cambridge: Cambridge University Press. Howard-Snyder, D. (Ed.). (1996). The evidential argument from evil. Bloomington: Indiana University Press. McGurk, H., & McDonald, J. (1976). Hearing lips and seeing voices. Nature, 264, 746–748. Putnam, H. (1975). Mind, language, and reality. Cambridge: Cambridge University Press. Reichenbach, H. (1925). Die Kausalstruktur der Welt und der Unterschied von Vergangenheit und Zukunft. In Sitzungsberichte der Bayerische Akademie der Wissenschaft, November, pp. 133–175. (Translated as The causal structure of the world and the difference between past and future. In R. Cohen & M. Reichenbach (Eds.), Hans Reichenbach—Selected Writings, 1909–1953 (1978, pp. 81–119)). Dordrecht: Reidel. Reichenbach, H. (1935). The theory of probability—an inquiry into the logical and mathematical foundations of the calculus of probability, 2nd edn. Berkeley: University of California Press, 1948. Reichenbach, H. (1938). Experience and prediction—an analysis of the foundations and structure of knowledge. Chicago: University of Chicago Press. (Reissued 2006 by University of Notre Dame Press with an introduction by A. Richardson). Reichenbach, H. (1956). The direction of time. Berkeley: University of California Press. Royall, R. (1997). Statistical evidence—a likelihood paradigm. Boca Raton, FL: Chapman and Hall. Salmon, W. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press.
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Salmon, W. (1999). Ornithology in a cubical world: Reichenbach on scientific realism. In D. Greenberger, W. Reiter, & A. Zeilinger (Eds.), Epistemological and experimental perspectives on quantum physics (pp. 303–315). Dordrecht: Kluwer. Skyrms, B. (1984). Pragmatics and empiricism. New Haven: Yale University Press. Sober, E. (1988). The principle of the common cause. In J. Fetzer (Ed.) Probability and causation: Essays in honor of Wesley Salmon (pp. 211–228). Dordrecht: Reidel. (Reprinted in E. Sober, From a biological point of view. Cambridge: Cambridge University Press, 1994). Sober, E. (2000). Quine’s two dogmas. In Proceedings of the Aristotelian Society, Vol. 74, pp. 237–280. Sober, E. (2001). Venetian sea levels, British bread prices, and the principle of the common cause. British Journal for the Philosophy of Science, 52, 1–16. Sober, E. (2007). Empiricism. In S. Psillos & M. Curd (Eds.), The Routledge companion to the philosophy of science (pp. 129–138). London: Routledge. Sober, E. (2008). Evidence and evolution—the logic behind the science. Cambridge: Cambridge University Press. Spirtes, P., Glymour, C., & Scheines, R. (2001). Causality, prediction, and search. Cambridge: MIT Press. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press. Yule, G. U. (1926). Why do we sometimes get nonsensical relations between time series? A study of sampling and the nature of time series. Journal of the Royal Statistical Society, 89, 1–64.
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Synthese (2011) 181:23–40 DOI 10.1007/s11229-009-9594-9
On Reichenbach’s argument for scientific realism Stathis Psillos
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 30 June 2009 © Springer Science+Business Media B.V. 2009
Abstract The aim of this paper is to articulate, discuss in detail and criticise Reichenbach’s sophisticated and complex argument for scientific realism. Reichenbach’s argument has two parts. The first part aims to show how there can be reasonable belief in unobservable entities, though the truth of claims about them is not given directly in experience. The second part aims to extent the argument of the first part to the case of realism about the external world, conceived of as a world of independently existing entities distinct from sensations. It is argued that the success of the first part depends on a change of perspective, where unobservable entities are viewed as projective complexes vis-à-vis their observable symptoms, or effects. It is also argued that there is an essential difference between the two parts of the argument, which Reichenbach comes (somewhat reluctantly) to accept. Keywords Scientific realism · Reichenbach · Bayesianism · Base-rate fallacy · Explanation 1 Introduction There is little doubt that Hans Reichenbach was a scientific realist. A good part of his Experience and Prediction, which appeared in 1938, while he was still in the University of Istanbul, aims to articulate an argument for scientific realism. In particular, it
An earlier version of this paper was presented at the conference A Philosopher of Science in Istanbul: Hans Reichenbach, Bogazici University, Istanbul, May 2008. Many thanks to Gurol Irzik and Elliott Sober for the kind invitation to participate and to the participants for very useful comments. S. Psillos (B) Department of Philosophy and History of Science, University of Athens, Panepistimioupolis (University Campus), 15771 Athens, Greece e-mail:
[email protected]
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aims to offer an argument suitable for empiricists, at least the post-positivist empiricists who were critical of a strict verificationist theory of meaning and unpersuaded by the claim that the problem of the reality of an external world of independently existing objects (some of which might well be unobservable) was a pseudo-problem. Surprisingly, Reichenbach’s argument for realism has not attracted a lot of attention. The only notable exceptions are Wesley Salmon and Hilary Putnam. In a series of papers,1 Salmon insisted that Reichenbach reconciled logical empiricism with scientific realism, but his considered view was that the argument Reichenbach offered in favour of realism is a common-cause argument. In his (2001), Putnam has unravelled some of the nuances of Reichenbach’s argument and has rightly stressed a point that is often neglected, viz., that Reichenbach took it that, ultimately, the difference between realism and positivism is a difference between two languages. But Putnam does not explain in sufficient detail how Reichenbach thought the choice between these two languages should be made. The aim of the present paper is to articulate and discuss in detail Reichenbach’s sophisticated and complex argument for scientific realism. The argument presupposes Reichenbach’s probability theory of meaning, so Sect. 2 presents the rudiments of this theory. Then, the paper proceeds with a careful reconstruction of Reichenbach’s argument. According to this reconstruction, the argument has two parts. The first part aims to show how there can be reasonable belief in unobservable entities, though the truth of claims about them is not given directly in experience. Reichenbach proceeds in two steps. In the first step (Sect. 3), he aims to secure some common inferential ground between empiricism and realism: there are inferential patterns that are accepted by both empiricists and realists which are such that the reality of unobserved observables is legitimately inferred on the basis of their effects. To this effect, Reichenbach introduces the example of the birds and their shadows. This argument (Sect. 3.1) presupposes a central distinction between reduction and projection, according to which two distinct entities X and Y can be such that X is irreducible to Y (or a set of Ys) and yet Y be a symptom for, a mark for, or the effect of X. In cases such as this, X can be a projective complex of Ys. Claiming some common ground between empiricism and realism renders plausible a second step in Reichenbach’s argument (Sect. 4), aiming to show that the inferential patterns that license a transition from an effect to its cause are blind to the observable/unobservable distinction. In other words, the difference between observable and unobservable entities is a difference that makes no epistemic difference. The argument Reichenbach offers is illustrated by a modification of the example of the birds and their shadows, the well-known story of the cubic world. An important element of Reichenbach’s point of view is that unobservable entities should be understood as projective complexes vis-à-vis their observable symptoms, or effects. But, unlike what Reichenbach seems to think, this kind of claim is not licensed by a probabilistic argument; rather it is presupposed by Reichenbach’s probabilistic inferential patterns to license belief in unobservable entities. What exactly is the probabilistic inferential pattern that Reichenbach favours? After flirting with the base-rate fallacy, Reichenbach (Sect. 4.1) endorses a straightforward
1 Most of them can be found in the posthumously published (2005).
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Bayesian inference and relies on prior probabilities of competing hypotheses. Being a frequentist about probabilities, he faces rather significant problems concerning the status of priors, but he (Sect. 4.2) does offer some insightful thoughts as to how prior probabilities can be fixed. Interestingly, Reichenbach’s argumentative strategy has a second part aiming to extent the argument of the first part to the case of realism about the external world, conceived of as a world of independently existing entities (projective complexes) distinct from sensations. Indeed (Sect. 5), he takes it that there is is a formal analogy between the kind of argument employed so far to legitimise belief in unobservables and the argument needed to support the realist conception of the external world. But he seems to realise (somewhat reluctantly) that this kind of move cannot be made. For the reality of an external world is not yet another hypothesis to be confirmed on the basis of evidence and prior probabilities. It is constitutive of a framework—the realist framework—and, as such, its adoption is based on a type of argument different from the type of argument that licenses acceptance of hypotheses within the realist framework. 2 Probability theory of meaning The kind of empiricism Reichenbach defends in his Experience and Prediction is very sophisticated. It is set up in such a way that makes room for ampliative inferences, or for what Reichenbach called “overreaching” inferences. It might be true that all substantive knowledge stems from experience, but the extent and therefore the limits of knowledge depend crucially on the kinds of inferences that are taken to be legitimate. Reichenbach puts all this primarily in terms of his probability theory of meaning (PTM), which allows that statements that are not directly verifiable be meaningful and confirmable on the basis of experience. Two are the principles of PTM. First, a proposition is meaningful if it is (physically) possible to determine a degree of probability for it. Second, two propositions have the same meaning if they have the same degree of probability on every possible observation. There is an obvious problem, however, with the second condition (noted by Ernst Nagel in his review of Experience & Prediction). The statements ‘this coin will land heads in the next toss’ and ‘this coin will land tails in the next toss’ are assigned the same probability by every possible observation (if this is a fair coin and a genuinely chancy effect), and yet they have different meaning. Hence, the antecedent of the second condition above cannot be sufficient for sameness of meaning, though it is necessary.2 2 To be more precise, Reichenbach uses the term ‘weight’ to capture the degree of probability of a prop-
osition (which is, strictly speaking, a concept in the logical theory of probability). ‘Weight’ is a predicate applicable to propositions and has to do with the degree of certainty with which a proposition is accepted. It therefore varies from utmost uncertainty to highest possible certainty and also varies with our knowledge or ignorance. Verified propositions have weight equal to unity. In §34, Reichenbach associates weights with wagers and we may safely say that the weight assigned to a given proposition is the fair betting quotient that the proposition is true (cf. 1938, p. 319). This way of putting things would amount to admitting that we can meaningfully talk about single-case probabilities. Reichenbach (1938, p. 314) does note that “A weight is what a degree of probability becomes if it is applied to a single case”. For him, however, all probabilities are frequencies. Hence, he is forced (1938, p. 325) to say that the concept of weight is “a fictional property of
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Probability, then, is the new element that Reichenbach brings to the logic of science. The key idea, if you like, is that probabilistic relations can capture the content-increasing, or ampliative, character of scientific inference. They can capture the relation between observations and theoretical hypotheses in a way that respects the mutual independence of both. Observational propositions can be the premises of (probabilistic) inferences to theoretical statements and yet the latter can have excess content over the former. Conversely, theoretical statements can be the premises of inferences to observational propositions even when there is no deductive entailment of them. With all this in mind, let us proceed with the reconstruction to Reichenbach’s argument for scientific realism. 3 Seeking some neutral ground Empiricists accept the truth of direct propositions, which concern “immediately observable physical facts” (1938, p. 83). But the kinds of entities they accept (or ought to accept) as real are not exhausted by the immediately given. In going beyond the given to the unobserved observable, they clearly engage in ampliative inferences. This means there are non-demonstrative inferential patterns that are accepted by empiricists and realists—at least they are not obviously denied by empiricists. To claim some neutral ground between empiricism and realism, Reichenbach introduces the example of the shadows cast by birds (1938, p. 108). Imagine some birds flying over us. The shadows of the birds are projected along two perpendicular axes (presumably by a set of vertical light-rays from above the birds and another set of horizontal light-rays from the sides of the birds). The birds are then inferred to be located at the point where the co-ordinates meet. This is clearly a non-demonstrative inference from the shadows to the birds: the shadows are marks of the presence of birds; they could be there without the birds being present and the birds could be there without casting a shadow (that is, without making any marks of their presence). What is important in this example is that there are two distinct kinds of existents which are however co-ordinated with each other. The birds are not reducible to shadows; nor talk about birds is exhausted by talk about shadows. It is precisely because of this that we can use the marks (viz., the effects) to infer something about the causes, though the inference is clearly non-deductive. Significantly, the birds (as well as the shadows) are observable. It is part of the first step of Reichenbach’s strategy that their presence can be identified independently of their being inferred on the basis of the shadows. But the observability of the birds is the appetiser for the main course that is about to follow. The first step aims to render plausible two thoughts: (a) it is one thing to talk about an entity and quite another to talk about the external symptoms of its presence; and (b) the existence of one type of entity can well be independent of the existence of another, even though the latter can be a (contingent) symptom of the presence of the former. This dual point forms the ground for the legitimacy of an inference from the effects to their causes. The fact Footnote 2 continued propositions which we use as an abbreviation for frequency statements”—which means that every weight should be determined, in principle, by a relative frequency.
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that the inferred entity is observable turns out to be a, perhaps pleasant, add-on, which does not affect the status of the inference.
3.1 Reduction vs. projection The philosophical presupposition of the example so far is that there can be distinct kinds of entity which are such that one can be a symptom (or the effect) of the other. To make a case for this presupposition, Reichenbach distinguishes between reduction and projection. Though reduction is introduced as a relation of meaning equivalence between propositions (cf. Reichenbach 1938, p. 95), Reichenbach (1938, p. 99) focuses his attention on a special case of reduction, viz., the relation between a complex and its internal parts, in virtue of which the complex is equivalent to its parts. He moves swiftly from conceptual reduction to ontic reduction because he is interested in cases in which there is reduction of existence: where the existence of an entity is reducible to the existence of others, or where “the complex vanishes with its elements” (1938, p. 114). Constitution, or the whole-part relation, is such a case of ontic reduction. A wall reduces to the set of bricks it is made of (and a certain spatial arrangement of them). It asymmetrically depends on them for its existence: it exists only insofar as the bricks are in place, but it can cease to exist (it can be pulled down) even if none of its constituent bricks is destroyed. We can say that the wall is constituted by (a certain configuration of) the bricks. Projection is a relation between two distinct types of entity such that one type constitutes a symptom, or an effect, or a mark of the other type. The marks of the presence of an entity (e.g., the sound of steps on the staircase or the footprints on the beach) are ‘external elements’ of a distinct entity, a means to infer the presence of something other than them. Reichenbach contrasts them to ‘internal elements’ that are the constituents (or the parts) of a type of entity. A type of entity, then, may well be reducible to its internal elements (constituents) but it is only projected to its external elements (symptoms; effects). In projection, there is no asymmetric dependence. It is not the case that if the external elements (the marks) cease to exist, the projective complex ceases to exist too. The example of the birds is meant to illustrate the difference between reduction and projection. The relation between the birds and the shadows is projective and not reductive. In a sense, this is so obvious that needs no arguing. Still, Reichenbach offers two reasons. First, the bird-propositions (that is, propositions that refer to birds) are not equivalent to shadow-propositions (that is, propositions that refer to shadows). This is so because one cannot deductively infer one from the other. On the contrary, the connection between bird-propositions and shadow-propositions, like all inferential connections between causes and effects, is ampliative—and in particular, probabilistic. Second, in the example at hand, “there is no reduction of existence” (1938, p. 109), viz., there are two distinct types of entity; the birds have independent existence over the marks. In the end, of course, the two reasons are one and the same. The nonequivalence implies distinct existence and conversely; and this is underwritten by the fact that the relation between claims about birds and claims about shadows is nondeductive.
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The very opening of the distinction between reduction and projection makes plausible the following thought: observable entities are symptoms (or effects) of unobservable ones (that is, unobservable entities are projective complexes, whose external elements are observable entities). This implies a certain inversion of the way empiricists view things. The unobservables become legitimate because, qua projective complexes, they are distinct existences whose external elements are observable entities. On the face of it, reduction and projection need not be in conflict provided they are performed on different bases. One and the same entity can be a projective complex vis-à-vis its external elements and a reductive complex vis-à-vis its internal elements. A bird, for instance, is a projective complex vis-à-vis its shadow and can be taken to be a reductive complex vis-à-vis its cells and molecules. The operative relations are clearly distinct. If reduction is, at least typically, constitution, projection is, at least typically, causation. There is a problem, however. Reichenbach (1938, p. 114) has claimed that in the case of reduction it is possible to define an entity in such a way that it “vanishes with its elements”. If the very same entity is a projective complex vis-à-vis a set of external elements, it is a distinct existence, whose reality is defeasibly inferred (by means of a probabilistic inference) from the external elements. It seems that the very same entity is real and independently existing and unreal (or less real, so to speak) and dependently existing. Besides, if reduction, qua conceptual relation, is such that the equivalence between the reductive complex and the reductive basis is ascertainable a priori (as Reichenbach suggests it is the case; cf. 1938, pp. 95 and 98–99), it follows that if macroscopic entities are reductive complexes of microscopic constituents, this must be knowable a priori—which would be absurd for an empiricist. Reichenbach does address this problem, but quite later on in the book and after he has completed his argument for realism. What he says, however, is very instructive and relevant to his argument. He (1938, p. 216) introduces the concept of “internal projection”, which—in effect—amounts to an a posteriori theoretical identification. A table is a collection of atoms—current physics tells us. Atoms are the constituents of the table. They fix the properties of the table, whatever they are. But the table is not, strictly speaking, a reductive complex vis-à-vis its constituent atoms because the relations that exist between the atoms and the table (in virtue of which the properties of the table are fixed by the properties of the atoms) can be known only a posteriori and by means of probabilistic inferences. In other words, the table is not a reductive complex of atoms because there are no deductive inferential relations (and hence no equivalence) between propositions about the table and propositions about its constituent atoms. The relation between the table and its constitutive atoms is projection (since it is captured by probabilistic inferences), but it is an internal projection (since, there are not two distinct existences: the table and the atoms). An internal projection, then, is a relation between an entity and its constituents which is such that (a) the entity is not something distinct from its constituents (for instance, there is the already noted asymmetric dependence between them) and (b) the constitutive relations between the entity and its constituents are knowable a posteriori. An internal projection, in other words, is a kind of reduction “which is ascertained by probability inferences, not by definition” (1938, p. 216).
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The notion of internal projection brings together reduction and projection. Though Reichenbach would not put it this way, ontically (but not conceptually) it is a reduction whilst epistemically it is a projection. Reichenbach, then, was wrong to identify, at least initially, two senses of reduction: an ontic relation of constitution and a deductive inferential relation, by means of which all truths about the reductive complex are deducible from truths about the reductive basis. These are not the same sense of reduction—at least not necessarily. Running them together obscured the idea of internal projection. It obscured, at least initially, an important subsequent element in Reichenbach’s argument for realism, viz., that apart from being independently existing entities (qua projective complexes), whose external elements are observable entities, unobservable entities are the constituents of observable entities (that is, observable entities are reductive complexes, whose internal projective elements are unobservable entities). 4 Reaching outside the C-world The example of the birds and their shadows has made plausible the view that there are inferential patterns (from external marks to projective complexes) that are shared between empiricists and realists. But in the example so far there is a two-way independent access to the marks and the causes: the birds are, after all, observable. One may naturally wonder: how can we proceed if there is only one-way independent access to the marks? How can we possibly infer the existence of something distinct from the marks? Something we cannot have an independent epistemic access to? More generally: how exactly do ampliative inferences generate the excess content attributed to the theoretical propositions of scientific theories? Reichenbach’s answer to this question is motivated by a modification of the example of the birds and their shadows—the example of the cubical world (C-world) (1938, §14). In this story, the inhabitants of the C-world are confined within a huge cube, whose walls are made of white cloth. It is soon observed that there are shadows dancing around the walls. Unbeknownst to the inhabitants, these are the shadows of birds flying outside the cubical world. A “friendly ghost” (a benevolent demon?) has set up a complex set of mirrors that project shadows of the birds on the walls. The birds (causes of the shadows) are, by hypothesis, unobservable—in fact, the laws of nature are presumed to be such that the birds cannot be seen. Is it possible for the inhabitants to come legitimately to believe that there are birds outside the C-world? Reichenbach points out that there in a sense in which the inhabitants of the C-world are in the same epistemic situation as those involved in the initial example of the birds. To bring this out, he introduces a local Copernicus who uses a telescope and finds out that the marks on the walls fall under regular patterns: the movements on the side wall are co-ordinated with movements on the top wall.3 The local Copernicus is pictured to engage in an inference from the marks on the walls to their causes and to infer 3 Reichenbach stacks his deck here a bit, since Copernicus is supposed to figure out that the dots on the walls have the shape of animals—of birds really—which seems to illicitly assume that there are birds within the c-world too and that people know a lot about them. But let us leave this to one side.
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the existence of unobservable birds as causes of the marks on the walls. Here is how Reichenbach (1938, p. 118) puts it: He [the local Copernicus] will maintain that the strange correspondence between the two shades of one pair cannot be a matter or chance but that these two shades are nothing but effects caused by one individual thing situated outside the cube within free space. He calls these things ‘birds’ and says that these are animals flying outside the cube, different from the shadow-figures, having an existence of their own, and that the black spots are nothing but shadows. Let us try to dig a bit deeper into the way the local Copernicus reasoned, since Reichenbach does not say much about it. Here is how I would put the matter. He observes the patterns on the walls and he forms a hypothesis that purports to explain them. This is a causal hypothesis: it posits a cause of the observed pattern in virtue of which this pattern is rendered intelligible. Copernicus, in other words, posits an entity (better: a type of entity) that brings some causal-nomological order in the world-view of the inhabitants of the C-world. Instead of taking a certain pattern as a brute fact, he offers an explanation of it—an explanation by postulation (of unobservable entities). As is stressed in the quotation above, the call for explanation is motivated by the thought that surprising coincidences should not be attributed to chance—there must be a reason for them to hold and hence an explanation. To my mind, this is clear case of what has been called inference to the best explanation (IBE). This claim might not amount to much—since IBE needs articulation. But the general point that needs to be driven home is this. Recall the question we (and Reichenbach) faced above: how can the existence of something distinct from the marks, something to which there is no independent epistemic access, be inferred? The answer is that explanatory reasoning does precisely this: it generates hypotheses with excess content over the observations that probe them. The projective complex (the birds), which has independent and distinct existence, is not strictly speaking the product of probabilistic reasoning. Rather, it is first posited as the best (causal) explanation of some marks or effects and then the issue is raised as to how probable it is relative to these marks. A probabilistic connection does hold between an explanatory hypothesis and some evidence for it, but it is not this probabilistic connection that generates the excess content; rather, the probabilistic connection suggests that ampliative hypotheses can be confirmed and hence that the excess content they possess in virtue of the fact that they are explanatory hypotheses can be legitimately accepted. So: the excess content is generated by the explanatory connection there is between the projective complex and its external elements. The relation of projection is an explanatory relation: it relates two distinct existences. I am not sure Reichenbach saw this point very clearly, though, as we are about to see, the way he went on to develop his argument in step 2 shows some appreciation of it. This way of viewing things explains why the observability of the birds does not matter to their being posited as causes of the shadows (or the dots). Both in step 1 and the step 2 of Reichenbach’s argument a physical entity is posited as a projective complex and its reality is accepted on the basis of the claim that it causes (and hence it
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causally explains) some observable events. It makes no difference to this function of the posited entity whether it is observable (as in step 1) or unobservable (as in step 2). 4.1 The base-rate fallacy (and how Reichenbach avoids it) After presenting the brief summary of Copernicus’s reasoning that we saw in the last quotation, Reichenbach went on to claim that the hypothesis of the local Copernicus is “highly probable” when “judged from the facts observed”. For, as he put it, it is “highly improbable that the strange coincidences observed for one pair of dots are an effect of pure chance” (1938, p. 120). Faced with improbable coincidences, he added, scientists will not believe that they are a matter of chance but instead they will look for a causal explanation (or for “causal connection”, as he put it). This suggests that Reichenbach saw the argument in step 2 as a straightforward probabilistic argument with a highly likely conclusion. But then the argument seems to be open to the charge that it commits the base-rate fallacy. Here is a brief reminder of the fallacy (introduced by the standard example in the literature, known as the Harvard Medical School test). Harvard medical school test A test for a disease has two outcomes, ‘positive’ (+) and ‘negative’ (−). Let a subject S take the test and let H be the hypothesis that S has the disease and −H the hypothesis that S doesn’t. The test is highly reliable: it has zero false negative rate: the likelihood that S tested negative given that S does have the disease is zero (i.e., prob(−/H) = 0). The test also has a very small false positive rate: the likelihood that S is tested positive though S doesn’t have the disease is, say, 5% (prob(+/−H) = .05). S tests positive. What is the probability that S has the disease given the positive test? That is, what is the posterior probability prob(H/+)? Given only information about the likelihoods prob(+/H) and prob(+/−H), the question above is indeterminate. This is so because there is some crucial information missing: we are not given the incidence rate (base-rate) of the disease in the population. If this incidence rate is very low, e.g., if only 1 person in 1,000 has the disease, it is very unlikely that S has the disease even though S tested positive: prob(H/+) would be less than .02. For prob(H/+) to be high, it must be the case that prob(H) be not too small. But if prob(H) is low, it can dominate over a high likelihood of true positives and lead to a very low posterior probability prob(H/+). Reichenbach has invited us to compare the likelihoods of two competing hypotheses, viz., H: the existence of unobservable birds; and not-H: there are no birds outside the cubical world (and hence that the observed coincidences are a matter of chance). More generally put, Reichenbach’s argument so far is this: there is an effect e (the strange coincidences) observed; e would be very unlikely if not-H were the case, but e would be very likely if H were the case; hence, H is very likely (or much more likely than not-H). Indeed, he says quite clearly: “Reflections like this would incline the physicists to believe in the hypothesis of Copernicus …” (1938, p. 121). But this kind
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of argument commits the base-rate fallacy. The likelihoods are not enough to fix the posterior probability of H, let alone to make it high. In order to avoid the fallacy, we need to take into account prior probabilities.4 The form of the argument, then, would be like this: (A) prob(e/H) is high. prob(e/−H) is very low. e is the case. prob(H) is not very low. Therefore, prob(H/e) is high. (A) is not fallacious. In fact, even with relatively low prob(H), the posterior probability prob(H/e) can be quite high. In any case, assuming prior probabilities, the degrees of confirmation of hypothesis in light of the evidence becomes quite definite. Reichenbach agonises a lot (and over several pages) about how different likelihoods could be attributed to the competing hypotheses, but in the end he rescues his argument from falling prey to the base-rate fallacy by admitting prior probabilities. He is clearly aware that the probabilistic inference he has in mind requires another element, viz., the prior probabilities of the competing hypotheses. Curiously, however, he relegates this important point to a brief and obscure footnote (under the pretentious heading “Remark for the mathematician”) (1938, p. 124). There he notes that the probabilistic inference he has in mind relies on “Bayes’s rule” (which, however, he never states). All he says is that one can use Bayes’s rule to specify the posterior (“backward) probability of a hypothesis given the evidence as a function of the likelihood (“forward probability”) and the “initial probability” of a hypothesis. More importantly, different prior probabilities make a difference to the posterior probabilities of competing hypotheses, even if the likelihoods are equal. Towards the end of the book, Reichenbach (1938, p. 390) notes that Bayes’s theorem is a rule “for inferring from given observations the probabilities of their causes”. Surprisingly little is said about the status of prior probabilities: “It is these initial probabilities that are involved in the reflections of the physicist about causal connections” (1938, p. 124, ft. 4). What he has in mind is this. The two competing hypotheses H (the existence of unobservable birds) and not-H (the observed coincidences are a matter of chance) can legitimately be given different prior probabilities on the basis of analogy and past experience. Even if a persistent positivist contrived a hypothesis such that a strange coincidence is the outcome of a (strange) causal law that did not involve projective complexes, one could point to the fact that in many other similar cases where strange coincidences were present, there had been a causal connection among them that involved projective complexes (simply put, there had been a common cause) (cf. 1938, p. 123). 4 One can always adopt likelihoodism, which uses the likelihood ratio to capture the strength by which the evidence supports a hypothesis over another, but it does not issue in judgements as to what the probability of a hypothesis in light of the evidence is (cf. Sober 2002). But this is clearly not the way Reichenbach proceeded.
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4.2 Prior probabilities to the rescue By bringing prior probabilities into play, Reichenbach is able to show that hypotheses about unobservables are confirmable on the basis of the evidence—provided of course they are allowed some non-zero initial probability. Besides, he is able to argue that the difference between forming beliefs about observables and forming beliefs about the unobservable on the basis of the evidence is one of degree. Both kinds of belief are ampliative; they concern projective complexes; their degree of confirmation is based on the same type of probabilistic reasoning. So probabilistic (Bayesian) inference is overreaching: it allows the justification of hypotheses (by showing how they are confirmed by the evidence) irrespective of whether or not their content is observationally accessible. For him, this type of probabilistic inference “is the basic method of the knowledge of nature” (1938, p. 127) and this is so for everyone—that is, positivists too have to rely on it (as the first step of the argument has shown). There is, of course, the issue of the status of prior probabilities. Reichenbach comes back to this issue quite late in the book (§30) and treats them as initial weights (or posits), and hence as estimates of how likely a hypothesis is (prior to the evidence). The overall tone of Reichenbach’s discussion (as well as his frequentist theory of probability) suggests that for him the assignment of prior probabilities to competing hypotheses is not a matter of subjective preference. But it is not quite clear how they are fixed. The first reaction of the critics of the book was to claim that Reichenbach leaves us in the dark. Eleanor Bisbee (of the neighbouring American College of Istanbul) noted in a review of Experience and Prediction (1938, p. 365): Dr. Reichenbach does not hesitate in the least to make a philosophy of gambling. His object is to find out how to gamble well. Every decision about a specific instance is a ‘posit’ of a possible outcome based on the highest known probability for similar cases. The trick is to choose a class of cases to which the similarities are significant. In passing, it may be noted that if instinctive appraisals are admitted, it seems as though a factor in the weight might be wishful thinking, which the author does not discuss. Presumably, his reply to this would be that clear knowledge of the probability basis of decisions would be the best check on that tendency. To be sure, the already noted reliance on analogy and past experience might also help Reichenbach to draw some connections between prior probabilities and relative frequencies. For at least there could be some pool of similar cases, from which an estimate of a weight of a new case could be made. But of course, a lot more would have to be said about the similarities among theories in virtue of which prior probabilities could be specified. Generally, Reichenbach’s conception of probabilities as limiting relative frequencies creates a number of problems. For one, it is not clear how relative frequencies can be specified for advanced hypotheses, viz., hypotheses for which analogy and past experience cannot be relied upon. For another, it appears that treating the prior probabilities of hypotheses concerning unobservables as relative frequencies would require independent access to these unobservable entities so that success frequencies
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are specified. But (a) there is no such independent access; and (b) this kind of requirement would remove the attraction of Reichenbach’s second step, since it would imply that probabilistic inference requires independent epistemic access to the entities whose existence is supported by the probabilistic inference. Though the criticism against Reichenbach’s frequentism is telling, the important point of the second step of the argument for realism is two-fold: (a) probabilistic inferences rely on prior probabilities and (b) by capturing explanatory relations of projection, they are blind to the observable/unobservable distinction. It would be unfair, however, to Reichenbach not to say something in his defence, since at the very end of his book (and in a way seemingly unrelated to the argument for realism) he pointed to what I think is the right general attitude about what kind of considerations play a role in fixing initial probabilities. Discussing the issue of weights attributed to scientific theories (which cannot be so easily equated with relative frequencies), he drew an all-important distinction between two levels of probability ascriptions (cf. 1938, pp. 397–398). When we try to specify the degree of confirmation of a scientific theory, that is when we look at how the evidence supports a certain theory, we can proceed at two distinct levels. At the first (or ground) level, we look into the specific information concerning the theory at hand: its predictions, its likelihood, and its initial probability, which might reflect an initial plausibility. We then calculate its degree of confirmation. We can however move to a second level and, as Reichenbach (1938, p. 397) put it, “consider the theory as a sociological phenomenon and (…) count the number of successful theories produced by mankind”. It is obvious that at this higher level, we are interested in the base-rate of truth among scientific theories. The relevant prior probability then assigned to a scientific theory is the prior probability that it is true given that it belongs to a pool of theories with certain characteristics. We don’t quite have this kind of statistical information. But had we had it, it would be a frequentist prior probability. Reichenbach was overly optimistic that this kind of information might become available. The key point, however, is that these two levels of determination of the (prior) probability of a theory need not (and as a rule will not) be the same. The kind of information that can be employed in the determination of the prior probability of a specific theory (assuming relevant background knowledge etc.) will be much more detailed and specific than the kind of information that can be employed at the second level—where information from the history of science and the past performance of scientific theories will be pertinent. Reichenbach thought that both kinds of consideration should be taken into account in fixing the probabilities of theories. He also suggested that there may be reason to trust second level probabilities more than first level one (and conversely). For, instance, there might be domains of inquiry where the truth is harder to get than others; or where theories have had a greater falsity rate.5 5 In my (2009, Chap. 4), I have drawn a similar distinction between first-order evidence in favour of a scientific theory and second-order evidence coming from the past record of scientific theories and/or from meta-theoretical (philosophical) considerations that have to do with the reliability of scientific methodology. I take it that when we think about scientific theories and what they assume about the world we need to balance both kinds of evidence.
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5 The problem of the external world If we were to recap the key point so far, I would say the following. The crucial element of Reichenbach’s argument for scientific realism, at least in the way I think it ought to be going, is that unobservable entities are seen as projective complexes that are detected by means of their effects, symptoms or marks. This kind of move is not the outcome of probabilistic reasoning, but of explanatory reasoning: the relation of projection is an explanatory relation between two distinct existences in virtue of which the first causally explains the second and the second becomes a mark of the first. Having this kind of relation in place (which cuts through the observable/unobservable distinction), probabilistic reasoning (with an ineliminable role assigned to prior probabilities) can yield definite degrees of confirmation of ampliative hypotheses concerning these projective complexes and underwrite their warranted acceptance. It turns out that Reichenbach has had a more ambitious aim in mind. He attempts to generalise the lessons drawn from the second step to the realism-positivism debate in general. So there is a second part (and a third step) in his strategy. His initial thought (1938, §15) is that the very question of the existence of the external world of physical things (what he (1938, p. 139) calls “the realistic conception of the world”) as distinct and independent from sense-impressions can be settled along the lines of the argument of the second step (see 1938, p. 154). After all, there are two rival hypotheses. One, favoured by Reichenbach, is that the physical objects of the external world are independently existing projective complexes, with the impressions being external elements of them—that is, signs or marks or effects of their presence. The rival (positivist) hypothesis is that physical objects are reduced to impressions—they are reductive complexes and as such, they are equivalent to collections of sense-impressions. It is crucial to Reichenbach’s argument that the realist claim (the projective hypothesis) is not equivalent to the positivist claim (viz., the reductive hypothesis). That they are not, in particular that the realist hypothesis has excess content over the positivist, is licensed by PTM. If the two hypotheses are not equivalent, there is, after all, a problem of the existence of the external world. PTM opens up a space for the problem of the external world to be a genuine problem and not merely a pseudo-problem as many of Reichenbach’s contemporaries would have it. By the same token however, he must offer a genuine solution to it. It is tempting then to think that the required genuine solution is simply an extension of the argument for the reality unobservable entities—sketched above. In particular, it is tempting to equate the shadows on the walls of the C-world with impressions and the birds that cause them from the outside with external physical objects (cf. 1938, p. 154). Note that Reichenbach’s contemplated move rests on the assumption that the very same method that is employed in science to accept hypotheses (probabilistic inference) can be employed in defence of realism as a philosophical position. There is, however, a difference between the argument of step 2 for the reality of unobservables and the argument of step 3 for the reality of independently existing physical objects (the external world). In step 2, the argument takes place within the framework of (independently existing) physical objects. Both the shadows (marks on the walls of the C-world) and the birds (outside the C-world) are distinct and independently existing physical objects. It’s just that the former are observable while the latter
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are unobservable and Reichenbach’s forcefully made point was that this is a difference that makes no epistemic difference. In particular, the (unobservable) birds are projective complexes vis-à-vis the shadows on the wall. But the very idea of their being projective (as opposed to reductive) complexes requires that they exist as physical things independently of their external symptoms. In generalising the argument to the realist conception of the world, there is a movement from (dependently existing) impressions to (independently existing) physical objects. Reichenbach (1938, p. 143) thinks that what matters is that in both steps 2 and 3, the relevant relation is projection and not reduction. But a committed reductive positivist would have objected that even if the argument in step 2 were to go through, the argument in step 3 generates new content out of nothing: it introduces an altogether different type of entity. Reichenbach (1938, pp. 136–138) tries to block this objection by noting that positing physical objects as distinct from impressions would result in an image of the world in which causal laws are homogeneous. That is, the very same causal laws would hold irrespective of whether or not anyone perceived anything. The positivist image, on the other hand, exhausted as it is by sense-impressions, requires strange and unhomogeneous causal laws. In particular, it would require causal laws that ensure continuity among sense impressions even when no-one observes anything. Reichenbach’s idea is that an image of the world based only on sense-impressions would have to mimic the fact that physical objects exist continuously, and in particular unperceived, and to achieve this it would need to posit two distinct and co-ordinated sets of causal laws: those that hold when someone perceives something and those that hold when no-one perceives anything. All this may well be right. But the fact remains that these considerations concerning causality and homogeneity can at most influence the prior probabilities of the two competing hypotheses—if they are indeed seen as theoretical hypotheses. For the argument for the reality of the external world to be of the same type as the argument for the reality of unobservable entities advanced in step 2, Reichenbach needs to rely on initial weights—as it became clear in the development of the argument in step 2. Here, for one, is where probabilities as frequencies are in their worst shape. What can plausibly be the reference class for which relative frequencies are determined? In his review of Experience and Prediction, Ernest Nagel (1938, p. 271) was quick to pick on this: How can a conception of probability, which takes its stand firmly upon interpreting probabilities as relative frequencies in empirical sequences, be made to apply intelligibly to a domain inaccessible to the requisite material investigation? Universes, with or without external worlds, are not so plentiful as blackberries; and not even Reichenbach’s ingenuity can make plausible the assumption that a statistical view of probability is relevant to solving such a problem. Perhaps, we should think of prior probabilities as based on plausibility considerations and analogy. The prior probability, one might say, of an external world distinct from impressions is significantly higher than the prior probability of a world of impressions because the former is such that it has simpler causal laws, it is more unified etc.
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But there is a problem. The very idea of assigning prior probabilities to the realist hypothesis and to the positivist hypothesis requires that there is another framework in place in which these two hypotheses are compared in terms of plausibility and the rest. This is clearly what happens in step 2 of the argument. There, the framework of physical things, qua independently existing projective complexes, is already in place. The issue then is to assign prior probabilities to the hypothesis that the shadows are caused by unobservable birds and the rival hypothesis that the co-ordination of the shadows is a coincidence. This can be done and hence, we can legitimately attach a degree of confirmation to the hypothesis that the shadows are caused by unobservable birds, without, as Reichenbach put it, digging a hole on the wall of the C-world (cf. 1938, p. 149). But in trying to extend the argument to the problem of the external world (step 3) at stake is the reality of the very framework of physical things, qua independently existing projective complexes vs its unreality. And there is simply no further framework in which this issue can be examined and in which the two rival hypotheses can be assigned different prior probabilities on the basis of their respective initial plausibilities. Here is another way to state the same problem. Reichenbach’s PTM requires the realist framework and cannot be a proof of it. PTM requires probabilistic relations between distinct types of entity, viz. the causes and the effects, or the projective complexes and their external elements, or the external physical objects and sense-impressions. Hence PTM cannot prove the distinctness of these types of entity; it presupposes it. What PTM does is to allow ampliative inferences between the marks and the projective complexes, after both have been admitted. In particular, as argued in Sect. 4, PTM does not yield the reality of the projective complexes. Based on the claim that talk about projective complexes has excess content over talk about their marks, PTM presupposes their existence and shows how there can be probabilistic relations between them and hence evidence for them, irrespective of their status visà-vis observability.
5.1 A perspectival approach to reality Interestingly, Reichenbach comes close to accepting all this—and hence to denying (or neutralizing) the third step of the argument in the form he did present it. It seems he is aware that the strategy of the first part of his argument in favour of unobservables cannot be generalised to the problem of realism in general. After all, the realist conception of the world is not a hypothesis at the same level as the hypothesis of birds outside the walls of the C-world. The choice of an overall framework (say an egocentric framework, where things are reduced to classes of impressions or a realist framework, where impressions are merely effects of independently existing objects) cannot be simply a matter of probability and confirmation of two competing hypothesis. Reichenbach (1938, §17) put the point in terms of languages. Ultimately, the problem of the external world is a problem of choosing a certain language (a language that allows us to talk about independently existing physical things) as opposed to another one (an “egocentric” language, as he put it). And choices of language are not factual but based on decisions (cf. 1938, p. 145). Reichenbach goes on to stress that the
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choice is, ultimately, between two different conception of meaning: his own PTM and a verificationist one. This choice does not answer to truth and falsity. The general problem of realism is then divided into two components—the first is the adoption of a language (framework; theory of meaning) as the result of a free (that is non-dictated by evidence or a priori considerations) decision; the second is the investigation of the adopted language (framework) by looking into its fruits. This consequentialist move is, for Reichenbach, a way to justify the choice of the language (framework)—especially by showing, in a comparative fashion, that one language is better suited than another to achieve certain aims or to satisfy certain desiderata (cf. 1938, pp. 146–147). This last move suggests that the original decision to accept a certain framework (the realist one that Reichenbach favours) is not arbitrary, though unforced by facts or reason. This kind of consequentialism fits well with Reichenbach’s overall approach to epistemology. He took it that the critical task of epistemology is to separate the factual from the conventional—a remnant of his Kantian heritage. The conventional element amounts to a decision to adopt a framework. Yet, it is not enough to point out that the choice of a framework does not answer to truth or falsity. Part of the critical task of epistemology is to examine what kinds of consequences follow from the adoption (the unforced adoption) of a certain convention. Reichenbach insisted that though the choice of a framework is based on an unforced decision, this decision entails others—what he (1938, p. 13) called “entailed decisions”—which, therefore, are far from arbitrary in that one is no longer free not to adopt them if one has already chosen the framework. By examining these ‘entailed decisions’ certain judgements can be made about the consequences of adopting a certain framework, their plausibility and their fruitfulness. As noted already, a case discussed by Reichenbach in some detail is the choice between an egocentric framework, in which objects do not exist while unperceived, and a realist one. Even if it is a matter of unforced decision to adopt an egocentric framework, one entailed decision that follows this is the adoption of strange and unhomogeneous causal laws. These entailed decisions may be contestable, or implausible, on independent grounds and this counts against the framework that implies them. The very presence of entailed decisions helps to build, as Reichenbach (1938, p. 15) put it, “a dam” against “extreme conventionalism”. This way of putting things neutralises the alleged similarity between steps 2 and 3. The argument of step 2 is not consequentialist. The bird hypothesis is better supported than the shadows-hypothesis. Conversely, step 3, unlike step 2, need not (in fact, it cannot) rely on prior probabilities. Having said this, Reichenbach did not clearly and forcefully uncouple the arguments of step 2 and 3. As noted already, the real problem is that we cannot talk of the probability of a framework as a whole, especially since the very idea of assigning probabilities to competing hypotheses within a framework (as in the second step of the strategy) requires that the framework is already in place.6
6 This is a point made by Feigl (1950, p. 54). For more on Feigl’s argument for realism, see my
(2010).
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Reichenbach characterised theoretical entities (like atoms) “illata”, meaning inferred entities. He (1938, p. 212) contrasted them to both concreta (which he took them to be immediately accessible to observations) and abstracta. Concreta are real beyond any doubt—they are immediately existent, as he put it. Illata, to be sure, “have an existence of their own” (1938, p. 212). But it seems that Reichenbach puts a premium on concreta because they are epistemically accessible and their knowledge is not probabilistic (nor inferential). On the other hand, he admitted that a possible basis for the construction of the world (a clear allusion to Carnap’s Aufbau) is the elementary particles posited by scientific theories, which are illata from the point of view of how their reality can be ascertained. He went as far as to claim that everything there is is a reductive complex of illata (as the atomic theory of physics implies) (cf. 1938, p. 215)—where, of course, the reductive relation he had now in mind was ontic: what we have already seen him calling internal projection. Seen from this point of view, only illata have objective existence. The world of observable things, the world of concreta, is taken to be a “substitute world”, “not the world as it is—objectively speaking” (1938, p. 220). The manifest image of the world is essentially false (cf. 1938, p. 221). To be more precise, Reichenbach had a perspectival approach to reality. He did use the notion of perspective and thought there is no perspective-free view of reality (cf. 1938, p. 221). This is perhaps a permanent loan from Kant, that Reichenbach kept even when he abandoned other key elements of his early Kantianism. Frameworks, then, can be seen as perspectives on reality. Occasionally, Reichenbach calls them “descriptional” frames by means of which we view the world (1938, p. 221). The manifest image of concreta then, is just one perspective on reality; it is “one-sided”: it reveals us only what is tuned to our perceptual capacities; and yet, “it shows some essential features of the world” (1938, p. 225). The realist framework of illata is yet another perspective on reality. It is a more objective perspective, since it is not anthropocentric (it is cosmological, as Feigl would put it). But it is still a perspective on reality. The task of epistemology then is to reveal these perspectives and to combine them. As Reichenbach (1938, p. 225) put it: We wander through the world, from perspective to perspective, carrying our own subjective horizon with us; it is by a kind of intellectual integration of subjective views that we succeed in constructing a total view of the world, the consistent expansion of which entitles us to ever increasing claims of objectivity.
6 Concluding thoughts Reichenbach’s argument for scientific realism (steps 1 and 2 in the argument) is an argument within the realist framework (the realist conception of the world) and not an argument for it. It presupposes, rather than proves, that there are projective complexes that cause certain observable phenomena. Given this presupposition, Reichenbach’s argument shows that hypotheses about unobservable entities are confirmable and confirmed on the basis of the evidence—provided that some non-zero initial weight is ascribed to them. The role of the realist framework is precisely to allow ascriptions
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of non-zero initial weights to hypotheses about unobservable entities. Differently put, the very fact that probabilities are assigned to hypotheses about unobservable entities requires the prior adoption of a realist framework within which such hypotheses are formulable and evaluable. It’s a different matter, of course, how prior probabilities are to be assigned after the framework is adopted. Here, Reichenbach’s interpretation of probability as limiting relative frequency might betray him, since as Feigl (1950) pointed out, it would require some estimation of the actual success of inferences from observable entities to hypotheses concerning unobservable entities—and, clearly, there is no independent assessment of the latter. But of course, the important point is not whether prior probabilities are relative frequencies but rather that (a) they are necessary and (b) their ascription requires a prior adoption of the realist framework. Seen in this light, the attraction of Reichenbach’s argument for scientific realism is in the thought that the very issue of observability of an entity is spurious. An entity is posited for explanatory reasons and the probabilistic inferential pattern by means of which some degree of belief in its existence is specified is blind to whether or not this entity is (un)observable. Here is where an appeal to common causes is important. Not as a distinct inferential pattern, but by way of reminding us that the relevant reference class for assigning prior probabilities to hypotheses should be inferences from correlations to common causes (that is, that, by and large, such correlations admit of further explanation by reference to third factors), irrespective of whether the common causes are observable or not. References Bisbee, E. (1938). A world of probability: Review of Experience and Prediction by Hans Reichenbach. Philosophy of Science, 5, 360–366. Feigl, H. (1950). Existential hypotheses: Realistic versus phenomenalistic interpretations. Philosophy of Science, 17, 35–62. Nagel, E. (1938). Review of Experience and Prediction. The Journal of Philosophy, 35, 270–272. Psillos, S. (2009). Knowing the structure of nature. London: Palgrave/MacMillan. Psillos, S. (2010). Choosing the realist framework. Synthese. doi:10.1007/s11229-009-9606-9. Putnam, H. (2001). Hans Reichenbach: Realist and verificationist. In J. Floyd & S. Shieh (Eds.), Future pasts (pp. 277–288). Oxford: Oxford University Press. Reichenbach, H. (1938). Experience and prediction. Chicago: The University of Chicago Press. Salmon, W. (2005). Reality and rationality (P. Dowe & M. Salmon, Eds.). Oxford: Oxford University Press. Sober, E. (2002). Bayesianism-its scope and limits. Proceedings of the British Academy, 113, 21–38.
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Synthese (2011) 181:41–62 DOI 10.1007/s11229-009-9590-0
Relativizing the relativized a priori: Reichenbach’s axioms of coordination divided Flavia Padovani
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 2 September 2009 © Springer Science+Business Media B.V. 2009
Abstract In recent years, Reichenbach’s 1920 conception of the principles of coordination has attracted increased attention after Michael Friedman’s attempt to revive Reichenbach’s idea of a “relativized a priori”. This paper follows the origin and development of this idea in the framework of Reichenbach’s distinction between the axioms of coordination and the axioms of connection. It suggests a further differentiation among the coordinating axioms and accordingly proposes a different account of Reichenbach’s “relativized a priori”. Keywords Relativized a priori · Axioms of coordination · Probability · Causality · Reichenbach · Cassirer · Friedman
1 Introduction In the years he spent in Istanbul, between 1933 and 1938, Reichenbach was mainly engaged in providing a more solid framework for the probabilistic picture he had started delineating in his doctoral dissertation of 1915, namely a probabilistic logic for scientific thought.1 These years are also characterised by his final attempt to refute the synthetic a priori, when he coined the pregnant expression “disaggregation (désagrégation) of the a priori” to describe the movement of ideas that led to the birth of logical
1 Cf. Reichenbach (1935, 1936b, 1937).
F. Padovani (B) Centre for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pittsburgh, PA 15260, USA e-mail:
[email protected]
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empiricism.2 Nonetheless, nowadays one of his most discussed, and certainly most interesting, contributions is considered to be the original proposal of a synthetic (or constitutive) yet revisable a priori, which he first formulated in his 1920 Habilitation thesis on relativity theory and cognition a priori.3 In this work, which deals with the possibility of reconciling Einstein’s theory with the Kantian system, the notion of constitutive a priori appears to be tied to a view of the cognitive coordination (Zuordnung) that is in general traced back to the influence of Moritz Schlick’s General Theory of Knowledge (1918/1974). In fact, in the secondary literature, it is largely accepted that Reichenbach first proposed a peculiar version of the synthetic a priori—and its correlated concept of cognitive coordination—only after his encounter with relativity theory, in the years 1917–1920.4 As Friedman puts it, [i]t is in no way accidental that coordination as a philosophical problem was first articulated by scientific philosophers deliberately attempting to come to terms with Einstein’s general theory of relativity. Indeed, Reichenbach in 1920, together with Moritz Schlick in virtually contemporaneous work, were the first thinkers explicitly to pose and to attempt to solve this philosophical problem. (Friedman 2001, p. 78) The aim of the present paper is to discuss neither Friedman’s proposal of a relativized a priori, nor the way he used it to ground his dynamical conception of the scientific development and its related philosophy from Newton to Einstein. Rather, it is to analyse and clarify Reichenbach’s conception of cognitive coordination in his early works in order to show that what he had in mind was more sophisticated than usually suggested and was also crucially linked with the role he assigned to probability in scientific representation. A philosophical framework for the notion of coordination, as functional correlation between a concept and its object, was indeed first provided by Reichenbach not with respect to the theory of relativity, and not primarily in line with Schlick’s 1918 conception, but against a totally different background, namely probabilistic, in his doctoral dissertation of 1915, The Concept of Probability in the Mathematical Representation of Reality.5 The fact that the issue of coordination makes its first appearance in such a framework is important in that the core of the relativized a priori is to be found, in nuce, in his doctoral thesis, not in his monograph on relativity theory. Moreover, as we shall see, Reichenbach’s concept of Zuordnung is mainly inspired by the one Cassirer elaborated in his “Kant und die moderne Mathematik” (1907) and in Substance and Function (1910/1923). 2 Cf. Reichenbach’s address in the section on logical empiricism at the famous Paris Congress of 1935, (1936a), as well as his (1936c). 3 Reichenbach (1920/1965). This text was presented by Reichenbach as Habilitationsschrift, a thesis written to obtain the qualification for university teaching under the formal supervision of Erich Regener, physics professor at the Stuttgart “Technische Hochschule”. 4 Reichenbach was one of the first five students attending Einstein’s lectures on general and special rela-
tivity, and on statistical mechanics in Berlin, between 1917 and 1920. His notebooks, like all the original material from the Hans Reichenbach Collection (HR) that I will quote in the next sections, are available at the Pittsburgh Archives of Scientific Philosophy, and they can be found in the folder HR 028-01-01/05. 5 Reichenbach (1916/2008).
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In the next section, I will briefly sketch some of the features of Reichenbach’s first work on probability and emphasise that this was the real ground of his move away from Kant, focussing on the specificity of his formulation of coordination. In Sect. 3, I will consider the way this notion is imported into his Habilitation thesis, where it turns into the distinction between axioms of coordination and axioms of connection. Finally, in Sect. 4, I will present some developments related to this distinction that Reichenbach considered right after the publication of his 1920 book and that imply a different reading of his relativized a priori. These developments are prior to the well-known correspondence with Schlick of the end of November 1920, which has in general been deemed the principal cause of Reichenbach’s adoption of a “conventionalist” viewpoint. In my view, two levels of constitutivity can be identified in his original proposal, along, so to speak, a vertical axis, as I suggest in the last section. This allows for an interpretation that regards his later shift towards conventionalism as only partial. 2 Elements of an attempted “(neo-)Kantian” proposal 2.1 Coordination in the dissertation. Or: from mathematics to physics and back (via an account of approximations) Reichenbach’s doctoral thesis initiated a reflection on the principles of causality and probability that he was bound to develop over the course of his entire intellectual life.6 In his first work, Reichenbach emphasised the importance of these two fundamental principles of knowledge, which appear to be compatible and whose validity is traced back to their status as synthetic a priori principles in the traditional Kantian fashion.7 In this work, the importance of the principle of probability is crucially linked with that of the principle of causality, which in 1915 Reichenbach still considered as complemented by the principle of probability. Following Kant, Reichenbach views the physical laws as describing (causal) connections among natural phenomena. These connections can be conceived, and are indeed justified, only by virtue of a synthetic a priori principle: the principle of causality, here also called “the principle of the lawful connection” (Prinzip der gesetzmässigen Verknüpfung). Physical laws are expressed in mathematical terms. The application of mathematical laws entails their coordination to empirical quantities, as represented in the physical equations. However, these quantities are never as exact as the quantities that enter into pure mathematics because they are scattered around certain values that need to be estimated. In this respect, the values that occur within physical laws are “fictions” for they do not mirror reality perfectly but merely with a certain, possibly high, degree of accuracy. Every physical law (i.e., every causal assertion) presupposes 6 For a synopsis of Reichenbach’s dissertation, see Eberhardt’s “Reliability via synthetic a priori— Reichenbach’s doctoral thesis on probability”, in this same volume. 7 Here, I only deal with the way these two principles interact in the process of cognitive coordination, not much with the question of their foundation. In particular, as far as the principle of probability is concerned, Reichenbach provides a justification that he reckons to be in line with the one Kant employed for the principle of causality, that is, a “transcendental deduction”. Cf. Reichenbach (1916/2008, 105 ff).
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a neglect of certain perturbing factors that are ineliminable from the observation. Since there are an infinite number of such factors, it is impossible to determine their precise values. Therefore, we have to make some hypothesis concerning the behaviour of these perturbations and their frequency. The idea is as follows. Our measurements are in principle imprecise. The measured values should represent the algebraic sum of an infinity of influential quantities, but for practical reasons, we have to consider them as the sum of finite factors, which we can use to calculate “backwards” the sought quantity. Our direct measurement, explains Reichenbach, never points to the real quantity that we are supposed to find, but only to its function. In this sense, the resulting numerical value is the one that we have chosen as representative for the class of available measured values. So the problem is that of being able to determine which of these values is the “correct” one. In other words, we have to find a lawful procedure to ground the choice among these various possibilities. This procedure is represented by a mathematical law expressing the errors distribution, a law that will “assign a frequency to every error.”8 This is the role played by the other fundamental synthetic a priori principle, which Reichenbach defines as the “principle of the lawful distribution” (Prinzip der gesetzmässigen Verteilung): the principle of probability. This principle asserts that each empirical distribution has a convergence limit, and it warrants (via a “transcendental” justification)9 that the observed convergence actually is representative of the “true” probabilities. This should finally enable us to formulate the physical laws, therefore making possible a prediction. Thus, Reichenbach’s principle of probability is meant to complete Kant’s principle of causality.10 It is in this context that Reichenbach first uses the concept of coordination to express the idea that the content of physical knowledge requires some specific form of coordination of certain mathematical structures to objects of empirical intuitions. Whereas the objects of mathematical judgments can be fully grasped, the objects of physical judgments require the coordination of the former to the unformed reality in order to produce the latter. In doing so, Reichenbach implicitly underlines that—the methodical Kantian assertion concerning the applicability of mathematics to the physical world notwithstanding—this coordination is in principle not complete, as we cannot do without approximations: a stance which is quite far from the Kantian spirit.11 8 Reichenbach (1916/2008, pp. 125–129). 9 For more details on these issues see again Eberhardt’s contribution to this volume. 10 There are several elements that would suggest that the principle of probability, as Reichenbach formulated it in 1915, cannot simply be placed beside that of causality. There, probability plays in fact a dual role: as a synthetic a priori principle, it serves to capture specific features of reality that cannot be subsumed under the principle of causality, and to give their representation for the subject; yet, the principle of probability is not only important from an “ontological” point of view, but also from a more methodological one. On the one hand, the principle of probability appears to be formulated in “causal” terms, namely in the treatment of causally dependent and independent trials. On the other hand, probability is the most fundamental tool allowing each natural science to account for real events, and in this very sense it is presupposed by causality itself, making it ultimately rely on probability, as Reichenbach will more thoroughly elaborate from (1932) onwards. 11 Despite Reichenbach’s Kantian terminology, in his work there is a tension in relation to the Kantian system: the principle of probability seems to suggest the statistical character of the laws of nature, and this would implicitly mean discarding the deterministic idea that is behind Kant’s fundamental principle of causality. This is in fact the direction that Reichenbach will take—with some vacillation—after the
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In the coordination of the mathematical structures to real ones required by physics (as well as by any empirical science), an important part is therefore played by the approximations with which we have to deal when we want to lay out natural laws. The values that appear within physical equations never stand for the measured values, which merely approximate the “real” ones (those which indeed satisfy the equations): hence, the crucial importance of probability in natural sciences. Physical knowledge, Reichenbach writes, consists in the coordination of equations, and consequently of numbers, to classes of objects of empirical intuition. The equality of these numbers for a number of actual objects of the class cannot be asserted, but only the approximate equality. The reason for this approximation is the existence of a law for the distribution of values. While mathematical judgments determine variables in such a way that they are the same for all their individual objects in all places at all times, the variables in a physical judgment are not equal for all individual objects in their class, but rather subject to a law of distribution in space and time. Instead of the general validity of mathematical claims, we have in the case of physical judgments the subsumption under the law of distribution. (Reichenbach 1916/2008, p. 127) In Reichenbach’s doctoral thesis, physical (but, in general, any empirical) knowledge puts forward an assertion about the validity of the coordination of a specified mathematical structure to reality. Thereby, with respect to the Kantian tradition, the question of validity is raised around two axes. On the one hand, the legitimacy of physical claims depends on our capacity to deal with the approximations rendered necessary by the shortcomings inherent in judgments of reality. On the other hand, the existence of such a function is itself justified from a transcendental viewpoint and it is explained, so to speak, bottom-up from the consideration of the empirical observations to which this function must conform. In other words, mathematical judgments, according to Reichenbach—and differently from Cassirer, as we shall see in the next subsection—although being synthetic a priori, acquire a meaning for cognition only insofar as they are consistently applied to reality. Above all, the role of mathematical syntheses appears somewhat secondary to the “imposition” determined by experience on the choice of the mathematical structures that are supposed to represent it. To a certain extent, what Reichenbach is considering here is a two-step “constructional” interpretation, in which the two levels, the set of formal assumptions and the set of empirical (approximate) data, cooperate in order to form a solid ground for scientific knowledge.12 An echo of this issue will be clearly reverberating in the idea Footnote 11 continued publication of his doctoral thesis. This tension in Reichenbach’s originally “Kantian” intentions has been ˇ already emphasised by Milic Capek long ago. As he remarked, “from [Kant’s] point of view, it is meaningless to claim that empirical reality is “rationally inexhaustible” and that the mathematical structure fits the observed data only loosely. […] [T]o postulate a special a priori status for the principle of statistical ˇ distribution, as Reichenbach did, was thoroughly un-Kantian.” (Capek 1958, pp. 88–90) 12 As Reichenbach makes clear, “it is precisely the task of experience to establish which are the important influences and which others may be neglected. Naturally, this experience can only be obtained by measurements; they establish whether the theoretically calculated numbers are anywhere close to the numbers occurring in reality. […] Hence, physical experience consists in the establishment of a numerical
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of the mutuality of the coordination, a central element of his 1920 formulation to which we shall return below. Let us first consider the impact of Cassirer’s conception of Zuordnung on Reichenbach’s thought. 2.2 Cassirer’s influence After the scientific—especially mathematical—developments of the nineteenth century, critical philosophy was confronted with a different form of objectivity.13 In a paper of 1907, “Kant und die moderne Mathematik,” and more extensively in the volume Substance and Function of 1910, Cassirer set out to clarify the new task of critical inquiry, that of accounting for the lately transformed manner of concept formation (Begriffsbildung), and providing a new logic of objective knowledge. In his 1910 monograph Cassirer, starting from an analysis of the evolution of modern mathematical natural sciences, and inspired by the new logicist currents in the foundations of mathematics, proposed a theory of the concept built on purely formal notions of function, series and order (or order system). Intuition, downplayed in favour of concept, takes part in the process of knowledge only once it is unified by pure thought. This unification can be understood as a subsumption under a system of relations and functional dependencies that is similar to the mathematical construction of concepts and series, and ordered accordingly. Each element of the series is constituted by the relation it bears to the other members of the series to which it is coordinated, while, at the same time, each is meaningfully correlated to members of other series. This network of dependencies and functional relations is grounded on this peculiar notion of coordination as constitutive of objects.14 Cassirer interpreted the historical development of mathematics and the mathematical sciences of nature according to a “genetic” conception of knowledge, as a generative progression of abstract structures (or “order systems”) converging towards a merely regulative ideal: the achievement of rational completeness of the conditions for the possibility of experience.15 In this framework, critical philosophy becomes a “universal invariant theory of experience,” for it ideally aims at identifying the ultimate logical invariants (the real a priori) “which lie at the basis of any determination of a connection according to natural law.”16 In the transition towards new stages of knowledge, Cassirer clarifies, it is the “functional form” itself, that changes into another; but this transition never means that the fundamental form absolutely disappears, and another absolutely new form arises in its place. The new form must contain the answer to Footnote 12 continued approximation by experiment, and conversely the physical principle assures by virtue of experience the approximate validity of certain numbers for a class of natural events.” (Reichenbach 1916/2008, pp. 123– 125) 13 See Richardson (1998, Chap. 5) and Ryckman (1991). 14 Cf. Ryckman (1991, 61 ff). 15 On all these issues, see Friedman (2005, 72 ff). 16 Cassirer (1910/1923, p. 269).
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questions, proposed within the older form; this one feature establishes a logical connection between them, and points to a common forum of judgment, to which both are subjected. The transformation must leave a certain body of principles unaffected; for it is undertaken merely for the sake of preserving this body of principles, and these reveal its real goal. Since we never compare the system of hypotheses in itself with the naked facts in themselves, but always can only oppose one hypothetical system of principles to another more inclusive, more radical system, we need for this progressive comparison an ultimate constant standard of measurement of supreme principles of experience in general. […] The goal of critical analysis would be reached, if we succeeded in isolating in this way the ultimate common element of all possible forms of scientific experience, i.e., if we succeeded in conceptually defining those moments, which persist in the advance from theory to theory because they are the conditions of any theory. At no given stage of knowledge can this goal be perfectly achieved; nevertheless it remains as a demand, and prescribes a fixed direction to the continuous unfolding and evolution of the system of experience. (Cassirer 1910/1923, pp. 268–269) In Cassirer’s early works, a pivotal position is assigned to mathematics for its specificity in exhibiting the very fundamental intellectual syntheses on which sciences rest, as displayed by their historical succession. Thus, mathematical concepts have a crucial philosophical significance in that they allow for a lawful ordering of phenomena, and for assigning them objective meaning. This fact assumes an even deeper importance once it is made clear that the critique of knowledge takes off precisely where mathematical reasoning stops, namely by elucidating the role that mathematical concepts play in constructing our “objectual” reality (“gegenständliche” Wirklichkeit).17 Reichenbach openly builds on Cassirer’s general approach in Substance and Function, where the most distinctive feature of scientific thought is that of proceeding according to a scheme of progressive dissolution of the concept of substance into that of function. As we have seen, for Cassirer the role of functions is that of constituting the objects of scientific representation through the connecting relation provided by the laws—a relation due to which each thing is mutually connected to every other. Reichenbach’s probability function plays a similar role in the representation of reality for it enables the connection that is described by the laws of nature. Further, following Cassirer, Reichenbach places an emphasis on the essential function performed by certain theoretic components (the constants) within and relative to a specific construction—constitutive elements that will become simple variables in the successive stage of scientific evolution.18 As he explains, [e]very constant is presented as a function; the natural constant which is simply given for certain laws and to whose measurement several experiments are 17 In Cassirer’s words: “Erst wenn wir begriffen haben, dass dieselben Grundsynthesen, auf denen Logik und Mathematik beruhren, auch den wissenschaftlichen Aufbau der Erfahrungserkenntnis beherrschen, dass erst sie es uns ermöglichen, von einer festen gesetzlichen Ordnung unter Erscheinungen und somit von ihrer gegenständlichen Bedeutung zu sprechen. Erst dann ist die wahre Rechtfertigung der Prinzipien erreicht.” (Cassirer 1907, pp. 44–45) 18 Cf. Cassirer (1910/1923, 265 ff).
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dedicated is brought into connection with completely different quantities, so that it appears as a function whose specific value in the previous laws is only attained under special circumstances. […] This is the general approach of physics: to resolve constants into functions, to find more general laws that contain the previous law as a special case. No end of this process is in sight. (Reichenbach 1916/2008, p. 115) Along with Cassirer and the Marburg tradition, Reichenbach’s doctoral thesis takes as a starting point science in its actuality and regressively tries to reconstruct its conditions of possibility, in line with the transcendental method presented in Kant’s Prolegomena. It is this same idea that will be at the core of Reichenbach’s wissenschaftsanalytische Methode, the inductive method of logical analysis of science that he will more fully elaborate in his Habilitation thesis.19 This method should lead to the identification of the actual principles presupposed by empirical sciences. It essentially represents the tool for detecting contradictions when comparing sets of coordinating principles (with their corresponding laws of nature) belonging to two different systems, one of which has developed from the other. Reichenbach will show the inconsistency of the Kantian System with the Einsteinian one precisely making use of this regressive approach. Most interestingly, in his Habilitation thesis these remodelled Cassirerian elements cooperate to shape a crucial, explanatory strategy that appears under the name of “procedure of the continuous expansion” (Verfahren der stetigen Erweiterung).20 The idea is that the inclusion of the old theory into the new one occurs as a generalisation of certain principles of knowledge—more specifically, coordinating principles constituting the actual concept of knowledge—that have become inconsistent with the old system. Contradictions can emerge and a generalisation (or extension) of a determinate system can also be obtained within the system itself, by virtue of this specific procedure. As he elucidates in 1920, [t]he contradiction that arises if experiences are made with the old coordinating principle by means of which a new coordinating principle is to be proved disappears on one condition: if the old principle can be regarded as an approximation [Näherung] for certain simple cases. Since all experiences are merely approximate laws [Näherungsgesetze], they may be established by means of the old principles; this method does not exclude the possibility that the totality of experiences inductively confirms a more general principle. It is logically admissible and technically possible to discover inductively new coordinating principles that represent a successive approximation of the principles used until now. We can call such a generalisation “successive” [stetig] because for certain approximately realised cases the new principle is to converge toward the old principle with an 19 And indeed, Reichenbach acknowledged the common approach in both writings, as he underlines in (1920/1965), p. 75: “The author was able to carry through such an analysis for a special domain of physics, for the theory of probability. It led to the discovery of an axiom that has fundamental significance for our understanding of physics, and as a principle of distribution finds its place next to causality, a principle of connection.” 20 The English edition quite freely translates it with “method of successive approximations”.
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exactness corresponding to the approximation of these cases. We shall call this inductive procedure the method of successive approximations [Verfahren der stetigen Erweiterung]. (Reichenbach 1920/1965, pp. 68–69) These are all motifs that Reichenbach inherited from Cassirer, although deprived of the regulative, ideal dimension in which they were originally embedded. Incidentally, this is a decisive element in Reichenbach’s 1920 book, for the absence of this dimension could well imply a move towards realism. In fact, in an account of a progressive generalisation of principles, there are two possible directions to take: either take a stance towards a form of dynamical idealism, as is the case of Cassirer (and somewhat of the 1920 Reichenbach), or take a step towards realism, a position that Reichenbach will explicitly embrace for the first time in “Metaphysics and Natural Science” (1925a/1978). The roots of this shift can be seen in the nuanced difference that there is between Reichenbach and Cassirer in assigning or not assigning a regulative meaning to the approximate generalisation of principles in the progress of science. Thus, it is clear that Reichenbach intends his early interpretation of Zuordnung to stay in line with that of his teacher.21 Nonetheless, in Reichenbach’s doctoral thesis the direction of the coordination is not only that of taking the mathematical structures and casting them onto the empirical material, almost assigning, as it were, the order from above, as it appears in Cassirer’s work. As I mentioned above, in Reichenbach’s interpretation the empirical sphere plays the crucial role of imposing the range of possible values and “controlling” the adequacy of the function through the given empirical frequency observed in the single case, and from there applied to the class which it belongs to. To accentuate the interesting difference with respect to the Kant-Cassirerian tradition Reichenbach intends to adhere to, let us recall that in Cassirer’s paper of 1907 the mathematical syntheses provide the ground for using the physical ones. Mathematics, there, grants the lawfulness of physics, whereas here it is the physical considerations themselves that select and warrant that a certain mathematical structure is applicable to reality. This takes place only by accepting (pace Kant) the constitutively imperfect character of the coordination of the mathematical sphere to the physical one. In other words, although Reichenbach does not extend this discussion further, the relations of primacy are the reverse in the two accounts. We shall soon see how this idea will be fruitfully strengthened in his 1920 monograph.
3 Elements of a revised “Kantian” proposal 3.1 Mathematical versus physical coordination The declared aim of The Theory of Relativity and A Priori Knowledge is the revision of the Kantian doctrine of the a priori in light of the theory of relativity. Along the same direction undertaken in the doctoral thesis, Reichenbach elaborates further on 21 Reichenbach attended Cassirer’s lectures on German idealism in the winter semester 1913–1914, while he was enrolled at the University of Berlin. In the bibliographic references to his (1916/2008), Reichenbach only mentions Cassirer (1910/1923), so it is not clear whether he was familiar also with his (1907).
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the issue of coordination, but now integrating Hilbert’s axiomatic model.22 In set theoretic language, he explains that the difference between mathematical and physical coordination depends on the difference between the mathematical and the physical types of concept. The former is “univocally determined by the axioms and definitions of mathematics,” i.e., it is implicitly defined through its relation to the other mathematical concepts so that it “receives meaning and content within the framework of definitions.”23 Definitions, in fact, indicate how a term is to be related to the others, whereas the rules according to which concepts are defined are given by axioms. The latter, however, cannot be determined by axioms and definitions. Whatever system of mathematical equations we may create and use to represent physical events, it will lack a fundamental statement, that is, the assertion concerning the validity of that system for reality. This fact implies a decisive asymmetry in the two types of coordination, precisely as Reichenbach underlined in his (1916/2008). But in the 1920 account, there is a new element that he acquires after reading Schlick’s General Theory of Knowledge (1918/1974): the concept of univocality (Eindeutigkeit). In the mathematical coordination both coordinated sets are wholly and univocally (eindeutig) determined in their terms and internal order. According to Reichenbach, the peculiarity of the coordination carried out in the cognitive process is that, when the set of well defined fundamental equations of physics is coordinated to the empirical matter, we have to face the very fact that one side of this coordination is not defined; neither can we define the direction of the coordination. As Reichenbach makes clear, the defined side does not carry its justification within itself; its structure is determined from outside. Although there is a coordination to undefined elements, it is restricted, not arbitrary.24 This restriction is called “the determination of knowledge by experience.” We notice the strange fact that it is the defined side that determines the individual things of the undefined side, and that, vice versa, it is the undefined side that prescribes the order of the defined side. The existence of reality is expressed in this mutuality of coordination. (Reichenbach 1920/1965, p. 42) Similarly to that of mathematical coordination, a criterion of univocality for physical coordination is introduced. We can deem a physical theory true when it leads to a consistent coordination, that is, when the coordination is univocal (or empirically confirmed). To characterise cognitive coordination as univocal means indeed that “a physical variable of state is represented by the same value resulting from different empirical data.” In this account, perceptions provide the required criterion.25 Furthermore, univocality is also essential for the consideration of a system of principles as a whole when compared to reality, as we shall see below. 22 This is an element that comes into his account after studying Schlick (1918/1974). 23 Reichenbach (1920/1965, pp. 34–35). 24 That there is a limit to the arbitrariness of physical coordination is a crucial point that Reichenbach will
keep emphasising also later, to characterise his account with respect to the conventionalists’. See especially his correspondence with Schlick, which I mention below, footnote 30. 25 Reichenbach (1920/1965, p. 44).
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The revised critical question now becomes: what principles allow for univocality? Reichenbach’s answer is that Kant’s system can be modified and made compatible with the evolution of science only by changing his doctrine of the a priori and by determining which principles of the coordination are the new ones, and what their new function is. 3.2 Two meanings of “a priori” and the distinction between axioms of coordination and axioms of connection As is well known, in The Theory of Relativity and A Priori Knowledge Reichenbach proposes an interesting version of the a priori—the so-called “relativized a priori”26 — that he views as divided according to its two components: “First it means ‘necessarily true’ or ‘true for all times,’ and secondly, ‘constituting the concept of object’.”27 Although the theory of relativity has shown the indefensibility of the first component, in 1920 Reichenbach still supported the second form of synthetic a priori as a constitutive element of knowledge in general, but revisable according to the evolution of science. Thus, again following an idea expressed by Cassirer, Reichenbach emphasised that “a priori” means “before knowledge,” but not “for all time” and not “independent of experience.” 28 Hence, he gave an interpretation of the cognitive coordination as based on contingent, coordinating principles that we need to presuppose in order to form, or constitute univocally, the objects of (scientific) knowledge—more specifically, in this case, the objects of physics. All these principles (including probability and causality) are constitutive a priori, yet nevertheless fallible, and theory-specific. One of the most interesting features of this little but very rich monograph is the repetition and re-elaboration of the distinction between the principle of the lawful distribution (probability) and the principle of the lawful connection (causality), which Reichenbach introduced in his doctoral thesis. Now this differentiation is presented in the form of a distinction between certain principles of knowledge called the axioms of coordination (Zuordnungsaxiome) and the axioms of connection (Verknüpfungsaxiome), where only the first ones are truly constitutive, even though contingently.29 In 1920, Reichenbach sketched an axiomatic conception of physics by stating a sharp distinction between these two types of axioms—a distinction that will later fall 26 To be sure, this expression was coined by Michael Friedman. Cf. his (1999, Chap. 3), and references therein. 27 Reichenbach (1920/1965, p. 48). 28 Reichenbach (1920/1965, p. 48). Cf. Cassirer (1910/1923, p. 269): “A cognition is called a priori not
in any sense as if it were prior to experience, but because and in so far as it is contained as a necessary premise in every valid judgment concerning facts.” [emphasis in the original] As Ryckman notices, “with this modification, the way is open towards viewing, as do Poincaré, Schlick, Einstein and Reichenbach, conventions as having the logical status of a priori elements.” (Ryckman 1991, p. 85) 29 Incidentally, some features assigned to causality in the dissertation are now integrated into the notion of probability. See below, Sect. 4.3. As I briefly indicated in footnote 10, in Reichenbach’s writings of the late 1920s, and especially in those of the 1930s, probability, instead of completing the principle of causality, will end up simply founding it, and causality will be expressed in probabilistic terms, like in (1925b/1978)—this in opposition to the approach displayed in the dissertation, where probability was first defined on the basis of causally dependent and independent trials.
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victim to his crucial shift from (constitutive) principles of coordination to (conventional) coordinative definitions. This shift followed a famous exchange with Moritz Schlick in autumn 1920, at the end of which Reichenbach was urged to accept the conventional nature of his constitutive principles.30 The axioms of connection are the empirical laws of physics, the fundamental equations of a theory. Reichenbach gets the term “Verknüpfungsaxiome”, which can be traced back to Hilbert’s Grundlagen der Geometrie, from the interpretation presented in an article by Arthur Haas (1919).31 There, Haas describes the history of the physical axiomatisation as an evolution in the direction of a more unitary image of nature, that is, an evolution in terms of a wider connection (Verknüpfung) created by the laws within different fields. In this respect, formulating new physical laws means disclosing previously unseen connections.32 Consequently, Reichenbach considers the axioms of connection as empirical laws in the usual sense, involving already sufficiently well defined concepts. Yet, as we have seen, the concepts in such equations require further qualification, viz., the assertion that they are valid for reality. It is only through the axioms of coordination that how these concepts can de facto apply to reality can be shown. And that is precisely their role: providing a “physical” definition of the concepts occurring within the axioms of connection. In that sense, the former determine the meaning of the latter and they are therefore constitutive of the concept of the physical object. Thus, the axioms of coordination determine the rules of the application of the axioms of connection to reality, that is, they determine the rules of the connection. Finally the axioms of coordination are required in order to state the univocal coordination of these concepts to reality. In Reichenbach’s words: Although [the coordinating principles] are prescriptions for the conceptual side of the coordination and may precede it as axioms of coordination, they differ from those principles generally called axioms of physics. The individual laws of physics can be combined into a deductive system so that all of them appear as consequences of a small number of fundamental equations. These fundamental equations still contain special mathematical operations; thus Einstein’s equations of gravitation indicate the special mathematical relation of the physical variable Rik to the physical variables Tik and gik . We shall call them, therefore, axioms 30 This exchange consists of five letters, in the order: HR 015-63-23, Schlick to Reichenbach, 25 September 1920; Reichenbach to Schlick, 17 October 1920 (in the Schlick Collection at the Wiener Kreis Stichting, Amsterdam); HR 015-63-22, Schlick to Reichenbach, 26 November 1920; HR 015-63-20, Reichenbach to Schlick, 29 November 1920; HR 015-63-19, Schlick to Reichenbach, 11 December 1920. This correspondence has been largely referred to and analysed in the secondary literature. Just to mention a few, see Coffa (1991, pp. 201–206), Hentschel (1990, 507 ff), Friedman (1999, pp. 62–65) and Ryckman (2005, 51 ff). Further, this exchange is also mentioned by Schlick in his (1921/1979)—a review of Cassirer (1921/1923)—and by Reichenbach in his (1922a/1959). All these letters are now entirely available at http:// echo.mpiwg-berlin.mpg.de/content/modernphysics/reichenbach1920-22. 31 The paper was emblematically entitled “Die Axiomatik der modernen Physik”—an idea that the young Reichenbach certainly found fascinating. 32 In his paper, Haas presents a survey of the axioms of physics (i.e., the axioms of connection) that he reckons complete. But although Reichenbach welcomes this classification, in footnote 15 to p. 54 he criticises Haas for not seeing the necessity of introducing physical axioms of coordination. Cf. Reichenbach (1920/1965, p. 111).
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of connection. The axioms of coordination differ from them in that they do not connect certain variables of state with others but contain general rules according to which connections take place. In the equations of gravitation, the axioms of arithmetic are presupposed as rules of connection and are therefore coordinating principles of physics. (Reichenbach 1920/1965, p. 54) Additionally, they must also be of such kind that they make the coordination univocal. Even if there are arbitrary elements in the principles of knowledge, their combination is no longer arbitrary. This is a crucial point, Reichenbach maintains, that had not been sufficiently accounted for by the conventionalists.33 Having said all this, however, the question remains whether among the axioms of coordination there are some that are more significant, or, to put it differently, whether there are principles that are “more constitutive” than others. Coordinating principles refer to the conceptual side of the coordination, and are purported to define what is real. Reichenbach indicates a non-exhaustive list of principles, like time and space, because they allow for the definition of a single real point by means of four numbers.34 Other important axioms of coordination are the principle of genidentity (or identity over time) and the principle of probability. This last principle is the variant of the principle of the lawful distribution that we encountered above and that is relativized, being still constitutive but revisable. This principle now simply “defines when a class of measured values is to be regarded as pertaining to the same constant.”35 The other principle is one that occurs for the first time in Reichenbach’s writings, with an expression, genidentity, that was officially coined by the Gestalt psychologist Kurt Lewin in 1922.36 Of this principle Reichenbach only says that it indicates how physical concepts have to be connected in sequences in order to define “the same thing remaining identical with itself in time.”37 For example, [w]hen we speak of the path of an electron, we must think of the electron as a thing remaining identical with itself; that is, we must make use of the principle of genidentity as a constitutive category. This connection between the conceptual category and the experience of coordination remains an ultimate, not as an analysable residue [nicht analysierbarer Rest]. But this connection clearly defines a class of principles that precede the most general laws of connection as presuppositions of knowledge though they hold as conceptual formulas only for the conceptual side of the coordination. These principles are so important because they define the otherwise completely undefined problem of the cognitive coordination. (Reichenbach 1920/1965, p. 55) What is striking in this account of the coordinating principles is the fact that even though Reichenbach does not provide a detailed account of all these axioms, he does 33 See also above, footnote 24. 34 Reichenbach (1920/1965, p. 53). 35 Reichenbach (1920/1965, pp. 54–55). 36 Lewin (1922). 37 This principle will play an important part in both his (1928/1958) and (1956), as I briefly mention in
Sect. 4.3.
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not seem to assign them the same significance. These last two principles in particular hold a pivotal position and play a more fundamental role with respect to the other coordinating axioms. Probability and genidentity are both indeed required by all other coordinating axioms that we use to assign content to the concepts occurring in the connecting axioms. The values appearing within the equations receive their physical meaning by virtue of the coordinating axioms, but the act of measuring itself is primarily dependent upon the principle of probability, as well as, more generally, on the principle of genidentity. These two constitutive axioms are, so to speak, meta-axioms of coordination: they are constitutive of the constitutive axioms, in that they represent an essentially underlying level of constitutivity, as I will argue more in detail in 4.1. The distinction between connecting and coordinating axioms has been understandably regarded as a very striking version of the relativized a priori.38 In The Theory of Relativity and A Priori Knowledge, this distinction serves well as a foundation for the outline of a model of scientific change, that is, of the evolutionary transformation in the concept of knowledge and the consequent shift in the logical conditions presupposed by the new object of physical knowledge. To illustrate how the advance from theory to theory takes place in light of these two types of axioms, Reichenbach uses the example of the metric. In Newtonian physics, he explains, the Euclidean metric was a coordinating axiom because it determined “the relations according to which space points combine to form extended structures independently of their physical quality.” In Einstein’s physics, on the contrary, the metric becomes a function of the totality of other surrounding bodies. Thus, Reichenbach concludes, “the metric is no longer an axiom of coordination but has become an axiom of connection.”39
4 Further developments in 1920 4.1 Coordinating properties, not just structures The distinction between axioms is a key element in the framework of this monograph, but unfortunately Reichenbach does not go into it more thoroughly. To be sure, The Theory of Relativity and A Priori Knowledge was conceived and written in only a few days in the spring of 1920.40 The manuscript, entirely available at the Pittsburgh Archives, was ready for publication, with minor modifications, during the summer of 1920. This material makes it clear that the distinction between axioms in these terms was inserted only later in revisions. Interestingly, in the drafts of this work there are traces of another specification in a marginal note, added later but eventually omitted from the published version. With respect to the passage of p. 54 that I have quoted above, Sect. 3.2, in this note he writes: 38 Friedman (1999, 60 ff). 39 Reichenbach (1920/1965, p. 100) [emphasis in the text]. See Friedman (1999, p. 66), for his reading of
Reichenbach’s account of theory change according to this scheme. Friedman’s own account of mathematical-physical theories has a tripartite structure (a mathematical, a mechanical and a proper physical-empirical part) and is partly shaped by Reichenbach’s. See his (2001, pp. 79–80). 40 Cf. his autobiographical notes of October 1927, HR 044-06-23.
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The specific laws can be combined into a deductive system so that all of them appear as consequences of a few fundamental equations. We will call these equations axioms of connection because they express the connection between the specific physical magnitudes. Opposite to these are the axioms of coordination, which represent the properties of all bodies, reduced to a minimum of propositions. An example of coordinating axioms of old physics are the axioms of geometry; Maxwell’s equations are an example of connecting axioms.41 (HR 026-03-01, 56 bis) Now, the Zuordnungsaxiome represent the possibility that the general properties of all bodies be reduced to a minimum of propositions. Here, the coordinating axioms are in fact entitled to deal with the properties of bodies. The system of equations is the general framework in which the connection among real things is actually achieved. Or better, this system represents the more general framework into which things have to be cast if they have to be thought of as real. This is an interesting specification, for above all it does not primarily associate the coordination directly with the idea that we saw at play in the dissertation, that is, the idea of “merely” representing a bridge between the formal structures and the real ones. Let’s briefly summarise what we have seen so far. In the doctoral thesis, the coordination was carried out by means of the notion of approximation. Formal structures could describe physical structures only by way of a certain approximation. The principle of probability was the tool Reichenbach implemented in order to treat the issue of approximation in formal terms and thus fill the gap between the two structures. In (1920/1965), the situation is complicated by the fact that not only is a principle of probability required in the same sense of the doctoral thesis, but there are also several other principles of the coordination (i.e., application) of these mathematical structures that are not strictly speaking related to the principle of probability. Some of these principles are, for instance, the axioms of arithmetic, which are presupposed as rules of connection in the equations of gravitation, as well as in allowing for the representation of certain physical relations by means of mathematical objects. This is the case of physical forces that we identify as vectors. It must be emphasised, though, that even if a number of other axioms of coordination can be isolated within the scientific construction, they also necessarily presuppose the principle of probability at a higher level, as the ultimate principle of the effective representation of material objects in any formal (mathematical) expressions. In my reading, probability is a meta-constitutive, coordinating axiom for it enables the other axioms of coordination to really perform the coordination of certain structures, like space and time, or the axioms of arithmetic, to real things (objects). Beside the principle of probability, the principle of genidentity also appears to be “more constitutive” than other constitutive principles. In fact, before deciding to coordinate 41 “Man kann die Einzelgesetze unter sich in ein deduktives System bringen, sodass sie alle als Folgerungen einiger weniger Grundgleichungen erscheinen. Wir wollen diese, da sie die Verknüpfung der einzelnen physikalischen Grössen angeben, als Verknüpfungsaxiome bezeichnen; wir stellen sie zu den Zuordnungsaxiomen gegenüber, welche die allgemeinen Eigenschaften aller Körper, auf ein Minimum von Sätzen reduziert, darstellen. Ein Beispiel für Zuordnungsaxiome der alten Physik sind die Axiome der Geometrie, für Verknüpfungsaxiome die Maxwellschen Gleichungen.” (HR 026-03-01, 56 bis)
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whatever formal structure to the unformed reality in order to constitute the object, an evident requirement is that this object persists over time as the same object. The idea behind both principles is that each eventually supplies some very general tool for the conceptual identification that is called for when applying formal structures to reality.
4.2 Axioms of connection, axioms of order and axioms of coordination Earlier I mentioned that in the original manuscript of The Theory of Relativity and A Priori Knowledge a distinction of axioms in terms of connection and coordination was introduced by Reichenbach only later in revisions. Moreover, among Reichenbach’s manuscripts and various drafts for the Axiomatik (1924/1969), there is evidence of a later attempt to clarify and further elaborate on this question in an unpublished short paper entitled “Der Begriff des Apriori und seine Wandlung durch die Relativitätstheorie” (The concept of a priori and its transformation through relativity theory).42 There, Reichenbach returns to Hilbert’s terminology of the Grundlagen, now presenting three different kinds of axioms: beside the previous two, he adds a third kind, the axioms of order (Axiome der Ordnung). These axioms share exactly the same features with the axioms of coordination. They are both constitutive a priori in the revised Kantian sense of (1920/1965), they are fallible (as is the distinction among axioms itself) and theory-specific. Unfortunately, this interesting distinction is only outlined in the paper, and Reichenbach does not expressly formulate the new axioms, but they clearly tend to be assimilated into the process of constituting a framework in which the representation of real things can in principle be embedded. However, these new axioms, which are placed between the connecting and the coordinating axioms, need to be supplemented by the axioms of coordination. Let us follow Reichenbach’s manuscript and start with the axioms of connection. They are again characterised in the same way we have seen so far, namely as special laws of physics. These axioms describe special relations, more specifically laws of experience (Erfahrungsgesetze). That is, they define individual things (Einzeldinge). The axioms of coordination and of order do not define individual things, but rather determine more generally what the object (Gegenstand) is. For instance, “the probability function determines identity.” This is to be understood in the same terms we have seen before, i.e., physical magnitudes can be represented by the same value resulting from different empirical data by virtue of the probability function. The constitutive axioms also specify the measurable relations of the objects that lead to the connection. In this, he continues, they constitute the physical, therefore measurable object. So it is right to say that the phenomena (Dinge qua Erscheinungen) conform to our thought. But this does not exclude the converse, namely that our thought is directed
42 HR 024-15-02.
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by them. That is why the special form of the coordinating and ordering axioms has to be modified when they no longer can ground the representation of our experience.43 In this manuscript, Reichenbach basically formulates a number of questions and sketches only a few answers. Despite the lack of a further elaboration, this text shows that the classical distinction in terms of coordinating and connecting axioms has to be construed differently from the way it is generally understood in the secondary literature. Interestingly, indeed, he asks: “How is cognition as coordination of fictitious magnitudes to reality possible? And how is the ordering of these magnitudes possible?” According to Reichenbach, only insofar as we make specific presuppositions about the coordination and the ordering can we define what an identical and real object is, and how it can be related to other things. Further, What is a real law in this framework? A real law is what remains invariant under coordinate transformations. What does measurability mean? Measurability means to assign an arbitrary order within the coordinates. A real thing is what appears in such laws as magnitude and that is measured according to these laws.44 (HR 024-15-02) Thus, there are two layers of constitutivity to be differentiated. Accordingly, the fundamental question regarding knowledge is to be answered on two levels. Cognition means, on the one hand, the coordination of certain fictitious magnitudes to reality and, on the other, the act of ordering these magnitudes within a specified structure. In the cognitive process, the real thing is what appears as magnitude within—and is measured according to—specific laws. But measuring requires a pre-constituted order. This order, in turn, acquires its meaning only by being referred to actual objects that can be identified according to certain ultimate principles. Therefore, in this unpublished manuscript, the cognitive component in the process of knowledge is deployed first by creating a determinate modality for ordering, and then by coordinating the
43 In his words: “Es gibt: Axiome der Zuordnung, der Ordnung, der Verknüpfung. Die V.[erknüpfungs] A.[xiome] sind die spez. Gesetze der Physik, z. B. Rik − 21 gik R = Tik . Sie geben nur die spez. Relationen, Erfahrungsgesetze. (Definieren die Einzeldinge). Die beiden ersten sind apriori. D.h. nichts zeitliches: es hat keinen Sinn zu sagen, dass sie sich nicht ändern. […] Ihre spez. Form ist durch den Stand unserer Erfahrung bestimmt. […] Aber: sie bestimmen welches der Gegenstand ist (W[ahrscheinlichkeits]f[un]kt[ion] bestimmt Identität), und welches die messbaren Relationen des Gegenstands sind, die zur Verknüpfung führen (ds 2 =). Sie konstituieren den physikalisch messbaren Gegenstand. Darum ist es richtig, dass sich die Dinge (d. Erscheinung) nach unserem Denken richten. Aber das schliesst die Umkehrung nicht aus: dass sich unser Denken nach den Dingen richtet. Vielmehr werden wir die spez. Form der Z.[uordnungs]A.[xiome] und O.[rdnungs]A.[xiome] ändern, sowie wir damit die Erfahrung nicht mehr darstellen können.” (HR 024-15-02) 44 “Frage: Wie ist die Erkenntnis als Zuordnung von fikt.[iven] Grössen zur Wirklichkeit und als Ordnung dieser Grössen möglich? Antwort: Nur dadurch, dass man bestimmte Vorauss.[etzungen] für die Zuordnung und die Ordnung macht, welche definieren, was ein identische[r], reale[r] Gegenstand ist und wie e[r] mit andern Dingen in Relation gebracht werden kann. […] Die Relativitätstheorie hat gezeigt, dass apriore Sätze wandelbar sind. Aber sie hat das nicht in jener flachen Form vollzogen wie die Empiristen, die da sagen ‘alles ist Erfahrung’, sondern sie hat eine wirkliche Wandlung des Gegenstandsbegriffes vollzogen. Reales Gesetz ist das, was invariant ist gegen Tr[ansformation] d. Koord[inaten]. Messbarkeit heisst beliebige Ordnung innerhalb d. Koord[inaten]. Wirkliches Ding ist das, was in solchen Gesetzen als Grösse auftritt u. nach solchen Gesetzen gemessen wird.” (HR 024-15-02)
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ordered structure to actual things (or also, by extension, to events), i.e., things (or events) that can be recognised as that specific individual thing (or event). In other words, here the Axiome der Zuordnung are concerned with stating what can be isolated and identified as the “real” to be ordered in the flux of perception. This ordering is possible only insofar as we have a framework in which the “real” can be inserted. This is not to be understood as the set of physical laws, but as the framework enabling these laws to be conceived. As in the example given in this manuscript, which Reichenbach also employed in (1920/1965), space and time are not characterised by and within the laws of physics, but rather provide the framework in which it is in principle possible to identify real things with the addition of the laws of physics. In the same sense, the axioms of arithmetic referring to the vectors are presupposed when we treat the force as a mathematical vector. But the final step in the coordination to reality is performed by way of another kind of coordinating principles. Before, I suggested that in the 1920 account there are two coordinating principles that appear to be more significant than others, namely the principle of genidentity and the principle of probability. These are clearly to be located at the level of the coordinating principles of the account that Reichenbach sketches on this occasion. The idea of the two-level co-ordination is confirmed by this manuscript, where the two constitutive moments are separated according to the two different functions they embody and serve in cognition.
4.3 A conventionalist shift? After the correspondence with Schlick and his consequent “conventionalist shift”, around the end of 1920, Reichenbach no longer talks about constitutive principles.45 The first development of this discussion is apparent in a report that he delivered at the Deutscher Physikertag in Jena, in September 1921, on his plan to axiomatise relativity theory.46 The fundamental methodological innovation of this short paper is to present an axiomatisation in which the starting point consists of making use of axioms that can ideally make direct contact with empirical (or experimentally testable) facts, and of complementing them by introducing a number of coordinative definitions for the construction of the conceptual content of the theory.47 In his second monograph on relativity theory, the Axiomatik (1924/1969), Reichenbach emphasises the importance of this novel approach, that it makes a clear-cut separation between the conventional component (the coordinative definitions) and the factual one (the empirical axioms). In fact, the axiomatisation has to be primarily based on observable facts, and it is only from these facts that the abstract conceptualisation will derive. For this approach Reichenbach now coins the expression “constructive
45 This expression actually last appears in (1922b/2006, pp. 152–154), but Reichenbach curiously combines it with a conventionalist stance. 46 Reichenbach (1921/2006). 47 Reichenbach (1921/2006, p. 45).
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axiomatisation”,48 a clear development of the regressive method—the wissenschaftsanalytische Methode—defined in (1920/1965). Despite the sharp distinction between definitions and axioms, in the Axiomatik, the principle of probability, in the form of the principle of induction (or of inductive simplicity), nevertheless reappears in the very general group of “epistemological principles”, i.e., principles presupposed by any factual statements: One of [these principles] is the assumption that the experiment, if subsequently repeated, will always yield the same result, the assumption of causality. Furthermore, the principle of induction is presupposed; for instance, certain values of measurement will be connected by a simple curve and this curve will be called an empirical law. (Reichenbach 1924/1969, p. 5) As is well known, all these issues will maintain a focal position in Reichenbach’s philosophical system. Let me just recall that as far as the principle of genidentity is concerned, Reichenbach no longer mentions it in his (1924/1969). However, this principle is in the background of his causal theory of time, even though Reichenbach will explicitly re-acknowledge its importance only in The Philosophy of Space and Time (1928/1958). There, he describes it as a very deep principle of natural knowledge (ein sehr tiefes Prinzip der Naturerkenntnis), an empirical but absolutely essential principle of time order without which it would be hard to conceive things and events in their individuality.49 What Reichenbach means by simply claiming that genidentity is an empirical principle is not completely clear. Neither does he seem to solve the issue in his posthumous The Direction of Time (1956), where this principle still plays a crucial, and actually constitutive, role. But I shall leave this discussion for another occasion. To return to the question of Reichenbach’s shift towards conventionalism, now we can ask: to what sort of assertions is this shift to be applied? Let us take the classic example of the coordinative definition represented by the concept of length unit elaborated in his 1924 axiomatisation. This concept is a mathematical one, and it states that “a certain particular interval is to serve as [standard of] comparison for other intervals.” The physical definition, to the contrary, needs to be able to project, as it were, the mathematical concept onto the unformed reality. But being coordinative, and thus conventional, such a definition is also arbitrary. In our example, it is represented by the designator of the Paris standard meter as the unit of length. This definition clearly presupposes the mathematical one. Therefore, he continues, physical (or coordinative) definitions are kinds of real definitions that coordinate a mathematical definition to a 48 As he elucidates, “the constructive axiomatisation is more in line with physics than is a deductive one, because it serves to carry out the primary aim of physics, the description of the physical world.” (Reichenbach 1924/1969, p. 5) 49 As he explains in 1928, this principle “enables us to speak of a unique time order and a unique now-point. Furthermore, it makes possible the concept of the individual that remains identical during the passage of time. It is therefore the most important axiom regarding time order, and we realize to what an extent the familiar concept of time order is based on this characteristic of causality. Of course, this axiom is a result of experience [es ist klar, daß es sich in diesem Axiom um einen Erfahrungssatz handeln kann].” (Reichenbach 1928/1958, pp. 142–143)
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“piece of reality”. Since the coordination must be univocal, the necessary requirements for this purpose are given by the axioms.50 According to what we have seen above, we can regard the axioms of order of the unpublished manuscript as the coordinative definitions of the constructive axiomatisation. The main feature that Reichenbach assigns them in that paper is that they determine the measurable relations that lead to the connection (that is, to a possible empirical law). Reichenbach also adds that measurability means to attribute an arbitrary order within the coordinates. Already in The Theory of Relativity and A Priori Knowledge, Reichenbach refers to the classical example of the length of a physical rod as “defined by a large number of physical equations that are interpreted as ‘length’ with the help of readings on geodetic instruments.”51 To conclude, in (1920/1965) there are clearly coordinating principles that are, as it were, constitutive of the constitutive principles. These cannot be turned into conventions, as is the case of probability. Although the spirit of Reichenbach’s constructive axiomatisation is oriented towards a conventionalist stance, the conventions only apply so far as a theory-specific package is concerned. In fact, his alleged conventionalist shift concerns only the Axiome der Ordnung, but not all constitutive axioms. 5 Relativizing the relativized a priori What consequences can be drawn from this new reading? If my interpretation of the two-level constitutive account of Reichenbach’s principles of knowledge is correct, the relativized a priori needs to be relativized in turn. In Reichenbach’s model, the constitutive order axioms can be turned into coordinative definitions (still holding an a priori status), whereas other (meta-)constitutive, coordinating principles, such as probability and genidentity, are relativized, or even “absolutised”, and turned into different assumptions in his later works. Although an attempt to provide a firmer axiomatic footing to the set of principles of knowledge is inscribed in Reichenbach’s empiricist tendency, he will not be able to do away with these two assumptions. He will try to provide a different kind of justification for probability, but he will uncritically assume genidentity simply based on the motivation that things would hardly be conceivable otherwise. This is not the place to start a discussion on the possible implications of a twolevel account of the constitutive, relativized a priori, but this tripartite distinction among axioms could be helpful in developing a more structured framework. As in Reichenbach’s account, a double layer of a priori could be envisaged, namely a set of very fundamental constitutive principles that should appear to be valid for scientific objects at the most general level, together with some subsets of other constitutive principles, which would themselves depend in turn on the most fundamental ones. These subsets would be specific to and would function in the special sciences they would have to be applied to. In conjunction with these, other sub-subsets of connecting axi50 Or, as he writes, “are derived from the facts laid down by the axioms.” Cf. Reichenbach (1924/1969, pp. 7–9). 51 Reichenbach (1920/1965, p. 40).
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oms could be thought of in terms of individual laws pertaining to each specific domain of science. The current debate over the possibility of maintaining some form of constitutive principles in the early Reichenbachian fashion should benefit from his lesson, and should, moreover, take account of the fact that the constitutive principles are not only different among themselves horizontally, or from a qualitative point of view, but should also be structured within themselves, as it were, vertically. Acknowledgements Special thanks goes to the Pittsburgh Centre for Philosophy of Science, which hosted me during the academic year 2008–2009, and to the group of visiting fellows for valuable comments on a previous draft of this paper, in particular to Claus Beisbart, Chris Pincock and Erik Curiel. Research for this paper was supported by a grant of the Swiss National Science Foundation. I also wish to thank the Directors of the Archives of Scientific Philosophy in Pittsburgh and Konstanz for their permission to quote from the Hans Reichenbach Collection. I am especially grateful to Brigitte Parakenings from the Konstanz Archives for her valuable help in finding and supplying unpublished material. All rights are reserved.
References ˇ Capek, M. (1958). Reichenbach’s early Kantianism. Philosophy and Phenomenological Research, 19(1), 86–94. Cassirer, E. (1907). Kant und die moderne Mathematik. Kant-Studien, 12, 1–49. Cassirer, E. (1910). Substanzbegriff und Funktionsbegriff. Untersuchungen über die Grundfragen der Erkenntniskritik. Berlin: Bruno Cassirer. Translated as Substance and function. Chicago: Open Court, 1923. Cassirer, E. (1921). Zur Einstein’schen Relativitätstheorie. Erkenntnistheoretische Betrachtungen. Berlin: Bruno Cassirer. Translated as Einstein’s theory of relativity. Chicago: Open Court, 1923. Coffa, J. A. (1991). The semantic tradition from Kant to Carnap: To the Vienna station. Cambridge: Cambridge University Press. Friedman, M. (1999). Reconsidering logical positivism. Cambridge: Cambridge University Press. Friedman, M. (2001). Dynamics of reason. Stanford: CSLI Publications. Friedman M. (2005). Ernst Cassirer and the philosophy of science. In G. Gutting (Ed.), Continental philosophy of science, 71–83. Oxford: Blackwell Publishing. Haas, A. (1919). Die Axiomatik der modernen Physik. Die Naturwissenschaften, 7, 744–750. Hentschel, K. (1990). Interpretationen und Fehlinterpretationen der speziellen und allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins. Basel: Birkäuser. Lewin, K. (1922). Der Begriff der Genese in Physik, Biologie und Entwicklungsgeschichte. Berlin: Springer. Reichenbach, H. (1916). Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit. Leipzig: Barth. Translated as The concept of probability in the mathematical representation of reality, F. Eberhardt & C. Glymour (Eds.). Chicago: Open Court, 2008. Reichenbach, H. (1920). Relativitätstheorie und Erkenntnis apriori. Berlin: Springer. Translated as The theory of relativity and a priori knowledge, M. Reichenbach (Ed.). Berkeley: University of California Press, 1965. Reichenbach, H. (1921). Bericht über eine Axiomatik der Einsteinschen Raum-Zeit-Lehre. Physikalische Zeitschrift, 22, 683–686. Translated as ‘A report on an axiomatization of Einstein’s theory of space-time’, in Reichenbach (2006), 45–55. Reichenbach, H. (1922a). Der gegenwärtige Stand der Relativitätsdiskussion. Logos, X, 316–378. Partially translated as ‘The present state of the discussion on relativity’, in Reichenbach (1959), 1–45. Reichenbach, H. (1922b). La signification philosophique de la théorie de la relativité. Revue philosophique de la France et de l’Étranger, 94, 5–61. Translated as ‘The philosophical significance of relativity’, in Reichenbach (2006), 95–160. Reichenbach, H. (1924). Axiomatik der relativistischen Raum-Zeit-Lehre. Braunschweig: Fried. Vieweg & Sohn. Translated as The axiomatization of the theory of relativity, M. Reichenbach (Ed.). Berkeley: University of California Press, 1969.
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Reichenbach, H. (1925a). Metaphysik und Naturwissenschaft. Symposion, 1(2), 158–176. Translated as ‘Metaphysics and natural science’, in Reichenbach (1978), Vol. I, 283–297. Reichenbach, H. (1925b). Die Kausalstruktur der Welt und der Unterschied von Vergangenheit und Zukunft. Sitzungsberichte der Bayerische Akademie der Wissenschaft, November: 1933–1975. Translated as ‘The causal structure of the world and the difference between past and future’, in Reichenbach (1978), Vol. II, 81–119. Reichenbach, H. (1928). Philosophie der Raum-Zeit-Lehre. Berlin–Leipzig: De Gruyter. Translated as The philosophy of space and time, M. Reichenbach & J. Freund (Eds.). New York: Dover, 1958. Reichenbach, H. (1932). Axiomatik der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 34(4), 568–619. Reichenbach, H. (1933). Die logischen Grundlagen des Wahrscheinlichkeitsbegriffs. Erkenntnis, 3(4/6), 401–425. Reichenbach, H. (1935). Wahrscheinlichkeitslehre. Leiden: Sijthoff. Revised English ed. in Reichenbach (1949). Reichenbach, H. (1936a). L’empirisme logistique et la désagrégation de l’a priori. In Actes du congrès international de philosophie scientifique, Paris, 1935. Vol. I: Philosophie scientifique et empirisme logique, 28–35. Paris: Hermann. Reichenbach, H. (1936b). Wahrscheinlichkeitslogik als Form wissenschaftlichen Denkens. In Actes du Congrès international de philosophie scientifique, Paris, 1935. Vol. IV: Induction et probabilité, 24–30. Paris: Hermann. Reichenbach, H. (1936c). Logistic empiricism in Germany and the present state of its problems. The Journal of Philosophy, 33(6), 141–160. Reichenbach, H. (1937). Les fondements logiques du calcul des probabilités. Annales de l’Institut Henri Poincaré, 7(5), 267–348. Reichenbach, H. (1949). The theory of probability. An inquiry into the logical and mathematical foundations of the calculus of probability. Berkeley: University of California Press. Reichenbach, H. (1956). The direction of time. Berkeley: University of California Press. Reichenbach, H. (1959). Modern philosophy of science: Selected essays. M. Reichenbach (Ed.). London: Routledge & Kegan Paul. Reichenbach, H. (1978). Selected writings: 1909–1953, 2 Volumes. R. Cohen & M. Reichenbach (Eds.). Dordrecht: Reidel. Reichenbach, H. (2006). Defending Einstein: Hans Reichenbach’s writings on space, time and motion. S. Gimbel & A. Walz (Eds.). New York: Cambridge University Press. Richardson, A. W. (1998). Carnap’s construction of the world. The Aufbau and the emergence of logical empiricism. Cambridge: Cambridge University Press. Ryckman, T.A. (1991). Conditio sine qua non? Zuordnung in the early epistemologies of Cassirer and Schlick. Synthese, 88(1), 57–95. Ryckman, T. A. (2005). The reign of relativity. Philosophy in physics 1915–1925. New York: Oxford University Press. Schlick, M. (1918). Allgemeine Erkenntnislehre (2nd rev. ed., 1925). Berlin: Springer. Translated as General theory of knowledge, H. Feigl & A. Blumberg (Eds.). LaSalle, IL: Open Court, 1974. Schlick, M. (1921). Kritizistische oder empiristische Deutung der neuen Physik? Bemerkungen zu Ernst Cassirers Buch ‘Zur Einsteinschen Relativitätstheorie’. Kant-Studien, 26, 96–111. Translated as ‘Critical or empiricist interpretation of modern physics?’ In H. Mulder & B. van de Velde-Schlick (Eds.), Moritz Schlick, Philosophical Papers, Vol. I (1909–1922), 322–334. Dordrecht: Reidel, 1979.
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Synthese (2011) 181:63–77 DOI 10.1007/s11229-009-9591-z
Reichenbach and Weyl on apriority and mathematical applicability Sandy Berkovski
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 30 June 2009 © Springer Science+Business Media B.V. 2009
Abstract I examine Reichenbach’s theory of relative a priori and Michael Friedman’s interpretation of it. I argue that Reichenbach’s view remains at bottom conventionalist and that one issue which separates Reichenbach’s account from Kant’s apriorism is the problem of mathematical applicability. I then discuss Hermann Weyl’s theory of blank forms which in many ways runs parallel to the theory of relative a priori. I argue that it is capable of dealing with the problem of applicability, but with a cost. Keywords
Relative a priori · Convention · Reichenbach · Weyl · Friedman
1 Introduction A view widespread already in the early 1900s was to see laws of nature as conventions. A popular example was the statement: Phosphorus melts at 44◦ C.
(1)
The melting temperature is not a sufficient characteristic, but a necessary one. Suppose there is a given solid substance X . To verify whether X is phosphorus we heat it to 44◦ C and observe its behaviour. If it starts melting, there are other tests to perform for establishing the nature of X . If it fails, we raise a hypothesis that X is not in fact phosphorus. Far from believing in the essential attributes of phosphorus that scientists uncover in the course of their experiments, many theorists believed that the statement (1) contributes to the way we understand the term ‘phosphorus’. Empirical regularities S. Berkovski (B) Department of Philosophy, Bilkent University, FA Building, 06800 Ankara, Turkey e-mail:
[email protected];
[email protected]
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observable in experiments affect the way we talk about material substances and the way we describe the experimental outcome. If such is the role of laws, they become akin to conventions, viz. arbitrary stipulations. I stipulate the term ‘phosphorus’ to refer to the substance melting at 44◦ C (plus a set of other characteristics), but there is nothing wrong with you if you decide to stipulate the same term to refer to something melting at 45◦ C. All we have to do is to find a way to correlate our respective linguistic habits. There is nothing wrong with either of those habits, since there is nothing in the string of noises and shapes ‘p h o s p h o r u s’ itself which singles out the correct way of using it. The parallel between laws and ordinary linguistic conventions is obvious: natural languages are likewise the products of history, a result of explicit and implicit conventions multiplied since time immemorial. Being conventions, laws are neither true, nor false. Statements about conventions can be true or false, and similarly statements using those conventions. The conventionalist view, in the form outlined here, is associated with the name of Poincaré. Although Poincaré’s concern is geometry, it is thought that conventionalism about geometry easily extends to conventionalism about physical sciences. The common perception is reinforced by his explicit appeal to the analogy with natural languages. Thus in Chap. III of Poincaré (1952) we find a little dictionary allowing mutual translation of statements of Lobatchevsky’s and Euclidean geometry. The common perception I am talking about is in point of fact misleading. Michael Friedman contributed significantly to clarifying Poincaré’s real position, and I shall say a few words about that below. Even if we deny the conventional character of natural laws, one may be reluctant to treat them as mere generalisations of observational data. That is, one may deny that laws are both empirical and contingent. In recent years this point has been stressed by Kripke’s theory metaphysical necessity elaborated in Lecture III of Kripke (1971, 1980). Kripke attributed metaphysical necessity to ‘theoretical identifications’ exactly of the sort displayed by the statement (1). Some theorists subsequently sought to eliminate the gap between metaphysical necessity and physical necessity. Metaphysically necessary statements receive their elevated modal status from certain very general physical laws which govern theoretical identifications. What is particularly important to us here is that Kripke regards the source of metaphysical necessity as being a priori. If we now identify metaphysical necessity with physical necessity of a special kind, then those general physical laws will in turn be known a priori. As we all know, there is a venerable tradition, according to which laws of nature are indeed known a priori. Descartes, Spinoza, and Leibniz should be counted among its adherents despite significant and subtle differences between them. However, with the advent of empiricism and naturalism the apriorist tradition has fallen out of favour. The most sustained recent attempt to resuscitate it was made by Michael Friedman. His studies of Kant’s philosophy of science showed that Kant, for better and for worse, was part of that same tradition. If the first Critique is concerned chiefly with the apriority of categories and pure intuition and tends to obscure Kant’s stance on natural laws, even a cursory perusal of Kant (1996) makes it plain: What can be called proper science is only that whose certainty is apodictic; cognition that can contain mere empirical certainty is only knowledge improperly
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so-called. . . . A rational doctrine of nature thus deserves the name of a natural science, only in case the fundamental natural laws therein are cognised a priori, and are not mere laws of experience. etc. etc. (Kant 1996, p. 468) Friedman’s ambition did not stop at merely making an historical correction vis-àvis Kant. His latest enquiries pursue a further twofold goal. One part of it consists in showing the continuity between Kant’s thought and the Vienna Circle, including Reichenbach (who resided in Berlin). That part of the project was started in Friedman (1983) and articulated in Friedman (1999). The second part of the project is less historical. In Friedman (2001) it is argued that a version of the aprioristic conception is the correct view on the nature of scientific theories. Furthermore, an aprioristic correction of positivism would gain us a more balanced and plausible interpretation of Kuhn’s historical data, as well as highlight the pitfalls of Quinean holism. In what follows I shall critically review Friedman’s interpretation of Reichenbach (1965). The main focus here will be on the notion of relative a priori and the tripartite distinction of physical sciences. I shall then discuss an alternative view on the same stock of issues due to Hermann Weyl. 2 Reichenbach on the relative a priori The Kantian notion of synthetic a priori was thought to be compromised by the development of non-Euclidean geometries. Whereas Kant claimed that the Euclidean geometry is a priori true, the development of non-Euclidean geometries showed that it is not to be believed a priori. The general theory of relativity (GTR) then showed that it is not even true. Such was the reasoning prominent in the late 1910s. Reichenbach resists it in Reichenbach (1965). His argument turns on distinguishing two connotations of a priori in Kant. One such connotation relates to eternal truth, to being ‘true for all times’. That is, S is a priori true just in case S is true at all times. This is an extraordinary view, exegetically and in content. I do not have the German source handy here, but I trust that the translation got it right. The view is remarkable, because Reichenbach’s Kant is made committed to believing that statements, or judgements, are true at some times, and false at other. This is a familiar medieval conception, perhaps also attributable to Aristotle; but I doubt very much that Kant has ever expressed sympathy with it. However, when we look at the textual evidence that Reichenbach gives in the footnote 17, we realise that no revolutionary exegesis is at stake. The first connotation of a priori equates it with strict universality. That is, S is a priori true just in case S is true in all possible circumstances. That formulation makes a link between apriority and necessity. It also does not distinguish between synthetic apriority and analytic apriority.1 The second connotation of a priori which Reichenbach attributes to Kant relates to the construction of objects of experience. Our experience obeys certain rules of organisation. The sensibility and the reason of the agent contribute to the way we perceive the world, and they do that in accordance with rules. Therefore, within this connotation, S is a priori just in case the truth-value of S is established solely through those ‘constitutive’ rules of experience. Reichenbach does not provide any textual 1 For an attempt to draw such a distinction see Hanna (2001, Sects. 5.2–5.3).
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evidence for his second connotation, because, as he says, it ‘will not be disputed’. He refers us to the Transcendental Deduction of the first Critique. Now, Reichenbach’s idea is to discard the first connotation and to keep the second one. Kantian rules that we have just mentioned are labelled as ‘axioms of coordination’ (synonymous with ‘coordinating principles’). Their role is in essence to control the way we reason about observational data. Says Reichenbach: The reality of things must be distinguished from the reality of concepts which, insofar as one wishes to call them real, have a mere psychological existence. But there remains a strange relation between the real thing and the concept, because only the coordination of the concept defines the individual thing in the “continuum” of reality; and only the conceptual connection decides on the basis of perceptions whether a conceived individual thing “is there in reality”. (Reichenbach 1965, pp. 50–51) This is the situation, according to Reichenbach, in analytic geometry. There we have algebraic representations of geometrical concepts. Thus, upon fixing the coordinate cross we can determine a one-parameter family of curves by the algebraic function f (x, y, z) = 0. In the case of Euclidean geometry, such a principle is embodied in the Euclidean metric which fixes the relation which is to be obtained for a collection of spatial points to form a spatially extended body. Similarly, we may coordinate certain mathematical symbols for vectors with physical forces and thereby conceive the latter as objects having vector-like properties. By discarding the first connotation of a priori we maintain that the Euclidean geometry is not necessarily, or universally, true. What does that mean? Here, I think, Reichenbach’s reasoning becomes fairly difficult to understand. On one hand, Reichenbach interprets apriority qua necessity and universality as immunity to revision.2 On the other hand, he effectively claims that revisability of coordinating principles does not amount to their ‘total’ falsehood. They should never be abandoned in their entirety as we might abandon a revised, viz. false, generalisation. Rather, we should always seek to replace them with those principles which differ from them only with respect to a limited number of instances of the available data. Reichenbach elaborates in the following key passage: Until now all results of physics have been obtained by means of the self-evident system. We discovered that this fact does not exclude a contradiction the existence of which can be ascertained—but how shall we obtain a new system? With respect to individual laws, this aim is easily reached because only those presuppositions that contain the individual law have to be changed. But we have seen that all laws contain coordinating principles, and if we wish to test new coordinating principles inductively, we must first change every physical law. It would indeed be nonsensical to test new principles by means of experiences still presupposing the old principles. If, for instance, space were tentatively assumed to be four-dimensional, to test the assumption, all methods of measuring lengths used until now would have to be abandoned and to be replaced 2 See Reichenbach (1965, p. 55).
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by a measurement compatible with four-dimensionality. Furthermore, all laws concerning the behavior of the material used in the measuring instrument, concerning the velocity of light, and so forth, would have to be given up. Such a procedure would be technically impossible. We cannot start physics all over again. (Reichenbach 1965, pp. 67–68) Interestingly, Reichenbach gives only pragmatic reasons for the ‘lax’ replacement of the old coordinating principles. The old principles are nothing but inductive approximations of the new ones. We, therefore, get a familiar chart of the cumulative development of science, in which theories—as time goes by—‘improve’, whether that means accounting for more and more phenomena or getting closer and closer to truth (although the cumulative chart might not require postulating any one single unreachable true theory). This is a view current among practicing scientists. Let us call it ‘the Folk View’. Kepler’s laws, according to that view, are regarded as approximations of Newton’s laws. The laws of stationary electric and magnetic fields are regarded as approximations of Maxwell’s equations. Some of these will no doubt qualify as what Reichenbach terms ‘axioms of connection’, that is, ordinary physical laws which are mere generalisations from experience. But of course the Folk View respects no sharp distinction between axioms of connection and axioms of coordination. For instance, a typical authoritative textbook tells us: Subatomic particles behave in a more complex way than the material points of the classical mechanics. The classical picture only approximately reflects the laws of nature. (Sivoukhin 1979, Sect. 5) Newton’s theory of gravitation was further developed in Einstein’s general theory of relativity. This latter gives not an intuitive explanation of gravitation, but a new way of describing it and a generalisation of Newton’s theory. (Sivoukhin 1979, Sects. 55–57) The theory of relativity and quantum mechanics are more general theories than Newtonian mechanics. The latter is contained in them as an approximate limiting instance. Relativistic mechanics merges into Newtonian mechanics in the case of low velocities. Quantum mechanics merges into Newtonian mechanics in the case of sufficiently massive bodies moving in smoothly varying fields. (Sivoukhin 1979, Sects. 0–5; italics added) According to the Folk View, then, the new principles extend the area of application of the old principles. The replacement of old principles is nothing but generalisation. Perhaps we should better talk about old principles being ‘superseded’ by new ones. Now, Reichenbach’s view amounts to the introduction of different standards of revision. Empirical laws, or the axioms of connection, may be abandoned in the course of scientific development as a result of obtaining new evidence. Coordinating principles of a given theory are those statements of the theory which are superseded, rather than completely abandoned, by their successors. However, Reichenbach supplies no systematic reason for thinking that there is a sharp distinction between two families of principles. The distinction appears to be based on a practical impossibility. Therefore, I think, Reichenbach’s conception of the relative a priori resembles the Folk View more closely than one might expect: the latter equally insists on incorporating
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the fundamental laws of the earlier theories into the novel ones.3 The earlier laws are approximations, or limiting cases, of the novel laws. We shall see in a moment that this resemblance is not accidental. 3 Friedman’s programme Quinean holism regards all individual beliefs as being inserted in a network. Abandoning one belief impinges on holding other beliefs in the network. To borrow John Carriero’s apt metaphor, it is as if the web of belief is composed of infinitely viscous fluid-like matter where the smallest local change reverberates throughout its farthest reaches. Therefore, no principled distinction between the a priori and the empirical is possible. If revising one belief on empirical grounds forces an adjustment of the whole network, logical and mathematical beliefs would also appear empirical. And holistic explanations seem congruent with Kuhn’s picture of scientific change. Since statements are never to be checked individually, but only as part of ‘theories’, those theories cannot be compatible. We can expand the notion of theory to include standards of experimentation, relevant textbooks, and so forth. We will then obtain Kuhn’s notion of structural lexicon. Projecting the resulting view on the history of a particular discipline, we will get a sequence of isolated paradigms eliminating each other without a trace. Friedman resists both Quinean holism and Kuhn’s picture of scientific change.4 His programme laid out in Friedman (2001) has many aspects, but these two of them seem to me the most important ones. More specifically, his claims are as follows: Contra Quine: historical developments in mathematical physics show that there is a hierarchy of beliefs. Mathematical beliefs are a priori and properly physical are empirical. There is a third class of beliefs characterised as relative a priori which mediates between the mathematical and the physical parts of the theory. Contra Kuhn: historical developments in mathematical physics show that there is far more continuity in successive paradigms than Kuhn allows. The fact of continuity is to be explained by the class of relative a priori beliefs. I will have little to say about Friedman’s polemic with Kuhn. As far as I can tell, Friedman happily endorses the Folk View in the outline. However, an important insight of Kuhn’s is preserved in that the a priori framework of an earlier theory cannot accommodate the framework of the later one. It is only in a retrospect, from a historical point of view, when we are already in possession of a later, ‘expanded’ theoretical framework, that we make sense of the earlier one.5 I will predominantly focus on the notion of relative a priori. Friedman derives it from Reichenbach (1965). The historical claim here is that before the logical positivists, and in particular Schlick and Reichenbach, adopted a thoroughly conventionalist outlook, they toyed with the idea of adapting the Kantian a priori to the development 3 Coffa draws a similar conclusion: see Coffa (1991, p. 203). 4 See also Friedman (2001). 5 See Friedman (2001, 63ff, 96ff). For a criticism see van Fraassen (2006, pp. 300–303).
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of relativistic mechanics. The result is a tripartite division of statements of physical theory. Apart from mathematical and empirical statements we also have a third class of relative a priori statements. They comprise mechanics which is sharply distinguished from the main body of physics. In Friedman’s hands, Reichenbach navigates skillfully between orthodox Kantianism, Poincaré’s conventionalism, and Helmholtzean empiricism. Relativised a priori is not a Kantian a priori, since there is a way in which it is revisable. It is, on the other hand, not a mere empirical law, since it occupies a different place in the hierarchy of our knowledge. Not only it is never fully abandoned, but also the scope of admissible evidence depends on which principles are accepted as relative a priori. For instance, classical mechanics allows absolute contraction, and therefore, treats length as an absolute property of bodies. Not so in special relativity, where length becomes dependent on the frame of reference. That relativisation of length in Lorentz transformations is very clearly not an empirical generalisation. Yet, why should one insist on regarding it as an a priori principle, and not a convention? In many ways Poincaré’s conventionalism occupies middle ground in the debate over the synthetic a priori. A convention does not reflect a property of reality, at least not literally, nor does it reflect our capacities allowing us to gain knowledge prior to all experience. Conversely, it is not an empirical statement: it would hardly be intelligible to try to test a convention by observation. If Reichenbach could successfully differentiate himself from Poincaré, he would be able to defend a second alternative position intermediate between apriorism and empiricism. From a historical perspective, too, the issue holds special importance for understanding Schlick’s criticism of Reichenbach’s 1920 book. Schlick interpreted the relative a priori as a form of convention. Reichenbach eventually came to accept Schlick’s criticism and endorsed conventionalism, albeit with qualifications.6 If a second intermediate position is available, Schlick would have misinterpreted Reichenbach, while the latter would have failed to see the novelty of his own approach. 4 The ghost of convention One key distinction between the relative a priori and the empirical lies in the way they are revisable. Empirical generalisations can be subjected to experimental tests and can be retained or abandoned depending on the results of those tests. Relative a priori statements behave differently. Consider the familiar story of the light principle of special relativity.7 It is not established by the Michelson–Morley experiment. The latter does not show the constant velocity of light in all inertial frames: it only shows that there are no identifiable differences in the velocity of light in different frames. Lorentz’s electrodynamics, based on Newtonian mechanics, was developed with the express purpose of accommodating the results of the experiment. Special relativity 6 See e.g. Reichenbach (1958, pp. 35–36). The Schlick–Reichenbach exchange is discussed in Coffa
(1991, pp. 202–203) and Friedman (1999, pp. 62–68). 7 See Friedman (2001, pp. 87–88).
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makes, therefore, a leap, unsupported by empirical input of the Michelson-Morley, when it postulates the light principle. Einstein uses it to define simultaneity and the new metric of the spatiotemporal framework. The Newtonian framework and the associated Euclidean metric were unseated as a result, not of an experimentum crucis, but of Einstein’s postulation. A Quinean holist reads this story as being essentially incomplete. True, there is no one experiment that would serve as a tiebreaker between alternative metrics. But there were multiple empirical results, notably in electrodynamics, that motivated the search for a non-Euclidean metric. The apriorist’s rejoinder is swift. Whatever motivation there was, it is at best a biographical episode. It is not sufficient to justify the choice of the new metric. The crucial factor involved in that choice was not coming from empirical testing. It is though much less clear how an apriorist fares against a conventionalist. From the introduction of the Minkowskian metric the conventionalist is happy to learn his conventionalist lesson: the light principle was a convention. Friedman and Friedman’s Reichenbach insist that it is an a priori statement. What is really at stake here beyond the terminological distinction? In one sense, the answer is relatively straightforward and uncomplicated. As Reichenbach notes in the very beginning of Reichenbach (1965), general relativity refuted Poincaré’s conventionalism. It showed that Euclidean geometry no longer represents the geometry of physical space–time. The curvature depends on the distribution of matter. And since the metric is chosen on the basis of physical considerations, geometry is transformed into a properly empirical science. But it is not a very satisfactory response. For it deals with a narrow conception of conventionalism which applies to geometry. One can extend its application to every theory. The epistemic status of the claims—empirical or conventional—is not permanent. They may be conventional in one theory, but regarded empirical in another. So whilst in Newtonian mechanics geometry was conventional, in GTR it becomes empirical. What remains conventional in it is, for example, the global topology of the universe. Now, that is precisely Friedman’s conception of ‘dynamic a priori’.8 The only difference, of course, is that the non-empirical, non-inductive, changeable level is called ‘a priori’, rather than ‘conventional’. A question arises about what exactly the gains of that shift in terminology should be. As far as I can tell, the point remains obscure. Whenever Friedman discusses Poincaré’s work, the emphasis is put always on the advances of GTR of which Poincaré was unaware, thus echoing Reichenbach’s own misgivings expressed in the letter to Schlick.9 But when he comes to examine Carnap’s version of conventionalism, he is prepared to identify Carnap’s ‘conventional’ L-rules from The Logical Syntax of Language with the relativised a priori. Indeed, he remarks that ‘Carnap articulates a version of Poincaré’s conventionalism that is as general as possible.’10 Schlick’s and Reichenbach’s own later reading of the theory presented
8 See e.g. Friedman (1999, p. 66). 9 See e.g. Friedman (1999, pp. 83–84). 10 See Friedman (1999, pp. 66–67).
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in Reichenbach (1965) was misleading only because they erroneously endorsed Poincaré’s conventionalism about geometry. They ignored its empirical status in GTR and along with it the possibility of a dynamic a priori. The Logical Syntax of Language restores to a large extent the vision first presented in Reichenbach (1965). Friedman’s reading of Reichenbach leads us, therefore, to a generalised version of conventionalism. And under a different, and Friedman’s preferred, angle, we have arrived at a circumscribed version of Kantian apriorism. We no longer believe in an eternal a priori, but we do still believe in a class of assumptions, whatever their name, that determine the conception of an object for a given theory. But I wish to draw attention to a particular issue, carrying special significance for Reichenbach’s and Friedman’s project, which divides sharply between the original version of apriorism and its watered-down version. If arithmetic and Euclidean geometry reflect immutable forms of pure intuition and if the objects of experience are equally determined by those forms, then there is no mystery in applying mathematics in empirical enquiry. Thus physical space necessarily possesses Euclidean metric: both have the same source. Kant triumphantly concludes in the Prolegomena: My doctrine of the ideality of space and time, therefore, so far from making the whole world of senses into mere illusion, is rather the only means of securing the application to real objects of one of the most important kinds of knowledge, namely that which mathematics expounds a priori, and of preventing it from being held to be mere illusion, because without this observation it would be quite impossible to decide whether the intuitions of space and time, which we take from no experience and which yet lie in our representations a priori, were not mere chimeras of the brain made by us to which no object corresponds, at least not adequately, and thus geometry itself a mere illusion; whereas on the contrary, just because all objects of the world of the senses are mere appearances, we have been able to show the indisputable validity of geometry in respect of them. (Kant 1953, p. 49) A Quinean holist, someone who believes in the empirical status of mathematics, may attempt at a similar argument. Since mathematics and natural science at bottom have the same empirical source, there is no wonder why mathematical concepts are found to be useful in empirical research. But if we recognise the a priori character of mathematics, we open up a gap: we create a problem of explaining why its concepts are useful in empirical disciplines. Now a host of issues must be resolved before a proper debate begins. Perhaps one should in the first place clarify why the problem deserves any explanation at all.11 But in the framework of Reichenbachian apriorism the problem receives a neat (Kantian) formulation. Since the role of the relative a priori is in mediating between the level of mathematics and the level of empirical laws, one should ask how the relative a priori is possible. We know that the mediation takes place. But we do not know why it has been successful. Indeed, most of its success is due to the advances in mathematical physics, the primary foci of Friedman’s account.
11 See Steiner (1998) and Berkovski (2002).
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I conclude that Reichenbach and Friedman have failed in formulating the second intermediate position referred to above. What I propose to do now is to look at Weyl’s views that in some aspects overlap Reichenbach’s and which, moreover, were developed at exactly the same time. Weyl’s account offers a solution to the problem of mathematical applicability—but with a considerable cost. 5 Weyl on mechanics and electromagnetism Hermann Weyl underwent many philosophical transformations in his career. At its various stages he was associated with constructivism, conventionalism, and formalism. Platonist sentiments can occasionally be found in his writings, while Duhemian holism is a running theme there. He was under the spell of the first Critique in his youth; later on Fichte and, more significantly, Husserl were among his major influences. The unusual diversity of Weyl’s philosophical beliefs was no accident. In his own words, he was like ‘a bumble-bee, flying between different flowers and trying to draw a little bit of nectar from each one of them’.12 It would therefore be futile to attribute a single well-argued philosophical doctrine to Weyl. We must regard him as a mathematician and physicist of the first rate deeply sensitive to the philosophical perplexities induced by his discipline. A particular argument to which I wish to draw attention here occurs in the discussion of stationary electromagnetism in Weyl (1922). Weyl gives a standard, if abridged, derivation of its field equations. Suppose we have two electric charges q1 and q2 in the given fragment of space. Coulomb’s Law allows us to describe the force existing between those charges when they occupy fixed positions. The force exerted on q1 is given by the formula: F1 =
1 q1 q2 r12 . 2 4π r12
Another notion is commonly introduced, namely, the notion of electric field which is just the force exerted upon the point-charge e: F = e · E. We generalise to the case of several charges. The field will be the sum of the contribution of all the charges at the given location: E=
1 qj r1 j . 4π r12 j j
Then we take the integral on the assumption that the charges are distributed in space with the ‘density’ ρ: 12 See Weyl (1955).
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E=
1 4π
ρ·r d V. r3
Now, on the other hand, we can introduce the notion of electric potential computed by the formula: 1 φ=− 4π
ρ d V, r
whence we get that: E = −∇φ = − grad φ. Therefore, since E is a gradient of the scalar field, we have: ∇ × E = curl E = 0.
(2)
By Gauss’ Theorem we also determine that the flux of E from an enclosed surface is equal to the quantity of charges within that surface; therefore: ∇ · E = div E = ρ.
(3)
After thus presenting a fairly standard account of electric field—reproduced here with only minor alterations—Weyl follows up with a densely argued philosophical gloss. I shall now try to unpack it. Coulomb’s Law describes action at a distance. If any of the charges is moved, the force exerted by it on another charge will change accordingly. But is such a situation even intelligible? The answer must be in the negative. Coulomb’s Law provides a way to compute the magnitude of force. But we should not regard it as explaining what force is. The real explanation is given by the field equations (2) and (3). And they embody a principle directly opposite to action at a distance. Combined together, they yield Coulomb’s Law, not vice versa. Yet, why should we adopt this particular explanatory order? Here is Weyl: [We] bow to the dictates of the theory of knowledge. Even Leibniz formulated the principle of continuity, of infinitely near action, as a general principle, and could not, for this reason, become reconciled to Newton’s Law of Gravitation, which entails action at a distance and which corresponds fully to that of Coulomb. The mathematical clearness and the simple meaning of the laws [(2) and (3)] are additional factors to be taken into account. (Weyl 1922, p. 66) The ‘general’ principle to which Weyl has resorted is most clearly not part of the physical theory itself. It is a philosophical principle and it determines the choice of the physical theory. Its precise epistemic role will have to be clarified further. Weyl, meanwhile, continues by linking mechanics to physics. There is no separate empirical science of mechanics. The concept of force is not provided by mechanics. Newton’s Second Law does not explain what force is; that is, force does not signify mass × acceleration. That is hardly a controversial view to hold. What one is expected
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to say instead is that Newton’s Second Law allows merely to compute force when the values for mass and acceleration are given. That is, indeed, what Weyl appears to claim a little later. But he also insists on a different cryptic remark: Mechanics does not, however, teach us what is force; that we learn from physics. The fundamental law of mechanics is a blank form which acquires a concrete content only when the conception of force occurring in it is filled in by physics. (Weyl 1922, pp. 66–67, his italics) What exactly does it mean to say that F = m · a is a blank form? A natural interpretation would be that, so long as we are confined to mechanics, we are dealing with a mere mathematical formula devoid of physical content. I believe that we cannot appreciate the significance of this claim without putting the role of mathematical symbolism into a wider perspective. Before we do that, let us finish with Weyl’s argument. For it ends with an energetic apology for holism. There is a network of laws which cannot be tested individually, but only as a whole. In the case of electrostatics we have electrons with constant mass and charge determining the density of the electric field. The field exerts a force calculated by Coulomb’s Law; in the general form, F = ρ · E. Given the value of this force, we calculate the acceleration of the matter by Newton’s Second Law. Weyl concludes: The laws thus constitute a cycle. . . . We require this whole network of theoretical considerations to arrive at an experimental means of verification,—if we assume that what we directly observe is the motion of matter. (Even this can be admitted only conditionally.) We cannot merely test a single law detached from this theoretical fabric! The connection between direct experience and the objective element behind it, which reason seeks to grasp conceptually in a theory, is not so simple that every single statements of the theory has a meaning which may be verified by direct intuition. (Weyl 1922, p. 67) Now, the argument does not explain why experience, i.e. an ‘individual’ experience, cannot intervene in the middle and break up the cycle. One may wonder, in other words, what that glue is which holds the cycle together and which prevents observations from falsifying laws in a discrete manner. In the last sentence of the quoted passage Weyl resorts to a version of meaning holism. On that view, abandoning one law impacts on the status of another law just by virtue of changing the meaning of the terms of that latter. But we have not yet seen any justification of it. 6 Symbolic representation Weyl’s brief discussion leaves us with an uncertain link between the non-intuitive status of physical laws—or ‘laws of nature’—and holism. The version of holism is a Duhemian one. Theories cannot be tested individually, and mathematics remains firmly outside the scope of the empirical. Weyl returns to the same issues nearly forty years later, shortly before his death in Weyl (1954).13 Let me summarise its major 13 Other congenial remarks are scattered in Weyl (1949) the bulk of which was published in 1926.
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claims. Physical science progresses towards the ever more increasing symbolisation. And this is to be welcomed. The goal of science is to remove the subjective element of experience. Symbolic constructions allow us doing exactly that. They do not appeal to any unique subjective element in cognition, and they are in principle accessible to every agent to the same extent. Phenomenal qualities are inadequate for understanding the world, since they are unreliable in generating predictions. They contain too many accidental features unique to the given experience. By stripping experience of those phenomenal qualities we arrive at symbolic constructions. They alone provide the required generality, strong enough to give us the predicting tools. Mathematical physics, according to Weyl, owes its success to just such a transition to symbolic representation. What of mathematical symbolism itself? Its key notion seems to be the notion of a variable. A typical mathematical theorem will have to be general. For example, given any three numbers a, b, and c, we say that if a < b and b < c, then a < c. Generality associated with the introduction of variables is interpreted as a possibility of continuing the procedure indefinitely. It is a hypothetical generality: if we can provide an actual construction of indefinitely reproducing the indicated operation, then we are engaging in a typical mathematical activity. And the same generality is present in other purely theoretical activities. Thus, for instance, we construct space as a continuum of possible locations. The claim has the following form. In science we have to account for phenomena which are not accessible to our immediate experience. Science is occupied with predictions. As such, it must possess generality. And if it has generality, it necessarily requires symbolic constructions involving variables. But there is a second, apparently independent argument to the same effect. If phenomenal qualities are subjective, we must strive to make them objective and subject-invariant. As we push the boundaries of the intuitive and visualisable further, we should ultimately remain with nothing but symbolic constructions. Thus: Whereas for Huygens colors were ‘in reality’ oscillations of the ether, they now appear merely as mathematical functions of periodic character depending on four variables that as coordinates represent the medium of space–time. What remains is ultimately a symbolic construction of exactly the same kind as that which Hilbert carries through in mathematics. (Weyl 1949, p. 113) And there should be no need for tracing the intuitive content of scientific explanations back to our ordinary perceptions. Such a procedure would require a purely qualitative explanation and would not even be intelligible. Weyl’s account contains, then, the following key elements. There is a hierarchy of disciplines. There is a level of ‘epistemology’, the philosophical enquiry. It supplies us with general principles, such as the principle of no action at a distance. There is a level of mechanics providing us with symbolic, that is, mathematical, constructions devoid of physical content. There is a level of physics that assigns physical meaning to the formulae of mechanics. But there is a hurdle to clear. The field equations themselves are mathematical formulae. Literally put, they cannot tell us what force or any other physical notion is. The empirical content is assigned to them by epistemological principles. Therefore, the latter are called to mediate between pure mathematics and mathematical physics. The idea here, one notices, is remarkably close to Friedman’s
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ideas: the choice of the relative a priori for a particular theory is similarly dictated by philosophical considerations.14 Given the interrelations between physics, mechanics, and philosophy, the scientific edifice becomes an organic body and holism is a natural outcome. On one hand, physical theories rely on the symbolism of mechanics, on the other—they ultimately follow epistemological assumptions. What of mathematical applicability? Since science progresses towards objectivity and, that is, towards increased symbolism and formalism, one suspects that the qualitative principles are whittling away in the process. What remains, or in any case should remain, is a symbolic construction of reality. Mathematics will be invading the domain of physics, replacing physical theories with its ‘blank forms’. Why would such an intrusion be legitimate in principle? Although never spelled out with clarity, Weyl’s ultimate answer is that reality is ‘endowed with a structure’.15 Structures, described axiomatically, would eventually provide us with a priori knowledge of the world. One feels that this cannot be the end of the story: there may be mutually inconsistent systems describing incompatible structures, and the choice will have to be made by means other than mathematical. Nevertheless the main programmatic claim is clear. Mathematics is applicable to the study of nature, since nature itself has mathematical properties.
7 Conclusion Terminological worries aside, Reichenbach’s 1920 theory should, I think, be regarded as a form of conventionalism. So far as they involve an element of arbitrariness and decision, relative a priori statements bear less resemblance to Kant’s a priori than Poincaré’s conventions. Compared with Poincaré’s or even Carnap’s original views, considerable modifications are involved. Friedman’s interpretation is at its best when it supplies the philosophical rationale for the Folk View and for the continuity in scientific paradigms. But since in attributing synthetic apriority to arithmetic and geometry Kant intends to dismiss the challenge of skepticism, there is a good systematic reason to contrast Kant’s a priori with relative a priori. Kant is able to solve the problem of mathematical applicability at the cost of making mathematics obey the nature of human cognition. The theory of relative a priori opens up a gap between the a priori nature of mathematics and the empirical nature of (mathematical) physics. It is, therefore, inept in answering the skeptic. Weyl’s theory, sketchy as it may be, is able to solve the applicability problem, but at no discount price. Its conclusion is a Pythagorean one: mathematics is useful in our theories of nature, since mathematical formalism reflects the deep structure of the world. Acknowledgements I am grateful to the audiences at LSE and Bo˘gaziçi, and especially to Philip Kitcher, Stathis Psillos, Alan Richardson, and Jon Williamson, for helpful comments on the earlier version of this paper.
14 See e.g. (Friedman, 2001, pp. 105–115). 15 See Weyl (1952, p. 144).
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References Berkovski, S. (2002). Surprising user-friendliness. Logique Et Analyse, 45, 283–297. Coffa, J. A. (1991). The semantic tradition from Kant to Carnap. Cambridge, MA: Cambridge University Press. Friedman, M. L. (1983). Foundations of space-time theories. Princeton, NJ: Princeton University Press. Friedman, M. L. (1999). Reconsidering logical positivism. Cambridge, MA: Cambridge University Press. Friedman, M. L. (2001). Dynamics of reason. Stanford, CA: CSLI Publications. Hanna, R. (2001). Kant and the foundations of analytic philosophy. Oxford: Clarendon Press. Kant, I. (1953). Prolegomena to any future metaphysics. Manchester: Manchester University Press. Kant, I. (1996). Metaphysical foundations of natural science. In Theoretical philosophy after 1781. Cambridge, MA: Cambridge University Press. Kripke, S. A. (1971). Identity and necessity. In S. P. Schwartz (Ed.), Naming, necessity, and natural kinds. Ithaca, NY: Cornell University Press. Kripke, S. A. (1980). Naming and necessity. Oxford: Basil Blackwell. Poincaré, J. H. (1952). Science and hypothesis. New York, NY: Dover (French edition published in 1905). Reichenbach, H. (1958). The philosophy of space and time. New York, NY: Dover (German edition published in 1928). Reichenbach, H. (1965). The theory of relativity and a priori knowledge. Berkeley, CA: University of California Press (German edition published in 1920). Sivoukhin, D. V. (1979). General physics (Vol. 1). Moscow: Nauka (in Russian). Steiner, M. (1998). The applicability of mathematics as a philosophical problem. Cambridge, MA: Harvard University Press. van Fraassen, B. C. (2006). Structure: Its shadow and substance. British Journal for the Philosophy of Science, 57, 275–307. Weyl, H. (1922). Space-time-matter (4th ed.). New York, NY: Dover (German first edition published in 1918). Weyl, H. (1949). Philosophy of mathematics and natural science. Princeton, NJ: Princeton University Press. Weyl, H. (1952). Symmetry. Princeton, NJ: Princeton University Press. Weyl, H. (1954). Über den Symbolismus der Mathematik und mathematischen Physik. Studium Generale, 6, 219–228. Weyl, H. (1955). Erkenntnis und Besinnung. Studia Philosophica, 15, 153–171.
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Synthese (2011) 181:79–93 DOI 10.1007/s11229-009-9588-7
Reichenbach on the relative a priori and the context of discovery/justification distinction Samet Bagce
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 8 July 2009 © Springer Science+Business Media B.V. 2009
Abstract Hans Reichenbach introduced two seemingly separate sets of distinctions in his epistemology at different times. One is between the axioms of coordination and the axioms of connections. The other distinction is between the context of discovery and the context of justification. The status and nature of each of these distinctions have been subject-matter of an ongoing debate among philosophers of science. Thus, there is a significant amount of works considering both distinctions separately. However, the relevance of Reichenbach’s two distinctions to each other does not seem to have enjoyed the same amount of interest so far. This is what I would like to consider in this paper. In other words, I am concerned with the question: what kind of relationship is there between his two distinctions, if there is any? Keywords Hans Reichenbach · Philosophy of science · The axiom distinction · The relative a priori · The context distinction 1 Introduction Hans Reichenbach (1891–1953) introduced two seemingly separate sets of distinctions in his epistemology at different times. One is between the axioms of coordination and the axioms of connections he introduced in his The Theory of Relativity and A priori Knowledge (TRAK) (1920). This distinction is introduced in the context of a given scientific theory.
An earlier version of this paper was delivered at the conference, A Philosopher of Science in Istanbul: Hans Reichenbach, Bogazici University, May 8–9, 2008. S. Bagce (B) Department of Philosophy, Middle East Technical University, 06531 Ankara, Turkey e-mail:
[email protected]
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The former are not empirical statements. One thus cannot test them empirically alone. The axioms of coordination should be laid down before one can determine empirically the relevant terms and concepts in the theory. The latter, on the other hand, are empirical statements in the traditional sense, describing empirical regularities. He introduces this distinction in order to argue that the traditional empiricism is at fault in not recognising the constitutive role in obtaining objective knowledge of Kant’s notion of a priori. So, the axioms of coordination are to play that role. By doing so, Reichenbach relativised Kant’s notion of a priori. The other distinction is between the context of discovery and the context of justification he presented in his Experience and Prediction (E&P) (1938). Reichenbach in the first chapter of his book E&P characterises epistemology as having three fundamental tasks: the descriptive, critical and advisory tasks. In this section he describes what these three tasks of epistemology are, and points to a particular difficulty of logical empiricism. In order to overcome this difficulty, the difficulty how to construct a theory of knowledge being both “logically complete and in strict correspondence with the psychological process of thought”, he distinguishes the task of epistemology from that of psychology. He employs the term rational reconstruction to indicate the task of epistemology. He then introduces “the terms context of discovery and context of justification to mark this distinction”. He later identifies the context of justification as the proper domain of epistemology. The status and nature of each of these distinctions have been subject-matter of an ongoing debate among philosophers of science. Thus, there is a significant amount of works considering both distinctions separately. Some honour them by seeing them as legitimate. Some try to abolish. There is no need to list here all the studies conducted until now. However, the relevance of Reichenbach’s two distinctions to each other does not seem to have enjoyed the same amount of interest so far. This is what I would like to consider here. In other words, I am concerned with the question of what kind of relationship there is between his two distinctions, if there is any.
2 The first distinction: TRAK and the philosophy of space and time Especially after Eddington’s 1919 eclipse expedition yielding the empirical confirmation of the prediction by the relativity theory of bending of light passing near the sun, the thread posed by the relativity theory to the standard views concerning space, time and gravitation as well as the predominant methodology of science and epistemology became acute. As a result a heated conflict between the neo-Kantians and the relativity theory was resulted in. Einstein and Schlick, while trying to provide a philosophical account of the general theory of relativity (GTR), were defending the theory against Kantian attacks. There was certainly a need for a new philosophy of science, which could establish the superiority of the theory over its predecessors, as well as which, in turn, would be legitimised by its success in justifying the achievements of the relativity theory. In order for this new account of scientific knowledge to do both required jobs, it has to negotiate “a careful path between a crudely reductive Machian positivism and the excesses of Kantian a priorism” (see Howard (1994), p. 47).
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Reichenbach’s TRAK grew out of such a need. In TRAK Reichenbach argues that the theory of relativity makes it impossible for one to maintain the synthetic a priori character of all the principles Kant had thought. So, one of the basic aims Reichenbach has in TRAK is to refute Kant’s philosophy. The other one is to provide a reinterpretation of Kant’s philosophy so that it would still be compatible with the relativity theory, as well as by means of which he would provide a good philosophical account of the relativity theory. But before going any further, let me ask the following question: what did Kant do that required such a refutation? To answer the question requires us to consider Kant’s philosophy briefly. Kant articulates an analysis of what counts as a genuine knowledge, i.e. scientific knowledge, in his Metaphysical Foundations of Natural Science (MFNS) (1786/1970). He provides his account in terms of two particular theories, Newtonian physics and Euclid’s geometry, which, in turn, is assumed as a background by Newtonian physics. In other words, he considers these two theories as providing us with what counts as genuine scientific knowledge. Kant’s account of scientific knowledge is based upon a distinction between pure and empirical, or form and content parts. Kant maintains that the pure part entirely consists of synthetic a priori judgements. Synthetic a priori judgments are actually obtained by the synthesis resulting from applying the pure concepts of the understanding to the content provided by the pure intuitions of the faculty of (human) sensibility. The pure forms of intuition together with the pure categories—yielding the synthetic a priori judgements—which, in turn, constitute the pure part of knowledge, then represent the very conditions of the possibility of the empirical part. Without the former, the latter cannot have well defined meaning, and any relation to objects, that is, truth values. So, one can have no judgement of experience, unless one has laid down the pure part in the first place. Thus, the pure part really constitutes the objects of the judgements of experience, i.e. genuine knowledge. This is why Kant regards them as constitutive. However, they are not only constitutive; they are at the same time to make synthetic a priori judgment as necessarily and unrevisable true for all times. According to Kant, the pure part in the case of Newtonian physics contains Euclid’s geometry, or more generally the whole applied mathematics required by the same theory, Galilean kinematics, or the absolute simultaneity and classical law of velocity addition, and Newton’s laws of motions. These are to provide the very background for Newtonian physics to formulate some specific laws of nature. As an example of these specific laws of nature, the law of universal gravitation can be cited. Not only this kind of laws, but any specific laws of motion that are to be obtained in terms of the Newtonian laws of motion are, in turn, to form the empirical part (see Friedman (1999), p. 61). According to Reichenbach, this articulation of genuine knowledge provided by Kant cannot be maintained in the light of the recent then developments in modern physics, i.e. the discovery of the theory of relativity, and in the foundations of geometry, that is, the works conducted by Gauss, Helmholtz, Lie, Klein, Poincaré and Hilbert concerning the foundations of geometry, which is culminated in the theory of relativity. This is because the relativity theory establishes that all the elements forming the pure part cannot be a priori and thus necessarily and unrevisable true for all times.
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However, the book TRAK has a more interesting consequence that the theory of relativity also makes possible to provide a reinterpretation of Kant’s conception of a priori, and by such a reinterpretation one can see what is right in Kant’s epistemology and at the same time what is wrong in the naïve empiricism, i.e. logical positivism. Thereby Reichenbach differentiates two separate meanings of Kant’s notion of a priori: (i) necessarily and unrevisably true for all times; (ii) constitutive of the concept of an object (see, 1920, p. 48). Reichenbach rejects the first meaning of a priori, but considers the second one as important. While he is clarifying these meanings, he introduces his famous distinction between the axioms of coordination and the axioms of connection (see, 1920, p. 54). By accepting the second meaning, he could provide a well articulated philosophical account of the general theory of relativity. He thereby could protect the theory against the neo-Kantians by maintaining that what Kant had once thought of some principles as a priori is true, but in the restricted sense of the a priori: we need those principles just to constitute the objects of experience, or better, these principles are just constitutive principles. Moreover, this was quite befitting with his general philosophical aim: to point out and account of the presence of the personal or subjective elements in human knowledge contributed by human beings, or reason. Reichenbach by his distinction between axioms of coordination and the axioms of connection aims at providing a more specific account of the character and the status of these constitutive principles. Briefly for Reichenbach, the axioms of coordination are themselves not empirical statements and one cannot empirically test them alone. However, they are the principles that make it possible for scientific theories to have any relation to reality and empirical content. Therefore, before we lay down these axioms, no meaningful question of truth or falsity of scientific theories can be raised. They are necessary assumptions for doing any scientific investigation and for understanding the world. These axioms are necessary to determine what objects, properties and so on, our scientific theories talk about. Therefore, they are to provide a framework for empirical theorising, and thus, they are constitutive of the objects of experience. Once these axioms are laid down and thereby a specific subject-matter is defined, one can then formulate the axioms of connection that make specific empirical claims about the subject-matter. The axioms of connection are empirical statements in the traditional sense, describing empirical regularities. When Reichenbach sees the axioms of coordination as being constitutive of the objects of knowledge, he agrees with Kant on the presence of a priori elements or principles in human knowledge. In other words, Reichenbach allows some subjective elements in human knowledge provided by reason as only to constitute the objects of knowledge, but not make our claims concerning these objects necessarily and unrevisably true. According to Reichenbach, in the case of Newtonian physics, Euclid’s geometry, Galilean kinematics, and the Newtonian laws of motion are all the axioms of coordination, and therefore constitutively a priori with respect to this theory. All the rest of specific empirical laws that are formulated within this framework are the axioms
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of connection (see Friedman (1999), p. 61). This is Reichenbach thinks exactly what Kant got right. So, Reichenbach believes that Kant’s articulation of human knowledge is correct historically.1 In the case of the special theory of relativity (STR), Reichenbach maintains that Euclidean geometry, Lorentzian kinematics, that is, the structure of Minkowski spacetime, are the axioms of coordination. On the other hand the axioms of connection in this theory, theories of particular forces and fields formulated in this structure such as Maxwell’s equations (see Friedman (1999), p. 62). In the context of the general theory of relativity, Reichenbach says that we have changed once again our framework and the axioms of coordination. “Now only the infinitesimally Lorentzian manifold structure—space-time topology sufficient to admit some or another (semi-) Riemannian metric—is constitutively a priori: the particular (semi-) Riemannian metrical structure realized within this framework then is determined empirically from the distribution of mass-energy, and thus the specific principles of metrical geometry now count as axioms of connection” (see Friedman (1999), p. 62). This is also according to Reichenbach to point to what is wrong with the naïve empiricism: they do not notice the role of the axioms of coordination in representing the “subjective form” of knowledge, i.e. the contribution of reason, since they claim that they can characterise all scientific statements indifferently as “derived from experience”; namely, as protocol sentences. In other words, Reichenbach does not hold the view that ordinary physical objects can be constructed solely out of sense data; instead, he thinks that to do so, some constitutive principles are also required. He does not think that there is a set of privileged sense perceptions being independent of these principles corresponding to physical objects. However, for Reichenbach, the axioms of coordination are not adopted for once and all. They can be developed, revised or given up with the progress of empirical science, that is, in the light of, and under the pressure of empirical findings. This is in fact what we have learnt from the theory of relativity: we have changed our axioms of coordination and, therefore, our concept of object of knowledge in moving from classical physics to relativity theory (1920, p. 94). As the development of relativity theory shows, the axioms of coordination are not unrevisable fixed points of empirical inquiry. As for The Philosophy of Space and Time (PST), (1928), published eight years after TRAK, is a book in which Reichenbach engages to unify certain ideas he had previously held with some modifications. It is an elegant work, and by employing better tools he provides his own account in addition to Helmholtz’s and Poincaré’s views concerning geometry with an analysis of Einstein’s special and general theories of relativity, some of which was already given in his Axiomatization of the Theory of Relativity (ATR), (1924). Some of these ideas include the distinction between universal and differential forces,normal systems, the synonymy of equivalent descriptions, the principle of the relativity of geometry, the distinction between inductive and descriptive simplicity, the
1 For more on this issue see, for example, Friedman (1999), pp. 59–79.
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requirement of postulating coordinative definitions beforehand, the conventionality of coordinating definitions, the conventionality of metrical simultaneity, an analysis of the logical structure of relativity theories in terms of causal relational properties. Reichenbach begins his work by establishing the interdependence between alternative ways of measuring length and alternative geometries, and thereby maintaining the same kind of relationship between properties and laws. This is to enable Reichenbach to argue that alternative systems of definitions and laws that account for the same empirical facts make the same claims and the same empirical content. In other words, these descriptions provided by these alternative systems of definitions and laws are equivalent ones. Thus, he no longer holds that relativity theory establishes a particular geometry as a background to this physical theory. But here by definitions Reichenbach means coordinative definitions, that is, they are specifying certain physical procedures to determine the values of quantities. Reichenbach also brings in Helmholtz’s idea of visualisation into discussion to argue against the view that pure visualisation has some normative function by maintaining that “the normative function of visualization is not visual but of logical origin” (1928, p. 91). PST in general does not deviate much concerning Reichenbach’s treatment of space and geometry from the one given in TRAK: each of the given theories, Newtonian, STR and GTR has a certain group of transformations that leaves certain things invariant. And each of such groups provides us with a range of possible and equivalent descriptions of nature. Reichenbach thinks that those elements remaining invariant are the elements that mark out the range of these possible and equivalent descriptions, and are the constitutive elements, the contributions of reason so to speak, that is, the definitions of coordination. And they also indicate that within the range of possible descriptions, the choice of one system over another one is arbitrary, that is, conventional. For Newtonian physics the relevant group of transformations is the Galilean group, and particular fields (of gravitational force, distribution of mass and etc.) formulated in this structure are empirical statements. In STR, it is the Lorentz group and particular fields defined in this structure such as the electromagnetic, the distribution of charge and etc., are the axioms of connection. And in GTR, it includes one-one bi-differentiable transformations, i.e. the underlying topology is constitutive but the metric of physical space is empirically determined (see Friedman (1999), p. 66). In PST, there does seem to be one striking change in Reichenbach’s language and epistemology. The term convention is not regarded as ill reputed any more, and employed instead of a priori.2 All his references in PST to a priori are in critical character. This may be taken to indicate a certain break with Kant’s epistemology. In PST, Reichenbach seems to have given up his association with neo-Kantianism (1928, p. xii). Thus, the epistemology underlying PST is intended to be basically more empiricist: the conventional elements in science are just the non-observational or theoretical ones. The only facts are the observable facts; all the rest is the “contribution of reason”. The distinction in TRAK between the elements of reason/facts, or if you like the conventional/factual distinction, is transformed into the theoretical/observational
2 For this please see Hoyningen-Huene (1987) and Popper (1934).
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one. But in TRAK, the former part of the first distinction is not identical to that of the latter’s; instead it is drawn within the realm of the theoretical: certain elements of theoretical structure, for example the choice of rest system and of inertial system, are conventional, other theoretical elements, such as the choice of metric, are not. Reichenbach seems to have developed two different epistemological positions, though they are complementary to each other: i) the earlier one, given in TRAK and ii) the later one, given in PST. However, there is the same concern underlying both positions. This is his concern to point to, and to account of, the presence of the elements in human knowledge contributed by reason, or subjective, conventional if you like—though Reichenbach does not use this appellation to describe his position in TRAK. He holds in TRAK that the form/content (convention/fact) distinction is essential for epistemology as well as the philosophy of science. In E&P he says that “the presentation of volitional—conventional that is—decisions contained in the system of knowledge constitutes an integral part of the critical task of epistemology” (1938, p. 9). Reichenbach’s positions both in TRAK and PST are neither strictly Kantian nor strictly naïve empiricist but in PST he seems to have liked to be less Kantian, and more empiricist. 3 The second distinction: experience and prediction In Experience and Prediction Reichenbach spells out the epistemology underlying PST and this is the book in which Reichenbach intends “to show the fundamental place which is occupied in the system of knowledge by this concept [the concept of probability] and to point out the consequences involved in a consideration of the probability character of knowledge” (1938, p. vi). In the very first section of the first chapter, Reichenbach characterizes epistemology as having three fundamental tasks: the descriptive, critical and advisory tasks. In this section he describes what these three tasks of epistemology are, and points to a particular difficulty of logical empiricism. In order to overcome this difficulty, the difficulty how to construct a theory of knowledge being both “logically complete and in strict correspondence with the psychological process of thought”, he distinguishes the task of epistemology from that of psychology in the descriptive task of epistemology: What epistemology intends to do is to construct thinking processes in a way in which they ought to occur if they are to be ranged in a consistent system, or to construct justifiable sets of operations which can be intercalated between the starting point and the issue of thought-processes, replacing the real intermediate links. Epistemology, thus, considers a logical substitute rather than real processes (1938, p. 5). For this logical substitute Reichenbach employs the term rational reconstruction to indicate this task of epistemology in its specific difference from that of psychology. He then says that “in spite of its being performed on a fictive construction, we must retain the notion of the descriptive task of epistemology. The construction to be given is not arbitrary; it is bound to actual thinking by the postulate of correspondence” (1938, p. 6).
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To illustrate the point he appeals to an example: The way, for instance, in which a mathematician publishes a new demonstration or a physicist his logical reasoning in the foundation of a new theory, would almost correspond to our concept of rational reconstruction; the well-known difference between the thinker’s way of finding this theorem and his way of presenting it before a public may illustrate the difference in question (1938, p. 6). He then introduces “the terms context of discovery and context of justification to mark this distinction” (1938, pp. 6–7). He later identifies the context of justification as the proper domain of epistemology (1938, p. 7 and 382). However, he immediately warns off the reader by saying that “even the way of presenting scientific theories is only an approximation to what we mean by the context of justification. Even in the written form scientific expositions do not always correspond to the exigencies of logic or suppress the traces of subjective motivation from which they started” (1938, p. 7). This descriptive task a bit further down in the book is supplemented by the second task of epistemology, that is, the critical task in which “the system of knowledge is criticised; it is judged in respect of its validity and its reliability. This task is already partially performed in the rational construction, for the fictive set of operations occurring here is chosen from the point of view of justifiability; we replace actual thinking by such operations as are justifiable, that is, as can be demonstrated as valid” (1938, p. 7). However, they are still different because “even the rational reconstruction contains unjustifiable chains”. It is interesting to see that the next time Reichenbach refers to this distinction is nearly at the end of the final chapter on probability and induction of the book. Before he brings in the distinction he talks about an objection to his account of induction “as an interpolation, as a method of continual approximation by means of anticipations”, the objection that Reichenbach’s theory of induction “may be good enough for the subordinate problems of scientific inquiry, for the completion and consolidation of scientific theories. Let us leave this task to the artisans of scientific inquiry—the genius follows other ways, unknown to us, unjustifiable a priori, but justified afterwards by the success of his predictions” (1938, pp. 379–381). The objection basically amounts to be claiming that all the important works of great scientific minds cannot be achieved only by the methods of simple induction and the employment of diagrams and statistics. To this objection Reichenbach’s reply runs as follows: “I know … that the working of their [the great men of science] minds cannot be replaced by directions for use of diagrams and statistics. I shall not venture any description of the ways of thought followed by them in the moments of their great discoveries; the obscurity of the birth of great ideas will never be satisfactorily cleared up by psychological investigation” (1938, p. 381). However, he does not see these facts as constituting any objection to his theory of induction “as the only means for an expansion of knowledge”. At this juncture Reichenbach once more refers to the context distinction as a reason why he does not see the facts mentioned above as a likely objection to his theory of induction:
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We emphasized that epistemology cannot be concerned with the first but only with the latter; we showed that the analysis of science is not directed toward actual thinking processes but toward the rational reconstruction of knowledge. It is this determination of the task of epistemology which we must remember if we want to construct a theory of a scientific research. What we wish to point out with our theory of induction is the logical relation of the new theory to the known facts. We do not insist that the discovery of our new theory is performed by the reflection of a kind similar to our expositions; we do not maintain anything about the question of how it is performed—what we maintain is nothing but a relation of a theory to facts, independent of the man who found the theory. There must be some definite relation of this kind, or there would be nothing to be discovered by the man of science (1938, p. 382). Reichenbach then asks the following question: why was Einstein’s theory of gravitation a great discovery, even before it was confirmed by astronomical observations? His answer is that: [B]ecause Einstein saw –as his predecessors had not seen- that the known facts indicate such a theory; i.e., that an inductive expansion of the known facts leads to the new theory. This just what distinguishes the great scientific discoverer from a clairvoyant. The latter wants to foresee the future without making use of induction; his forecast is a construction in open space, without any bridge to the solid domain of observation, and it is a mere matter of chance whether his prediction will or will not be confirmed. The man of science constructs his forecast in such a way that known facts support it by inductive relations; that is why we must trust his prediction. What makes the greatness of his work is that he sees the inductive relations between different elements in the system of knowledge where other people did not see them; but it is not true that he predicts phenomena which have no inductive relations at all to known facts. Scientific genius does not manifest itself in contemptuously neglecting inductive methods; on the contrary, it shows its supremacy over inferior ways of thought by better handling, by more clearly using the methods of induction, which always will remain the genuine methods of scientific discovery” (1938, pp. 382–383). One may find this passage a bit confusing; for Reichenbach, on the one hand, asserts that the context of discovery is not the proper domain of epistemology, and on the other hand, claims that methods of inductive reasoning is and will always remain the genuine methods of scientific discovery. However, there is not anything confusing here. This is because Reichenbach rejects the context of discovery as the actual process of discovery being a proper domain of epistemology; but he does not reject the formal or normative aspects of discovery which is basically directed at finding the objective inductive relations of the known facts to the theory. Gathering the objective inductive relations between the known facts to the theory is a part of justification, and is independent of how the discoverer actually got them or of the psychological, social and cultural basis of this process of discovery. Reichenbach maintains that such relations should exist physically between the known facts and the theory. Otherwise
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“there would be nothing to be discovered by the man of science”. He also iterates this point by saying that “the inductive connections of modern physics are constructed analytically…” (1938, p. 385). We can and should be interested in providing a rational account of how these relations, which are supposedly exist between the facts and the theory or that particular new piece of knowledge, are obtained. Reichenbach also adds the remark that the difference of the context of justification from the context of discovery is not restricted only to inductive thinking alone. The same distinction can also be made with respect to deductive operations of thought (see 1938, p. 383). He states a particular example in geometry, “the construction of a triangle from three given parameters”. He maintains that “the objective relations from the given entities to the solution and the subjective way of finding it are clearly separated for problems of a deductive character; we must learn to make the same distinction for the problem of the inductive relation from facts to the theories” (1938, p. 384). Reichenbach stresses the difference between the logical relations existing between the set of the givens and the conclusion and the way one sees or discovers those relations in the problems of deductive character. Although, as it is pointed out, the discovery/justification distinction seems to have been present before Reichenbach reintroduced in his E&P,3 it seems that Reichenbach takes his cue for the context distinction from this difference in deduction. This characterisation thereby makes the distinction as the one between factual and formal/normative. Reichenbach by this distinction basically intended to show that the psychological, sociological, cultural origins of statements, theories have nothing to do with the way of determining their truth values, and thereby having no epistemological concern. What is relevant epistemologically is the possibility of confirming statements. Giere argues that this distinction is a matter as deeply personal as it was philosophical. He thinks that “there may well exist additional documentary evidence regarding Reichenbach’s personal motivations for insisting on a distinction between discovery and justification around 1935” (1999, p. 230). So, Reichenbach wanted to have a scientific epistemology dictating as a precondition that rules out the possibility of Jewish or any national or culturally identifiable science. Giere also thinks that “that had to be a very useful stance for anyone in his position”, given the historical evidence such as he was called back to Berlin prior to 1938 and he was looking for safe heaven in the States, as well as completed the book in English in 1934–1937 (see 1999, pp. 13–15 and 227–230). There is one more role for this distinction to play: Reichenbach criticises in E&P a doctrine to which a number of early positivists had been committed: phenomenalism. The roots of Reichenbach’s rejection of phenomenalism go back to his alliance with Kantianism: in TRAK, he rejects the synthetic a priori status of Euclidean geometry and of causality, but he retains the idea of a priori to play an essential role in constituting objects of knowledge. From this, one can safely say that he did not hold the view that ordinary physical objects could be constructed solely out of sense data or that statements about such objects are logically equivalent to a finite set of “protocol” statements; instead, he holds that to do so, some sort of constitutive principle 3 Reichenbach earlier had given a clearly obvious statement of this anti-Machian view in his paper of 1929. See also Salmon (1979), pp. 43–44.
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was also required. Since his theory of empirical confirmation is probabilistic, then he thinks, it is easy to adopt a kind of empiricism and to maintain a consistent empiricist epistemology without appealing to any form of phenomenalism.4 However the distinction is introduced by Reichenbach not as a logical conclusion of any series of arguments. This is also the case with the first distinction as well. It is introduced as a precondition for doing a normative epistemology which deals with the “three predicates of propositions”, meaning, truth-value, and weight (probability). It is clear that none of these predicates has anything to do with questions concerning the psychological, sociological, cultural origins of propositions or theories. Put it in another way, the way a particular theory is discovered or constructed has no bearing upon the way it is to be justified. So the legitimate domain of any epistemology that aims at providing a scientifically articulated account of human knowledge is not the context of discovery, but that of justification.
4 The relationship between Reichenbach’s two sets of distinctions Let me begin by asking the following question: Is there any relation between these two sets of distinctions Reichenbach introduces? There does not appear to be so. Reichenbach never states that these two distinctions are in one way or other related to each other. But can they be related by asking the question of justification concerning the definitions (earlier axioms) of coordination, or conventions? One may think that this is a legitimate question given Reichenbach’s original definitions of the descriptive and critical task of epistemology. However, one can immediately raise an objection here: their justification cannot arise given the fact that they are the ones that facilitate the normative justification procedure. Prior to this distinction no question of justification can meaningfully be asked. So they cannot be subjected to any procedure of justification. But let’s assume that a permission be granted to ask the aforementioned question just to see what Reichenbach can say on the issue. With respect to this issue, the justification of the axioms or definitions of coordination, Reichenbach in his earlier epistemology says almost nothing except that “… the principles of coordination are determined by the nature of reason; experience merely selects from among all possible principles” (1920, p. 87). And he also adds that “the contribution of reason is not expressed by the fact that the system of coordination
4 Moreover, Reichenbach assumes a certain link between the definitions (earlier the axioms) of coordination in each of Newtonian physics, STR and GTR, and thereby the mathematical structures associated with each theory and the empirical findings or experience. However, the link between these definitions and the invariance groups is not something to be assumed, but something to be demonstrated (see Friedman (1999), p. 70). Hence, here a series of independent arguments is required. However such an argument is not forthcoming in Reichenbach. A similar assumption is made by Kant concerning an a priori link between the appearances and the a priori forms of intuition. However, this link is not there to suppose, but to be demonstrated. Kant tried to provide such arguments in order to justify such a link in the Transcendental Aesthetic of the first Critique (1787/1987). However, he failed to demonstrate this a priori link between the appearances and the a priori forms of intuition. The absence of such a demonstration is one of the reasons that Kant’s a priorist project in epistemology fails. Furthermore, Torretti claims that coordination as described by Reichenbach can hardly be said to define the individual elements of reality (1983, p. 235).
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contains unchanging elements, but in the fact that arbitrary elements occur in the system” (1920, pp. 88–89). In his later epistemology, there seems to be one more thing Reichenbach could say: these definitions of coordination or conventions, say, in the case of GTR, are chosen simply because they have produced a system which contains no universal forces, i.e. normal system. Although his theory of probability is defective, especially with respect to the distributing the prior probabilities, he could still argue for the claim that by appealing to the idea of induction and descriptive simplicity, we can justify our choice of these conventions over others as the best posits exhibiting the objective inductive relation from the known facts to the theory. But in this case Reichenbach would face some serious difficulties. The first one is that one cannot guarantee that the so called objective relations between the known facts and the theory can only accounted for and discovered simply by the application of inductive methods. There are other formal methods, such as group theory, deductive quasi-empirical methods, that might be at work in establishing the link. The second one is that Reichenbach’s account of induction cannot be powerful enough to lead us necessarily to one unique scientific theory. It is perfectly possible the same objective relations can also be captured by more than one scientific theory. After all, there are in principle infinitely many ways to generalise on the basis of the given empirical data. This is a possibility that Reichenbach himself does not rule out, and because of this fact, Reichenbach introduces his definition of equivalent descriptions and of synonymy. According to Reichenbach, all these equivalent descriptions express the same physical content, but in different languages. The question here is not which of the equivalent descriptions is the true one; for that question is ill-formed: they all are either true or false. If one of these equivalent descriptions contains no universal force, (or, say, it involves a normal system), according to Reichenbach, it is the one that we should choose. Justification of choosing the normal system as the preferred description is given by means of the principle of descriptive simplicity. But this is the point where Reichenbach goes wrong when he says that the objective relations can only be discovered by the application of inductive methods. One of the equivalent systems is denying the existence of some universal forces, and the other one positing their existence. Since one cannot empirically confirm or falsify such claims, we cannot maintain that one has obtained such objective relations by means of the theory. The only way one can argue for the objectiveness of such claims is through justifying the theory altogether in question, that is, the one that denies the existence of such forces.5 This means that one has to have constructed the theory beforehand in order to argue for the objective character of the relations between the theory and the known facts. Otherwise it would be an impossible task to achieve. In other words, in Reichenbach’s case, he should have committed to the truth of the relativity theory; he could then argue that those objective relations between the known facts and the theory could be obtainable by induction alone. It is clear that Reichenbach was only interested in justifying
5 For more on these issues, see Peckhaus (2006) and Floridi (1996).
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the choice of certain conventions lying at the very basis of the relativity theory. Put it in other way, Reichenbach’s account of knowledge outlined in his E&P is supposed to yield a justification for scientific knowledge exemplified by the relativity theory. This is exactly the primary reason for Reichenbach to introduce the context diction: to safeguard those coordinative definitions or conventions upon which the theory was erected so that they could not be subjected to a further justification. This is the point where the relationship between these two sets of distinction seems to arise. Because of this, Reichenbach seems to have introduced separately these two different sets of the distinctions. The justification of the relativity theory is an empirical matter, and depends upon the number of the correct predictions it makes. The relativity theory had made some correct predictions by the time Reichenbach got interested in the theory. There is no question that Reichenbach’s trust in the theory must have been affected by these predictions. However, these correct predictions cannot be the only reason for his trust in the success and truth of the theory. Howard outlines other important factors in the following way: It is, of course, not surprising that three [Schlick, Reichenbach and Carnap] bright, technically sophisticated, young philosophers would be excited by the relativity, especially in the wake of the wave of public interest after Eddington’s 1919 eclipse expedition yielded confirmation of the predicted bending of the light near the sun. With its radical challenge to received views about the nature of space and time, and gravitation, with its implicit challenge even to the method whereby physics had earlier been done, general relativity suited the rebellious temperaments of young thinkers who were coming of age at a time of political and cultural upheaval and eager to lead a revolt against the philosophy of their elders similar to the revolt then underway against the politics of their elders [...]. Certainly Schlick and Reichenbach were also attracted not only to the theory, but to its author. Einstein was more than just a world-famous scientific genius. He was a pacifist who was notorious in Germany for his early expression of doubts about German war aims. He was a socialist who was sympathetic to the aims of young Berlin student radicals, like Reichenbach [...]. He was a Jew in a Germany already showing the first signs of a vindictive anti-Semitism. How could one not be drawn to such a man and his science? How could one not seek to develop a philosophy of science that would legitimate the relativity theory’s claims to superiority over its predecessors, a philosophy of science that would be legitimated in turn by its success in thus rationalizing the achievements of relativity? (1994, p. 46). As Howard points out, these additional factors must have played some considerable role in Reichenbach’s belief in the achievement of the theory. These factors are not something that can be inferred by the logical analysis and justification of the theory. They are the so called “social” elements that have contributed to his belief in the theory. Thus, the context distinction is already blurred. The path Reichenbach followed in introducing these distinctions separately is the path followed by Kant in articulating his theory of knowledge. By the transcendental method of his first Critique Kant intended to provide a justification of scientific knowl-
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edge exemplified by Newtonian physics as well as Euclid’s geometry. As pointed out by Reichenbach himself, Kant’s theory of knowledge was historical. In other words, it was with respect to these particular theories at his period. He wanted to provide an indisputable epistemological basis for the aforementioned theories so that no form of scepticism could arise. There was only one way to do so and this move to suppress any scepticism should be made right at the beginning, that is, by providing such an a priori basis for these theories which could immunise them for further justification. By this move, Kant was able to put some restriction on what aspects of the nature were knowable and to legitimise what kinds of questions were epistemologically permissible. This is exactly the job for Reichenbach that was intended to be done by the introduction of the context distinction so that no possible form of scepticism and any question of the origin and justification could arise concerning the coordinative definitions in the case of the general theory of relativity. Thus, his account of knowledge is too historical, with respect to a particular scientific theory, the general theory of relativity. Reichenbach, like Kant, was introducing certain restrictions to determine the domain of epistemological activity. Reichenbach’s account of knowledge becomes susceptible to the same pitfalls Kant had. Moreover, after Kant there was a discussion about the problem of the foundation of epistemology raised by K. L. Reinhold concerning the first Critique. This problem later was formulated as a trilemma by Jakop Friederich Fries—dogmatism, infinite regress, and psychological basis. Later on with the revival of Fries’s philosophy through the works of Leonard Nelson, the foundational problem was discussed as the distinction between genesis and validity in epistemology. Reichenbach must have been aware of these discussions. So, one reason for him to introduce the context distinction might be to provide a solution to the foundation problem then.6 To conclude: Reichenbach was not interested in how to account for the role of human creativity in providing genuine scientific knowledge; but interested in accounting for a kind of knowledge provided by a specific scientific theory. Since he was primarily interested in justifying the relativity theory, he introduced the context distinction. He was still Kantian in E&P too, though much he wanted to disassociate himself from it, and the reason why Kant failed are the reasons why Reichenbach fails. The so called personal or social or conventional elements play important roles in producing scientific knowledge. These are exactly the elements for Reichenbach that need to be pointed to and accounted of. This was the gist of his general epistemological programme. To map out what kinds of roles and how conventional, subjective or social elements in human knowledge play in constructing certain structures yielding scientific knowledge is certainly a proper job for epistemology. However, introducing certain restrictions on what aspect of nature one can know and what kinds of epistemological questions are allowable to ask is certainly not a step in the right direction in dealing with fundamental epistemological questions. By doing so, one would definitely lead to an epistemological impoverishment.
6 This is what I suspect what he means by saying that the relation between philosophy and science should
not be considered as an absolute but as an historical category.
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This is what writes in the Preface to E&P and later forgets all about it: The idea that knowledge is an approximate system which will never become “true” has been acknowledged by almost all writers of the empiricist group; but never have the logical consequences of this idea been sufficiently realized. The approximate character of science has been considered as evil, unavoidable for all practical knowledge, but not to be counted among the essential features of knowledge; the probability element in science was taken as provisional feature, appearing in scientific investigation as long as it is on the path of discovery but disappearing in knowledge as a definite system. Thus a fictive definite system of knowledge was made the basis of epistemological inquiry, with the result that the schematized character of this basis was soon forgotten, and the fictive construction was identified with the actual system. It is one of the elementary laws of approximative procedure that the consequences drawn from schematized conception do not hold outside the limits of the approximation; that in particular no consequences may be drawn from features belonging to the nature of the schematization only and not to the co-ordinated object (1938, p. vi). Acknowledgements I wish to thank Alan Richardson for instructive remarks on the topic of this paper; Stathis Psillos for enlightening talks and comments on an earlier draft; and Thomas Uebel for valuable discussions and observations while formulating the problem of this paper.
References Floridi, L. (1996). Scepticism and the foundation of epistemology: A study in the metalogical fallacies. Leiden: Brill.. Friedman, M. (1999). Reconsidering logical positivism. Cambridge: Cambridge University Press.. Giere, R. N. (1999). Science without laws. Chicago: The University of Chicago Press.. Howard, D. (1994). Einstein, Kant, and the origins of logical empiricism. In W. Salmon & G. Wolters (Eds.), Logic, language, and the structure of scientific theories (pp. 45–105). Pittsburgh: University of Pittsburgh Press.. Hoyningen-Huene, P. (1987). Context of discovery and context of justification. Studies in History and Philosophy of Science, 18, 501–515. Kant, I. (1786/1970). Metaphysical foundations of natural science. (J. W. Ellington, Trans.). Indianapolis: The Bobbs-Merrill. Kant, I. (1787/1987). Critique of pure reason. (N. K. Smith, Trans.). London: Macmillian. Peckhaus, V. (2006). Psychologism and the distinction between discovery and justification. In J. Schickore & F. Steinle (Eds.), Revisiting discovery and jutification (pp. 96–116). Dordrecht: Springer. Popper, K. R. (1934/1980). The logic of scientific discovery. London: Hutchinson. Reichenbach, H. (1920/1965). The theory of relativity and a priori knowledge. Berkeley & Los Angeles: University of California Press. Reichenbach, H. (1924/1969). Axiomatization of theory of relativity. Berkeley & Los Angeles: University of California Press. Reichenbach, H. (1928/1958). The philosophy of space and time. New York: Dover. Reichenbach, H. (1929). Ziele und Wege der physikalischen Erkenntnis. Handbuch der Physik, 4, 1–80. Reichenbach, H. (1938). Experience and prediction. Chicago: The University of Chicago Press. Salmon, W. C. (1979). The philosophy of Hans Reichenbach. In W. C. Salmon (Ed.), Hans Reichenbach: Logical empiricist (pp. 1–84). Dordrecht: D. Reidel. Torretti, R. (1983). Relativity and geometry. Oxford: Pergamon Press.
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Synthese (2011) 181:95–111 DOI 10.1007/s11229-009-9589-6
On Hans Reichenbach’s inductivism Maria Carla Galavotti
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 1 July 2009 © Springer Science+Business Media B.V. 2009
Abstract One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach’s inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises’s perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach’s inductivism, with special reference to his book Experience and prediction. Keywords
Probability · Induction · Epistemology
1 Reichenbach’s probabilism Wesley Salmon, a prominent pupil of Hans Reichenbach, wrote of his mentor: “Just as Hume was the great empiricist of the eighteenth century, so it may be, will Reichenbach be remembered as the great empiricist of the twentieth century” (Salmon 1979, pp. 2–3). There is no doubt that this statement features a distinctive trait of Reichenbach’s philosophy. Echoing Salmon’s statement, one could also claim that as Hume was the great inductivist of the eighteenth century, Reichenbach was the great
M. C. Galavotti (B) Department of Philosophy, University of Bologna, via Zamboni 38, 40126 Bologna, Italy e-mail:
[email protected]
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inductivist of the twentieth century. Like Hume, Reichenbach was deeply convinced that prediction is the main task of science, and that induction is the essential tool for making predictions. Unlike Hume’s, though, Reichenbach’s inductivism is probabilistic: he regarded the combination of induction and probability as a decisive step forward in the direction pointed by Hume. Reichenbach’s empiricism is characterized by a constant attention to scientific practice flanked by a distrust of the notion of truth. In fact Reichenbach’s epistemology is rooted in the conviction that it is probability, not truth, that provides the toolbox for a reconstruction of scientific knowledge in tune with scientific practice. In his address delivered to the Neuvième Congrès International de Philosophie (Paris, 1937) he maintained that “the ideal of an absolute truth is a phantom, unrealizable; certainty is a privilege pertaining only to tautologies, namely those propositions which do not convey any knowledge” (Reichenbach 1937, p. 90. My translation). When dealing with matters of experience, truth can at best represent the limiting case of probability, namely “a special case in which the probability value is near to one or zero. It would be illusory to imagine that the terms ‘true’ or ‘false’ ever expressed anything else than high or low probability values” (Reichenbach 1936, p. 156). The attitude adopted in this connection inspired Reichenbach’s criticism of the position assumed by Rudolf Carnap and the “Viennese school” aimed “to show that every proposition has a verifiable meaning” (Reichenbach 1936, p. 143). While sharing Carnap’s concern for the problem of meaning, Reichenbach opposed the verifiability theory, calling attention to the close ties between the significance of scientific statements and their predictive character, which is a condition for their testability. Ever since the early days of logical empiricism, Reichenbach held that “the concept of probability was fundamental to any theory of knowledge” (Reichenbach 1951, p. 47).1 By contrast, he heralded a probabilistic theory of meaning which “substituted probability relations for equivalence relations and conceived of verification as a procedure in terms of probabilities rather than in terms of truth” and “abandoned the program of defining ‘the meaning’ of a sentence. Instead, it merely laid down two principles of meaning; the first stating the conditions under which a sentence has meaning; the second the conditions under which two sentences have the same meaning” (Reichenbach 1951, p. 47). It is worth recalling how back in the Thirties Carnap’s interest in probability was triggered by the need to overcome the shortcomings of the verifiability theory of meaning. Evidence of the fact that Carnap’s theory of probability is rooted in the problem of cognitive significance is the fact that he was the first to suggest the idea of “degree of confirmation” towards the end of “Testability and meaning” (1936–1937). Unlike Reichenbach, though, Carnap did not distrust the notion of truth, and strived to bring the notion of confirmation as close as possible to that of truth. In the Thirties and Forties Carnap regarded confirmation as a semantic concept, by definition time-independent, expressing a relationship between the meanings of two sentences, describing a certain hypothesis and a given body of evidence supporting it. Sentences expressing degrees of confirmation are analytic and their logic, namely inductive logic, is seen as
1 In his (1951) Reichenbach dates his opposition to the verifiability theory of meaning back to 1921.
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analogous to deductive logic. The only difference between the statements of inductive logic and those of deductive logic amounts to “the fact that the first contain the concept of degree of confirmation and are based on the definition of this concept, while the latter are independent of it” (Carnap 1946, p. 591). The theory of partial definability put forward by Carnap in “Testability and meaning” was bitterly criticized by Reichenbach. To his eyes the testability criterion of meaning was quite inadequate because it did not take into account probability, and Carnap’s reduction chains were “too primitive instruments for the construction of scientific language” (Reichenbach 1951, p. 48). Reichenbach’s review of the Aufbau charged Carnap with reductionism and lack of consideration for the probabilistic aspects of science: “It is a puzzle to me just how logical neo-positivism proposes to include assertions of probability in its system, and I am under the impression that this is not possible without an essential violation of its basic principles” (Reichenbach [1933] 1978, vol. I, p. 407). For Reichenbach the distinctive feature of scientific statements lay in their predictive character: “the theory of knowledge is a theory of prediction” (Reichenbach 1937, p. 89). Statements about the future are not certain, but rather probabilistic, and the theory of knowledge requires the theory of probability, which is a “theory of propositions about the future . . . in which the two truth-values, true and false, are replaced by a continuous scale of probabilities” (Reichenbach 1936, p. 159). Such a theory rests on the frequency interpretation of probability, which is the cornerstone of Reichenbach’s entire epistemology. Before dealing with Reichenbach’s frequency theory in some detail, it is worth mentioning that following the logical empiricist orthodoxy he set himself the task of building a “probability logic”. This called for some way of bringing together probability, which can take many values, with the two values of truth and falsehood. The problem according to Reichenbach was solved by the frequency theory, which combines in the proper way statements about single events and statements about frequencies because “the frequency interpretation derives the degree of probability from an enumeration of the truth values of individual statements” (Reichenbach 1933, 1949, p. 311). When interpreted as frequency, probability refers to sequences of statements, whereas truth refers to single sentences, but since the propositional sequence “can be conceived as an extension of the concept of statement” (Reichenbach 1933, 1949, p. 312), probability logic can be seen as a logic of propositional sequences and “appears as a generalization of the logic of statements” (Reichenbach 1933, 1949, p. 313). Reichenbach’s probability logic encountered a number of criticisms but they will not be dealt with here.2 Let us instead explore the main features of Reichenbach’s frequentism. 2 Reichenbach’s frequentism We start our overview of Reichenbach’s version of the frequency interpretation of probability by comparing it with that developed by Richard von Mises, his colleague in Berlin and Istanbul. Reichenbach was concerned about distinguishing his own position 2 See Eberhardt and Glymour (in press) for a more detailed treatment of Reichenbach’s probability logic.
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from that of von Mises. In a letter to Bertrand Russell written in 1949 Reichenbach wrote the following with reference to Russell’s book Human Knowledge: I was surprised to find myself hyphenated to von Mises . . . - as much surprised, presumably, as he. You even call my theory a development of that of von Mises. I do not think this is a correct statement. My first publication on probability [Der Begriff der Wahrscheinlichkeit für die mathematische Dartstellung der Wirklichkeit, Leipzig, 1915], which is earlier than Mises’ publications, has already a frequency interpretation and a criticism of the principle of indifference . . . Mises’ merit is to have shown that the strict-limit interpretation does not lead to contradictions and, further, to have provided a means for the characterization of random sequences. . . . But my mathematical theory is more comprehensive than Mises’ theory, since it is not restricted to random sequences; furthermore, Mises does not connect his theory with the logical symbolism. And Mises has never had a theory of induction or of application of his theory to physical reality (Reichenbach 1978, vol. II, p. 410). The major differences between Reichenbach’s and von Mises’s versions of frequentism can be summarized by saying that Reichenbach (1) admitted of a weaker notion of randomness; (2) opted for a “practical limit” instead of “strict limit”; (3) admitted of single case probability attributions; (4) developed a theory of induction; (5) had an argument for the justification of induction. Compared to von Mises’s, Reichenbach’s frequentism is more flexible. The overall difference between the their viewpoints, which gave rise to the divergencies just outlined, was Reichenbach’s constant interest in all sorts of practical applications. By contrast, von Mises was more concerned with the mathematical development of the frequency theory and devoted great effort to laying its foundations upon the notion of randomness. Moreover, von Mises focused on the application of the theory to fields endowed with a well developed theoretical apparatus, like the kinetic theory of gases, Brownian motion, radioactivity, Planck’s theory of black-body radiation.3 Randomness is the cornerstone of the theory developed by von Mises, who reaffirms the theoretical priority of this notion over that of probability. Von Mises gave an operative definition of randomness in terms of insensitivity to place selection. This obtains when the limiting values of the relative frequencies in a given sequence of observations—a ‘collective’ in von Mises’s terminology—are not affected by any of all the possible selections that can be performed on it. In addition, the limiting values of the relative frequencies in the sub-sequences obtained by place selection equal those of the original sequence. This randomness condition is also called principle of the impossibility of a gambling system, because it reflects the impossibility of devising a system leading to a certain win in any hypothetical game. By adopting insensitivity to all possible place selections von Mises adopts an absolute, unrestricted notion of randomness. Soon after it was put forward, such a notion raised serious objections on the part of a number of authors including Abraham Wald and Alonzo Church.4
3 Such applications are discussed by von Mises in the last chapter of his (1939). 4 For more on this and other issues addressed in this article the reader is addressed to Galavotti (2005).
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In addition Reichenbach adopted a critical attitude towards von Mises’s view of the matter, and embraced a weaker notion of randomness, not referred to an absolute invariance domain, but rather to a restricted domain of selections “not defined by mathematical rules, but by reference to physical (or psychological) occurrences” (Reichenbach 1949, 1971, p. 150). In his words: Random sequences are characterized by the peculiarity that a person who does not know the attributes of the elements is unable to construct a mathematical selection by which he would, on an average, select more hits that would correspond to the frequency of the major sequence. In other words, such selections will be included in the domain of invariance. In this form, the impossibility of making a deviating selection is expressed by a psychological, not a logical, statement; it refers to acts performed by a human being. This may be called a psychological randomness (ibid.). Although aware of the weakness of a definition that “instead of speaking of logical impossibilities, refers only to a limitation of the technical abilities of human observers”, Reichenbach believed that “such a psychological reference is indispensable . . . when selections in terms of physical observations are to be incorporated in the domain of invariance” (ibid.). Reichenbach’s attitude towards randomness reflectd his concern for scientific practice, as testified by the following passage: All types of probability sequences are found in nature. A mathematical theory of probability should not be restricted to the study of one specific type of sequence but should include suitable definitions of various types, chosen from the standpoint of practical use (Reichenbach 1949, 1971, p. 151). In the same spirit, Reichenbach weakened the notion of strict limit adopted by von Mises by introducing the notion of practical limit. This applied to “sequences that, in dimensions accessible to human observation, converge sufficiently and remain within the interval of convergence” (Reichenbach 1949, 1971, pp. 347–348). Reichenbach justified his viewpoint by the claim that “it is with sequences having a practical limit that all actual statistics are concerned” (ibid.). His position towards the notion of limit was obviously motivated by the same concern for practical applications imprinting his concept of randomness. Like von Mises, Reichenbach held an empirical view of probability, according to which degrees of probability can only be ascertained a posteriori, namely based on experience alone. Such an attitude led naturally to the frequency view of probability, for the simple reason that what can be extracted from experience are frequencies. Reichenbach called the method by which probability values are obtained induction by enumeration. This is based on counting the relative frequency [of a certain attribute] in an initial section of the sequence, and consists in the inference that the relative frequency observed will persist approximately for the rest of the sequence; or, in other words, that the observed value represents, within certain limits of exactness, the value of the limit for the whole sequence (Reichenbach 1949, 1971, p. 351).
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The procedure described amounts to inductive inference, to be stated in more precise terms by what Reichenbach called the Rule of induction: if the sequence has a limit of the frequency, there must exist an n such that from there on the frequency f i (i > n) will remain within the interval f n ± δ, where δ is a quantity that we can choose as small as we like, but that, once chosen, is kept constant. Now if we posit that the frequency f i will remain within the interval f n ± δ, and we correct this posit for greater n by the same rule, we must finally come to the correct result (Reichenbach 1949, 1971, p. 445). As one can gather from these definitions, for Reichenbach probability and the inductive method were inextricably intertwined: on the one hand probabilities are determined by induction by enumeration and on the other hand induction is performed in a probabilistic fashion.
3 The theory of posits and the notion of weight Echoing the terminology dear to logical empiricists who labelled metaphysical concepts ‘meaningless’, von Mises maintained that to talk of the probability of single events “has no meaning” (von Mises 1939, p. 11). For him probability referred only to collectives. Reichenbach was convinced that single-case probability attributions were required for practical applications, and made an effort to accommodate them within the frequency theory. The pivotal notion in this connection is that of weight, framed in his theory of posits. As suggested by the above formulation of the Rule of induction, a probability attribution was what Reichenbach called a posit, that is “a statement with which we deal as true, although the truth value is unknown” (Reichenbach 1949, 1971, p. 373). Whenever we assess the probability of an uncertain event, we make a wager, pretty much like the gambler who “has to make a prediction before every game, although he knows that the calculated probability has a meaning only for larger numbers; and he makes his decision by betting, or as we shall say, by positing the more probable event” (Reichenbach 1949, 1971, p. 314). The theory of probability, or inductive inference, which as we saw amounts to the same thing, is a theory of posits. Posits differ depending on whether they are made in a context of primitive or advanced knowledge. Reichenbach called appraised the posits made in a state of advanced knowledge, whereas posits made in a state of primitive knowledge were called anticipative, or blind. Within primitive knowledge no information on probabilities is available, while advanced knowledge includes some information about probabilities. In the context of primitive knowledge the Rule of induction is used to obtain probability values. By contrast, “all the questions concerning induction in advanced knowledge . . . are answered in the calculus of probabilities” (Reichenbach 1949, 1971, p. 432). Typically, scientific hypotheses are confirmed within advanced knowledge by Bayes’s rule. In this connection Reichenbach embraced a kind of Bayesianism that qualifies as strictly objective, because it requires prior probabilities to be determined on the basis of frequencies alone.
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Reichenbach took posits to represent “the bridge between the probability of the . . . sequence and the compulsion to make a decision in a single case” (Reichenbach 1949, 1971, p. 315). This leads us to Reichenbach’s proposed solution of the single-case problem left open by von Mises’s frequentism. The central notion in this connection is that of weight, which is taken to represent the “predictional value” of sentences referring to single events. Posits made by such sentences receive a weight from the probabilities attached to the reference class to which the event in question is assigned. The reference class should satisfy the criterion of homogeneity, namely it should be chosen in such a way as to include as many cases as possible similar to the one under consideration, excluding dissimilar ones. Homogeneity is obtained through successive partitions of the reference class by means of statistically relevant properties. A reference class is homogeneous when it cannot be further partitioned in this way. Reichenbach’s recommendation was to choose “the narrowest class for which we have reliable statistics” (Reichenbach 1938, p. 316). Taking an example from Reichenbach, let us say that one wants to know the probability of death of a man of forty who contracted tuberculosis. Starting with the class of tubercular men of forty, a physician would presumably be in a position to narrow the reference class by taking an X-ray, and partition the initial class by means of the condition he observes. He could proceed to more and more partitions by taking into consideration further attributes, such as smoking or the environment. All relevant information available will improve the homogeneity of the reference class, while all information that does not alter the probability is irrelevant and can be neglected. Needless to say, identification of the reference class raises serious problems, because in principle one can never be sure that all of the properties relevant to a phenomenon under study have been taken into account. The issue is well known and discussed at length in the statistical literature. Although aware of such difficulties, Reichenbach believed that the theory of probability, being the theory of prediction of uncertain events, should lead to single case assignments, simply because it would otherwise fail to accomplish its main task. In everyday life as well as in science we are compelled to act on the basis of uncertain predictions, and the theory of probability is the tool that allows us to evaluate uncertainty. In Reichenbach’s words: The statement about a single case is not uttered by us with any pretence of its being a true statement; it is uttered in the form of a posit, or as we may also say . . . in the form of a wager. The frequency within the corresponding class determines, for the single case, the weight of the posit or wager. . . . we stand in a similar way before every future event, whether it is a job we are expecting to get, the result of a physical experiment, the sun’s rising tomorrow, or the next world-war. All our posits concerning these events figure within our list of expectations with a predictional value, a weight, determined by their probability (Reichenbach 1938, pp. 314–315). One of the main tasks of Experience and Prediction is “to develop the theory of weight, which shall turn out to be identical with the theory of probability” (Reichenbach 1938, p. 24), and weight receives great attention in the book. A fundamental role of the notion of weight is that of providing the essential ingredient of the probabilistic theory of meaning that Reichenbach’s opposed to the verifiability theory fostered by
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the “Viennese school”. Reichenbach’s theory of meaning is based on two fundamental principles. First, a proposition is said to be meaningful if its weight can be determined on the basis of observation; secondly, two propositions have the same meaning if their weight is the same for every possible observation that can be made. The fundamental principle underlying such a theory maintains that “there is as much meaning in a proposition as can be utilized for action” (Reichenbach 1938, p. 80; italics original). The strict link established by Reichenbach between meaning and action, together with the consideration that action is guided by prediction, explains the crucial role played by the notion of weight. The importance ascribed to action gives a pragmatical flavour to Reichenbach’s epistemology. Well aware of this, Reichenbach held that the importance assigned to the notion of weight within his own perspective was an improvement over other versions of pragmatism. All posits are characterized by a weight, but while appraised posits, which are made in the context of advanced knowledge, have a definite weight, blind posits, which are made in the context of primitive knowledge, have unknown weight and are approximate in character. However, if the sequence has a limit anticipative posits can be corrected. According to Reichenbach, this is simply a consequence of the convergence assured by the Rule of induction. The method of posits gives rise to a hierarchical system, whose basic idea is described by Reichenbach as follows: if we know the limit of the frequency in a sequence, this value can be regarded as the weight of an individual posit concerning an unknown element of the sequence. The weight may be identified with the probability of the single case . . . In order to find the limit of the frequency we use an anticipative posit; its weight is unknown. In order to determine this weight we must make an anticipative posit on a higher linguistic level; the former anticipative posit is then transformed into an appraised posit, that is, a posit of known weight. The procedure can be extended to higher and higher levels (Reichenbach 1949, 1971, p. 465). Reichenbach called the procedure that starts with blind posits and goes on to formulate appraised posits that become part of a complex system the method of concatenated inductions. As an example, in Experience and prediction he described the case of three urns containing white and black balls, of which it is known that the ratios of the white balls to the total number of balls is 1:4; 2:4 and 3:4, but it is unknown to which of the three urns each of these ratios belongs. After four draws are made from an urn (putting back the drawn ball after each draw) three white balls are obtained. It may then be asked what is the probability of a white ball. This question can be answered by formulating a blind posit, according to which the sought probability is 3/4. At this point, one can proceed to ask what is the probability that the probability of a white ball is 3/4, which is tantamount to asking, on the basis of the draws that have been made, what is the probability that the ratios of white balls in the chosen urn is 3:4. This question regards a probability of the second level, to be expressed by an appraised posit. Reichenbach tells us that such probability, calculated by means of the probability calculus, is 27/46, so that the next drawing has two weights: “the weight 3/4 for the drawing of a white ball, and the weight 27/46 for the value 3/4 of the first weight” (Reichenbach 1938, pp. 367–368). In this case the second level weight, being greater than 1/2, confirms the blind posit. In other cases the second level weight
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could suggest correcting the initial blind posit. According to Reichenbach, this kind of methodology can be applied to more complicated cases, to be dealt with by means of complex lattices of higher order probabilities forming systems of blind and appraised posits. The fundamental feature of the method of concatenated inductions is that of being self-correcting: By means of the inductive rule we set up posits concerning the limit of the frequency in a sequence and thus establish probability values. The probabilities so constructed can be used as the weights of certain other posits; we are thus able to construct appraised posits by means of anticipative posits. The appraised posits can even be identical with some of the anticipative posits; in other words, we can transform an anticipative posit into an appraised posit. Since the weight thus constructed can be used for a change in the posited value of the limit, we speak here of the method of correction (Reichenbach 1949, 1971, p. 461). Since the method of concatenated inductions allows one to move from experience of frequencies to predictions on probabilities, it provides the bed rock underpinning the interplay between experience and prediction, the fundamental constituent of scientific method. Reichenbach ascribes “the overwhelming success of scientific method” (Reichenbach 1938, p. 364) to the procedure described above, or more generally to its core notion of inductive inference. The motivation underlying Reichenbach’s wholehearted trust in the inductive method, and the reason compelling him to develop his theory of posits, is the fact that induction provides the link between experience and prediction. In Reichenbach’s words: The connecting link, within all chains of inference leading to predictions, is always the inductive inference. This is because among all scientific inferences there is only one of an overreaching type: that is the inductive inference. All other inferences are empty, tautological; they do not add anything new to the experiences from which they start. The inductive inference does; that is why it is the elementary form of the method of scientific discovery. However, it is the only form; there are no cases of connections of phenomena assumed by science which do not fit into the inductive scheme (Reichenbach 1938, p. 365). As argued in Sect. 2, for Reichenbach induction is strictly intertwined with probability, defined in terms of frequency. He clarifies that the frequency interpretation played a twofold role in connection with probability. On the one hand, “a frequency is used as a substantiation for the probability statement; it furnishes the reason why we believe in the statement” (Reichenbach 1938, p. 339; italics original), on the other hand “a frequency is used for the verification of the probability statement; that is to say, it is to furnish the meaning of the statement” (ibid., italics original). Taken together, these two related albeit different functions account for the fact that the observed frequency from which we start is only the basis of the probability inference; we intend to state another frequency which concerns future observations. The probability inference proceeds from a known frequency to one
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unknown; it is from this function that its importance is derived. The probability statement sustains a prediction, and this is why we want it (ibid.; italics original). While epitomizing the nature of scientific method, the interplay between experience and prediction calls into question the justification of induction. Given the strict link established by Reichenbach between induction and probability, the problem of justifying induction mingles with that of justifying the frequency notion of probability.
4 The justification of induction Unlike von Mises, who did not address the problem of the justification of induction, Reichenbach thought that “the theory of probability involves the problem of induction, and a solution of the problem of probability cannot be given without an answer to the question of induction” (Reichenbach 1938, p. 339). Reichenbach’s proposed solution lay in the success of the inductive method. Starting from the tenet that induction cannot be justified on logical grounds, as convincingly argued by David Hume, Reichenbach sought a justification on pragmatical grounds, through “an analysis of the situation in which we employ probability statements” (Reichenbach 1938, p. 309). Since probability statements serve the purpose of guiding decisions leading to actions, they will be justified if it can be shown that they are the best possible guide to action. The path was indicated by Hume, whose theory of inductive belief as a habit was “put forward with the intention of veiling the gap pointed out by him between experience and prediction” (Reichenbach 1938, pp. 345–346). Instead of appealing to belief, for Reichenbach one should start from the incontrovertible assertion that inductive inference “cannot be dispensed with because we need it for the purpose of action” (ibid.) and show that it is a procedure of which one can say that it gives the best possible guide to the future. It turns out that the frequency interpretation is amenable to this kind of pragmatical justification because it satisfies what Reichenbach calls the “principle of the greatest number of successes”, namely it leads to act in the most successful way possible. In Reichenbach’s words: The meaning of probability statements is to be determined in such a way that our behavior in utilizing them for action can be justified. It is in this sense that the frequency interpretation of probability statements can be carried through even if it is the happening or not happening of a single event which is of concern to us. The preference of the more probable event is justified on the frequency interpretation by the argument in terms of behavior most favourable on the whole: if we decide to assume the happening of the most probable event, we shall have in the long run the greatest number of successes. Thus although the individual event remains unknown, we do best believe in the occurrence of the most probable event as determined by the frequency interpretation; in spite of possible failures, this principle will lead us to the best ratio of successes which is attainable (Reichenbach 1938, pp. 309–310; italics original).
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Reichenbach’s argument relies on the self-correcting character of the method of concatenated inductions and on the approximate character of the rule of induction, which makes it precisely the kind of method being sought, namely “a procedure which is to furnish us the best assumption concerning the future” (Reichenbach 1938, p. 348). Given the impossibility of proving that the inductive method is truth preserving, or even that it leads to probable conclusions, it can still be shown that induction is a necessary condition of prediction. As a method of prediction, induction is subject to scientific testing, and this bears the conclusion that if successful predictions are attainable at all, the application of induction will assure attainment of that goal. Furthermore, Reichenbach claimed that the rule of induction “is the only method that can be used in the test of other methods of approximation, because it is the only method of which we know that it represents a method of approximation” (Reichenbach 1949, 1971, p. 477; italics original). Since Reichenbach regarded knowledge as a system of posits or wagers, the argument for the justification of induction acquires a crucial relevance for his epistemology, because it impinges upon the question whether scientific knowledge is the best wager we can make. In other words, his argument does not provide a justification only for induction, but for scientific method and knowledge in general. This is emphasized by the passage ending Experience and prediction: we wager on the predictions of science and wager on the predictions of practical wisdom: we wager on the sun’s rising tomorrow, we wager that food will nourish us tomorrow, we wager that our feet will carry us tomorrow. Our stake is not low; all our personal existence, our life itself, is at stake. To confess ignorance in the face of the future is the tragic duty of all scientific philosophy; but, if we are excluded from knowing true predictions, we shall be glad that at least we know the road toward our best wagers (Reichenbach 1938, p. 404). Borrowing Herbert Feigl’s terminology, Reichenbach can be said to put forward a vindication of induction, that is a pragmatic argument that justifies the use of induction in view of the attainment of what is taken to be its end, namely the formulation of good predictions. Feigl distinguishes between two kinds of justifying procedures, called ‘vindication’ and ‘validation’. The validation procedure, commonly used within deductive logic, consists in appealing to more and more general standards until the fundamental principles of a theory are reached. To justify such principles, what is needed is a validation by means of pragmatic considerations, typically based on the success obtained in view of the achievement of a certain goal. Given that the task of induction is to acquire new knowledge while formulating successful predictions, Feigl proposes to regard an inductive method as vindicated if it can be shown that it allows for good predictions about the future.5 Reichenbach’s justification of induction found favour with Wesley Salmon, who made original developments of a number of Reichenbach’s ideas. According to Salmon, a great merit of Reichenbach’s argument is that it does not require the presupposition that there exists an order in nature. On the contrary, it avoids precisely this kind of
5 See Feigl (1950) for further details.
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presupposition, for if nature is uniform, there is also the possibility that other methods of inference work, but we are not able to demonstrate it, as we can for the rule of induction. In case nature is not uniform, the rule of induction will not work, but other methods will not work either, for, if some other method led us to make correct predictions habitually, this fact alone would constitute a uniformity to which we could apply induction. Where induction fails, no other method can succeed. As observed by Salmon, “it should be clear that a solution such as Reichenbach’s to the problem of justification of induction avoids the necessity of any such assumption as the principle of uniformity of nature. The whole force of the justification is that the use of induction is reasonable whether or not nature is uniform, whatever may be meant by the assertion ‘Nature is uniform’ ” (Salmon 1953, p. 48). Being grounded on the sole criterion of convergence, Reichenbach’s justification applies equally well to a whole class of asymptotic rules. Reichenbach did not regard it as too problematic and admitted all asymptotic rules, since the probability values determined by them converge in the long run. He simply claimed the superiority of the rule of induction over other methods on account of its descriptive simplicity. This does not satisfy Salmon, who points to a gap in Reichenbach’s argument because asymptotic rules do not converge uniformly, which means that they “are not in any sense empirically equivalent” (Salmon 1963, p. 28). According to Salmon descriptive simplicity would be a sufficient criterion for justifying the choice of a particular rule from the class of asymptotic rules only if these rules were empirically equivalent, but this is not the case. In various articles published in the fifties and sixties Salmon attempted to vindicate the rule of induction by imposing requirements that, once applied to the great variety of inductive rules, make it possible to isolate the rule of induction, thereby justifying it. The problem has been also tackled by Ian Hacking, who proved that the three conditions of consistency, symmetry and invariance taken together are necessary and sufficient to fulfill the goal.6 Hacking’s conditions partly match those proposed by Salmon. In particular, Hacking’s consistency condition is a stronger version of Salmon’s normalizing, or “regularity” condition, imposing that no relative frequency m/n, observed in any initial section of a sequence whatsoever, can be negative, and that for every possible n so obtained all the corresponding values of m i must add up to one. Hacking’s invariance is a stronger version of Salmon’s “requirement of linguistic invariance”, aimed to avoid the choice of the language used to describe the available evidence having any bearing on the conclusions obtained by means of inductive rules. Lastly, the symmetry condition advanced by Hacking corresponds to exchangeability, and requires that for any given value of the relative frequency observed in a sample the posited value of the limiting frequency must be insensitive to the order in which the items of the sample were observed to occur. Salmon’s attempts to combine this requirement with his vindication of induction were unsuccessful, and at the beginning of the nineties he wrote that “for 25 years, it has seemed . . . an unsurmountable obstacle to the kind of vindication I had hoped to provide” (Salmon 1991, p. 107). Put briefly, the problem raised by symmetry (alias exchangeability) is as follows. The condition
6 See Hacking (1968).
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can easily be accepted by subjectivists, who hold that any evaluation of probability, although making use of empirical information provided by experience, is ultimately the expression of subjective opinion. By contrast Reichenbach and Salmon, who embrace an objective interpretation according to which the evaluation of probability is entirely based on empirical data, would have interpreted symmetry as a factual assumption on the nature of the population under investigation. As we have seen, Reichenbach locates the rule of induction within primitive knowledge, where no previous inductive information is available. Thus, according to Salmon, Reichenbach would have argued that “since we have no results of previous inductions to establish these factual assumptions, we are not entitled to make them” (Salmon 1991, p. 117). This makes the symmetry condition recalcitrant to a vindication in tune with Reichenbach’s approach. Having deemed his own previous attempts unsuccessful, at the beginning of the nineties Salmon turned to a different approach. This was meant to combine the justification of induction with Reichenbach’s distinction between “context of discovery” and “context of justification”. Such a distinction was introduced right at the beginning of Experience and prediction, with reference to “the well-known difference between the thinker’s way of finding his theorem and his way of presenting it before a public” (Reichenbach 1938, p. 6). The idea is that epistemology is concerned with the context of justification, or in other words with the “rational reconstruction” of knowledge, whereas the context of discovery belongs to the realm of psychology. With Salmon, it may be asked to which of these contexts the rule of induction belongs. His answer is that the decision to examine a given sequence to calculate the relative frequency of one of its attributes belongs to the context of discovery. Furthermore, “the use of the rule of induction to arrive at a value to posit is also part of the context of discovery; at the same time, it looks like part of the context of justification as well, for the posit is justified by virtue of the rule of induction” (Salmon 1991, pp. 117–118; italics original). In other words, according to Salmon the application of the distinction between context of discovery and context of justification to Reichenbach’s inductive rule reveals an interplay such that assumptions introduced as hypotheses at the discovery level are to be confirmed or rejected at the justification level. Applying the same kind of reasoning to Bayesian method—which as we saw was also embraced by Reichenbach—Salmon observes that the assumption that the sampling procedure is random can be seen as a guess that can be subjected to statistical testing. In fact “what the subjective Bayesian takes as a personal probability the objective Bayesian can regard as a guess in the context of discovery” (Salmon 1991, p. 118). The symmetry condition, which would obviously be satisfied in case of random sampling, would then represent a wager in the context of discovery, to be tested in the context of justification. The conclusion drawn by Salmon is that: Reichenbach sought to solve Hume’s problem of the justification of induction by means of a pragmatic vindication that relies heavily on the convergence properties of his rule of induction. His attempt to rule out all other asymptotic methods by an appeal to descriptive simplicity was unavailing. We found that important progress in that direction could be made by invoking normalizing conditions (consistency) and methodological simplicity (as a basis for invariance), but that they did not do the whole job. I am proposing that, in the end, Reichenbach’s
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own distinction between discovery and justification holds the key to the solution (Salmon 1991, p. 119). The “principle of methodological simplicity” mentioned by Salmon in the above passage is borrowed from Clendinnen, and embodies a version of simplicity that applies to rules instead of statements. It requires us to “adopt the simplest system of predicting rules which are compatible with, and exemplified in, the set of known facts” (quoted from Salmon 1991, p. 114). In spite of its originality, Salmon’s argument for the justification of induction is not fully convincing. For one thing, the distinction between context of discovery and context of justification is disputable, as testified by the ongoing debate on the topic.7 In addition, the arguments put forward by both Reichenbach and Salmon face a fundamental difficulty in connection with convergence, the fundamental criterion underpinning the rule of induction. The problem is that with respect to any given sequence one cannot predict how far one must go before obtaining evaluations—posits in Reichenbach’s terminology—that fulfil a desired degree of accuracy. Furthermore, “even if we have arrived at that point, we have no way of knowing that we are there” (Salmon 1991, p. 103). In spite of Reichenbach’s and Salmon’s efforts, this remains an open problem.8 Obviously, Salmon’s strenuous attempts to justify Reichenbach’s rule of induction were inspired by their shared conviction that the inductive method rests on the frequency theory.
5 Concluding remarks Commenting on Experience and prediction, Salmon observed that Reichenbach places great stress on what he calls the ‘overreaching character’ of probabilistic reasoning, but he tells us very little about how this is accomplished. In fact, from Reichenbach’s general characterization of his theory of probability and induction, as given in the final chapter of Experience and Prediction, it is by no means obvious how probabilistic reasoning can achieve his goal (Salmon 1994, p. 244). According to Salmon, the goal aimed at, namely knowledge of nature, could be reached by combining the theses advanced by Reichenbach in Experience and prediction with those he put forward in his volume The direction of time, which appeared posthumously in 1953. There Reichenbach developed a causal theory of time revolving around the “principle of the common cause”, stating that whenever an improbable coincidence occurs one should look for a common cause. Salmon believed that the combination of this principle with Bayes’s rule offered a canon for assigning different priors to general hypotheses, on the account that hypotheses embodying common causes should have higher prior probabilities than those involving improbable coincidences. Once again, Salmon’s proposal is interesting and original, but the principle of common cause is 7 See for instance Schickore and Steinle (2006). 8 Eberhardt and Glymour (in press) contains an extensive discussion of the problem.
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not free from difficulties.9 Therefore the approach outlined by Salmon can hardly be hold to admit of wide applicability. Reichenbach’s epistemology represents a unique blend of empiricism and pragmatism, originating from an unshakable trust in empiricism combined with the deeply felt conviction that our knowledge is uncertain and relies on induction. He set himself the goal of building an epistemological perspective which, although probabilistic, rested on a basis sound enough to guarantee objectivity. Such a solid bedrock was provided by the frequency interpretation of probability. Reichenbach was altogether concerned that the rational reconstruction of science by epistemology should never lose sight of scientific practice, nor of everyday life. He identified the main task of scientific statements with prediction, and held that success is the hallmark of science. Moving from this kind of perspective, Reichenbach was able to spot some crucial weaknesses of logical empiricism, to embrace a pragmatically oriented epistemology. It is somewhat ironic that in spite of his strong concern for practice his views fail precisely on application grounds. One may contend that the problematic aspect of Reichenbach’s construction lies in its core notion, the frequency interpretation of probability. An alternative, more flexible approach is offered by the subjective theory of probability. Granted that frequencies, whenever available, are the best guide to prediction and action, a subjectivist would not regard frequencies as the only ingredient for probability evaluations. By contrast, according to the subjective approach the evaluation of probability is a complex procedure that depends on objective as well as subjective elements combined in ways that are by and large determined by the context. While sharing Reichenbach’s empirical and pragmatic stand, and his confidence in the Bayesian method, the subjective viewpoint abandons the distinction between context of discovery and context of justification, in the conviction that a number of contextual elements that do not fall within the realm of the context of justification, like the degree of expertise of the evaluating subject and the way in which evidence has been collected, have an important role to play. The objective character that Reichenbach attached to science and epistemology included both a commitment to scientific realism and the quest for objectivity. As convincingly argued by Salmon, Reichenbach embraced a non-metaphysical form of realism.10 This included the tenet that there are unknown probabilities, a concept totally alien to the subjective approach according to which probability belongs to our knowledge rather than to the facts. In addition, Reichenbach requires the objectivity of probability evaluations and thought that this was guaranteed by the rule of induction, which is a purely empirical method of evaluating probability. In point of fact, objectivity is also taken seriously by subjectivists, who address the problem of devising good probability appraisers and have developed an array of methods for the validation of probability assessments. One should not forget that Bruno de Finetti, the strongest opponent of “objectivism” taken as the idea that probability depends entirely on some aspects of 9 In this regard see for instance Van Fraassen (1882). Van Fraassen’s article deals with Salmon’s version of
the “common cause principle”, but some of the objections it raises impinge upon Reichenbach’s formulation as well. For Salmon’s use of that principle in connection with his causal theory of explanation see Salmon (1998). 10 See Salmon (1994) and (1999).
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reality, gave substantial contributions to the problem of objectivity of probability evaluations.11 The subjective viewpoint embodies a view of epistemology and rationality that strays from Reichenbach’s in a number of respects. In particular, subjectivists do not share his conviction that there are correct—generally unknown—probability values to be approached by a self-correcting procedure based on an entirely empirical method like the rule of induction. They rather commit themselves to a weaker view of rationality that regards scientific knowledge as the product of the concurrence of logical and empirical elements, as well as personal and social factors.12 While there is no question that whenever plenty of evidence is available probability assessments tend to converge in the long run, in those situations characterized by scant information subjectivism seems to have more to offer than frequentism, but the choice between these options also depends on philosophical considerations. References Carnap, R. (1936–1937). Testability and meaning. Philosophy of Science, 3, 419–471; 4, 1–40. Carnap, R. (1946). Remarks on induction and truth. Philosophy and Phenomenological Research, 6, 590–602. Dawid, P., & Galavotti, M. C. (2009). De Finetti’s subjectivism, objective probability, and the empirical validation of probability assessments. In M. C. Galavotti (Ed.), Bruno de Finetti, radical probabilist (pp. 97–114). London: College Publications. Eberhardt, F., & Glymour, C. (in press). Hans Reichenbach’s probability logic. In D. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the history of logic X: Inductive logic. Amsterdam: Elsevier. Feigl, H. (1950). De principiis non disputandum . . .? On the meaning and the limits of justification. In M. Black (Ed.), Philosophical analysis (pp. 119–56). Ithaca, NY: Cornell University Press (Reprinted in H. Feigl, Inquiries and provocations: selected writings 1929–1974, pp. 237–68, by R. S. Cohen, Ed., 1980, Dordrecht: Reidel). Galavotti, M. C. (2001). Subjectivism, objectivism and objectivity in Bruno de Finetti’s Bayesianism. In D. Corfield & J. Williamson (Eds.), Foundations of Bayesianism (pp. 173–186). Dordrecht, Boston, London: Kluwer. Galavotti, M. C. (2003). Kinds of probabilism. In P. Parrini, W. C. Salmon, & M. H. Salmon (Eds.), Logical empiricism. Historical and contemporary perspectives (pp. 281–303). Pittsburgh: University of Pittsburgh Press. Galavotti, M. C. (2005). Philosophical introduction to probability. Stanford: CSLI. Hacking, I. (1968). One problem about induction. In I. Lakatos (Ed.), The problem of inductive logic (pp. 44–59). Amsterdam: North-Holland. Reichenbach, H. (1933, 1949). Die logischen Grundlagen des Wahrscheinlichkeitsbegriffs, Erkenntnis, 3, 401–425. (English edition with modifications of The logical foundations of the concept of probability. In H. Feigl & W. Sellars (Eds.), 1949, Readings in philosophical analysis (pp. 305–323). New York: Appleton-Century-Crofts). Reichenbach, H. (1933, 1978). Carnap’s logical structure of the world. Kantstudien, 38, 199–201 (Reprinted in English in Reichenbach 1978, Vol. I, pp. 405–408). Reichenbach, H. (1935). Wahrscheinlichkeitslehre. Leyden: Sijthoff. Reichenbach, H. (1936). Logicist empiricism in Germany and the present state of its problems. Journal of Philosophy, 6, 141–160. Reichenbach, H. (1937). La philosophie scientifique: une esquisse de ses traits principaux. In Travaux du IX Congrès International de Philosophie (pp. 86–91). Paris: Hermann. 11 More on this point is to be found in Galavotti (2001). For more details on the subjective way of addressing
the problem of objectivity see Dawid and Galavotti (2009). 12 The reader is addressed to Galavotti (2003) for a comparison between the notions of probability devel-
oped by Reichenbach and de Finetti.
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Reichenbach, H. (1938). Experience and prediction. Chicago: University of Chicago Press. Reichenbach, H. (1949). The theory of probability. Berkeley-Los Angeles: University of California Press. (Second edition 1971. English translation of Reichenbach 1935 with modifications). Reichenbach, H. (1951). The verifiability theory of meaning. Proceedings of the American Academy of Arts and Sciences, 53, 46–60. Reichenbach, H. (1978). Selected writings, 1909–1953. In M. Reichenbach & R. S. Cohen (Eds.), (Vols. I–II). Dordrecht, Boston: Reidel. Salmon, W. C. (1953). The uniformity of nature. Philosophy and Phenomenological Research, 14, 39–48. Salmon, W. C. (1963). On vindicating induction. Philosophy of Science, 30, 252–261. Salmon, W. C. (1979). The philosophy of Hans Reichenbach. In W. C. Salmon (Ed.), Hans Reichenbach: Logical empiricist (pp. 1–84). Dordrecht: Reidel. Salmon, W. C. (1991). Hans Reichenbach’s vindication of induction. Erkenntnis, 35, 99–122. Salmon, W. C. (1994). Carnap, Hempel, and Reichenbach on scientific realism. In W. C. Salmon & G. Wolters (Eds.), Logic, language, and the structure of scientific theories (pp. 237–254). Pittsburgh: University of Pittsburgh Press and Konstanz: Universitätsverlag. Salmon, W. C. (1998). Causality and explanation. Oxford: Oxford University Press. Salmon, W. C. (1999). Ornithology in a cubical world: Reichenbach on scientific realism. In D. Greenberger, et al. (Eds.), Epistemological and experimental perspectives on quantum physics (pp. 303–315). Dordrecht: Kluwer. Schickore, J. & Steinle, F. (Eds.). (2006). Revisiting discovery and justification. Dordrecht: Springer. Van Fraassen, B. (1882). Rational belief and the common cause principle. In R. McLaughlin (Ed.), What? Where? When? Why? (pp. 193–210). Dordrecht: Reidel. von Mises, R. (1939). Probability, statistics and truth. London, New York: Allen and Unwin (Reprinted New York: Dover, 1957. English revised edition of Wahrscheinlichkeit, Statistik und Wahrheit. Vienna: Springer, 1928).
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Synthese (2011) 181:113–124 DOI 10.1007/s11229-009-9586-9
Grounds and limits: Reichenbach and foundationalist epistemology Jeanne Peijnenburg · David Atkinson
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 14 July 2009 © The Author(s) 2009. This article is published with open access at Springerlink.com
Abstract From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form ‘x is probable’ only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis’s idea, calling it “a remnant of rationalism”. The last move in this debate was a challenge by Lewis, defying Reichenbach to produce a regress of probability values that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it on his behalf, as it were. By presenting a series converging to a limit, we demonstrate that x can have a definite and computable probability, even if its justification consists of an infinite number of steps. Next we show the invalidity of a recent riposte of foundationalists that this limit of the series can be the ground of justification. Finally we discuss the question where justification can come from if not from a ground. Keywords
Foundationalism · Reichenbach · Probability
1 Introduction In the debate between epistemic foundationalists and anti-foundationalists, Hans Reichenbach is clearly on the side of the latter. Already in his discussions with early logical positivists, Reichenbach’s anti-foundationalist stance is noticeable: he rejects the positivistic idea that a theoretical sentence is equivalent to a set of observational sentences, arguing instead for a connection in terms of probability relations
J. Peijnenburg (B) · D. Atkinson Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, Groningen 9712 GL, The Netherlands e-mail:
[email protected]
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(Reichenbach 1938). Reichenbach’s anti-foundationalism is, however, most obvious in his debate with the American logician and epistemologist C. I. Lewis (1883–1964). The disagreement extended over more than two decades, from 1930 until 1952, and it is well-documented in letters and in contributions to journals. Both Lewis and Reichenbach agree that epistemic justification is probabilistic in character: both believe that it makes sense to say that a proposition or a belief justifies another proposition or belief, even if the former does not logically imply the latter but merely gives probabilistic support. However, Lewis insists that probabilistic justification only makes sense if it springs from a ground that is not merely probable, but is certain. Reichenbach disagrees, holding that probabilistic justification remains coherent, even if it is not rooted in firm ground. In the present article we analyse the debate (Sects. 2–4), and explain its relevance to contemporary epistemology (Sects. 5–7). We start in Sect. 2 by describing the basic difference between Lewis and Reichenbach. In Sect. 3 we explain Lewis’s main argument for his claim that probability judgements presuppose certainties, namely that any regress of probability judgements, justified by probability judgements ad infinitum, has the absurd consequence of always yielding zero. Reichenbach explains to Lewis that this argument is flawed; but, as we will see, he is unable to convince his opponent. Rather, Lewis challenges Reichenbach to produce a counterexample, i.e., a particular regress of probability judgements that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it in Sect. 4. By presenting a series that converges to a nonzero limit, we demonstrate that a probability judgement can have a definite, reasonable and computable value, even if its justification is infinitely postponed in the sense that it consists of an infinite number of steps. In this manner we show that Reichenbach, not Lewis, was correct, thereby also refuting later claims of Van Cleve (1977) and Legum (1980). In Sects. 5 and 6 we discuss further the relevance of the Lewis–Reichenbach debate to present-day foundationalism. We first explain a recent riposte, which claims that foundationalism can be consistent with an infinite series of reasons. The riposte involves a particular example of a series which, although infinite, is claimed nevertheless to be foundational. We argue that the example is flawed for three reasons. First, its structure is quite different from a standard epistemic chain. Second, it is based on a confusion between the outcome of an infinite series and its origin. Third, and most seriously, the series in question implies that the probability of the target proposition is always one, independently of the nature and probability of the purported foundation. Finally, in Sect. 7, we address the question whence epistemic justification can spring if not from a primordial source.
2 Reichenbach versus Lewis In his first major work, Mind and the World-Order. An Outline of a Theory of Knowledge (1929), Lewis starts from the traditional view that our knowledge is partly mathematical and partly empirical. The mathematical part deals with knowledge that is a priori and analytic, the empirical part concerns our knowledge of nature. The crucial issue for any theory of knowledge, according to Lewis, is the character and the validity of empirical knowledge. Since “all empirical knowledge is probable only” (ibid.,
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p. 309), the essential problem for a theory of knowledge is “that of the validity of our probability judgements” (ibid., p. 308). A recurring theme in Mind and the World Order is that probability judgements only make sense if they are based on grounds that are certain: The validity of probability judgements rests upon truths which must be certain. (ibid., p. 311) …the immediate premises are, very likely, themselves only probable, and perhaps in turn based upon premises only probable. Unless this backward-leading chain comes to rest finally in certainty, no probability-judgment can be valid at all. (ibid., pp. 328–329) From a letter that Lewis writes to Reichenbach on 26 August 1930, we can infer that Reichenbach had questioned these claims 1 month earlier, in a letter to Lewis that is now lost. Whatever the precise content of Reichenbach’s letter may have been, it is clear that it did not convince Lewis. For 16 years later, in An Analysis of Knowledge and Valuation, Lewis stresses the same point again: If anything is to be probable, then something must be certain. The data which themselves support a genuine probability, must themselves be certainties. (Lewis 1946, p. 186) The disagreement between Lewis and Reichenbach reached its height in December 1951, when, at the 48th meeting of the Eastern Division of the American Philosophical Association at Bryn Mawr College, Reichenbach and Lewis both read papers relevant to this dispute. These papers were subsequently published in the The Philosophical Review of April 1952. In Lewis’s contribution we read that he sticks to his guns: The supposition that the probability of anything whatever always depends on something else which is only probable itself, is flatly incompatible with the assignment of any probability at all. (Lewis 1952, p. 173) Reichenbach, as is clear, strongly disagrees with this foundationalist claim. Already in his major epistemological work, Experience and Prediction, he found an apt metaphor to summarize his own anti-foundationalist position: All we have is an elastic net of probability relations, floating in open space. (Reichenbach 1938, p. 192) Lewis’s claim that this is not so, and that probabilities must be grounded in certainties, is called by Reichenbach “just one of those fallacies in which probability theory is so rich” (Reichenbach 1952, p. 152). In an attempt to understand the root of the fallacy Reichenbach writes: We argue: if events are merely probable, the statement about their probability must be certain, because …Because of what? I think there is tacitly a conception involved according to which knowledge is to be identified with certainty, and probable knowledge appears tolerable only if it is embedded in a framework of certainty. This is a remnant of rationalism. (Reichenbach 1952, p. 152)
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Lewis, in turn, rejects the accusation of being an old fashioned rationalist and replies that, on the contrary, he is trying to save empiricism from what he calls a modernized coherence theory like that of his opponent (Lewis 1952, pp. 171, 173). He writes: …[Reichenbach’s] probabilistic conception strikes me as supposing that if enough probabilities can be got to lean against one another they can all be made to stand up. I suggest that, on the contrary, unless some of them can stand up alone, they will all fall flat. (Lewis 1952, p. 173) In an attempt to arbitrate the matter, we will in Sect. 3 look at the argument with which Lewis defends his claim that probabilities presuppose grounds that are certain.
3 Lewis’s argument Lewis’s argument, as it appears in Mind and the World Order, is the following: Nearly all the accepted probabilities rest upon more complex evidence than the usual formulations suggest; what are accepted as premises are themselves not certain but highly probable. Thus our probability judgement, if made explicit, would take the form: the probability that A is B is a/b, because if P is Q, then the probability that A is B is m/n, and the probability of ‘P is Q’ is p/q (where m/n × p/q = a/b). But this compound character of probable judgement offers no theoretical difficulty for their validity, provided only that the probability of the premises, when pushed back to what is more and more ultimate, somewhere comes to rest in something certain. (Lewis 1929, pp. 327–328) So Lewis’s argument amounts to this. He first stresses that the statement ‘the probability that A is B is a/b’ or P(‘A is B’) = a/b
(1)
is elliptical for ‘the probability that A is B is m/n, if P were Q, but the probability that P is Q is p/q’. In symbols: P(‘A is B’) = P(‘A is B’|‘P is Q’) P(‘P is Q’) = (m/n) × ( p/q) = a/b.
(2)
Now of course the probability that P is Q may also be elliptical. If this series were to go on and on, then, because all the factors in the multiplication are probabilities (positive numbers less than one), the probability of the original proposition ‘ A is B’ would always tend to zero. But this is ridiculous, so the series of probability judgements must come to a stop in a statement that is certain.
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Lewis’s argument is, however, simply mistaken. For P(‘A is B’) is not elliptical for the product P(‘A is B’|‘P is Q’) P(‘P is Q’), but is elliptical for the sum of products P(‘A is B’|‘P is Q’) P(‘P is Q’) + P(‘A is B’|not-‘P is Q’) P(not-‘P is Q’).
(3)
Lewis forgets that, if the probability of ‘ A is B’ is conditioned by the probability of ‘P is Q’, then you can only calculate the probability of ‘ A is B’ if you also take into account what the probability of ‘A is B’ is in case ‘P is Q’ is false. Almost 20 years later, Bertrand Russell also champions the Lewisian claim that probabilities require grounds that are certain. It is interesting, to say the least, that he defends this claim with exactly the same erroneous argument that Lewis had used (Russell 1948 , pp. 433–435). Reichenbach notices this and he explains it to Russell in a letter on 28 March 1949 (Reichenbach and Cohen 1978, pp. 405–411). Three weeks later, on the 22nd of April, Russell sends a reply in which he acknowledges his mistake. Lewis, however, seems to have persisted in the error of his ways, and Reichenbach confronts him with this fact in 1951, at the 48th meeting of the APA at Bryn Mawr. Lewis appears however not to be impressed by Reichenbach’s amendment. Apparently failing to see the relevance of the second term in (3), he simply states: I disbelieve that this will save [Reichenbach’s] point. For that, I think he must prove that, where any regress of probability-values is involved, the progressively qualified fraction measuring the probability of the quaesitum will converge to some determinable value other than zero; and I question whether such a proof can be given. (Lewis 1952, p. 172) In other words, Lewis simply does not believe that an infinite regress of probabilities can converge to some value other than zero. Even if we do take Reichenbach’s amendment into account, then for Lewis it is still the case that an infinite series of probability statements conditioned by probability statements will always converge to zero. And he defies Reichenbach to prove the contrary. Reichenbach never took up the challenge, but in the next section we will do so, as it were on Reichenbach’s behalf.
4 Meeting Lewis’s challenge Reichenbach in fact corrects Lewis and Russell by citing a theorem that follows directly from the probability axioms. For Eq. 3 is an instance of the rule of total probability: P(E 0 ) = P(E 0 |E 1 )P(E 1 ) + P(E 0 |¬E 1 )P(¬E 1 ),
(4)
where E 0 = ‘A is B’ and E 1 = ‘P is Q’. If E 1 itself is only probable, grounded in E 2 = ‘R is S’, then formula (4) must be iterated, and this produces a much more complicated regression than the simple product that Russell and Lewis had envisaged.
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Below we will give an example in which Eq. 4 is iterated infinitely many times. We will show that, even when the iteration is infinite, it need not converge to zero.1 Let P(E 0 ) in Eq. 4 be the probability that a man will have a certain hereditary disorder. Let P(E 0 |E 1 ) be the conditional probability that he will have the complaint, given that his father had it. Under the assumption that not all people with this disorder have fathers with a similar affliction, P(E 0 |¬E 1 ) is not zero. On the other hand, we know that a man is more likely to contract the disorder if his father had it than if he did not. That means that 1 > P(E 0 |E 1 ) > P(E 0 |¬E 1 ) > 0, and we may assume that approximate empirical values of these two probabilities have been estimated from the study of large populations. With α = P(E 0 |E 1 ) and β = P(E 0 |¬E 1 ), we may rewrite formula (4) in the form P(E) = α P(E 1 ) + β(1 − P(E 1 )) = α P(E 1 ) + β − β P(E 1 ) = β + (α − β)P(E 1 ).
(5)
P(E 1 ) is the probability that the father had the disorder, and of course this probability can be in turn conditioned by the fact that his father did, or did not similarly suffer. Thus we have P(E 1 ) = β + (α − β)P(E 2 ), where P(E 2 ) is the probability that the man’s paternal grandfather contracted the infirmity. Of course, the value of P(E 2 ) is calculated in the same way, giving: P(E 2 ) = β + (α − β)P(E 3 ), where P(E 3 ) is the probability that the man’s paternal great-grandfather contracted it. After n steps we have:
P(E 0 ) = β + β(α − β) + β(α − β)2 + · · · + β(α − β)n + (α − β)n+1 P(E n+1 ).
(6)
The remainder term in Eq. 6, (α − β)n+1 P(E n+1 ), is the product of two factors. The factor P(E n+1 ) is the probability that the primal grandfather had the disease. The other factor, (α − β)n+1 , gets smaller as n gets bigger, and in the limit that n goes to infinity, (α − β)n+1 tends to zero. But if (α − β)n+1 tends to zero, the entire remainder term dwindles away to nothing. In other words, with an infinite number of steps, the remainder term vanishes and what remains is the infinite series 1 See also Sect. 4 of Atkinson and Peijnenburg (2006) .
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P(E 0 ) = β + β(α − β) + β(α − β)2 + . . . = β[1 + (α − β) + (α − β)2 + . . .] ∞ (α − β)n . =β
(7)
n=0
Since 0 < α − β < 1, this geometric series is convergent and its sum is P(E 0 ) =
β . 1−α+β
(8)
And this is certainly not zero. For example, if α = 0.8 and β = 0.05, then the value of P(E 0 ) is 0.2. Conclusion: Lewis is mistaken. It is not the case that an infinite series of probability statements conditioned on probability statements always tends to zero—we have just seen an example of such a series that does not do so.2 5 A foundationalist reply Contemporary foundationalists are of course very different from Lewis, yet they resemble him in some of their views. For example, like Lewis many have a probabilistic view of epistemic justification. They believe that it makes sense to say that E n+1 justifies E n even if the former does not logically imply the latter; it is enough if E n+1 only probabilistically supports E n (with respect to some measure and with some degree of epistemic support). Moreover, like Lewis, they feel uneasy when confronted by a series in which the epistemic support is continued ad infinitum, never reaching firm ground. Presumably most of them will not fall into the trap of thinking that an infinite regress of probability values must yield zero, but they do have the feeling that such a regress is incoherent in one way or another. And this feeling should of course not come as a surprise. After all, what could be more central to foundationalism than the claim that there has to be a foundation, a last member that serves as the basis of the entire edifice, the source from which the whole justification springs? This foundation may be a certainty, as it is in Lewis’s philosophy, or a fixed probability, as it is for moderate foundationalists, or a probability that is not fixed, as it is for so-called weak foundationalists (Bonjour 1985). But however he twists and turns, a genuine foundationalist seems attached to a foundation, a last link in the chain. Nevertheless there have recently been foundationalists who argue that an epistemic chain need not have a last link. John Turri, for example, writes: A series of reasons, supporting a belief in a questioned non-evident proposition, need not have a last member in order to have a foundational (properly basic) member. …Foundationalism is consistent with there being available …an infinite, non-repeating series of reasons, of the sort the infinitist prizes. In other 2 The objection that the series in our example is not really infinite, because it starts off with a primal grandfather, begs the question. For a primal grandfather does not enter the scene as a deus ex machina: he has ancestors too, in the form of primates, vertebrates, invertebrates, etc., eventually going back to the Big Bang. And the question is precisely whether that was the beginning, indeed whether there was a beginning.
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words, foundationalists needn’t limit themselves to a finite series of reasons. (Turri 2009, pp. 162–163) Here is Turri’s example of an infinite series that he claims to be compatible with foundationalism: Suppose that Fran sees that it is 2:05. Suppose further that she practices a version of foundationalism according to which such external-world beliefs can be properly basic, and that in the present case her belief that it is 2:05 satisfies all the relevant criteria. Now Fran asserts that it is past 2:00 …She …believes it is past 2:00 because it is past 2:04 …why think that it is past 2:04? Because it is past 2:04:30. Why think that? Because it is past 2:04:45 …But proceeding this way ensures that she will approach the limit of, but never arrive at, 2:05. In other words, she has available to her an infinite series of non-repeating reasons, each of which is entailed by its successor. Moreover, the foundationalist has a principled story to tell about how each member of this infinite series gets justified for her: namely she can see that it is 2:05! (ibid., p. 163) In other words, Turri claims that the limit serves as the ground of the infinite and convergent series. Is that tenable? 6 Limits as grounds? There are three things that should be noted about Turri’s example. The first is that it is not a standard epistemic chain. When infinite, a standard epistemic chain has the form E 0 ←− E 1 ←− E 2 ←− E 3 . . . . . . ∞,
(9)
where each link E n is justified by E n+1 . Turri’s idea is that the whole infinite chain is supported by the basic belief , and thus has the form E 0 ←− E 1 ←− E 2 ←− E 3 . . . . . . ←− .
(10)
But in fact the structure of Turri’s example is quite different. It may be pictured as follows: E 0 ←− E 1 ←− E 2 ←− E 3 . . . ↑ ↑ ↑ ↑ where is Fran’s basic belief “It is 2:05”, and where E 0 : “It is past 2:00” E 1 : “It is past 2:04” E 2 : “It is past 2:04:30” E 3 : “It is past 2:04:45”
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and so on. In (11), each E n is entailed by E n+1 , just as was the case in the array (10). In contrast to (10), however, in (11) directly entails each of the E n separately; rather than an epistemic chain, (11) constitutes an infinite number of single implications, all having the same antecedent, . The fact that each E n is also entailed by E n+1 does not add anything at all to its credibility. The second remark to be made about Turri’s example concerns his use of the term ‘limit’. Normally, the limit denotes the value or outcome of a series when its length grows beyond all bounds, not its origin. In casu this refers to the probability of the non-evident target proposition E 0 . In the Fran example, however, Turri tries to identify the limit with the alleged origin of the series, namely . He thereby confuses the result of an infinite series with its supposed initiator. The third and final thing we may note about the Fran example is that entails each E n , which is more than merely making each E n more probable. Similarly, the relation between E n+1 and E n is that of logical implication rather than of probabilistic support. With the notation αn = P(E n |E n+1 ) and βn = P(E n |¬E n+1 ), we have αn = 1, since E n is entailed by E n+1 . However, βn could be nonzero. After all, E n can be true when E n+1 is false. If it were not the case that E n could be true when E n+1 is false, the structure would not be that of entailment, but bi-entailment. We would not just have E n+1 −→ E n , but also E n −→ E n+1 . Such bi-entailment would be equivalent to having αn = 1 and βn = 0. Be that as it may, in Turri’s scenario it is certainly the case that βn is not zero. Take for example β0 = P(E 0 |¬E 1 ). If E 1 were false, i.e., if it were not the case that it is past 2:04, E 0 could still be true, for it might be 2:02, for example, and then it would indeed be past 2:00. So β0 is greater than zero, and the same goes for each of the βn . However, when αn = 1 and βn > 0, there are serious consequences if the chain is of infinite length. For an infinite chain will then always lead to the conclusion that the target belief E 0 , or in Turri’s words the “belief in a questioned non-evident proposition”, has probability unity. This in itself is not bad news for Turri, for he works after all with implication, and not with probabilistic support. What is, however, disastrous for his claim is that P(E 0 ) = 1 quite independently of what is. Indeed, even if were replaced by not- = ‘It is not past 2:05’, the infinite chain would still lead to certainty. This can be further elucidated as follows. Appealing once more to the rule of total probability, now in the form P(E n ) = P(E n |E n+1 )P(E n+1 ) + P(E n |¬E n+1 )P(¬E n+1 ), we find that P(¬E n ) = P(¬E n |¬E n+1 )P(¬E n+1 ),
(12)
with use of P(E n |E n+1 ) = 1. 3 The relation (12) can be iterated from n = 0 to n = s: 3 The steps in the derivation of Eq. 12 are
P(E n ) = P(E n+1 ) + P(E n |¬E n+1 )P(¬E n+1 ) 1 − P(E n ) = 1 − [P(E n+1 ) + P(E n |¬E n+1 )P(¬E n+1 )]
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P(¬E 0 ) =
s
P(¬E n |¬E n+1 ) P(¬E s+1 ).
(13)
n=0
What happens as we take s to infinity? P(E n |¬E n+1 ) is not 0, as we noted, therefore, P(¬E n |¬E n+1 ) is a positive number less than 1, since the sum of P(E n |¬E n+1 ) and P(¬E n |¬E n+1 ) equals 1. When s in (13) tends to infinity, the product of factors between the parentheses has an infinite number of terms, each less than one. In this limit the product will normally be zero. But of course, this means that the whole right hand side of (13) equals zero. From this it follows that P(¬E 0 ) = 0 and thus that P(E 0 ) = 1.4 Far from supporting Turri’s hope that his infinite chain can serve the foundationalist’s purpose, the above reasoning has provided ammunition for an infinitist new-style (see Peijnenburg 2007). For, in complete accordance with the Weltanschauung of the latter, we have here a proposition that is entailed (up to measure zero) by an infinite chain of conditional probabilities.5 No anchoring of the infinite sequence of propositions to a basic belief is required. Nor is it possible, as we have just shown. 7 Where then does the justification come from? If the justification of a target proposition by means of an infinite regress of epistemic support does not come from a basic belief, where does it come from? How can we make sense of the idea that there can be justification without a ground? The answer is that the justification by an infinite chain comes entirely from the conditional probabilities that constitute its links. We do not need a single source from which justification springs in order to have justificatory relations between beliefs or propositions. Recall the manner in which we (probabilistically) justified a non-evident target proposition E 0 : we calculated its unconditional probability on the basis of a series of conditional probabilities. If the series is finite, then there is a last link, a basic belief that constitutes the starting point of the chain. Part of the justification comes from this basic belief and part comes from the conditional probabilities that connect the basic belief to the target proposition. If the chain is very long but still finite, the Footnote 3 continued = 1 − P(E n+1 ) − P(E n |¬E n+1 )P(¬E n+1 ) P(¬E n ) = P(¬E n+1 ) − P(E n |¬E n+1 )P(¬E n+1 ) = [1 − P(E n |¬E n+1 )]P(¬E n+1 ) = P(¬E n |¬E n+1 )P(¬E n+1 ).
4 In general a product like the one in Eq. 13 could fail to tend to zero in the limit that s tends to infinity, but only if the conditional probabilities tend very rapidly to unity as n tends to infinity. In the normal case, however, and certainly if the conditional probabilities have a uniform upper bound that is less than 1, the infinite product is zero. 5 A special case of this result can be obtained from the example (7), in which the conditional probabilities were the same from step to step of the iteration. It suffices to set α = 1 in Eq. 8 to obtain P(E 0 ) = 1, on condition that β = 0.
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justificatory role of the basic belief diminishes while the combined contribution of the conditional probabilities to the justification increases. The longer the chain becomes, the less the justification by the basic belief and the more the justification provided by the conditional probabilities. This is no surprise, for the conditional probabilities do not arise out of thin air: they are part and parcel of the epistemic chain. If the series is infinite (and convergent), then all of the justification is carried by the conditional probabilities, and none by the basic belief. Indeed, the basic belief has then become completely irrelevant. It is instructive to illustrate our answer by means of another example. Consider an inheritable trait, T, conducive to survival in a particular environment, which a girl is sure to have if her mother had it. Suppose though that the child might also carry T if her father had it, whether or not mother did so. Thus the probability that the child has T, given that mother has T, is 1; but the probability that she has T if mother lacks T is not zero, since there is a chance after all that father has T (assuming that there is no other way that the child can get T). In terms of our symbolism, this situation satisfies αn = P(E n |E n+1 ) = 1 and βn = P(E n |¬E n+1 ) > 0, where E n is the proposition that a female in the nth generation carries T, and E n+1 is the proposition that her mother has T. So the structure of the example is formally the same as it was in Turri’s example.6 The new example has the advantage that further investigation will yield insight into the origin of the justification of the claim that a given girl has the inheritable trait, as symbolized by P(E 0 ) = 1. The probability that a girl has T is greater than the probability that mother had T (on condition that the latter probability is not 1) simply because there is a nonzero probability that father carries T. The probability that the child has T is even greater than the probability that her maternal grandmother had T, since the possibilities are more numerous: there are after all three other grandparents, each of whom could be a T-carrier. It is intuitively clear—reaching further and further back into the family tree—that the genetic condition of a great-great-grandmother in the nth ancestral generation contributes less and less, as n increases, to the probability that the girl has T. In the formal limit of an infinite number of generations, all the contributions to the probability that the child has T are coming from the conditional probabilities: the contribution of a remote ancestress diminishes more and more as the ancestress is further and further away, until she is hidden in the mists of time and her influence has vanished completely.7 A final worry seems to remain. If a basic belief about a primal grandfather or a first ancestress has no influence on the probability of our target proposition, then how could our chain of reasons apply to the world? Are we not, in concluding that all epistemic support comes from conditional probabilities, detaching our epistemic chain from the real world around us? And if so, how can we distinguish our reasonings from those 6 In Turri’s example there is of course also , which is absent here; but, as we have explained, in infinite series the justificatory role of basic beliefs such as is nihil. 7 The fact that the child is sure to carry T, in the case that the number of generations is infinite, is a consequence of the assumption that it is certain that she will carry T if her mother does so. If this conditional probability is reduced, the unconditional probability that the child carries T is also reduced (cf. Eq. 8 for the case that the conditional probabilities are the same from generation to generation).
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occurring in fiction, in the machinations of a liar, or in the hallucinations of a heroin addict? In terms of our example: how can we ever distinguish the story about a real trait T from a fairy tale with the same structure in which, instead of T, there is an inheritable magical power M to turn a prince into a frog? The distinction is not far to seek. It lies in the mundane fact that in the former, but not in the latter, the conditional probabilities connect to that possible world which is the actual world. Research in many empirical case studies might have established that all T-carriers had at least one parent who carried T. In the fairy tale, on the other hand, the only ‘evidence’ that M is inheritable is contained in the story itself—outside the tale there is no evidence at all. We realise that this answer will not convince the confirmed sceptic, but our opponent after all is the foundationalist, not the sceptic. To our friend the foundationalist we say: the fact that conditional probabilities are connected to the real world does not imply that they must have an origin in the sense of a basic belief. An infinite series of conditional probabilities can refer to the real world without their being tied to an unconditional probability. Some foundationalists might not be convinced, objecting that an appeal to notions like ‘as applying to the real world’, ‘outside evidence’ and ‘empirical case studies’ only makes sense within a framework of foundationalism. But if all that is left of foundationalism is the acceptance of estimated empirical conditional probabilities, then perhaps even Reichenbach might have joined the foundationalist club. Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
References Atkinson, D., & Peijnenburg, J. (2006). Probability without certainty. Studies in History and Philosophy of Science, 37, 442–453. Bonjour, L. (1985). The structure of empirical knowledge. Cambridge, MA: Harvard University Press. Lewis, C. I. (1929). Mind and the world-order. An outline of a theory of knowledge. New York: C. Scribner’s Sons. Lewis, C. I. (1946). An analysis of knowledge and valuation. La Salle, IL: Open Court. Lewis, C. I. (1952). The given element in empirical knowledge. The Philosophical Review, 61(2), 168–172. Legum, R. A. (1980). Probability and foundationalism. Philosophical Studies, 38(4), 419–425. Peijnenburg, J. (2007). Infinitism regained. Mind, 116, 597–602. Reichenbach, H. (1938). Experience and prediction. Chicago: University of Chicago Press. Reichenbach, H. (1952). Are phenomenological reports absolutely certain?. The Philosophical Review, 61(2), 147–159. Reichenbach, M. & Cohen, R. (Eds.). (1978). Hans Reichenbach. Selected writings 1909–1953. Dordrecht: Reidel. Russell, B. (1948). Human knowledge. London: George Allen and Unwin. Turri, J. (2009). On the regress argument for infinitism. Synthese, 166(1), 157–163. Van Cleve, J. (1977). Probability and certainty. Philosophical Studies, 32(4), 323–334.
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Synthese (2011) 181:125–136 DOI 10.1007/s11229-009-9587-8
Reliability via synthetic a priori: Reichenbach’s doctoral thesis on probability Frederick Eberhardt
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 7 July 2009 © Springer Science+Business Media B.V. 2009
Abstract Hans Reichenbach is well known for his limiting frequency view of probability, with his most thorough account given in The Theory of Probability in 1935/1949. Perhaps less known are Reichenbach’s early views on probability and its epistemology. In his doctoral thesis from 1915, Reichenbach espouses a Kantian view of probability, where the convergence limit of an empirical frequency distribution is guaranteed to exist thanks to the synthetic a priori principle of lawful distribution. Reichenbach claims to have given a purely objective account of probability, while integrating the concept into a more general philosophical and epistemological framework. A brief synopsis of Reichenbach’s thesis and a critical analysis of the problematic steps of his argument will show that the roots of many of his most influential insights on probability and causality can be found in this early work.
1 Historical background Hans Reichenbach wrote his thesis Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit (The Concept of Probability in the Mathematical Representation of Reality) largely independently in 1914. It was accepted in March 1915 by Paul Hensel and Max Noether at the University of Erlangen. Unlike his later views, the thesis was deeply influenced by the Kantian view dominant in philosophy and epistemology at the time. Reichenbach took synthetic a priori principles to form the foundation of empirical knowledge, and transcendental arguments to be the appropriate method to support such principles. Reichenbach had studied with Ernst
F. Eberhardt (B) Department of Philosophy, Washington University in St Louis, Wilson 208, Campus Box 1073, One Brookings Drive, St Louis, MO 63130, USA e-mail:
[email protected]
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Cassirer, and had hoped (unsuccessfully) to write his dissertation with the neo-Kantian Paul Natorp (Gerner 1997, p. 15). In 1914 the mathematics of probability was already reasonably well developed but there was not yet an agreed upon axiomatization. First proposals were around (e.g. Bohlmann 1901), but Andrey Kolmogorov only published the now standard set of axioms in 1933, while Reichenbach published his own (structurally, but not semantically similar) axiomatization in a paper in 1932. In 1914 the discussion surrounding the formal definition of randomness (involving von Mises 1919; Church 1940; Ville 1936; Copeland 1928; Wald 1938, etc.), which is generally regarded as one of the main impediments in the early development of an axiomatization of probability, had not yet started. Emile Borel had published a few papers on this topic, (Borel 1909) but Reichenbach does not appear to have been familiar with them at the time. Without an axiomatization or any other widely accepted foundation, probability claims and their corresponding inferences supplied successful heuristics, but were without any epistemological grounding. 2 Thesis synopsis Reichenbach’s thesis set out to change this situation by giving a detailed account of the concept of probability as it was used in the sciences, and by tying this concept into a broader philosophical and epistemological framework. Reichenbach intended to provide a purely objective account of the meaning of probability claims, conditions for the assertibility of probability claims and a foundation for a rational expectation that is based on judgments of probability. Reichenbach contrasted his view with those of von Kries (1886) and Stumpf (1892a, b), both of whom he appears to have regarded as representative of two different accounts of probability common at the time. Kries’ account of probability was based on equi-probable events: The probability of a particular event E is determined by the proportion of equi-probable ‘ur-events’ it derives from. These ur-events can be found by tracing back the (causal) history of E and its compliment, tracking each of their causal ancestor events, until an event space is found for which no reason is available to consider one event in the space more likely than any other. This space then constitutes the space of equi-probable ur-events. The inference from events for which there is no reason to believe that one is more likely than the other, to the claim that these events are equi-probable is licensed by the principle of insufficient reason,1 which states that if there is no reason to distinguish the probability of two events, then the two events have equal probability. By tracing the dependency on its ur-events, the probability of the event E can be determined. It is not obvious how a space of ur-events should be determined practically, whether practical constraints on the tracing of the causal history limits judgments of probability, or whether there always is a unique space of ur-events. A failure of uniqueness would 1 The principle of insufficient reason is now also referred to as the principle of indifference, a term coined
by the economist John Maynard Keynes in 1921. While there may be minor differences in the precise usage of the two terms, those are not relevant here.
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imply problems similar to those in the Bertrand paradox (Bertrand 1889), where the probability of events is undetermined because symmetry conditions can be applied in different ways to yield conflicting probability judgments for events. In modern terminology Kries could be described as an objective Bayesian. He believed that probabilities are objective and that there is in some sense one correct objective probability for any event, but that ultimately, a human judgment enters into the account when the space of equi-probable events is determined.2 Reichenbach took issue with this human, and therefore in his view subjective component of the principle of insufficient reason. He considered such a subjective element alien to the scientific use of probability. Consequently, Reichenbach sought to develop Kries’ account of probability in such a way that the principle of insufficient reason became redundant and that probability claims could be couched in a purely objective framework.3 Both Kries’ and Reichenbach’s views contrasted with that of Carl Stumpf. Stumpf had a purely subjectivist view of probability. He took probability to represent degrees of belief. He did not present his view explicitly in terms of wagers, but it could have been framed in those terms. Stumpf took the realization that a die is biased to constitute a change in probability as opposed to a correction. He did not view the prior belief that all sides of a die have equal probability as false. Instead, probability only constitutes a summary of the current knowledge an individual has about the events under consideration—and that can be updated. Stumpf did not give a detailed account of belief update or the constraints that beliefs are subject to, but it is obvious that he only required that a probability claim about an event reflect the considered knowledge of an individual. Events, for which an agent has no reason to believe that their probabilities differ, are assigned equal probability—until there is evidence to the contrary. Unsurprisingly, Reichenbach rejected this account as unsuitable for a description of probability in science, since it would replace the aim for objectivity with what appears to be subjective whim and autobiography. Reichenbach proposed a foundation of probability based on Henri Poincaré’s argument of arbitrary functions (1912). In modern terms one would describe this argument as an analysis of strike ratios.4 For illustration, Reichenbach considered a moving tape that is punctured (repeatedly) by a projectile shot from a cylinder fixed above the moving tape. The event space (possible locations of punctures on the tape) is divided into narrow equally wide alternating black and white stripes orthogonal to the movement 2 Salmon (1979) describes Reichenbach as having attempted to be an ‘objective Bayesian’. While this may be an accurate description of Reichenbach’s mature views, I think it is a misleading description of Reichenbach’s early views. Reichenbach rejected (or at least tried to reject) any component of human judgment in the foundation of probability, and consequently he struggled with an account of how we come to know probabilities. In contrast, an objective Bayesian admits a component of human judgment in the assessment of probability, as did Reichenbach with the introduction of posits in his mature view on probability. The synthetic (a priori) part of Reichenbach’s early view of probability admittedly constitutes an introduction of human constraints into the concept of probability, but I consider this to be of a more necessary nature than an objective Bayesian would require. 3 “In particular, we will strive to get rid of the principle of insufficient reason, which Kries could not avoid
and which, since it is purely subjective, would preclude the objective validity of the laws of probability.” Reichenbach (1916, p. 13) translation by author. 4 See, for example, Michael Strevens, Bigger than Chaos (2003).
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Fig. 1 Strike ratio: If the black and white stripes are equally wide, the probability of a white outcome is the same as the probability of a black outcome. (Figure taken from Reichenbach’s thesis.)
of the tape. In a sequence of trials (shots at the moving tape) the number of punctures of the tape that fall within each stripe are counted and plotted as a histogram. As the number of outcomes increases and the width of the stripes decreases,5 the histogram approximates a Riemann integrable function, as shown in Fig. 1. Furthermore, the number of hits on white stripes is approximately equal to the number of hits on black stripes. That is, we find that the ratio of hits on white to hits on black stripes is approximately equal no matter what the Riemann integrable function is that the histogram converges towards. Reichenbach thereby was able to argue that it is not the equi-probability of the ur-events that is required to make sense of probability claims, but rather the existence of a convergence limit of the empirical frequency distribution to a continuous function. This result does not even depend on an equal partition of the event space: If the black stripes were twice as wide as the white ones, one would converge to a strike ratio of 2:1. As long as the empirical distribution converges to a continuous function, one is able to specify a probability distribution. Thus, Reichenbach could replace the principle of insufficient reason with an assumption about the existence of a convergence limit.6 Which conditions are necessary to justify the assumption that the empirical distribution has a convergence limit? Reichenbach identified two: causally independent and causally identical trials: Reichenbach deemed an assumption of convergence to a limiting distribution justified when (i) the shots of the projectile are independent of one another (that is, in particular, if the movement of the tape is independent of the shooting device) and (ii) if the repeated shots are generated by the same mechanism subject to the same forces. If the projectile were somehow attracted to the black stripes, or if the shooting mechanism varied between shots, one would not expect the distribution of hits to be equal or even stable. Reichenbach then attempted to show that causally independent and causally identical trials imply probabilistically independent and identically distributed trials. Reichenbach did not provide a proof of this inference, but he did hint at an argument 5 Reichenbach is not particularly precise about the nature of the limit. He explicitly states the decrease in stripe width, but like Poincaré he appears to assume that there are always enough events so that the histogram bins do not suddenly only contain one or no “hit”. 6 Thesis, pp. 21–26.
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based on invariance constraints of a distribution generated by a causal structure that is subject to an intervention. He claimed that the marginal distribution of one of two causally independent variables is invariant when the other variable is subject to an intervention. This in turn implies the factorization of the joint probability into the two marginals over the variables, which constitutes probabilistic independence. The details of the argument are opaque, and its generalization to more complex scenarios is far from obvious.7 We return to this point in the analysis. Probabilistically independent and identically distributed trials provide a foundation for the weak law of large numbers. The weak law of large numbers guarantees that the sample average of a sequence of (probabilistically) independent and identically distributed trials converges to the distribution mean with probability 1, i.e. for all ε lim P(|X − μ| < ε) = 1
n→∞
In a sequence of Bernoulli trials the sample mean is an estimator of the probability of the event occurring, hence the weak law of large numbers would be of interest as a convergence guarantee towards a limiting distribution. Reichenbach did not follow this line of argument, nor did he discuss the relevance of the weak law of large numbers to his argument, even though there is reasonable evidence8 that he was familiar with the law at the time. One explanation for this neglect is that the weak law of large numbers only guarantees convergence in probability. Since probability is exactly what Reichenbach was attempting to define, convergence in probability would have implied a circular definition. Instead, he attempted to provide a guarantee of convergence with certainty. In retrospect it might be obvious that search for convergence with certainty is hopeless. But in his thesis Reichenbach argued that the existence of a convergence limit of the empirical frequency distribution is guaranteed by a synthetic a priori principle: the principle of lawful distribution. The argument for the synthetic a priori status of this 7 “Consider the experiment in which two different variables x and y are simultaneously physically real-
ized in repeating trials; then a vast variety of different combinations of x and y will be observed. Let each observed combination x, y be represented by a point in the x–y-plane. If the y variable is now forced to remain within an interval c–d, then all these points will lie in a band parallel to the x-axis. The distribution along this band is proportional to ab f 1 (x)d x if the interval from a to b varies arbitrarily. Each point on the band corresponds to an x-value and their distribution remains unchanged when the distribution of y-values is restricted: this is the condition of independence. Hence, if the limits c and d are fixed while a and b vary arbitrarily, the following equality must hold: b d
f (x, y)d xd y = k
a c
b f 1 (x)d x a
The same is true when a and b are fixed while c and d vary, i.e. b d
b f (x, y)d xd y = k
a c
d f 1 (x)d x
a
f 2 (y)dy, c
Reichenbach (1916, p. 33), translation by author. See also pages 33–36. 8 In notes pertaining to Reichenbach’s thesis preserved in the Reichenbach Archives the weak law of large
numbers is mentioned, but there is no elaboration.
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principle is, in short, as follows. It is a transcendental argument in the spirit of Kant’s argument for the synthetic a priori principle of causality.9 Reichenbach claims that our scientific knowledge is represented in the laws of nature. These laws, or at least some of them, are causal laws. In his view at the time, causal relations were assumed to be relations between individual token events, not between types of events—entirely in line with Kant’s view of causality (or at least one of its interpretations). Hence, if our causal knowledge is restricted to token events, then in order to attain knowledge in terms of causal laws, one needs some procedure that aggregates token causal events into scientific laws. This aggregation is achieved by the calculus of probability. But we only ever have finitely many token causal events to aggregate. If we had no guarantee that the empirical frequency distribution of these finitely many token causal events converges, then we could not have the knowledge represented in the laws of nature. But we do have this knowledge and use it successfully, and hence we must have a guarantee of convergence. Hence, the principle of lawful distribution, stating that each empirical distribution has a convergence limit, is a necessary ingredient for the attainment of scientific knowledge; it is a synthetic a priori principle that complements Kant’s principle of causality.10 Reichenbach claimed that if convergence did not occur (though it is not clear how or when that would be judged) then it is an indication that the conditions (causal independence of trials, causally identical trials) have not all been satisfied. However, such lack of convergence supposedly does not refute the principle of lawful distribution. Reichenbach admitted that his argument implies that the principle of lawful distribution is untestable, but he pointed out that the same criticism applies to Kant, whose principle of causality also fails to be testable. We apparently simply have to accept the lamentable nature of synthetic a priori principles.11 Reichenbach thus provided what he regarded to be an entirely objective account of probability. It is objective in the sense that it is only dependent on necessary constraints of experience, and it is not circular, since it builds on causally independent and causally identical trials. The principle of insufficient reason is replaced by the assumption of the existence of a convergence limit of the empirical frequency distribution, which in turn is guaranteed by the synthetic a priori principle of lawful distribution. On his view, the transcendental deduction of the principle of lawful distribution matches Kant’s transcendental argument for the principle of causality. Kant had argued that Hume’s 9 Reichenbach (1916, ch. 3). 10 “If there were a fully exact measurement of real things, then one should be able to claim that the value
obtained once can be found again at any time at any place. Since we cannot claim that the value remains constant we have no choice but to assume that if it is not constant then there exists some law for its distribution in time and space. This is the synthetic a priori judgment which we must make. It should be added that the same judgment must hold for the combination of several processes. As before, we cannot claim that the calculated value remains constant, and we have to replace it with its lawful distribution in space and time. Hence we conclude that the principle of lawful connection of all events, which causality brings about, is insufficient for the mathematical representation of reality. A further principle has to be added, which connects the events—one could say—orthogonally; this is the principle of lawful distribution.” (Reichenbach 1916, pp. 62–63); “Natural knowledge is only possible when this principle is added to the principle of causality, thereby, so to speak, connecting events orthogonally to the direction in which the relation of cause and effect connects them.” (Reichenbach 1916, p. 74). (italics original, translation by author). 11 Reichenbach (1916, p. 71).
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skepticism towards causal knowledge disregarded the fact that causal knowledge is necessary for empirical knowledge, and hence that the principle of causality must be synthetic a priori. Reichenbach considered his argument to complete the missing link in Kant’s account from token causal relations to causal relations of types, as they are represented in the (causal) laws of nature. The meaning of (scientific) probability statements is thus given by a relative frequency of an event within a sequence of trials, and the justification of probability claims hinges on conditions concerning the relation between the trials that give rise to the frequencies. Reichenbach embedded his account in an epistemology that was regarded as standard at the time, and he claimed that this account provides grounds for a rational expectation: Given the convergence guarantee one could take the empirical distribution to be indicative of the limiting distribution. Though the empirical distribution may at any point diverge again before it converges, the guarantee of convergence at some—albeit unknown—finite point is (supposedly) sufficient to regard any expectation based on the empirical distribution as rational.12 Convergence at some unknown point is (supposedly) better than no guarantee of convergence at all, and since this assurance is, so to speak, better than nothing, it is (supposedly) rational. Reichenbach’s argument that belief in the accuracy of the empirical distribution is the best available strategy (and therefore rational) is not made explicit in the thesis; this line of argument only surfaces later as a justification of the straight rule (see below). 3 Analysis of thesis Reichenbach successfully criticized accounts based on equi-probability and instead proposed a version of Poincaré’s argument from strike ratios. He thereby avoided paradoxes resulting from the lack of uniqueness in determining the event space of equi-probable events (e.g. Bertrand’s paradox). His new contribution was the synthetic a priori foundation with the principle of lawful distribution. It enabled him to abandon Kries’ principle of insufficient reason and substitute a supposedly justified assumption about convergence. While the result might appear to successfully establish a more objective foundation of probability, it is not obvious that the account can hold what it promises. We will consider some of the problematic issues, and in many cases we will find that Reichenbach had much more to say about these points in his later works on probability. In his thesis Reichenbach did not provide any guidance on how the trials that form the basis of his account of probability are supposed to be judged (i) causally independent, and (ii) causally identical. Reichenbach claimed that causal identity is satisfied when repeated trials are of the “same” process. Two processes are the same if they differ only in their position in space and time and all physically measurable variables have the same value. He must have assumed some caveat restricting the measurement to all relevant physically measurable variables, and we can guess that the judgment of relevance of variables was given by knowledge derived from the Kantian synthetic a priori principle of causality. None of this is elaborated in the thesis. 12 Reichenbach (1916, pp. 70–72).
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The argument for causal independence had to be similar. Without recourse to probabilistic features (since those were to be defined in terms of these causal relations), it is unclear how causal independence can be judged. Unless this knowledge is supplied by some a priori principle, it would seem that a subjective—or at least somewhat arbitrary—assessment of causal independence would enter the supposedly objective foundation. After publishing his thesis Reichenbach attended Albert Einstein’s lectures in Berlin. Einstein’s findings concerning the nature of space spelled trouble for the supposedly synthetic a priori assumption that space is Euclidean. As a result Reichenbach almost immediately became uneasy with the Kantian notion of causality as synthetic a priori. But as the above analysis shows, without the synthetic a priori principle of causality, Reichenbach loses the foundation of his account of probability in terms of causal independence and identical causal trials. In his mature view on probability in The Theory of Probability (1935/1949), Reichenbach abandoned any attempt to build probability on token causal events. Instead, probability was defined in terms of properties of sequences. These sequences were supposed to correspond to sequences of trials, but the causal properties of the trials were no longer deemed relevant to the determination of probabilities. Instead, the sequences had to satisfy the mathematical conditions of normality. The class of normal sequences is more general than that of sequences generated from independent identically distributed trials (or random sequences), but excludes deterministic or patterned sequences. The motivation for recourse to normal sequences resulted from the difficulties that had been identified with a precise formal characterization of randomness in the early part of the twentieth century. For Reichenbach this generalization to normal sequences not only avoided the problems associated with randomness, but also seemed appropriate in light of sequences of trials in science. The condition of full independence and causal identity of trials is excessively strong, since, for example, a coin might be found to measurably wear down in a long sequence of flips. Nevertheless, it might still exhibit a stable probability of 1/2 for heads. Reichenbach considered the weakening to normal sequences to provide a more general foundation that would be appropriate even for such sequences. While Reichenbach ultimately abandoned the causal foundation expounded in his thesis and concluded that probability could not be founded on causal notions, there is a sequence of papers published after his thesis in which he goes back and forth in taking causality or probability to be the more fundamental notion. (See Reichenbach 1925, 1929, 1930, 1932a.) The assessment of the connection between causality and probability is one of Reichenbach’s greatest influences. In the thesis Reichenbach’s derivation of probabilistically independent and identically distributed trials from causally independent and causally identical trials is far from complete. In order to complete the proof, Reichenbach would have needed a bridge principle that connects features of the causal structure to features of the probability distribution over that structure. Throughout his life there are indicators of the development of such a principle (Reichenbach 1920a,b, 1932b), but he only stated it explicitly as the principle of common cause in The Direction of Time (1956), published posthumously. By that time he regarded the scientific notion of causality to be a relation of event types rather than of token events. The principle of common cause links the causal feature of ‘screening off’ to proba-
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bilistic independence. Intuitively, a cause screens off its effects from any prior causal ancestors. This ‘screening off’ is reflected in the probability distribution generated by the causal structure, and so the principle of common cause states that a dependence between two variables is due to one causing the other, or the existence of a common cause of both variables. This contribution to the connection between probability and causality is widely regarded as one of Reichenbach’s most influential achievements. Reichenbach’s ideas were generalized to arbitrary causal structures in the causal Markov assumption,13 first mentioned by Kiiveri and Speed (1982), which underlies most of the contemporary procedures of causal discovery. The basic issue already featured prominently in Reichenbach’s thesis. The second aim of Reichenbach’s thesis was to supply a justification of why probability judgments determined in the way described supply a normative guide to action. The aim was to explain why probability claims supported a rational expectation for the occurrence of events. In this regard his conclusions are unsatisfying. Reichenbach unfortunately succumbed to the strong influence of the Kantian philosophy, which seems to have prevented him from presenting interesting results. He essentially claimed that we must assume that the strike ratios of the process under consideration will converge, since otherwise the knowledge represented in the laws of science would be impossible to attain. Reichenbach hinted at the weak law of large numbers, but did not lay out its relevance to the problem he was trying to tackle, nor did he discuss why he considered it to be inadequate. Instead, he argued that a guarantee of convergence could be given with certainty. But the claim is—even if one accepts the transcendental deduction—extremely weak and practically useless: Convergence is guaranteed at some point after some finite number of trials, but the actual point is unknown. This claim makes no headway into the actual question of how we are supposed to interpret the empirical distribution after a finite number of trials, what the empirical distribution tells us about future events or future distributions and how we could verify or falsify any probability claim. Furthermore, it is an extremely weak support for the basis of a rational expectation: Use the empirical distribution as basis for inferences because at some point the empirical distribution converges to the true distribution. No measure of confidence in the empirical distribution or measure of distance between the empirical and true distribution is provided. A synthetic a priori assurance that the empirical distribution of a finite number of trials converges at some point begs the question of what assurance we have regarding probability claims based on empirical facts. Reichenbach does not deny this and admits that there is no way to disprove the principle of lawful distribution. But rather than admitting that he has provided an unsatisfactory argument, he argues that Kant’s argument for the principle of causality was no better. Sadly, reference to a poor argument of a greater authority does not make the present argument any better. Later in his career, Reichenbach took several different approaches to address this problem. He developed a framework of higher-order probabilities that guarantee 13 The causal Markov condition states that each variable in a causal structure (directed acyclic graph) is
independent of its non-descendents given its parents (in the graph). Note that Reichenbach’s principle of common cause (Reichenbach 1956) is a special case of the causal Markov condition when taken to apply to distributional properties.
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convergence (in higher-order probability)14 and argued for what came to be known as the straight rule. The straight rule states that one should take the empirical distribution as representative of the limiting distribution. Although the empirical distribution might at any point be quite distinct from the limiting distribution or there might not actually be a limiting distribution, Reichenbach later argued that adherence to the straight rule is the best strategy available to find the truth, even if no guarantee of convergence is provided.15 This view is controversial, and within the sciences that use search procedures, there is a lively debate of how to handle situations in which one either has to accept such a weak convergence guarantee (known as pointwise convergence) or commit to stronger assumptions—whose support is dubious—to achieve a convergence guarantee that supports confidence intervals (so-called uniform convergence). In The Theory of Probability Reichenbach claims that the probability of convergence can be estimated by integration of convergence results across different domains16 using higher order probabilities combined with subjective posits. These posits, which basically amount to subjective guesses of probability values, seem like a peculiar reversal of Reichenbach’s orginal aim at an objective foundation of probability. Reichenbach claimed that where possible, these guesses should be informed by available frequency information, but could otherwise just be blind guesses. He considered them to be innocuous, since their effect would “wash out” in the long run, as the probability assessment is updated in light of new data. Scientific objectivity would be reached in the limit. Needless to say, even this considered view was not spared from criticism (see, e.g. Nagel 1938), but it certainly addresses the problems of the thesis in more detail.
4 Conclusion I have tried to argue that Reichenbach’s thesis leaves us with a technical account of an (well, let us say) objective foundation of probability (strike ratios approximating a continuous function), but with no satisfactory meaning to our probability claims, as the convergence guarantee is bogus. The guarantees it provides, even if one accepts the Kantian spin, are useless for scientific inference. In that sense, Reichenbach failed to achieve his aim. But he achieved what a doctoral thesis should perhaps most importantly achieve: It furnished him with a lifetime’s supply of interesting problems, to which he would make influential, though rarely uncontroversial, contributions. I have not read Reichenbach as a limiting frequentist in 1915 (though he is obviously a frequentist), since he does not explicitly identify the probability with the limit of the relative frequency in an infinite series and he points out in later work that he 14 Reichenbach (1932a, p. 614). 15 Reichenbach (1949). For a development of Reichenbach’s theory of induction see Reichenbach (1936,
1938, 1940) 16 The domain of cross-integration was given by Reichenbach’s theory of reference classes. We will not
go into any detail of that theory here. Suffice it to say that Reichenbach’s account of reference classes was problematic.
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did not do so in his thesis.17 The role of the limit is taken up by the synthetic a priori assurance given by the principle of lawful distribution. But since Reichenbach does require some kind of convergence the synthetic a priori principle seems very much like a limiting frequency wolf in the coat of some kind of sheep. 5 Epilogue In unpublished autobiographical notes from August 6, 1927, Reichenbach gives a brief review of the main results of his thesis. He lists the following18 : (i) “The assumption of equi-probable events can be replaced by a continuity assumption. (ii) The continuity assumption is essential to an understanding of causal claims. (iii) An attempt to provide a guarantee of certain convergence. (iv) An attempt to show that the principle of lawful distribution is a synthetic a priori principle and necessary for all knowledge.” In 1927 Reichenbach views points (iii) and (iv) as failures. His work in The Theory of Relativity and a priori Knowledge 1920, 1965, resulting from the lectures Reichenbach attended with Einstein after his doctoral thesis, convinced him of the impossibility of synthetic a priori principles. On (iii) he concedes that one can only guarantee convergence in probability (as is the case in the weak law of large numbers), rather than convergence with certainty. However, he considers (ii), the link between probability and causality, to be one of the most important discoveries since Hume. The results of this importance that Reichenbach attached to this point can be found in several of his later works, and Reichenbach’s insights on the relationship between probability and causality contributed crucially to the modern understanding of causality developed by Salmon (1984, 1998) and Suppes (1970), and the causal Bayes net representation in Spirtes et al. (2000). Acknowledgements I am extremely grateful to Clark Glymour for many discussions on Reichenbach’s thesis and work, and to an anonymous reviewer. This research was supported in part by a grant from the McDonnell Foundation.
References Bertrand, J. (1889). Calcul des probabilités. Paris: Gauthier-Villars. Bohlmann, G. (1901). Lebensversicherungs-Mathematik. In Encyklopadie der Mathematischen Wissenschaften, Bd. I, Teil 2, Artikel ID4b, Akademie der Wissenschaften (pp. 852–917). Leipzig: Teubner. Borel, E. (1909). Les probabilités d enombrables et leurs applications arithmétiques. Rendiconti del Circolo Matematico di Palermo, 27, 247–271. Church, A. (1940). On the concept of random sequence. American Mathematical Society Bulletin, 46, 130– 135. 17 Reichenbach (1932a, pp. 576–577). 18 HR 044-06-21, Reichenbach Collection, Special Collections, University of Pittsburgh. All rights
reserved. (translation by author).
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Copeland, A. (1928). Admissible numbers in the theory of probability. American Journal of Mathematics, 50, 535–552. Gerner, K. (1997). Hans Reichenbach, sein Leben und Wirken. Osnabrück: Phoebe Autorenpress. Kiiveri, H., & Speed, T. (1982). Structural analysis of multivariate data: A review, sociological methodology. San Francisco: Jossey-Bass. Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer. Nagel, E. (1938). Principles of the theory of probability. In R. Carnap, C. Morris, & O. Neurath, Foundations of the unity of science. Chicago: University of Chicago Press. Poincaré, H. (1912). Calcul des Probabilités. Paris: Gauthier-Villars. Reichenbach, H. (1916, 2008). Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit. J. A. Barth, Leipzig. Translated by F. Eberhardt and C. Glymour as The Concept of Probability in the Mathematical Representation of Reality. Open Court. Reichenbach, H. (1920a). Die physikalischen Voraussetzungen der Wahrscheinlichkeitsrechnung. Die Naturwissenschaften, 8, 46–55. Reichenbach, H. (1920b). Philosophische Kritik der Wahrscheinlichkeitsrechnung. Die Naturwissenschaften, 8, 146–153. Reichenbach, H. (1925). Die Kausalstruktur der Welt und der Unterschied von Vergangenheit und Zukunft. In Sitzungsberichte—Bayerische Akademie der Wissenschaften, mathematisch-naturwissenschaftliche Klasse (pp. 133–175). Reichenbach, H. (1920, 1965). The theory of relativity and a priori knowledge, translated and edited by Maria Reichenbach. Berkeley: University of California Press. Reichenbach, H. (1927). HR 044-06-21, Unpublished autobiographic notes from the Reichenbach collection, special collections. University of Pittsburgh. All rights reserved. Reichenbach, H. (1929). Stetige Wahrscheinlichkeitsfolgen. Zeitschrift für Physik, 53, 274–307. Reichenbach, H. (1930). Kausalität und Wahrscheinlichkeit. Erkenntnis, 1, 158–188. Reichenbach, H. (1932a). Axiomatik der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 34, 568–619. Reichenbach, H. (1932b). Die logischen Grundlagen des Wahrscheinlichkeitsbegriffs. Erkenntnis, 3, 410– 425. Reichenbach, H. (1936). Warum ist die Anwendung der Induktionsregel für uns notwendige Bedingung zur Gewinnung von Voraussagen?. Erkenntnis, 6, 32–40. Reichenbach, H. (1938). On probability and induction. Philosophy of Science, 5, 21–45. Reichenbach, H. (1940). On the justification of induction. The Journal of Philosophy, 37, 97–103. Reichenbach, H. (1949). The theory of probability. Berkeley, CA: University of California Press. Reichenbach, H. (1956, 1971). The Direction of Time. Berkeley, CA: University of California Press. Salmon, W. C. (1979). Hans Reichenbach: Logical empiricist. Dordrecht: D. Reidel Publishing Company. Salmon, W. C. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press. Salmon, W. C. (1998). Causality and explanation. New York: Oxford University Press. Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, Prediction and Search. New York: MIT Press. Strevens, M. (2003). Bigger than chaos. Cambridge, MA: Harvard University Press. Stumpf, C. (1892a). Über den Begriff der mathematischen Wahrscheinlichkeit. In Sitzungsbericht der philosophisch-historischen Klasse der königlich bayerischen Akademie der Wissenschaften zu München. Stumpf, C. (1892b). Über die Anwendung des mathematischen Wahrscheinlichkeitsbegriffs auf Teile eines Continuums. In Sitzungsbericht der philosophisch-historischen Klasse der königlich bayerischen Akademie der Wissenschaften zu München. Suppes, P. (1970). A probabilistic theory of causality. Amsterdam: North-Holland. Ville, J. A. (1936). Calcul des Probabilités—Sur la Notion de Collectif. Comptes Rendus Académie Des Sciences, 203, 26–27. von Kries, J. (1886). Die Prinzipien der Wahrscheinlichkeitsrechnung. Tübingen: J. C. B. Mohr. von Mises, R. (1919). Grundlagen der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 5, 52–99. Wald, A. (1938). Die Widerspruchsfreiheit des Kollektivbegriffs. Actualités Scientifiques et Industrielles, 735, 79–99.
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Synthese (2011) 181:137–155 DOI 10.1007/s11229-009-9595-8
The road to Experience and Prediction from within: Hans Reichenbach’s scientific correspondence from Berlin to Istanbul Friedrich Stadler
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 31 July 2009 © Springer Science+Business Media B.V. 2009
Abstract Ever since the first meeting of the proponents of the emerging Logical Empiricism in 1923, there existed philosophical differences as well as personal rivalries between the groups in Berlin and Vienna, headed by Hans Reichenbach and Moritz Schlick, respectively. Early theoretical tensions between Schlick and Reichenbach were caused by Reichenbach’s (neo)Kantian roots (esp. his version of the relativized a priori), who himself regarded the Vienna Circle as a sort of anti-realist “positivist school”—as he described it in his Experience and Prediction (1938). One result of this divergence was Schlick’s preference of Carnap over Reichenbach for a position at the University of Vienna (in 1926), and his decision not to serve as a co-editor with Reichenbach for the journal Erkenntnis that they jointly established in 1930 (which was then co-edited by Carnap and Reichenbach from 1930 to 1938). A second split rooted in different views on induction and probability, which culminated in the Hans Reichenbach’s refusal to serve as an invited author on probability within the International Encyclopedia of Unified Science series ed. by Rudolf Carnap, Charles Morris and Otto Neurath from 1938 onwards. In this regard it is remarkable that also Richard von Mises, who was the second leading figure of Logical Empiricism in Turkish exile, criticized the theory of probability put forward by his former Berlin colleague. In this
F. Stadler (B) Department of Philosophy, University of Vienna, University Campus, Hof 1. Spitalgasse 2, 1090 Vienna, Austria e-mail:
[email protected] F. Stadler Department of Contemporary History, University of Vienna, University Campus, Hof 1. Spitalgasse 2, 1090 Vienna, Austria F. Stadler Vienna Circle Institute, Vienna, Austria
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paper I analyse this controversial exchange, drawing on the relevant correspondence and asking whether these (meta)philosophical differences were a typical feature of the pluralism inherent in Logical Empiricism in general. Keywords Logical Empiricism · Vienna Circle · Berlin Group · Probability Theory · Hans Reichenbach · Experience and Prediction
1 Introduction Hans Reichenbach1 is still well known to the scientific community as the leading figure of the Berlin Group and one of the main proponents of Logical Empiricism—along with Moritz Schlick who founded the Vienna Circle. With the latter he was a pioneer “In Defending Einstein” (Gimbel and Waltz 2006) against “school philosophy” and in popularising modern scientific philosophy focusing primarily on inductivism and probability linked to the distinction between discovery und justification. Together with Rudolf Carnap he founded and edited the journal Erkenntnis—as the (re-founded in 1975) international forum for the movement of Logical Empiricism from 1930 to1940. (Spohn 1991). One common image of Logical Empiricism is that of a family resemblance that united the circles in Berlin, Vienna, Prague and Warsaw despite of specific personal and collective features. Nevertheless, there remain questions as to the concrete philosophical profiles and personal relations within the groups between the wars: e.g., the reasons why Reichenbach was not invited by Schlick to come to Vienna in 1925 and—surprisingly—why he did not serve as author of the International Encyclopedia of Unified Science in exile.2 In order to elucidate these developments I want to deal with the internal relations of Logical Empiricism (LE) referring primarily to the correspondence3 between: 1. Reichenbach and Schlick, who mainly addressed Neo-Kantianism (relativized a priori) and Einstein, and the failed project of founding a “Journal for Exact Philosophy” in 1923—which was realized only in 1930 with the publication of the periodical Erkenntnis. 2. Reichenbach and members of the Vienna Circle in his Istanbul years, in particular his contacts with Otto Neurath regarding the Unity of Science movement.
1 On Reichenbach’s Life and Work: Hans Reichenbach, Gesammelte Werke (HRGS). Ed. by Andreas Kam-
lah and Maria Reichenbach. Braunschweig und Wiesbaden: Vieweg 1977ff. In addition: Danneberg et al. (1994), Kamlah (2006), Glymour (2008). 2 Publications on the occasion of the centenaries of Carnap and Reichenbach: Haller and Stadler (1993), Stadler (1993), Danneberg et al. (1994). 3 The correspondence and papers of Schlick are located at the Vienna Circle Archives (VCA) in Haarlem (North-Holland), the correspondence and papers of Reichenbach in the Archives of Scientific Philosophy (ASP), University of Pittsburgh. Both collections are also available at the University of Konstanz, and partly at the Institute Vienna Circle (IVC) in Vienna. My thanks go to the archives for the permission of quoting from the correspondence.
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3. Summarizing, I will speculate on the causes of the split in the philosophy of science—which seems to be inherent in the pluralism of LE, and is even reflected in the historiography—as another hidden “positivism”—dispute. To be sure, the intellectual road to Reichenbach’s Experience and Prediction (1938) was determined by the historical circumstances in Berlin, Vienna and in the Turkish exile, where another renowned proponent of LE, the mathematician Richard von Mises was also employed by Kemal Atatürk in Istanbul till the outbreak of WW II.4
2 Reichenbach and Schlick: from philosophical coincidence to divergence The personal acquaintance between Schlick and Reichenbach was planned to take place in 1923 when Schlick was invited to the conference in Erlangen, where the project of founding a new journal for scientific philosophy was launched. This event marked the beginning of an intense as well as ambivalent communication between the two main figures in Berlin and Vienna—a communication that lasted up until Schlick’s death.5 This first common project was initiated by Carnap and Reichenbach with the aim of establishing a special journal for the growing “exact philosophy” in Germany and Austria with Springer Verlag. Schlick was the author of one of the earliest philosophical interpretations of Einsteins’s theory of relativity: Raum und Zeit in der gegenwärtigen Physik. Zur Einführung in das Verständnis der allgemeinen Relativitätstheorie (1917/1919), which was highly praised by Einstein himself (Engler and Neuber 2006).6 In addition, in 1918 Schlick published the first edition of his Allgemeine Erkenntnislehre (General Theory of Knowledge), a cornerstone of scientific philosophy conceived as critical realism (Wendel and Engler 2009 = MSGA 1). The correspondence between Schlick and Reichenbach goes back to 1920. Their contact began with Reichenbach’s publication Relativitätstheorie und Erkenntnis a priori (1920a), dedicated to Einstein, who later on helped Reichenbach get a university position in Berlin. Schlick largely endorsed Reichenbach’s booklet, but mentioned some specific points of philosophical differences related to the Neo-Kantian conception and the (relativized) a priori. And Reichenbach, in turn, appreciated Schlick’s agreement commenting on the differences as follows: If I had to contradict your studies on several issues, then that probably lies partly in our different approaches. While you were bent on contradicting Kant, my intention was to rescue him from the Kantians. (R–S, October 17, 1920).7 4 Regarding the intellectual emigration to Turkey: Dahms (2004), Erichsen (1998). 5 Reichenbach’s warm obituary of Schlick (1936a) in Erkenntnis, Vol. 6, p. 141f. 6 Edited as volume 2 of the Schlick Edition Project (Moritz Schlick Gesamtausgabe = MSGA) in Rostock and Vienna, ed. by Friedrich Stadler and Hans Jürgen Wendel. 7 „Wenn ich Ihren Untersuchungen in einigen Punkten widersprechen musste, so liegt das vielleicht z.T. in einer Verschiedenheit unserer Tendenz begründet. Denn wenn es Ihnen darauf ankam, Kant zu widerlegen, so war es meine Absicht, ihn vor den Kantianern zu retten“ (R–S, 17.10.1920).
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Schlick, in his long reply to Reichenbach, agreed to this interpretation and elucidated their problem of the a priori as principles, which constitute objects, and could be seen also as hypotheses or mere conventions, although he concluded that he was not able to identify the difference of Reichenbach’s a priori judgments from conventions proper.8 A second difference arose from the relation of Euclidian and Non-Euclidian geometry employing the principle of simplicity—given the acceptance of General Relativity Theory (GRT) (as exemplified by the logical status of coordination principles, the socalled Zuordnungsprinzipien). According to Schlick the conclusion is that any version of a synthetic a priori is to be rejected as metaphysical aberration. After this, Schlick’s final review of Reichenbach’s book in Arnold Berliner’s Die Naturwissenschaften (10, 1922)9 was a repetition of his above-mentioned critique but ended with a striking tribute to his work—despite his own successful interpretation of GRT. There seems to have been established a sense of considerable philosophical convergence between the two, if we take into account also Reichenbach’s friendly review of Schlick’s General Theory of Knowledge in Zeitschrift für Angewandte Psychologie (Journal for Applied Psychology) (1920b).10 From March 5 to 15, 1923 Carnap and Reichenbach organized a conference in Erlangen to bring together scholars in the emerging field of exact philosophising against “school philosophy”. With the founding of the Vienna Circle in 1924 this marked a sort of anniversary of German-speaking Logical Empiricism.11 Amongst the invited participants we find philosophers like Heinrich Behmann, Walter Dubislav, Abraham A. Frenkel, Fritz Heider, Paul Hertz, Kurt Lewin, but the invited Moritz Schlick was unable to attend. Regrettably, there are no proceedings left, but we know that Reichenbach presented his views on causality with the principle of probability as the more general explanatory tool. Together with Schlick, Einstein, Russell, Cassirer and Berlin Gestalt psychologists Wolfgang Köhler and Kurt Lewin a new journal titled “Zeitschrift für exakte Philosophie” (Journal for Exact Philosophy) with Springer Verlag was projected. Springer was highly sceptical because of the economic crisis in Germany and Austria and doubted there would be enough subscribers. The publisher urged the initiators to include also proponents of Geisteswissenschaften for a renamed “Zeitschrift für philosophische Forschung” (Journal for Philosophical Research)—amongst them Karl Jaspers, Martin Heidegger, Hans Freyer, Moritz Geiger, Nicolai Hartmann, Eduard Spranger, Max Wertheimer, and (more plausibly) Heinrich Scholz—on which not surprisingly no consensus was reached by the young activists of the “New philosophy” according to Reichenbach (Gerner 1997, p. 57f). Only the discontinuation of the journal Annalen der Philosopie (Annals of Philosophy), edited by Raymund Schmidt and Hans Vaihinger, made possible the inception of the new journal Erkenntnis in 1930, which was jointly commissioned by the Viennese “Verein Ernst Mach” and the Berlin “Gesellschaft für empirische Philosophie” 8 Schlick–Reichenbach, November 26, 1920. “… ich nicht herauszufinden mag, worin sich ihre Sätze a priori von den Konventionen eigentlich unterscheiden”. 9 Schlick (1922). 10 Reichenbach (1920). 11 The Erlangen Conference is described in: Thiel (1993).
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and edited by Reichenbach and Carnap, Schlick withdrew his editorship because of a difference in opinion—in his view too many concessions were given to traditional philosophy.12 This was to be expected, as the title of the journal was the reason for differences between Berlin and Vienna. Schlick’s decision was caused by Reichenbach’s first introductory note “Zur Einführung” (Introduction) and his “Die philosophische Bedeutung der modernen Physik” (The Philosophical Meaning of Modern Physics) (Erkenntnis I, 1930/1931, pp. 1–4 and 49–92). It was follwed by Schlick’s programmatic “Die Wende der Philosophy” (The Turning-Point in Philosophy).13 Schlick was confirmed by some Vienna Circle members who complained about Reichenbach assuming a privileged position as editor, so that only the “lowest common denominator” prevailed. Questions concerning the profile of the journal continued to be the subject of debates which were overshadowed by the pressure of Nazi-Germany on Meiner Verlag after 1933 to dismiss the “non-Aryan” editor Reichenbach (Hegselmann and Siegwart 1991). The sad result is well known: volume 7 appeared with only as Carnap as editor, and the last volume 8 was printed 1939/1940 jointly with the Dutch publisher Van Stockum & Zoon and Chicago University Press (for the USA) as Erkenntnis/Journal of Unified Science with Carnap and Reichenbach again as main editors, along with Philipp Frank, Joergen Joergensen, Charles W. Morris, Otto Neurath, Louis Rougier and Susan Stebbing who served as “associate editors” (Gerner 1997, pp. 157–162). Following the pioneering years between 1920 and 1925 and Reichenbach’s return to Berlin in 1926, a growing alienation can be detected between Schlick and Reichenbach, which became manifest by Reichenbach’s gradual distancing himself from the “positivist” Vienna Circle in general during his Turkish exile, from 1933 to 1938: There was Schlick’s clear preference for Carnap to come to Vienna (instead of Reichenbach) in 1926 to take on a position in theoretical philosophy. Already in 1924 Schlick had invited Carnap to write an “Abriss der symbolischen Logik”14 (published as Abriss der Logistik in 1929) after Schlick had accepted Carnap’s wish to submit his Habilitation at the Vienna University (Ferrari 2009). In two subsequent letters to Carnap (March 7, 1926 and October 2, 1927) Schlick expressed his disagreement with Reichenbach’s recent publications on “Metaphysik und Naturwissenschaft” (Metaphysics and Natural Science) (1925a) and on “Die Kausalstruktur der Welt und der Unterschied zwischen Vergangenheit und Zukunft” (The Causal Structure of the World and the Difference between Past and Future) (1925b). Moreover, he was embarrassed about Reichenbach’s critique of Feigl’s article “Zufall und Gesetz” (Chance and Law) (1927).15 As already mentioned, these philosophical differences led to Schlick’s deciding not to serve as the editor of the new journal Erkenntnis together with Reichenbach from the beginning in 1930, which resulted in both Reichenbach and Carnap serving as editors. There existed different thematic tensions in LE like the logic/language
12 Schlick to Felix Meiner, May 18, 1930. 13 English translation: Schlick (1979, Vol. II, pp. 154–160). 14 Schlick to Carnap, October 21, 1924. 15 Feigl (1927).
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distinction versus philosophy of nature and science with alternative options regarding probability and induction.16 Given this gradual distancing, it is not surprising, but still worth mentioning that in 1931 Schlick wrote an official assessment for the “Preußisches Ministerium für Wissenschaft, Kunst und Volksbildung” (Prussian Ministry for Science, Arts and Adult Education), in which he critically described Reichenbach’s scientific merits. This letter is worth quoting because it documents the reasons behind the philosophical tensions:17 He was endowed with a rare talent for analysing the basic concepts of natural science and he certainly made excellent use of this talent in his early writings that deal with the theory of relativity. Especially his main work—the ‘Philosophy of Space and Time’ gives an exemplary clear, comprehensive and, in a certain sense, also conclusive account of physical space-time issues—a contribution that in itself can be seen as a high achievement and only prompted misgivings in few items. Reichenbach’s later works do not stand on the same high level. I see his basic ideas on the analysis of causality and probability … as failed. It is as if Reichenbach had stopped himself from pursuing these issues further by his strange, rigid adherence to ideas. Perhaps this was also due to the enormous expansion of his activities in the last years … To propagate scientific insights Reichenbach had certainly made ever greater achievements but as a researcher he had not been able to fulfil the hopes that had, justifiably, been set in him ten years earlier. Whether personal traits are to blame for this or whether these very traits could lead him back to the path of truly productive research, eludes my knowledge.18 I think that these two actions were evidence for the split between Reichenbach and Schlick—with Carnap attempting unsuccessfully to mediate between the two—and in some sense also between the Berlin Group and the Vienna Circle, which was followed by a second overlapping conflict, namely between Reichenbach and the Unity of Science proponents. In any case, different approaches to causality and probability—especially Reichenbach’s “Das Kausalproblem in der Physik” (The Problem of 16 Galavotti (2005). 17 Schlick to Wolfgang Windelband, February 15, 1931. 18 “Er besitzt eine seltene Gabe zur Analyse naturwissenschaftlicher Grundbegriffe, und er hat von dieser Gabe in seinen früheren Schriften, die von der Relativitätstheorie handeln, auch einen vortrefflichen Gebrauch gemacht. Besonders sein Hauptwerk – die ,Philosophie der Raum-Zeitlehre’ – gibt eine vorbildlich klare, umfassende und in gewissem Sinne abschließende Darstellung der physikalischen RaumZeit-Fragen, die als eine selbständige Leistung hohen Ranges angesehen werden muss und nur an wenigen Punkten Bedenken erregt. Die späteren Arbeiten Reichenbachs stehen nicht auf der gleichen Höhe. Seine Grundgedanken zur Analyse der Kausalität und der Wahrscheinlichkeit … halte ich für verfehlt. Es ist, als ob Reichenbach auf diesem Gebiete durch ein eigentümlich starres Festhalten an Ideen gehindert würde, in diesen Fragen in die letzte Tiefe zu dringen. Vielleicht ist hieran auch schuld die gewaltige Ausdehnung in die Breite, die seine Tätigkeit in den letzten Jahren genommen hat … Um die Verbreitung wissenschaftlicher Einsichten hat sich Reichenbach zweifellos immer steigende Verdienste erworben, aber als Forscher hat er die sehr grossen Hoffnungen, die man vor zehn Jahren auf ihn zu setzen berechtigt war, nicht erfüllt. Ob Eigenschaften seiner Persönlichkeit hierfür verantwortlich zu machen sind, und ob sie ihn wieder auf den Weg wahrhaft fruchtbarer Forschung zurückführen können, entzieht sich meiner Beurteilung.“
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Causality in Physics) (1931/1978) in response to Schlick’s different Spielraumtheorie (range of interpretation theory) of probability (1931a)19 —led to this alienation with all its unfortunate consequences: With regard to the specific conflict, Reichenbach’s ideas (usage of probability logic including probability implication and probability propositions resulted) in the following summary: It has now been shown that the meaning of every assertion about reality is given through a prediction, and in just the same sense that the meaning of every probability assertion is given through a prediction. The inquiry into the meaning of truth of reality assertions is therefore synonymous with that into the meaning truth of probability assertions (Reichenbach 1931, p. 338). Schlick—in a letter to Carnap (September 19, 1931)—commented with disappointment and some resignation: I already read Reichenbach’s article on causality in the Naturwissenschaften yesterday. It struck me as rather meagre so that I don’t really feel like responding. However, something should be written on Reichenbach’s far-fetched ideas on probability—or do you not regard them as important enough?20 Schlick’s sudden tragic death in 1936 obscured the first wave of divergence. In his obituary of Schlick, Reichenbach praised and honoured his Viennese colleague (Erkenntnis VI, p. 141f.) as a pioneer of the anti-metaphysical “scientific conception of the world” and founder of the Vienna Circle. But some 15 years later Schlick, as well as the Vienna Circle, were not mentioned at all in Reichenbach’s successful popular book The Rise of Scientific Philosophy (1951). With a development towards an anti-Kantian position still apparent in Reichenbach’s Philosophie der Raum-Zeit-Lehre (The Philosophy of Space and Time) (1928), we can see an increasing rift with reference to causality, probability and induction—a pluralist field, which generated a split within LE especially in the Istanbul period— where mathematician Richard von Mises was one more prominent player. It seems that only Reichenbach’s lifelong friendship with Carnap did not suffer from these controversies, which cannot be addressed in detail in this study.
3 Reichenbach and the Vienna Circle/logical empiricism in Istanbul: between unity and plurality The road to Experience and Prediction was certainly one of the subjects addressed in the scientific communication between Vienna, Prague, The Hague and Istanbul which 19 English edition: Reichenbach, The Problem of Causality in Physics, in Reichenbach (1978, Vol. I,
pp. 326–342). 20 “Reichenbach’s Aufsatz ueber Kausalität in den Naturwissenschaften habe ich gestern gelesen. Er scheint
mir ziemlich kümmerlich, sodass ich keine Lust zu einer Antwort habe. Aber es sollte doch einmal jemand etwas ueber Reichenbach’s verdrehte Wahrscheinlichkeitsideen schreiben – oder hältst Du es nicht fuer wichtig genug?“
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ultimately converged in the “Americanisation” of LE (Richardson and Uebel 2007) including the “International Congresses for the Unity of Science”21 The “First Conference on the Epistemology of the Exact Sciences” held in Prague from September 15–17, 1929 was a meeting organized jointly with the German Societies of Physicists and Mathematicians (DPG/DMG). It included an introductory and controversial debate on probability and causality with Reichenbach proposing the frequency interpretation and postulating inductivism based on the idea of the uniformity of the world. A probabilist logic would enable an inductivist decision making as the real practice of scientists. And predictability therefore was seen as a reasonable pragmatic aim of science compliant with a (critical) realism—which was rejected by Schlick as a metaphysical “Wirklichkeitsphilosophie” (reality philosophy) whereas Reichenbach pleaded for realism as opposed to the so-called (Machian) “positivism” (further discussants were Richard von Mises, Paul Hertz, Friedrich Waismann and Herbert Feigl). At the same time Reichenbach turned down a professorship (Extra-Ordinarius) for natural philosophy (“Naturphilosophie”) in Prague in 1929—a decision, from which his friend Carnap was later to benefit in 1931. The “Second Conference on the Epistemology of the Exact Sciences” in Königsberg (today Kaliningrad, Russia) in 1930, organized mainly by the mathematician Kurt Reidemeister, focused on the foundational debates in mathematics and quantum mechanics (with Kurt Gödel’s famous discoveries being announced for the first time along with reports by Friedrich Waismann on conversations with Wittgenstein including the principle of complete induction). In one session in which Werner Heisenberg participated, Reichenbach criticized “The Physicalist Conception of Truth” (1931b) and took part in discussions on causality and quantum mechanics. (Erkenntnis 3/1931, pp. 91–190). He argued for the priority of a (non-causal) concept of probability over the concept of truth in modern physics, for example, in the application of Heisenberg’s uncertainty relation:22 There is no truth for physical assertions; probability is all that is attainable. If we nonetheless wish to use the concept of truth, it can play in physics only the role of the limiting case of the concept of probability. In addition, he demanded a much more sophisticated interpretation of the existing objective world than the one that had been used in physics until then: truth, causality and probability stayed on the agenda for the next decade. Four years later the “Preliminary Conference of the International Congresses for the Unity of Science” was held again in Prague, from August 31 to September 2, 1934—organized as a pre-conference to the 8th International Congress of Philosophy. Its purpose was to plan and prepare the “First International Congress for the Unity of Science” in Paris 1935 whose main topic was to be “Scientific Philosophy”. This conference was to respond to a growing need for scientific cooperation and to promote the anti-metaphysical empiricism incorporating investigations in “the logical foundations of the entire area of science” (Erkenntnis 5/1935, p. 1). In the section 21 Stadler (2001, pp. 339–392). 22 Reichenbach (1931, p. 182), quoted after (1978, Vol. I, p. 354f).
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on physics, probability, and biology with Philipp Frank and Edgar Zilsel (chaired by Louis Rougier), Reichenbach contributed a paper on “Many-Valued Logic” and chaired a discussion on induction. He also delivered a paper on “The Importance of the Concept of Probability for Knowledge” (still only available in German) to the Congress of Philosophy. The committee for the International Encyclopedia of Unity of Science (IEUS) consisted of Carnap, Frank, Joergensen, Łukasiewicz, Morris, Reichenbach, Rougier and Schlick—with Neurath’s Mundaneum Institute in The Hague serving as an organizational platform. This meeting was the first public cooperation with the Warsaw School and the North American neo-pragmatists headed by Charles Morris. Morris was later to become decisive for Reichenbach’s academic career in the USA, especially for his appointment to the chair in Los Angeles. In his programmatic speech at the Prague conference 1934, Neurath outlined the future Encyclopedia claiming that “The system is the great scientific lie” (ibid., p. 116): He already mentioned the theory-ladenness of empirical propositions and the indeterminacy of all terms as further elements of this pragmatic and historical conception of science that were diametrically opposed to the common image of “positivism”. Carnap pointed to the tri-partition of semiotics (syntax, semantic, pragmatics) as a (possible) common future agenda, even if he himself adhered to the distinction of analytic/synthetic sentences and the formal and empirical sciences. Already in Prague, a controversial discussion emerged between Reichenbach, Neurath, and Popper on induction. Popper, after rejecting Reichenbach’s theory of induction and concept of probability, offered his well-known falsificationism and hypothetical knowledge as described in the Logic of Scientific Discovery (1934). This intervention prompted Reichenbach to devote an entire article to this matter, in which he called Popper’s methodology as “completely untenable” (Reichenbach 1935a)— a verdict, which, by the way, was also directed against Carnap’s favourable review of Popper’s book in the same volume of Erkenntnis. And Reichenbach continued to attack Popper as “a naïve guy”, who was bringing the Vienna Circle into disrepute.23 The schism concerning the problem of induction had thus been anticipated. With respect to the forthcoming Congresses, Reichenbach objected early on to the term “Einheit der Wissenschaft” (Unity of Science) and proposed instead “wissenschaftliche Philosophie”/scientific philosophy.24 Neurath praised the “First Congress for the Unity of Science” at the Sorbonne in Paris 1935 (September 16–21) on “philosophie scientifique”, with Bertrand Russell giving the opening lecture, as “a scholar’s republic of logical empiricism” (Erkenntnis 5/1935, p. 377). In this optimistic air the Encyclopedia project was launched by Logical Empiricism in exile with the official support of a large international committee of some 38 philosophers of science. At the congress Reichenbach spoke on “L’empirisme logistique et la desegregation de l’apriori”, and—not surprising—on “Induction as a Method of Scientific Knowledge” (in German) as well as on “The Logic of Probability as a Form of Scientific Thinking” in a session with Carnap, Schlick, Bruno de Finetti, Zygmunt Zawirski, and Janina Hosiasson.
23 See Popper’s remembrances of this episode in (Stadler, 2001, p. 493). 24 Reichenbach to Neurath, January 8, 1935.
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In the meantime, Reichenbach had published his book Wahrscheinlichkeitslehre. Eine Untersuchung über die Logischen und Mathematischen Grundlagen der Wahrscheinlichkeitsrechnung (1935b),25 which he saw as a definitive solution to the problem of induction and a comprehensive presentation of the theory of probability (to be summarized as chapter 5 of his Experience and Prediction). In 1936, Reichenbach made a striking attempt to profile himself and the Berlin Group as distinct from the Vienna Circle in an article published in the renowned Journal of Philosophy entitled “Logistic Empiricism in Germany and the Present State of its Problems”.26 It can be read as a sort of Berlin manifesto in exile after the official manifesto Wissenschaftliche Weltauffassung. Der Wiener Kreis in 1929.27 Reichenbach’s individual account privileged his method of analysis of science (wissenschaftsanalytische Methode) and presented his probability theory since 1920. According to Reichenbach it was to be seen an alternative to the so-called “logical positivism” of the “Viennese circle” as a verificationist school with the quest for certainty:28 In line with their more concrete working-program, which demanded analysis of specific problems in science, they avoided all theoretical maxims like those set up by the Viennese school and embarked upon detailed work in logistics, physics, biology, and psychology. The central problem selected for analysis was probability and induction. Their enquiries led to a new mathematical theory of probability, and to a solution of the problem of induction. Subsequently, Reichenbach claimed he had initiated a turn from a possible generalization of the “causality-connection” of the world to a “probability-connection” (Wahrscheinlichkeitszusammenhang),29 convinced that he had “arrived at a definitive solution for a theory of propositions about the future, based on a theory of probability which answers all mathematical and logical questions involved”30 —a “probabilitylogic” as presented already in his Wahrscheinlichkeitslehre (1935)/ The Theory of Probability (1935/1949). In spite of all these tensions and differences, Reichenbach was invited by Neurath to join the Advisory Committee of the “International Unity of Science Encyclopedia”31 and to write one of the first brochures (with some 70 pages) on the “Weltbild der modernen Physik” (World View of Modern Physics) under the proposed title “Cosmology”. But Reichenbach refused to deliver an article on “Cosmology” and instead offered to write one on “Logical Analysis of Physics”, which Neurath felt did not fit into the general frame because of possible overlappings with Victor Lenzen, Philipp Frank, 25 English: The Theory of Probability (1949). 26 Journal of Philosophy 33/6/1936, pp. 141–160. 27 Abridged English translation: R.S. Cohen and M. Neurath (1973, pp. 299–319). Regarding the history of the manifesto: Uebel (2008). 28 Reichenbach, op.cit., p. 144. 29 Ibid., p. 147. 30 Ibid., p. 153. 31 Neurath to Reichenbach, January 22, 1937.
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and Ernest Nagel. As an option he suggested publishing a special monograph on probability and induction in one of the subsequent volumes. In his next letter (May 7, 1937) Neurath recommended the title “Relativity and Empiricism” and asked that it be coordinated with Frank and Lenzen. As Reichenbach still hesitated, Neurath continued with his persuasive actions. He reported that Ernest Nagel, who was offered the contribution on probability, was also expected not to deliver his own position on probability. He went on with a first compromise: namely the option of “Logical Analysis of Physics”—to which he had agreed with Morris—provided that an agreement could be reached and adopt the same format as Philipp Frank’s “Foundations of Physics”. Nevertheless, Reichenbach was still embarrassed and accused the editors of adhering to “unobjectivity”. Despite of all these differences, Neurath invited Reichenbach again, to take over the contribution on “Logical Analysis” although he was personally offended by the former (“completely clueless”/“völlige Ahnungslosigkeit”) and reminded Reichenbach of his own critical account in the Journal of Philosophy which was cited above. Once more, he renewed his offer to Reichenbach to write on his own theory of probability in one of the future volumes. In June 1937 (June 6, 8, 22), Reichenbach did not budge an inch: he refused to write generally on “analysis of physics”, and withdrew from the Advisory Committee of the IEUS on which he had served as a member. Neurath was apparently disappointed about this uncompromising rejection but proceeded to organize the forthcoming project—with 19 brochures including Erwin Finlay-Freundlich on “Cosmology” and Ernest Nagel on “Principles of the Theory of Probability”. These conflicts in a setting of theoretical pluralism led to a sort of disentanglement of Reichenbach from the Encycopedia project. At the Third International Congress for the Unity of Science—Encyclopedia Conference in Paris, (July 29–31, 1937), he did not join the organizational committee and withdrew completely as invited author for the first two volumes of the Encyclopedia with the University of Chicago Press.32 The background of this intellectual falling-out was alluded to by Neurath:33 Paris also saw two discussions devoted to settling undecided questions. One, introduced by Carnap and Neurath, dealt with the concept of truth; the other, introduced by Carnap and Reichenbach, with the concept of probability. The Encyclopedia was to be arranged like an onion, around a core of the first two volumes with 20 introductory monographs, 19 of which were actually published. After this basic “foundation” section a second series was to be devoted to problems of methodology, a third one to an overview of the current state of individual sciences, and a final one to discussions on the possible application of scientific results and methods. Each of these sections was planned to comprise several volumes of 10 monographs each. Altogether, the Encyclopedia was to have amounted to 26 volumes with 260 monographs in English and French, rounded off by a 10-volume pictorial statistical supplement with global surveys as a “visual thesaurus”—all of them dealing with philosophy, sociology and history of science. This concept was mod32 Republicationof the 19 monogaphs in 2 Volumes: Neurath et al. (1955/1971). Remarkable, Reichenbach was listed again as a member of the Advisory Committee in this Reprint. 33 Einheitswissenschaft 6 (1938, p. 3f). English in McGuinness (1987).
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elled after a (utopian) non-reductive naturalism, and non-foundational empiricism—a cooperative enterprise as an option to systems of philosophy and methodological absolutism, including verification or falsification (Nemeth and Stadler 1996). It was only at the subsequent “9th International Congress of Philosophy” (Congrés Descartes) that Reichenbach spoke on “La philosophie scientifique une equisse de ses traits principaux”. He missed the 4th International Congress for the Unity of Science in Cambridge (UK) in 1938, but he participated again in the 5th Congress for the Unity of Science in Harvard, September 3–9, 1939, after his emigration from Istanbul to the US just before the outbreak of WW II, presenting a paper “On Meaning”. At the last and 6th Congress for the Unity of Science at the University of Chicago in September 1941 he had already switched to the philosophy of quantum mechanics. Reichenbach’s emigration with his appointment as Professor for Philosophy of Science at the University of California, L.A., in 1938 was made possible by Charles Morris’s intervention and his book Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge (Chicago University Press, 1938), written in Turkish exile. In the Preface he presented the book as result of a world wide movement, including “Austrian positivists”, and German representatives of the analysis of science, now called “logistic empiricism” (as a variation on Neurath’s “logical empiricism”, etc.)—with the intention of uniting both the empiricist conception of modern science and the formalistic conception of logic, as expressed in logistics.34 But the book was written, because former investigations did not sufficiently take into account one concept which penetrates into all the logical relations constructed in these domains: that is, the concept of probability. It is the intention of this book to show the fundamental place which is occupied in the system of knowledge by this concept and to point out the consequences involved in a consideration of the probability character of knowledge35 Therefore, the approximate nature of science is an essential and unavoidable feature of knowledge, which demanded a construction of foundations different from those constructed by some of my philosophical friends. I concentrated my inquiry on the problem of probability which demanded at the same time a mathematical and logical analysis. It is only after having traced out a logistic theory of probability, including a solution of the problem of induction, that I turn now to an application of these ideas to questions of a more general epistemological character.36 Here, obviously, lies the clue to the increased split within Logical Empiricism around 1938: the presentation of one version of the theory of probability and induction as an exclusive individual solution compared to all other variants from Carnap to Zilsel—and which was seen as not fitting into the general framework and concept 34 Reichenbach (1938, V). 35 Ibid., VI. 36 Ibid., VII.
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of the foundations of knowledge and science of the growing Encyclopedia project. This “logistic empiricism” was to be transformed by Reichenbach into a new form of “probabilistic empiricism” as an alternative to all “positivist writers”. Now it seems clear also that with Experience and Prediction Reichenbach challenged mainly the “Machian” fraction with Philipp Frank and Richard von Mises, but astonishingly also the realist Popper and in a certain sense the “Vienna positivism” of Carnap and Neurath after their “behavioristic turn”37 (whose manuscript already had been completed in July 1937!). But this book was seen by the proponents of “Logical” Empiricism not at all as the path-breaking “probabilist revolution”. Here we are facing another, so far unexplored “positivism dispute” from within (after Lenin versus Mach, Planck versus Schlick, Horkheimer versus Neurath, and Adorno versus Popper). Experience and Prediction is partly an open, but also a coded critical account of (or counter-narrative to) the Viennese group—as was elaborated by Alberto Coffa in his informative comments to the German edition of Experience and Prediction in 1983.38 Reichenbach critically dealt with Mach, Schlick, Carnap and especially with Neurath’s position (as a non-foundationalist and holistic philosophy of science incorporating values and theory choice from an historical and pragmatic point of view). In this regard Reichenbach’s invention of the discovery-justification dualism can be interpreted as directed against Neurath’s vision of an enlightened “science in context”.39 In 1938, Experience and Prediction was seen by the community as one more valuable, maybe anachronistic contribution to the growing pluralist project of LE and International Encyclopedia, as Carnap had expressed ironically in a letter to Neurath:40 Have you seen Reichenbach’s latest book ‘Experience and Prediction’ (University of Chicago Press)? It contains all sorts of interesting discussions, but also a number of attacks on ‘positivism’ that in reality are only directed against Wittgenstein and our older views. Hempel would like to know at how many points of the book have you already exploded?41 Neurath did not explode, but replied in an untypical resignating manner:42 “I was very much concerned about a lot”. Reichenbach’s colleague in Istanbul, Richard von Mises, was also reluctant to write a monograph on probability for the Encyclopedia, but he instead submitted a different contribution to the “Library of Unified Science, Book Series, Vol. I” (ed. by 37 Reichenbach (1938, p. 163). 38 Alberto Coffa in Reichenbach (1983, pp. 255–304). 39 Hempel (1993), Howard (2002). Regarding the issue of realism with reference to the “cubical world” in Experience and Prediction cf. Salmon (1999), Sober in this volume. 40 Carnap to Neurath, April 21, 1938. 41 “Hast Du Reichenbach’s neues Buch ‘Experience and Prediction’ (University of Chicago Press) schon
gesehen? Es enthält allerhand interessante Diskussionen, aber auch eine Menge Angriffe gegen den ‘Positivismus’, die sich aber in Wirklichkeit nur gegen Wittgenstein und unsere älteren Auffassungen richten. Hempel möchte gerne wissen, an wie vielen Stellen des Buches Du schon zersprungen wärest?“ 42 Neurath to Carnap, May 18, 1938: “ich war sehr betroffen ueber vieles”.
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Neurath)—his book Kleines Lehrbuch des Positivismus. Einführung in die empiristische Wissenschaftsauffassung (Positivism) (1939/1951).43 In this regard it is perhaps surprising that Mises, his former colleague in Berlin, and since 1933 working and teaching at the same university in Istanbul—he was one of the pioneers of applied mathematics and probability theory (claiming a similar objective notion of statistical probability with relative frequency interpretation employing collectives (“Kollektiva”)—is mentioned by Reichenbach only once as a proponent of the first form of mathematical probability, “occurring in mathematics, mathematical physics and all kinds of statistics”.44 But for Reichenbach the more important was the second concept, namely the logical concept of probability, although it admittedly “has not been able to attain the same degree of perfection as the theory of the mathematical concept of probability”.45 These different approaches were disputed in Paris 1937 and the discussion continued (between Los Angeles and Istanbul) with a controversy in German on the probability of hypotheses between Reichenbach and Mises’ later wife, the mathematician Hilda Geiringer-Mises in the last volume of Erkenntnis/The Journal of Unified Science (8, 1939/40): – Reichenbach replied with “Über die semantische und die Objektauffassung von Wahrscheinlichkeitsausdrücken” (on the semantic and object conception of probability notions)46 to Carnap and Tarski. As a result, probability logic can be seen as a generalization of two valued logic. – Geiringer, in „Über die Wahrscheinlichkeit von Hypothesen“ (On the Probability of Hypotheses),47 with reference to Paris 1937 deplored the misunderstandings of the notion of probability in connection with the probability of hypotheses from the perspective of mathematical theory of probability (like R. von Mises), and addresses the so called dilemma riddle: if one does not know of a sentence, whether it is true or false, maybe it is possible at least to formulate a statement on its probability.48 As distributed hypotheses (according the Bayes’ Theorem (instead of Reichenbach’s “rule of induction”) this is possible for hypotheses and events—with the restriction to “Verteilungshypothesen” (distributed hypotheses) again with reference to Bayes’s Theorem. – Reichenbach replied with „Bemerkungen zur Hypothesenwahrscheinlichkeit“ (Remarks on the Probability of Hypotheses)49 that each probability of hypotheses can be interpreted with frequency; the problem of induction is a problem related to truth; and the application problem (“Anwendungsproblem”) has to do with questions of probability. 43 English translation: Richard von Mises (1951). Second German edition (1990) introduced by Friedrich Stadler, “Richard von Mises (1883–1953)—Wissenschaft im Exil” pp. 7–64. 44 Reichenbach (1938, p. 298). 45 Ibid., p. 299. 46 Reichenbach (1939/1940a, pp. 50–68). 47 Geiringer (1939/40, pp. 151–176). 48 “wenn man von einem Satz nicht weiß, ob er wahr oder falsch ist, so ist es vielleicht doch möglich, über die Wahrscheinlichkeit dieses Satzes eine Aussage zu machen”. 49 Reichenbach (1939/1940b, pp. 256–264).
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– Geiringer closed this dispute critically “Zu Bemerkungen zur Hypothesenwahrscheinlichkeit ” (On ‘Remarks on the Probability of Hypotheses’)50 challenging the exclusive status of probability theory as overcoming the difficulties of all concept formation in the sciences. In parallel, Richard Mises himself referred in his 1939 book to Reichenbach’s theory of probability (= Wahrscheinlichkeitslehre) in a chapter on the transgression of the borderline (“Grenzüberschreitungen”): he dealt with the application of probability calculus in order to solve the problem of induction based on the frequency interpretation (§14/6, p. 171ff).51 In particular, he criticized Reichenbach’s generalisation of the rule of induction aiming at applications in everyday life as totally inadequate and as violating the criterion of linguistic connectibility.52 And last not least, he classified Reichenbach’s concept of probability (as an objective property of natural phenomena) as a misleading metaphysical statement.53
4 Summary From my point of view, Reichenbach’s linkage of epistemology, probability and induction to the context of discovery/justification distinction is anything but coincidental. It appears in Experience and Prediction54 and re-occurs in his The Rise of Scientific Philosophy55 in the chapter on “Predictive Knowledge” in defence of inductive inference as a method of justification based on observational data. And in his Preface, Reichenbach established a second important link, namely to philosophical objectivism and relativism—once again, directed against Neurath. As I argued already in “Induction and/or Deduction in the Philosophy of Science”:56 these dualism were to be contextualized in the classical period of Logical Empiricism before its emigration. Besides the often forgotten vindicationist (not justificationist) position of Herbert Feigl compliant with Reichenbach’s inductivism and epistemological realism since 1934, and later on, the distinction refers also to Carnap’s rational reconstruction (in his Der Logische Aufbau der Welt/The Logical Structure of the World) (1928/1967) and appears in Popper’s Logik der Forschung (1934)/Logic of Scientific Discovery (1959)—whose English title should better read Logic of Research or Logic of Justification). Of course, this idea can be traced back to Kant, John Herschel, or William Whewell, but it has special meaning in the historiography of the “received view”. Only in the two last decades the image of the Vienna Circle/ 50 Geiringer (1939/1940b, p. 352f). 51 Mises 1939, §14/6, p. 263. English 1951, p. 171ff. 52 Ibid., p. 265. 53 Ibid., p. 283. (English 1951, p. 174f.). See also Mises, Wahrscheinlichkeit, Statistik, Wahrheit
(1928/1936) as a sort of„ Anti-Reichenbach“ reprinted in his Istanbul years. English translation (1939/1957). 54 Reichenbach (1938, p. 239). 55 Reichenbach (1951, p. 231). 56 Stadler (2004).
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Logical Empiricism as an exclusive anti-historical “positivist” school has been challenged convincingly.57 Examining the so-called “Dogmas of Logical Empiricism” since Quine it becomes clear that we are facing a research field with syntactic, semantic and pragmatic methods and that the Vienna Circle as well as the broader movement of Logical Empiricism certainly does not represent a homogenous school regarding inductivism or verificationism.58 A critical historical review of the two major dualisms (i.e., discovery-justification, relativism-objectivism) from the Methodenstreit to the “Science Wars” allows us to conclude that an epistemological alternative to the controversial relativism (with Frank and Neurath as prominent candidates) appears to be more of a philosophical absolutism, and certainly not an objectivism. A possible replacement for the contested relativism would be a less contested fallibilism—may be bridging the gaps between the controversial dualisms and continuing the road since Reichenbach’s Experience and Prediction—thereby avoiding a context free “Whig Historiography”.59 Acknowledgements Thanks go to Thomas Uebel for critical comments and to the Archive of Scientific Philosophy, University of Pittsburgh, Archives of Philosophy, University of Konstanz (Germany), and the Vienna Circle Collection, Haarlem (NL) for the permission of quoting from the correspondence of Carnap, Neurath, and Reichenbach. I am grateful to Camilla Nielsen (Vienna) for her editorial work and translation of the German correspondence.
References Dahms, H.-J. (2004). Die Türkei als Zielland der wissenschaftlichen Emigration aus. Österreich. In Stadler, F. (1988). Vertriebene Vernunft. Emigration und Exil österreichischer Wissenschaft 1930– 1940, Band II (pp. 1017–1020). Münster: LIT Verlag. Danneberg, L., Kamlah, A., & Schäfer, L. (Eds.). (1994). Hans Reichenbach und die Berliner Gruppe. Braunschweig-Wiesbaden: Vieweg. Erichsen, R. (1998). Türkei. In K.-D. Krohn, et al. (Eds.), Handbuch der deutschsprachigen Emigration 1933–1945 (pp. 426–433). Darmstadt: Wissenschaftliche Buchgesellschaft. Feigl, H. (1927). Zufall und Gesetz. In Wissenschaftlicher Jahresbericht der Philosophischen Gesellschaft an der Universität Wien. A summary of his dissertation. Reprinted in Zufall und Gesetz. Drei Dissertationen unter Schlick: H. Feigl – M. Natkin – Tscha Hung, pp. 1–191, by R. Haller & Th. Binder, Ed., 1993. Amsterdam-Atlana: Rodopi. Feigl, H. (1934). The logical character of the principle of induction. Philosophy of Science, 1, 20–29. Reprinted in Feigl, 1980, pp. 153–163. Feigl, H. (1980). Inquiries and provocations. Selected writings, 1929–1974. Ed. by R. S. Cohen. Dordrecht, Boston, London: Reidel. 57 See Stadler (2007), Richardson and Uebel (2007) and Uebel (2007) as an overview. 58 Stadler (2003). 59 In some misleading and privileging sense “Logical Empiricism” (by the way, a term coined by Eino
Kaila and Otto Neurath) as the exclusive heritage of the Berlin Group and Reichenbach is continued in the historiography, esp. in writings of Reichenbach’s renowned adherents—e.g., in Salmon (2001, p. 241): “Undeniably, many philosophers today consider logical empiricism wrongheaded or passé; often this results from a confusion of logical empiricism with logical positivism. For this reason, as well as of historical accuracy, it is important to recognize the fundamental differences between the two movements. Not only in America—where several important figures found refuge from Hitler—but throughout the world, many philosophers continue to find the approach philosophically rewarding.” Compare also Hilary Putnam (2007) on the compatibility of Reichenbach’s realism and verificationism as distinct of Carnop’s position.
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Ferrari, M. (2009). 1922: Moritz Schlick in Wien. In F. Stadler & H. J. Wendel (Eds.), Stationen, op.cit. (pp. 17–62). Galavotti, M. C. (2005). Philosophical induction to probability. Stanford: CSLI Publications. Geiringer, H. (1939/1940a). Über die Wahrscheinlichkeit von Hypothesen. Erkenntnis/The Journal of Unified Science, 8, 151–176. Geiringer, H. (1939/1940b). Zu “Bemerkungen zur Hypothesenwahrscheinlichkeit”, Ibid. (p. 352f). Gerner, K. (1997). Hans Reichenbach. Sein Leben und Wirken. Eine wissenschaftliche Biographie. Osnabrück: Phoebe-Autorenpress. Gimbel, St. & Waltz, A. (Eds.). (2006). Defending Einstein. Hans Reichenbach’s writings on space, time, and motion. New York: Cambridge University Press. Glymour, C. (2008). Hans Reichenbach. Stanford Encyclopedia of Philosophy. August 24, 2008. http:// plato.stanford.edu/entries/reichenbach/. Haller, R., & Stadler, F. (1993). Wien – Berlin – Prag. Der Aufstieg der wissenschaftlichen Philosophie. Zentenarien Rudolf Carnap, Hans Reichenbach, Edgar Zilsel. Wien: Hölder-Pichler-Tempsky. Hegselmann, R., & Siegwart, G. (1991). Zur Geschichte der Erkenntnis. In W. Spohn (Ed.), Erkenntnis Oriented, op.cit. (pp. 461–471). Hempel, C. G. (1993). Empiricism in the Vienna Circle and the Berlin society for scientific philosophy. Recollections and reflections. In Stadler, F. (Ed.), Scientific philosophy, loc.cit. (pp. 1–10). Hentschel, K. (1990). Interpretationen und Fehlinterpretationen der speziellen und der allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins. Basel, Boston, Berlin: Birkhäuser. Howard, D. (2002). Lost wanderers in the forest of knowledge: Some thoughts on the discovery-justification distinction. In Schickore, J., & Steinle, F. (Eds.), Revisiting discovery and justification (pp. 41–58). Berlin: Max Planck Institute for the History of Science. Kamlah, A. (2006). Hans Reichenbach. In S. Sarkar & J. Pfeifer (Eds.), Philosophy of science. An encyclopedia (pp. 703–712). New York, London: Routledge. Lehrer, K. (1993). Carnap and Reichenbach on probability with Neurath the winner. In F. Stadler (Ed.), Scientific philosophy, loc.cit (pp. 143–156). McGuinness, B. (Ed.). (1987). Unified science. The Vienna Circle Monograph Series originally edited by Otto Neurath, now in an English edition. With an introduction by R. Hegselmann. Dordrecht: Reidel. Nemeth, E. & Stadler, F. (Eds.). (1996). Encyclopedia and utopia. The life and work of Otto Neurath (1882–1945). Reidel: Dordrecht, Boston, Kluwer. Neurath, O., Carnap, R., & Morris, Ch. (Eds.). (1955/1971). Foundations of the unity of science. Toward an international encyclopedia of unified science (Vol. 2). Chicago, London: The University of Chicago Press. Popper, K. (1934). Logik der Forschung. Zur Erkenntnistheorie der modernen Naturwissenschaft. Wien: Springer. (= Schriften zur wissenschaftlichen Weltauffassung, Band 9. Ed. by Ph. Frank & M. Schlick). English edition: Logic of scientific discovery (London 1959). Putnam, H. (2007). Hans Reichenbach: Realist and Verificationist. In J. Floyd & S. Shich (Eds.), Future Pasts. The Analytic Tradition in Twentieth Century Philosophy. (pp. 277–287). Oxford and New York: Oxford University Press. Reichenbach, H. (1920a). Relativitätstheorie und Erkenntnis Apriori. Berlin: J. Springer. Reprint: The theory of relativity and a priori knowledge, 1965. Berkeley, Los Angeles: University of California Press. Reichenbach, H. (1920b). Review: M. Schlick Allgemeine Erkenntnislehre/general theory of knowledge (1918). (In Zeitschrift für Angewandte Psychologie, Vol. 16/1920, pp. 341ff.): English Translation in Gimbel & Waltz, 2006, pp. 15–19. Reichenbach, H. (1925a). Metaphysik und Naturwissenschaft. In Symposion I/2, pp. 158–176. English translation in Reichenbach, 1978, I, pp. 283–287. Reichenbach, H. (1925b). Die Kausalstruktur der Welt und der Unterschied zwischen Vergangenheit und Zukunft. Sitzungsberichte der Bayerischen Akademie der Wissenschaft (Nov. 1925) (pp. 133–175). English translation in Reichenbach, 1978, II, pp. 81–119. Reichenbach. (1928). Philosophie der Raum-Zeit-Lehre. Berlin, Leipzig: Walter de Gruyter. English translation: 1958, The philosophy of space and time. New York: Dover. Reichenbach, H. (1931a/1978). Das Kausalproblem in der Physik. Die Naturwissenschaften, 19/34, 713–722. English translation in Reichenbach, 1978, pp. 326–342.
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Reichenbach, H. (1931b). Der physikalische Wahrheitsbegriff (the physicalist conception of truth). Erkenntnis, 2, 156–171. English translation in Reichenbach, 1978, pp. 343–355. Reichenbach, H. (1935a). Über Induktion und Wahrscheinlichkeit. Bemerkungen zu Karl Poppers Logik der Forschung. Erkenntnis, 5, 267–284. English translation in Reichenbach, 1978, II, pp. 372–388. Reichenbach, H. (1935b). Wahrscheinlichkeitslehre. Eine Untersuchung über die logischen und mathematischen Grundlagen der Wahrscheinlichkeitsrechnung. Leyden: A.W. Sijthoff. English Translation, 1949. Berkeley and Los Angeles: University of California Press. Reichenbach, H. (1936a). Logistic empiricism in Germany and the present state of its problems. Journal of Philosophy, 33(6), 141–160. Reichenbach, H. (1936b). Die Bedeutung des Wahrscheinlichkeitsbegriffs für de Erkenntnis. In Actes du huitiéme Congrés International de Philosophie, Prague, Sept. 2–4, 1934, pp. 163–169. Reichenbach, H. (1938). Experience and prediction. An analysis of the foundation and the structure of knowledge. Chicago, Illinois: The University of Chicago Press. Third impression 1949. English reprints 1961 and 1976. German translation 1977, Vol. 4. Reichenbach, H. (1939/1940a). Über semantische und die Objektauffassung von Wahrscheinlichkeitsausdrücken. Erkenntnis/The Journal of Unified Science, 8, 50–68. Reichenbach, H. (1939/1940b). Bemerkungen zur Hypothesenwahrscheinlichkeit. Ibid, pp. 256–264. Reichenbach, H. (1949). The theory of probability. An inquiry into the logical and mathematical foundations of the calculus of probability. Berkeley, Los Angeles: University of California Press. Reichenbach, H. (1951). The rise of scientific philosophy. Berkeley, Los Angeles: University of California Press. Second edition 1954. German translation, 1951: Der Aufstieg der wissenschaftlichen Philosophie. Berlin Grunewald: Herbig Verlagsbuchhandlung. Second edition, 1977, Vol. 1. Reichenbach, H. (1977ff.). Hans Reichenbach: Gesammelte Werke in 9 Bänden. (HRGW). Ed. by A. Kamlah & M. Reichenbach. Braunschweig-Wiesbaden: Vieweg. Band 1: Der Aufstieg der wissenschaftlichen Philosophie. Band 2: Philosophie der Raum-Zeit-Lehre. Band 3: Die philosophische Bedeutung der Relativitätstheorie. Band 4: Erfahrung und Prognose. Band 5: Philosophische Grundlagen der Quantenmechanik und Wahrscheinlichkeit. Band 6: Grundzüge der symbolischen Logik. Band 7: Wahrscheinlichkeitslehre. Band 8: Kausalität und Zeitrichtung. Band 9: Wissenschaft und logischer Empirismus. Reichenbach, H. (1978). Selected writings, 1909–1953, 2 volumes. Ed. by M. Reichenbach & R. S. Cohen. Dordrecht, Boston, London: Reidel. Reichenbach, H. (1983). Erfahrung und Prognose. Eine Analyse der Grundlagen und der Struktur der Erkenntnis. Mit Erläuterungen von A. Coffa. Braunschweig, Wiesbaden: Vieweg. Richardson, A., & Uebel, Th. (Eds.). (2007). The Cambridge companion to logical empiricism. Cambridge: Cambridge University Press. Salmon, W. (1999). Ornithology in a cubical world. In D. Greenberger, W. L. Reiter, & A. Zeilinger (Eds.), Epistemological and experimental perspectives on quantum physics (pp. 303–315). Dordrecht, Boston, London: Kluwer. Salmon, W. (2001). Logical empiricism. In W. H. Newton-Smith (Ed.), A companion to the philosophy of science (pp. 233–242). Oxford: Blackwell. Schlick, M. (1917/1919). Raum und Zeit in der gegenwärtigen Physik. Zur Einführung in das Verständnis der allgemeinen Relativitätstheorie. Berlin: Springer. MSGA 2: H. J. Wendel & F. O. Engler (Eds.). Wien-New York: Springer, 2006. Schlick, M. (1922). Review: Hans Reichenbach, Relativitätstheorie und Erkenntnis Apriori. Die Naturwissenschaften, 10, 873–874. Schlick, M. (1931). Die Kausalität in der gegenwärtigen Physik (causality in contemporary physics). Die Naturwissenschaften 19, pp. 162. English translation: Schlick, M. (1979). Philosophical papers II, Ed. by H. Mulder & B. van der Velde-Schlick, II, pp. 176–209. Schlick, M. (1979). Die Wende der Philosophie (The turning point in philosophy). Ibid., Vol. II, pp. 54–160. Schlick, M. (2006ff.). Kritische Gesamtausgabe MSGA. Ed. by F. Stadler, & H. J. Wendel. Wien, New York: Band 1: Allgemeine Erkenntnislehre. Ed. by H. J. Wendel & F. O. Engler (2009). Band 2: Über die Reflexion des Lichtes in einer inhomogenen Schicht. Raum und Zeit in der gegenwärtigen Physik. Ed. by F.O. Engler & M. Neuber (2006). Band 3: Lebensweisheit. Versuch einer Glückseligkeitslehre/Fragen der Ethik. Ed. by M. Iven (2006). Band 6: Die Wiener Zeit. Aufsätze, Beiträge, Rezensionen 1926–1936. Ed. by J. Friedl & H. Rutte (2008).
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Sober, E. (2008). The birds outside—Reichenbach’s cubical universe and the problem of the external world. Manuscript 2008. Publication in this volume. Spohn, W. (Ed.). (1991). Erkenntnis oriented: A centennial volume for Rudolf Carnap and Hans Reichenbach. Dordrecht, Boston, London: Kluwer (= Erkenntnis, Vol. 35, Nos. 1–3, 1991). Stadler, F. (Ed.). (1993). Scientific philosophy: Origins and developments. Dordrecht, Boston, London: Kluwer. Stadler, F. (2001). The Vienna Circle. Studies in the origins, development, and influence of empirical empiricism. Wien, New York: Springer. Stadler, F. (2003). The Vienna Circle and logical empiricism. Re-evaluation and future perspectives. Dordrecht, Boston, London: Kluwer. Stadler, F. (2004). Introduction and deduction in the philosophy of science: A critical account since the Methodenstreit. In F. Stadler (Ed.), Induction and deduction in the sciences (pp. 1–15). Dordrecht, Boston, London: Kluwer. Stadler, F., Wendel, H., & Glassner, E. (Eds.). (2009). Stationen. Dem Philosophen und Physiker Moritz Schlick zum 125. Geburtstag. Wien, New York: Springer (= Schlick-Studien, Band I). Thiel, Chr. (1993). Carnap und die wissenschaftliche Tagung auf der Erlanger Tagung 1923. In R. Haller & F. Stadler (Eds.), Wien – Berlin – Prag. Der Aufstieg der wissenschaftlichen Philosophie (pp. 175–188). Wien: Hölder-Pichler-Tempsky. Uebel, Th. (2007). Empiricism at the crossroads. The Vienna Circle’s protocol-sentence debate. Chicago, La Salle: Open Court. Uebel, Th. (2008). Writing a revolution: On the production and early reception of the Vienna Circle’s manifesto. Perspectives on Science, 16(1), 70–102. von Mises, R. (1928/1936). Wahrscheinlichkeit, Statistik und Wahrheit. Wien: Springer. English translation: Probability, statistics, and truth. London 1939; New York 1957. von Mises, R. (1939/1990). Kleines Lehrbuch des Positivismus. Einführung in die empiristische Wissenschaftsauffassung. Den Haag: Van Stockum. Reprint ed. and introduced by F. Stadler (1990) (Ed.) (Frankfurt/M.: Suhrkamp). Revised English edition: R. von Mises (1951) Positivism. Study in human understanding. Harvard University Press. 2nd edition New York: Dover Publications. Wissenschaftliche Weltauffassung. Der Wiener Kreis. (1929). Ed. by H. Hahn, O. Neurath, & R. Carnap on behalf of the Verein Ernst Mach/Ernst Mach Society. Wien: Verlag Artur Wolf. Abridged English translation in Neurath, O. (1973). Empiricism and sociology. Ed. by R.S. Cohen and M. Neurath. Dordrecht, Boston: Reidel.
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Synthese (2011) 181:157–180 DOI 10.1007/s11229-009-9592-y
Hans Reichenbach in Istanbul Gürol Irzık
Received: 13 May 2009 / Accepted: 8 June 2009 / Published online: 4 July 2009 © Springer Science+Business Media B.V. 2009
Abstract Fleeing from the Nazi regime, along with many German refugees, Hans Reichenbach came to teach at Istanbul University in 1933, accepting the invitation of the Turkish government and stayed in Istanbul until 1938. While much is known about his work and life in Istanbul, the existing literature relies mostly on his letters and works. In this article I try to shed more light on Reichenbach’s scholarly activities and personal life by also taking into account the Turkish sources and the academic context in which Reichenbach taught and worked. Keywords
Reichenbach · Life · Work · Istanbul University · German émigrés
1 The University Reform of 1933 and the Road to Istanbul In 1933 Adolf Hitler became the chancellor of Germany, and the very same year a comprehensive university reform was being put into effect in the Republic of Turkey, which had been founded only 10 years earlier in 1923 under the leadership of Mustafa Kemal Atatürk. As a result of historical coincidence, what was a disastrous event in Germany gave an opportunity to the Turkish government to implement its goal of reforming higher education in Turkey. Between 1923 and 1933 a series of revolutionary reforms—political, social, legal, and cultural—were put into effect in order to modernize Turkish society, and reforming the system of education was among the top priorities of the leaders of the young Republic who knew that the success of modernization depended heavily on education. For this purpose the famous philosopher John Dewey was invited by the ministry of education back in 1924, only 1 year after the founding of the Republic. Dewey stayed
G. Irzık (B) Philosophy Department, Bo˘gaziçi University, 34342 Istanbul, Bebek, Turkey e-mail:
[email protected]
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for two months and submitted a report about how the educational system in Turkey should be reformed. His report, however, focused on the primary and secondary school system and contained very little about higher education. With respect to the latter, it said: I was not able to give attention to higher education. In general, the university1 seems to have made a most promising beginning. Of course special attention should be paid to the selection of its teachers, to secure men who are throughly trained in modern methods and who are devoted to the improvement of the intellectual condition of Turkey. A system of fellowships for foreign continued studies to be awarded to students in subjects in which they have made the best record and shown unusual promise would be an assistance. (Dewey 2007, p. 135) At the time there was only one “university,” or more correctly, only one institution of higher education in Turkey, namely, Darülfünun in Istanbul, and its condition and function were still a matter of constant public debate almost a decade after the formation of the Republic. In 1931 the Turkish government took a decisive step to initiate a reform regarding Darülfünun and invited Albert Malche, a professor of pedagogy at the University of Geneva, to write a report about it. Malche visited Turkey in early 1932 and then submitted his report in May 1932. The report was very critical of the existing state of Darülfünun and called for a comprehensive reform. Basically, the report said that Darülfünun was no more than a teaching institution that produced no research or publications; it had so great an autonomy that it had lost touch with the government and the rest of the society; the teaching methods of the professors were archaic, resulting in students’ rote memorization; professors’ salaries were low, forcing them to take extra jobs; very few students knew any foreing language, and so on (Widmann 1999, pp. 75–76). Malche came to Turkey in May 1933 again and stayed almost a year as an official adviser to the Turkish government. The real architect of the university reform, however, was Re¸sit Galib, the minister of education at the time. Especially with his efforts, the university reform law was passed during the last day of May of 1933, and accordingly Darülfünun was abolished on July 31st and Istanbul University was founded the next day. It soon became clear that the reform at the same time meant liquidation. 157 out of 240 faculty members of Darülfünun were dismissed from their positions, and 71 of those who lost their jobs were full professors (Bilsel 1943, p. 37).2 In a letter to Philipp Schwartz, who, as we shall see, played a critical role in hiring refugee professors at the newly founded Istanbul University, Re¸sit Galib wrote that Darülfünun, from its buildings to its professors, was so old that it had to be overhauled completely (Kazancıgil and Er 1999, p. 62). With a speech he gave the very next day, in which he complained that Darülfünun did not enthusiastically embrace, and often stayed “impartial” to the political, legal and cultural reforms of the young Republic, Darülfünun was abolished (Bahadır 2007, 1 Dewey is referring to Darülfünun here. See below. 2 Among those who were fired was ˙Ismail Hakkı Baltacıo˘glu, one of the former rectors of Darülfünun from
1923 to 1924. However, it should be noted that a good many of them were appointed to other (often lesser) positions at one or another level of the educational system.
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p. 65; Bilsel 1943, pp. 34–35). Thus, the reasons behind the dismissals were not only academic, but also political. As Emily Apter has observed, firings at both ends played a critical role in the Turkish university reform and it was “nothing short of historical irony that, in many cases, a Turk’s job lost was a German’s job gained” (Apter 2003, p. 266), even though the émigré professors could not have known this. On the other hand, what the Turkish reformers did was simply sieze a unique opportunity that history presented to them. In May of 1933, Malche contacted Philipp Schwartz in Zürich, informing him of possible teaching positions in Istanbul (Widmann 1999, pp. 91 and 380). Schwartz was a doctor of medicine who had become the informal leader of a group of German scholars in exile in Zürich, called “Emergency Assistance Organization for German Scholars” (EAOGS, for short). The group had quickly and successfully organized itself, prepared profiles of German scholars on exile and looked for opportunities to find them jobs. For this purpose Schwartz visited Turkey twice, once on July 5 and another on July 25, 1933. During his brief first visit, he met Re¸sit Galib and his 20 staff in Ankara on the 6th of July. Schwartz presented the profiles of German scholars he had brought with him. Hans Reichenbach’s name first came up in this meeting (Widmann 1999, p. 96). At the end of a long day, Schwartz was thrilled that Turkey was willing to hire 30 professors from his list. This was the first big success of EAOGS. Moreover, Re¸sit Galib also offered his government’s help with those scholars who were in concentration camps or under detention. Indeed, soon after three professors were freed from arrest thanks to the intervention of the Turkish government. These were sociologist Gerhard Kessler, radiologist Friedrich Dessauer and dentist Alfred Kantorowicz (Tachau 2002, p. 237). While visiting Turkey, Schwartz was also asked to help with the building and organization of new facilities such as an observatory. The task was beyond his powers. Thus, upon his recommendation, three world-famous scientists from Göttingen were brought to Turkey as advisors: mathematician Richard Courant, Nobel laurate physicists Max Born and James Franck. Their stay of a few weeks was important for two reasons. Their valuable scientific advice and evaluation not only played an important role in convincing the Turkish officials that the reform plan would be a success, but also created a positive image of Turkey in the eyes of the scholars in exile (Schwartz 2003, p. 51). A definitive agreement was reached on July 6, but a temporary setback occurred unexpectedly. In mid-August Re¸sit Galip, the minister of education, resigned from his post, which was taken over temporarily by Refik Saydam, who was the minister of health at the time. For 2 weeks the process was interrupted. At the end of August, Schwartz demanded a statement from Turkish officials, and he got it the next day from Refik Saydam, assuring him that the Turkish government would honor its commitments. Indeed, contracts were signed by the professors and the Turkish consulate in Geneva in the presence of Malche (Widmann 1999, pp. 95–96).3 All 30 German 3 On September 17, Albert Einstein, as the honorary president of World Union “OSE”, had sent a letter to ˙Ismet ˙Inönü, the prime minister of Turkey at the time, urging him to allow “forty experienced specialists and prominent scholars” to work in Turkey. It may be that Einstein was asked to intervene due to the temporary setback. “Who contacted Einstein?” and “why forty?”, on the other hand, are questions whose answers I do
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refugee professors, including Hans Reichenbach, arrived in Istanbul with their families in October 1933. Some of them, though not Reichenbach, had brought their assistants with them. Reichenbach came with his wife and two children. It is estimated that altogether a total of 150 refugees came at that time (Cremer and Przytulla n.d., p. 22). The major criterion for the selection of émigré scholars invited to Turkey was that they be “accomplished”. None of them were interviewed, their cv’s were simply communicated in the 6th of July meeting by Schwartz to Re¸sit Galib and his staff, who generally agreed. Reichenbach clearly satisfied the condition of being accomplished, but it is also worth mentioning that his being a leading representative of scientific philosophy happily coincided with the “positivistic” founding ideology of the early Republic. Mustafa Kemal Atatürk’s famous saying “The true path in life is positive/natural science,” which decorates every school in Turkey even today, is a good expression of this outlook. More tellingly, during his visit to Samsun High school in 1930 Atatürk attended a philosophy class, and after hearing the lecture that contained much metaphysics, he turned to the students and said: Students, I listened to your valuable teacher with attention and pleasure. I saw that you paid similar attention and listened to the lecture with pleasure. I learned from him and I thank him. But I did not quite get where philosophy was in all this. For me, philosophy means science; thoughts which are founded not on positive science, but only on metaphysical issues are not called “philosophy”, but “theology” (“ilm-i kelam”). The philosophy wanted and longed for by the Turkish people is a philosophy that would take them to positive science, positive facts. Any other philosophy is a waste of time, a futile effort after useless ideas. (Quoted in Kafadar 2000/2001, p. 55)4
2 Reichenbach’s reasons for choosing Istanbul University Even though Reichenbach received an offer from Oxford as well, he chose to go to Istanbul University. In a letter to Hook, he explained that Istanbul University’s offer was better. Whereas Oxford University offered him only a one-year position, Istanbul University’s offer was for 5 years and renewable. Furthermore, at Istanbul University Reichenbach would be employed as a full (“ordentlicher”) professor and paid well: “The personal position is good, indeed. We get a salary of 6,600 pounds = 5,300 dollars, which is considerably more than the same amount over there because of the
Footnote 3 continued not know. Einstein’s letter appeared in Turkish daily Hürriyet on 29 October 2006. A copy of the Turkish translation of Reichenbach’s contract in Istanbul University Archives indicates that Reichenbach signed his contract, effective from 15 October 1933, on the October 4 in the same year in Geneva. 4 Interestingly, Adnan Adıvar, a prominent doctor of medicine, politician and author who wrote the first book on the history of Ottoman science, met Reichenbach at the philosophy of science conference in Paris in 1935 and asked him head on whether he was chosen to teach at Istanbul University because his philosophical outlook was in congruence with the new university’s ideology. Reichenbach replied that he did not know but that he had not come across any evidence to that effect (see Adıvar 1945, p. 127).
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cheapness of living costs”.5 In addition, Reichenbach’s contract allowed him to cover his and his family’s moving expenses both to and from Istanbul upon his departure for good as well as his travel expenses to attend academic meetings. Finally, in case of illness he would receive one year’s salary and in case of death the same amount would be paid to his wife or non-adult children. There is another reason why Reichenbach chose to go to Istanbul University. In the same letter to Hook, Reichenbach cited the following reason before any other: “The prospect of contributing to the foundation of a new university in a position of responsibility lured me a great deal…”6 This implies that he had not only heard about the Istanbul University reform before coming to Turkey, but also held the hope that he could contribute to it. In an interview, Maria Reichenbach confirmed this: At the hands of Mustafa Kemal Pasha, or Atatürk, the father of the Turks, as he used to be called, Turkey experienced quite an intellectual revolution. He saw this great opportunity to build up the university of Istanbul with the help of about 35 refugee professors in all major fields…This foreign faculty was outstanding. Its members were given five year contracts and ample financial support to build up whatever institutes were needed. (Güzeldere 2005, p. 78) Reichenbach had a clear idea about what a university must be like, or at least he did in his lengthy article “Socializing the University”, which he wrote back in 1918 as a young academician (Reichenbach 1918/1978). This article was the result of Reichenbach’s early participation with the student movements such as the Freistudentenschaft (see Wipf 1994 for details). It summarizes his vision of the university and sheds light on his academic activities, hopes and disappointments at Istanbul University. In that article Reichenbach argued that both knowledge and the university as the principal site for knowledge production are ends in themselves. In a Millian and Popperian spirit before Popper, he took the critical approach as crucial to the functioning of the university: we can err but learn from our mistakes. Thus, the plurality of viewpoints and their free expression and dissemination are essential. The university must be autonomous, and the faculty should have complete freedom over their courses. All academic rights must be granted regardless of class, political view, religion and sect, race, sex, or citizenship. The sole criterion for being a member of the university community is scientific qualification. This applies not just to teachers but also to students. The university is only for the most gifted students, not for everybody. Of course, all students—male or female, rich or poor—must be given equal opportunity to be admitted to the university, based on talent and academic achievement. As a socialist, Reichenbach was well aware of the impact of social class on the scholarly success of students. He discussed at some length the materialist conception of history, according to which economic conditions influence the development of 5 “Zwar, die persönliche Stellung is gut. Wir bekommen hier ein Gehalt von 6600 türkischen Pfund = 5,300 Dollar, was wegen der Billigkeit der Lebenshaltung hier noch wesentlich mehr ist als die gleiche Summe drüben”. HR 013-46-99. Letter from Reichenbach to Hook, 31 January 1935. Reichenbach’ salary was more than four times the highest salary paid to his Turkish equivalents (see Bilsel 1943, p. 42). 6 “Die Aussicht, an der Gründung einer neuen Universität in verantwortlicher Stelle mitzuwirken lockte
mich sehr”.
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intellectual and cultural life and argued that this should be understood probabilistically, not deterministically as if there were a one-to-one relationship between the two. At any rate, formal democratic equality must be supplemented by economic equality, which, he believed, could only be achieved in a socialist state. Nevertheless, there are a number of policies that can be put into effect even in the existing system to improve the chances of poor students, such as the removal of all fees and tuition, the building of dormitories and the like. Reichenbach placed special emphasis on the equality of men and women. The selection of the faculty requires, according to Reichenbach, the highest scientific standards. Scientifically unqualified teachers must be removed. All teachers must be paid a full salary regardless of rank, and all must be included in retirement pension schemes. They must be actively involved in the governance of the university through faculty councils. Their teaching must conform to pedagogical principles; that is, classes must be taught in the form of seminars in which students must learn to think critically and independently, large classes must be divided into smaller discussion groups, exams should not measure sheer information which encourages rote memorizing, and so on. Rich libraries (both general and special) are sine qua non for a good education. At the end of the article, Reichenbach laments that philosophy has degenerated into a historical discipline and demands that systematic philosophy, which is problem oriented, must be given priority over history of philosophy. He explicitly states that philosophy should be the systematic study of the sciences and nothing else, signaling the conception of scientific philosophy that he later adopted and articulated more fully. The following may serve as a conclusion of Reichenbach’s article: “But all these improvements…can be carried out within the framework of a new university, dedicated to science and learning” (Reichenbach 1918/1978, pp. 176–177). By 1933 Reichenbach had become one of the leading representatives of scientific philosophy and started teaching at Istanbul University. What was Istanbul University like at the time? To what degree did it coincide with his vision of the new university and how much was he able to accomplish at his new home? It is to these questions that I now turn.
3 The best German University of its time Although numerous German professors came to teach at Istanbul University in the thirties, this was not the first time German scholars were employed at Darülfünun, the precursor of Istanbul University. For example, about 20 of them taught there between 1915 and 1918. Their areas of specialization varied more or less evenly among natural sciences, social sciences including law, and humanities. None were philosophers. Due to the war, however, their impact was extremely limited.7 After the war, the interest shifted to the French. Between 1920 and 1933 about two dozen French teachers were employed in the faculties of medicine, science, letters, law and theology. Some of them continued to teach even after the 1933 reform. With the exception of two, however, 7 For a list of them see Dölen (2007, pp. 97–98).
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none held PhD degrees, and again there were no philosophers among them.8 Thus, before the influx of German émigré scholars, Istanbul University was mainly under French influence in most disciplines. This situation changed radically after 1933. German scholars flooded into Istanbul University, and scientific quality skyrocketed. As Friedrich Riemann, an émigré professor of medicine put it, Istanbul University was “the best German university of its time” and this was especially true of medicine (Widmann 1999, p. 118, footnote 28). Indeed, even a cursory look at some of the names would confirm this. But first some numbers. In the 1933–1934 academic year, there were 65 full (“ordentlicher”) professors, 38 of whom were non-Turkish, 22 professors (“ausserer ordentlicher”), four of whom were non-Turkish, and 98 instructors (“Privatdozenten”), all of whom were Turkish (Aslanapa 1983, p. 27; see also Widmann 1999, p. 107). A vast majority of the nonTurkish faculty was German. In the 1936–1937 academic year, there were 31 Turkish and 38 non-Turkish full professors, 20 Turkish and six non-Turkish professors, and 86 lecturers, all of whom were Turkish. As can be seen, all non-Turkish faculty had high ranks; moreover, almost all of the full professors were department heads. Interestingly, none of the foreign professors (full or otherwise) were women. In addition, there were a total of 33 non-Turkish assistants and technicians, some of whom were females, mostly in the faculty of medicine (Dölen 2007, p. 128). While some left, many more scholars kept coming to Istanbul University well after 1933, and according to one estimate, the total number of émigré scholars (including assistants and technicians) at Istanbul University was over a hundred (Tachau 2002, p. 240). There were a number of French, Italian, Austrian and Hungarian scholars as well. Clearly, in the 1930s and 1940s Istanbul University was truly cosmopolitan. As for the scientific quality of the scholars, consider just the following names: Richard von Mises, Erwin Finley Freundlich, William Prager, Arthur von Hippel, Eric Auerbach, Leo Spitzer, Helmut Ritter, Andreas Tietze, Alexander Rüstow, Wilhelm Köpke, Gerhard Kessler, Fritz Neumark, and Ernest Hirsh.9 Along with Reichenbach, the most famous of them was the mathematician Richard von Mises. Mises left his position at Berlin University and became the chair of mathematics and statistics at Istanbul University in 1933, and taught until 1939, after which he left for the USA and became a professor of mathematics at Harvard.10 He wrote Kleines Lehrbuch des Positivismus (translated as Positivism) when he was in Turkey. Erwin Finley Freundlich was an astronomer who received his PhD at Göttingen under Felix Klein and was the director of the Einstein Institute in Berlin before joining the Astronomy Department of Istanbul University in 1933. He published a number of books and articles on relativity theory and was famous for successfully testing Einstein’s general theory of relativity in 1929. He taught at Istanbul University for 3 years, established an observatory there and later went to the St. Andrews University.11
8 For a complete list see Dölen (2007, pp. 104–105). 9 For a comprehensive list with brief biographical remarks see Widmann (1999) and Reisman (2006). 10 For a scientific biography of Mises, see Siegmund-Schultze (2004). 11 See Klüjber (1965) for a short biography of Freundlich.
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Before coming to Istanbul University, William Prager served as the director of the Institute of Applied Mathematics at Göttingen. He was best known for his work on elastic solids. He taught applied mathematics and mechanics at Istanbul University and was very productive there. In addition to articles in international journals, he published two books for Turkish readers, one in descriptive geometry and one on mechanics. He stayed in Turkey until 1941, after which he became the director of Advanced Instruction and Research in Mechanics at Brown University.12 Arthur von Hippel obtained his PhD in physics in 1924. In his autobiographical article he remarked that “the ‘Bohr Festspiele’ (festival) in Göttingen in June 1922, organized by Hilbert, Franck, and Born, proved a decisive event” for him to pursue a career in physics (Hippel 1980, p. 2). Before joining the physics department at Istanbul University in 1933, he had worked at the Second Physics Institute, under the directorship of James Franck of Göttingen University. Hippel was a pioneer in material science, radar technology, and what we today call “nanotechnology.” He taught at Istanbul University for only a year and a half, after which he first went to the Niels Bohr Institute in Copenhagen upon Bohr’s invitation and then joined the engineering faculty at MIT in 1936. In addition to these eminent scientists, there were also a number of very good social scientists and professors of law at Istanbul University during the same period. Consider, for example, Alexander Rüstow, who had an extraordinary background and career. He first studied mathematics, economics, law, and philosophy at Göttingen, Munich and Berlin, and then received a PhD at the University of Erlangen, where Reichenbach had also received his PhD, by writing a dissertation on Russellian set theoretical paradoxes in 1908, which was published under the title Der Lügner. Theorie, Geschichte und Auflösung 2 years later (Peckhaus 1995). Apparently, he was also knowledgable about the pre-Socratic philosophers, especially Parmenides. Afterwards, he served as an expert for the Ministry of Economy and made a reputation as one of the forerunners of German social market economics, which enabled him to get a professorship of economics at Istanbul University from 1933 to 1949. He then moved to Germany and taught at the University of Heidelberg until his retirement. Wilhem Röpke was a professor of economics who taught at Jena, Graz and Marburg before joining the department of economics at Istanbul University in 1933. His views about economics were similar to those of Rüstow, who had had a shaping influence on him, along with Ludwig von Mises, the brother of Richard von Mises. In 1937 Röpke left for a position at the Institute of International Studies in Geneva. Röpke and Rüstow were known as “ordoliberals,” associated with the journal Ordo, and played an important role in shaping the principles of economic policy (known as social market economics) in Germany after the War (Reisman 2006, pp. 109–112). Gerhard Kessler studied social sciences at the Universities of Berlin and Leipzig. Among his teachers were Wilhelm Wundt and Karl Büchner. He received a PhD at the University of Leipzig in 1905. He was a socialist and a pioneer in the field of social policy and taught at Jena and Leipzig Universities. He played an important role in the founding of Turkish Worker’s Syndicate. After leaving Istanbul University, he taught
12 For more on Prager, see O’Connor and Robertson (2005).
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at the University of Göttingen with the help of his old friend Theodore Heuss, the president of Germany between 1949 and 1959 (Hanlein 2006). Fritz Neumark remained in Turkey for nearly two decades from 1933 to 1952 and made significant contributions to Turkey’s modernization, especially in finance law. Before coming to Istanbul University he taught economics and finance at the University of Frankfurt, where he later twice served as its rector. His memoirs, published under the title Zuflucht am Bosphorus, sheds much light on the lives and experiences of the refugee scholars between 1933 and 1952 (Neumark 2008). Leaving his post at the University of Frankfurt, Ernest Hirsch taught philosophy of law, sociology of law, and commercial law at Istanbul University from 1933 to 1943, after which he taught at Ankara University until 1952. Like Neumark, he contributed much to the modernization of Turkish law and, like him, published a very detailed autobiography under the title Aus des Kaisers Zeiten Durch Weimarer Republik in das Land Atatürks. Upon returning to Germany, he twice served as the rector of the Free University, Berlin (Hirsch 1997). Finally, there is a distinguished group of scholars in humanities that is worth mentioning. The most famous of them were Eric Auerbach and Leo Spitzer, the founding fathers of the discipline we call “comparative literature” today. Spitzer was a brilliant linguist and literary critic who received his PhD under Wilhelm Meyer-Lübke. After teaching at the universities of Marburg and Cologne, he came to Istanbul University in 1933 and became the chair of Romance Languages and Literatures and the director of the School of Foreign Languages. In 1936 he left for USA and became a professor of Romance Studies at Johns Hopkins University. Although he stayed only for 3 years in Turkey, Spitzer was instrumental in attracting a number of bright scholars to Istanbul University, including Eric Auerbach, Herbert Dieckmann, Adreas Titze and Traugott Fuchs. I will mention only Auerbach. Before coming to Turkey, Auerbach taught philology at the University of Marburg. He took the position in 1936 that later Spitzer had occupied and taught at Istanbul University until 1947. He wrote his masterpiece, Mimesis, considered to be the founding text of comparative literature, while in Istanbul. After moving to USA, he taught at Penn State University, spent some time at Institute for Advanced Study at Princeton and finally became a professor of Romance philology at Yale. This list would not be complete without including the names of Helmut Ritter and Ernst von Aster. Ritter was a famous arabist who taught at the University of Hamburg. He came to Istanbul University in 1936 and served as the chair of Oriental Studies until 1949, after which he moved to University of Frankfurt a.M. By all counts, Istanbul University had some of the best minds in literary criticism, philology and oriental studies. Other than Reichenbach, Ernst von Aster was the only philosopher among the émigré scholars who taught at Istanbul University during this period. He was a wellknown historian of philosophy and Reichenbach’s teacher back in Germany. It was Reichenbach who brought him to Turkey. I will say more about him in the next section. This completes my cursory biographical summary of some of the most eminent professors at Istanbul University in the thirties. The list above does not include the professors of medicine. They formed the largest group by far, and modern medicine in Turkey owes a great deal to them and their students.
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Needless to say, the quality of the teaching staff is only one (even if the most important) component of a first-rate university. Its infrastructure (its buildings, libraries, labs and equipment), its student body and personnel, a collegiate atmosphere, and above all, a sense of what a university must be like are equally crucial. Istanbul University did not lack buildings, but had still a long way to go in other aspects, as the memoirs of émigré scholars amply demonstrate. According to Cemil Bilsel, who served as the rector of Istanbul University between 1934 and 1943, overall Istanbul University was at the level of a central European University (Bilsel 1943, p. 55). Even if one found the title of “the best German university of its time” exaggerated, Istanbul University certainly came close to Reichenbach’s vision of a university so far as the scientific qualifications of its professors are concerned.
4 Reichenbach as a teacher and the Chair of the Philosophy Department As we saw, Istanbul University as a whole was changing rapidly after the 1933 reform. This was also true of the philosophy department under Reichenbach’s leadership. Indeed, both the teaching staff and the structure of the department went through a complete overhaul. While professor Mustafa Sekip ¸ Tunç (who taught psychology and pedagogy) and lecturer Orhan Sadettin (who taught history of philosophy) kept their positions, professors Ahmet Naim Babanzade (who taught metaphysics, classical logic and morality), Halil Nimetullah Öztürk (who taught classical logic), and ˙Ismail Hakkı Baltacıo˘glu (who taught pedagogy) were dismissed from theirs (Bahadır 2007, pp. 79 and 83). Mustafa Sekip ¸ Tunç had studied psychology and pedagogy at the Jean-Jacques Rousseau Institute in Geneva. He was a follower of Bergson and critical of the excessive holism of Durkheimian sociology, which tended to overemphasize the importance of the social over the individual. Back then it was customary to keep philosophy, psychology and pedagogy under the same organizational structure, so the philosophy department continued to offer courses in psychology and pedagogy even after the reform, and to these were added courses in general philosophy, logic, sociology, and also the history of Turkish civilization. On the other hand, courses in metaphysics, and in Islamic thought and philosophy, were either shut down or moved to the faculty of theology (Kafadar 2000/2001, pp. 51–52). Although not initiated by Reichenbach, this was certainly a right move from his perspective; scientific philosophy had nothing to do with them. Since Turkish students had very little knowledge of Western philosophy, Reichenbach wanted to strengthen the area of history of philosophy by recommending to the university administration that a full professor in this area be hired. He lobbied very hard for Ernst von Aster. Aster was a neo-Kantian philosopher and Reichenbach’s teacher in Münich during the 1912–1913 academic year. Reichenbach respected Aster very much and wanted to secure a descent job for him in Turkey since at the time Aster’s financial situation in Sweden was bad. Reichenbach met an unexpected resistance in his efforts, coming from his German colleagues Spitzer and Mises, who tried to appoint Karl Löwitz, a student of Heidegger, and lobbied against Aster on the grounds that he was not much different from Reichenbach, philosophically speaking. In return, Reichenbach obtained strong letters in support of Aster from Edmund Husserl, Ernst
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Cassirer, Henri Bergson and Léon Brunschvicg, and convinced the Istanbul University administration to appoint Aster.13 However, the final word in regard to the hiring of foreign faculty belonged to the ministry of education in Ankara, and they thought that another candidate should also be considered. This was how Cassirer’s name came up, and Reichenbach informed Cassirer of the situation,14 but unfortunately, Cassirer cabled back saying that he had already accepted a four-year position at the University of Göteborg.15 Aster, on the other hand, did accept the offer and taught from the Fall of 1936 until his unexpected death in 1948.16 After Reichenbach left, the department became heavily historical under Aster’s influence. One cannot help wondering how events would have turned out if Cassirer rather than Aster had joined the philosophy department. In addition to strengthening the history of philosophy component of the philosophy department, Reichenbach tried to do the same with respect to psychology. Although there was Sekip ¸ Tunç as a professor of psychology in the department, Reichenbach was not satisfied with him, since he lectured “in the French tradition”. He finally convinced the Istanbul University administration that a full professor of psychology should be recruited in the “scientific direction,” and the offer was made to Adhemar Gelb. Gelb, who had studied with Carl Stumpf, was a gestalt psychologist. Later he became a collaborator of Kurt Goldstein’s, a very philosophically oriented pioneer in neuroscience (Pickren 2003).17 Gelb was also highly esteemed by philosophers such as Cassirer.18 However, he died unexpectedly before coming to Istanbul, so a new search began. Reichenbach contacted Kurt Lewin in desperation and asked him whether he would be willing to accept the position even though he knew that it would not be attractive to him.19 As is known, Lewin was Reichenbach’s close friend and colleague who had helped him found the journal Erkenntnis. He too had studied with Carl Stumpf and was involved with gestalt psychology and the early Frankfurt School. As expected, Lewin declined the offer. In the end, the position went to David Katz.20 Katz too was a gestalt psychologist and had contributed to the journal Psychologische Forschung like Reichenbach.21 That all three names, Gelb, Lewin, and Katz, whom Reichenbach tried hard to recruit, were associated with gestalt psychology is not a coincidence. Reichenbach was very much interested in gestalt psychology and emphasized the “gestalt charac13 HR 013-39-29. Letter from Reichenbach to Ernest von Aster, dated 24 May 1936. 14 HR 013-41-71. Letter from Reichenbach to Cassirer, dated 27 August 1936. 15 The cable is dated 1 September 1936. Courtesy of the archive of Istanbul University Rectorate personnel office. 16 The website of the Philosophy Department of Istanbul University. http://felsefe.istanbul.edu.tr/node/49.
Accessed on 1 February 2009. 17 Interestingly, Goldstein and Cassirer were related; Cassirer was a cousin of Goldstein. 18 HR 013-41-72. Letter from Reichenbach to Cassirer, dated 19 January 1936. 19 HR 013-49-35. Letter from Reichenbach Letter to Lewin, dated 24 September 1936. 20 HR 013-48-05. Letter from Reichenbach to David Katz, dated 22 September 1936. 21 For more details about the relationship between scientific philosophers and gestalt psychologists, see Ash (1994, 1995) and Feest at http://www.mpiwg-berlin.mpg.de/en/research/projects/ DeptIII_Feest_Gestaltpsy. Accessed on 19 February 2009.
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ter” of our experiences in his writings, most notably in his Experience and Prediction. He wrote: “We do not see things as amorphous but always as framed within a certain description…In the same sense the objects of our sensations have always a “Gestalt character.” They appear as if pressed into a certain conceptual frame; it is their being seen within this frame which we call existence” (Reichenbach 1938, p. 221). This is an early and remarkable denial of “the myth of the given,” and a statement of the theory-dependence, or, more accurately, the concept-ladenness of experience. Nevertheless, I did not come across any evidence of a collaboration between Katz and Reichenbach in Istanbul. After Reichenbach became the chair, a number of young and promising assistants such as Nusret Hızır, Macit Gökberk, Vehbi Eralp, Hilmi Ziya Ülken, Niyazi Berkes and Neyire Adil Arda joined the department. There is also some evidence that presiding over the philosophy department with full authority, Reichenbach wrote negative reports about some members of the department, disputing their competence. This caused resentment within the department (Kaynarda˘g 1986b, p. 12).22 Furthermore, he changed the philosophy curriculum radically, in line with his conception of philosophy, requiring philosophy majors to take “two theoretical science [courses] and one experimental one each semester for four years” (Kamber 1978, p. 37). It is fair to say, therefore, that under Reichenbach the philosophy department had little in common with the one that existed before the 1933 reform. Reichenbach also tried hard to build a good library for the philosophy department. The government had allocated a good sum of money for this purpose. Although Reichenbach faced some bureaucratic difficulties, eventually he did succeed in getting many books and journals for the departmental library, which his students remembered with gratitude even years later (Kaynarda˘g 1986a, pp. 37 and 181; compare, however, Traiger 1984). It is worth mentioning in this context that Reichenbach showed no tolerance for philosophies which he thought were antithetical to the scientific outlook. He removed all of Bergson’s and other similar philosophers’ books from the department library and sent them to the library of the literature department despite the fact that his colleague Sekip ¸ Tunç, the only Turkish professor left in the philosophy department after the 1933 reform, was a follower of Bergson (Berkes 1997, p. 105).23 It is not difficult to imagine how he must have felt. As a teacher, Reichenbach was “the star of the department” (Berkes 1997, p. 105). He brought not only a new philosophy but also a fresh air. His lectures were clear, lively and exciting. He encouraged students to ask questions, valued their opinions,
22 According to Kaynarda˘g, Ziyaeddin Fahri Fındıko˘glu was one of them, and this explains, Kaynarda˘g
argues, why he later wrote a bitter paper about Reichenbach with the title “A Page from the History of Education in Philosophy or the Problem of Reichenbach.” Fındıko˘glu had studied sociology and philosophy at Strasbourg University and then became a lecturer in sociology and moral philosophy at Istanbul University from 1933 to 1937. In 1937 he moved to the department of economics and taught sociology there. I do not know whether Reichenbach’s report played a role in this change of position. 23 Regarding the philosophical systems of Bergson, Fichte, Schelling, Hegel, Schopenhauer and Spencer, Reichenbach wrote: “Yet, considered historically, these systems would better be compared to the dead end of a river that after flowing through fertile lands finally dries out in the desert” (Reichenbach 1951, p. 122). Notice that this did not prevent Reichenbach from using Bergson’s letter in support of Aster.
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and taught that philosophy was more than repeating what this or that philosopher said (Kaynarda˘g 1986a, pp. 67 and 181). Since his students did not speak any language other than Turkish, his lectures had to be translated consecutively by an assistant. Reichenbach was lucky in this respect. His first assistant, Macit Gökberk, was fluent in German and served as Reichenbach’s assistant during the 1933–1934 academic year, after which he went to Germany and received a PhD in philosophy under Eduard Spranger. Before each class Reichenbach either gave his lecture notes to his assistant or summarized his lecture to him (Kaynarda˘g 1986a, p. 22). His second assistant was Nusret Hızır. Hızır had studied physics, mathematics and philosophy in Germany and served as Reichenbach’s assistant from 1934 to 1937. He enthusiastically embraced the new logic and scientific philosophy. Hızır became a well-known philosopher of science and successfully disseminated logical empiricism in Turkey. Vehbi Eralp, who was appointed as a lecturer in the philosophy department in 1933, also translated Reichenbach’s lectures. Eralp had studied philosophy at Bordeaux and Sorbonne. Since at the time Eralp spoke only French and not German, Reichenbach had to lecture in French (Kaynarda˘g 1986a, p. 67). According to some commentators, Reichenbach rarely taught his specialty and concentrated on the history of philosophy because of the poor level of students (see, for example, Traiger 1984 and Gerner 1997). This is an exaggeration. It is true that he taught history of philosophy, but probably no more than for a year when Orhan Saadettin, who normally taught it, became ill (Kaynarda˘g 1986a, p. 67).24 As we saw, Aster joined the department in 1936 and took over the history of philosophy classes. Reichenbach taught, especially during his last two years, symbolic logic, epistemology and what we today call philosophy of science, though not at advanced levels. In a letter to Philipp Frank, for instance, Reichenbach named symbolic logic, epistemology, and philosophy of space and time among the topics he taught.25 This is also well documented by the memoirs of his assistants and students, by the prefaces of books Reichenbach wrote while in Turkey (see Reichenbach 1938, p. viii, Reichenbach 1947, p. ix, Kamber 1978, p. 37, and Kaynarda˘g 1986a, p. 67). Moreover, a plan for the philosophy curriculum of the 1937–1938 academic year also confirms this.26 The plan shows all the courses, including the name of instructors next to each, a philosophy student must take within four years. Reichenbach was assigned the following courses: logic and theory of knowledge (to be taught to freshmen and sophomores), contemporary philosophy (to be taught with Aster on a rotational basis), space and time, the image of the world in natural sciences, and advanced logic (to be taught to juniors and seniors).27 Finally, I must also mention that Reichenbach’s logic lectures
24 This must be in the year 1935. See also Reichenbach’s letter to Carl Hempel dated 25 February 1935 (HR 013-46-12) in which Reichenbach wrote that he was teaching some history of philosophy. That same year Adnan Adıvar met Reichenbach in the Paris conference who told him that “I am for now also teaching some history of philosophy…But I am bringing a professor of history of philosophy” (Adıvar 1945, p. 127; my emphasis). As we saw, that professor turned out to be Ernest von Aster. 25 HR 013-44-08. Letter from Reichenbach to Frank, dated 26 February 1938. 26 Courtesy of the Istanbul University archive. 27 Each of these courses were to be taught for 2 h per week. It is to be noted that at the time Istanbul
University did not have a semester system. Each course was for the whole academic year.
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were translated into Turkish by Vehbi Eralp and published under the title Lojistik in 1939. Lojistik is a 95-page booklet that includes the following topics: propositional logic, functions, classes, classical logic, induction, paradoxes, infinity, and axiomatic systems. Chapter of Two, entitled “Introduction to Symbolic Logic”, of his The Theory of Probability is entirely contained in that booklet, which also found its place in his Elements of Symbolic Logic. Reichenbach organized many interdisciplinary seminars and lectures, both formal and informal. Among those attending were members of the philosophy department, especially his assistants, Aster, Rustow, Auerbach, and Eleanor Bisbee, who was at the time a teacher of philosophy at the American College for Girls at Arnavutköy, Istanbul.28 Reichenbach also continued his editorship of Erkenntnis from Istanbul for a while. In 1934 he became a founding member of the “Turkish Association of Physics and Natural Sciences” and gave lectures there (Kaynarda˘g 1986b, p. 5). He was much respected both inside and outside Istanbul University, and even gained some popularity in non-academic spheres. News about him appeared in French newspapers published in Istanbul (Kaynarda˘g 1986b, p. 14).
5 Reichenbach’s works between 1933 and 1938 Reichenbach was extremely productive during his five-year stay at Istanbul University. As is well known, he wrote Experience and Prediction, published in 1938, in Istanbul. This was the first book he wrote and published in English. He also wrote The Theory of Probability (in German, 1935) and more than a dozen essays, some of which were written for international conferences such as the one in Prague in 1934 and the one in Paris in 1935. Most of his essays in this period appeared in Erkenntnis and Philosophy of Science. In addition, several of his lectures appeared in Istanbul University publications in Turkish. In those days, Istanbul University had the custom of opening the academic year with general lectures in each discipline by a professor, often the department chair. Four of these were delivered by Reichenbach, and it appears that all of them found their place in The Rise of Scientific Philosophy: ˙ (1) “Felsefe ve Tabiat Ilimleri” (Philosophy and the Natural Sciences), Üniversite ˙ Konferansları 1933–1934, Istanbul Üniversitesi Yayınları, 1934. In this opening lecture of the “General Philosophy” course for the 1933–1934 academic year, Reichenbach discusses the relationship between the natural sciences and the “system philosophies” of Descartes, Hume and Kant. (2) “˙Ilmi Felsefenin Bugünkü Meseleleri” (Today’s Issues of Scientific Philosophy), Üniversite Konferansları 1936–1937, ˙Istanbul Üniversitesi Yayınları, 1937. In this paper Reichenbach describes scientific philosophy as the analysis of knowledge, of the language of science.
28 See Reichenbach’s letter to Katz, dated 22 September 1936, HR 013-48-05; Bisbee’s letter to Reichenbach dated 12 August 1938, HR 37-03-149; and Reichenbach’s letter of recommendation for Bisbee, dated 30 September 1942, HR 37-03-143.
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(3) “Tabiat Kanunu Meselesi” (The Problem of Law of Nature), Üniversite Konferansları, ˙Istanbul Üniversitesi Yayınları, 1937–1938. This lecture seems to have formed Chap. 10, on Laws of Nature, of The Rise of Scientific Philosophy. (4) “˙Illiyet ve ˙Istikra” (Causality and Induction), Felsefe Semineri Dergisi, Istanbul University Yayınları, 1939. Here, Reichenbach discusses Hume’s and Kant’s views on causality and induction and argues that a probabilistic approach promises to solve the problem of induction. 6 Reichenbach’s disillusionment with Istanbul University Despite the fact that Reichenbach had a productive five years at Istanbul University, he left for UCLA at the end of his contract. The reasons were emphatically not financial. As we saw earlier, he had a very good contract which allowed him to lead a comfortable life. This provided some measure of security, but his position had no retirement benefits, something that was not unique to his contract. He had two very young children and was worried about their future (Kaynarda˘g 1986a, p. 28). Towards the end of his contract, the Turkish government asked him whether he would become a Turkish citizen, but he declined. As Maria Reichenbach put it, “everybody knew we were not going to be able to put our roots down there…We kept the German conventions and customs. I do not think there was very much social interaction with the Turks” (Güzeldere 2005, p. 20 ). In this context I should perhaps also mention that Reichenbach, like many refugees, saw his exile in Turkey as a temporary situation. As Sydney Hook points out in his memoirs, Reichenbach was skeptical that Hitler would come to power (Hook 1978, p. 34). Even after Hitler’s seizing of power, he did not think that Hitler was to remain for long, as his assistants noted (Kaynarda˘g 1986a, p. 28; Berkes 1997, p. 106). In his early letters Reichenbach was optimistic about what he could accomplish at Istanbul University. In a letter to his friend and former colleague Walter Dubislav soon after his arrival, for example, he wrote that “I have made a very nice hit with the university. I have a big institute with an auditorium of my own, library, a room of my own etc, I am to get funds to buy books as well…I’m in charge of the whole philosophical section and therefore I can do quite a lot. The students naturally haven’t a clue but they are willing and intelligent.”29 In a similar vein, in a letter to von Laue, he wrote: We’ve all been received very heartily at the university. Everywhere, everybody is very obliging towards us, we can arrange our scientific work, as we see fit. I have been assigned with the task of making a fresh start with the philosophy department. You can imagine that I am very happy doing that! I have a nice institute with a number of rooms, among them an auditorium for philosophy. 29 “In der Universität habe ich es sehr schön getroffen. Ich habe ein großes Institut mit eigenem Hörsaal, Bibliothek, eigenem Zimmer usw. Auh einen Fonds zum Anschaffen von Büchern soll ich noch kriegen…Die Leitung der ganzen philosophischen Sektion habe ich und kann daher allerhand machen. Die Studenten sind natürlich ohne alle Ahnung, aber gutwillig und intelligent.” (HR 013-09-04. Letter from Reichenbach to Dubislav, dated 29 November 1933).
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I have also been granted a fund to extend the library. My next task is now to win over the students of natural sciences to philosophy, who keep themselves quite far from philosophy. It is very nice for me, to have the opportunity for the first time to have organizational influence on the philosophical teaching and with the influence of the ordinarius…In the seminar I speak German, French and English with the students, all mixed up, additionally there is the Turkish translation so that there is a babylonic chaos of languages. But one gets used to that as well and I am quite pleased with the progresses of my students, who are now learning for the first time to discuss independently. It also seems that the students are quite satisfied with us German professors and that does make one happy.30 In another early letter, he even found teaching history of philosophy somewhat interesting. He wrote: “I am now giving lectures on the history of philosophy; that is quite interesting if one takes the people more in a psychological sense and adds some general sociological points of view to it.”31 However, by the end of the 1933–1934 academic year, Reichenbach’s optimism was gone, and he expressed regret over not having accepted Oxford University’s offer.32 When Sydney Hook contacted him about giving a series of lectures at NYU, he was ready to accept the offer with the hope that it might become a permanent one. In a number of letters, Reichenbach complained that the level of students was very low, that the university administration—not withstanding a few idealists—did not quite understand what a scientific education was supposed to be, that the country was too poor to sustain a modern scientific university, that the Turkish reform from above, a sort of “enlightened absolutism,” was not quite working, and that he felt completely isolated. He wrote: We are always forced to decrease the level of instruction and to turn the university into some sort of a higher secondary school. I can’t talk at all about the things which interest me, so scientifically I am wholly isolated…The country doesn’t seem to be ripe for such things that interest me; my ideas of a scien-
30 “In der Universität sind wir alle sehr herzlich empfangen worden. Man kommt uns überall mit großer Bereitwilligkeit entgegen, und wir können die wissenschaftliche Arbeit einrichten, wie wir für richtig halten. Mir ist die Aufgabe zugefallen, den Betrieb der Philosophie hier auf neue Beine zu stellen. Sie können sich denken, daß ich das sehr gern mache! Ich habe eine schönes Institut, darunter eigenem Hörsaal für Philosophie. Ein Fonds zur Erweiterung der Bibliothek ist mir auch bewilligtt worden. Meine nächste Aufgabe ist nun, die Studenten der Naturwissenschaften die sich hier ganz von der Philosophie fern hielten bisher, für die Philosophie zu gewinnen. Es ist für mich sehr schön, daß ich nun zum ersten Mal Gelegenheit habe, in den philosophischen Lehrbetrieb organisatorisch und mit dem Einfluß des Ordinarius einzugreifen. (…) Im Seminar “spreche ich durcheinander Deutsch, Französisch und Englisch mit den Studenten, daneben wird auch noch ins Türkische übersetzt, so daß ein babilonisches Sprachengewirr herrscht. Aber daran gewöhnt man sich auch und ich bin schon ganz zufrieden mit den Fortschritten meiner Studenten, die jetzt zum erstenmal lernen, selbstständig zu diskutieren. Es scheint übrigens, daß auch die Studenten mit uns deutschen Professoren ganz zufrieden sind, und das freut einen doch!” (HR 013-49-11. Letter from Reichenbach to von Laue, dated 10 January 1934). 31 “Ich halte jetzt Vorlesungen über Geschichte der Philosophie; das ist ganz interessant, wenn man die Leute mehr psychologisch nimmt und ein paar allgemeine soziologische Gesichtspunkte hinzunimmt…” (HR 013-46-12. Letter from Reichenbach to Carl Hempel, dated 25 February 1935). 32 HR 013-41-73. Letter from Reichenbach to Ernst Cassirer, dated 27 July 1934.
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tific philosophy do require a higher level of scientific education. Under these circumstances, it seems that America is a better option for me.33 Although Reichenbach asked to be released from his contract in 1936, the ministry of education refused to let Reichenbach go. Naturally, Reichenbach felt very bitter and, according to Hook, gave up studying Turkish “as a gesture of retaliation” (Hook 1978, p. 35).34 Reichenbach’s complaints about and, indeed, disappointment with his academic life in Turkey are closely connected to his vision of the university discussed earlier. Istanbul University, for Reichenbach, simply fell short of that vision in many respects, as his letters indicated. Furthermore, the way the 1933 university reform was carried out from above (e.g., by firing dozens of Turkish faculty members, replacing them with émigré professors who were appointed as department heads) also caused much resistance, resentment and envy among the remaining Turkish academicians who saw themselves being practically as being reduced to second-class status. As Hirsch wrote in his memoirs, if the émigré professors were informed from the beginning about the 1933 university reform, its aims, its difficulties and how it fit into the larger series of socio-political reforms, “many misunderstandings, frictions and crises” between them and their Turkish colleagues could have been avoided (Hirsch 1997, p. 211) Finally, and this was the decisive factor, Reichenbach felt extremely isolated intellectually. His intellectual isolation had two aspects. On the one hand, he missed the Berlin Circle, his interactions with students such as Carl Hempel and the members of the Vienna Circle, especially Carnap. On the other hand, he was worried that the Berlin Circle was being forgotten, with the result that scientific philosophy was being represented exclusively by the members of the Vienna Circle. It is perhaps for this reason that in his “public university lectures” published in Turkish (listed in the previous section) there is no mention of the Vienna Circle or even Carnap. He also realized that the future of scientific philosophy was in the US, the country to which Vienna Circle philosophers were moving one by one. He feared that staying in Istanbul would have meant that his distinctive version of logical empiricism, with its strong endorsement of scientific realism and its emphasis on probability theory as the key to a host of problems in scientific methodology and epistemology, would have fallen into oblivion (Gerner 1997, p. 151). Thus, he desperately tried to find a job in the US. After the NYU incident, he made another effort in 1936 by asking Einstein to recommend him to Princeton. His hope was that if Carnap, who had received offers both from Princeton and Chicago, declined Princeton’s offer, he himself might get it. Unfortunately, this did not happen. Apparently, Princeton did not want to hire any Jews (Gerner 1997). Reichenbach was finally offered a job at UCLA through Charles Morris’s efforts. 33 Letter from Reichenbach to Hook, dated 31 January 1935 (HR 013-46-99). See also letters from Reichenbach to Kurt Lewin dated 13 December 1934 (HR 013-49-36) and to Cassirer dated 27 July 1934 (HR 013-41-73). 34 In this period Reichenbach also exchanged a number of letters with Louis von Rougier who was teaching in Egypt at the time. In these letters, which invite a comparative analysis of the experiences and difficulties encountered by the two philosophers who were living in two different non-European countries, one can see how hard Reichenbach tried to find a position in the USA. See Padovani (2006) for a detailed study of the Reichenbach-Rougier correspondence.
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Although Reichenbach felt an acute intellectual isolation from the philosophical world, we should not lose sight of the fact that he shared the same academic space with first-rate scholars such as Mises, Aster, Freundlich, Prager, Hippel, Rüstow and Auerbach, whose intellectual backgrounds and interests intersected with his in one way or another. He tried hard to make the most of this and so formed a small philosophical circle that included Aster, Auerbach, Rüstow (who was also teaching pre-Socratic philosophy in the philosophy department); this group participated in the formal and informal philosophical seminars Reichenbach organized. To these seminars also attended Eleanor Bisbee and Reichenbach’s assistants, especially Neyire Adil-Arda, whom Reichenbach thanked very generously in the preface to Experience and Prediction: “The ideas of this book have been discussed in lectures and seminars at the University of Istanbul. I welcome the opportunity to express my warmest thanks to friends and students here in Istanbul for their active interest which formed a valuable stimulus in the clarification of my ideas, especially my assistant Miss Neyire Adil-Arda, without whose constant support I should have found it very much harder to formulate my views” (Reichenbach 1938, p. viii). In the same preface Reichenbach also thanked Bisbee, among others, for “help in linguistic matters and reading of proofs” of his book. Bisbee, who at the time was a teacher of philosophy at the American College for Girls in Istanbul, had received her PhD from the University of Cincinnati in 1929. Before coming to Istanbul in 1936, she was an assistant professor at her alma mater. Specializing in logic and Greek philosophy, she also taught scientific method and problems of philosophy.35 She published several reviews and articles (especially on logical forms of propositions) in Journal of Symbolic Logic, Philosophy of Science, Journal of Philosophy and Philosophical Review. Bisbee became friends with Reichenbach and his family, visited them often and did more than helping him “in linguistic matters and reading of proofs” of Experience and Prediction. She wrote one of its earliest reviews to help Reichenbach become better known in the US. In a letter to him, she said: “Thank you for your comments on my review of Experience and Prediction. My impatience to get it published was to get into print some personal remarks about you to remind American readers of your arrival in America and of your special interests.”36 While Reichenbach was able to establish a small, modest circle of philosophy, I came across no evidence to the effect that Reichenbach had any serious scholarly interaction with mathematicians Prager and Mises or with physicist Hippel, despite the fact that they were all outstanding scientists. Reichenbach’s almost nonexistent relationship with Mises is the most puzzling. Reichenbach and Mises were colleagues at Berlin University, and fate brought them together again in Istanbul. Here were two distinguished professors on exile, whom one would expect would collaborate fruitfully, especially since they were both interested in probability theory and both held the frequency interpretation of probability. This was not the case. As the hiring process regarding Aster revealed, Reichenbach and Mises did not get along well. Even though Reichenbach wrote The Theory of Probability (published in 1935) and Mises 35 Extracted from Bisbee’s letter of application to American College for Girls, which, incidentally includes a letter of recommendation from John Dewey as well. Courtesy of the Robert College archives. 36 HR 037-05-146. Letter from Bisbee to Reichenbach, dated 9 December 1938.
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wrote Positivism (published in German in 1939) in Turkey, neither of them thanked the other in his preface. Whereas Reichenbach’s book contains a number of references to Mises’ various views and works in relation to the theory of probability, Mises’ book contains only two references to Reichenbach. Reichenbach both acknowledges Mises’ contributions to the theory of probability and at the same time takes pains to distinguish his views from those of Mises. For instance, he writes: “An essential feature of my theory of order is that it deals with all possible forms of probability sequences and is not restricted to sequences of one type of order, such as normal sequences. In this respect my probability theory differences from others—in particular, from that developed by R. von Mises” (Reichenbach 1949, p. 132). By contrast, Mises totally ignores Reichenbach’s theory of probability in his book. Of the two references he gives to Reichenbach, the first one criticizes Reichenbach’s rule of induction, and the other dismisses as “metaphysical” Reichenbach’s view that probability is an objective feature of natural events (Mises 1951, pp. 171–174 and 187). Thus, while Mises found Reichenbach too metaphysical, Reichenbach found Mises too positivistic! One cannot help feeling that what separated the two were emblematic of the continuing divide between the practising mathematician and the philosopher of science, in addition to personal differences. The discussion continued for several years between Reichenbach and the mathematician Hilda Geiringer, who was Mises’ assistant at Istanbul University and who later married Mises.37 Finally, mention should be made of the social and political mood in Turkey in the thirties as another factor behind Reichenbach’s decision to leave. It should be recalled that the Turkish Republic was born out of an independence war won against the Western imperialist powers that had invaded Anatolia. The Republic was only 10 years old in 1933, the year when Reichenbach came to teach at Istanbul University. The process of modern nation building, which relied heavily on a nationalist ideology, was still continuing with full speed in the thirties. Being a victim of Nazi nationalism, Reichenbach naturally felt no sympathy for any form of nationalism. To this must be added Turkey’s love-and-hate relationship with the European West. Turks on the one hand wanted to have a modern country, but on the other hand were afraid of losing their cultural identity. Modernization in the Turkish experience meant Westernization, but “the West” also signified “the enemy” that had invaded the country a decade ago. A series of political, legal and cultural reforms were being carried out to Westernize a traditional society, but they were being imposed from above, causing a kind of a schizophrenia, schism and resistance. This was equally true of the 1933 university reform, which relied heavily on the émigré scholars who occupied the positions of many Turkish academicians who were fired. In the case of Reichenbach, even though he was admired, the scientific philosophy he represented and was trying to implement was foreign to Turkey. Philosophy in Turkey at the time had no unity or direction; most philosophers practiced Islamic philosophy, and those educated in the West were under the influence of French thinkers such as Bergson and Durkheim. They were interested more in social and political, historical and metaphysical issues than with natural science. 37 For more on the differences between Reichenbach, Mises and Geiringer, see Stadler’s and Galavotti’s
articles in this issue.
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As the war neared, life became more difficult for all German refugees. The Nazi government started putting pressure on them through diplomatic channels. For example, they were sent questionnaires and asked whether they would attest to their wives’ and their own status as Aryans (Tachau 2002, p. 242). Some of them, though not the academicians, lost their passports or German citizenship. The Nazi government was also pressuring the Turkish government, and as a result the political mood was also changing, “becoming more chauvinistic somehow” as Maria Reichenbach put it. So, the Reichenbachs left for UCLA in the summer of 1938. 7 Concluding remarks Despite the many hardships Reichenbach faced, as we saw, he was extremely productive in Turkey. As one commentator put it, “although isolated from the philosophical world and deeply aware of the lack of his old Berlin circle, Reichenbach was extremely productive during the Istanbul years. In fact, it appears that he turned the isolation and adversity to a positive advantage.”(Traiger 1984, p. 507) Furthermore, in Istanbul Reichenbach found a secure home for himself and his family, however temporary and imperfect it was. He was loved and respected by his students, assistants and many of his colleagues, even by those who found his philosophy incomprehensible. He became friends with many of them, often took them on long walks in Istanbul and even went to skiing with them in Uluda˘g near Bursa. He is still remembered as a great, innovative teacher who brought fresh air to the philosophy department and indeed as one of the giants of 20th century philosophy of science.38 His impact in Turkey, limited as it was, is felt even today as the conference that occasioned this special issue attests. How lucky we are that philosophy of science proper was introduced to us through him, and indeed philosophy of science became a respected discipline in Turkey thanks to him. His colleagues knew this, and his administrators knew this, despite their occasional misbehavior. What better proof for this can I present than reminding the reader of the fact that when he left in 1938, his successor was planned to be Philipp Frank, though, alas, without success.39 Despite his disillusionment with Istanbul University, Reichenbach genuinely cared about the future of scientific philosophy in Turkey and expressed some optimism during his last year in a letter to Frank: “I myself would be most pleased, for I could not imagine anyone else who could continue my work here as well as you could. A tradition in scientific philosophy has already been founded here, with a few very nice young people; and I would go away with a very heavy heart if I had to see how this position falls in the hands of a philosopher of the customary sort.”40 38 See the interviews with Turkish philosophers such as Macit Gökberk, Vehbi Eralp and Bedia Akarsu in (Kaynarda˘g 1986a). 39 At the time Frank was at the university of Prague. He then moved to USA and became a professor of physics and mathematics at Harvard. 40 “(…) am meisten wäre ich selbst froh, denn ich könnte mir niemand denken, der so gut wie meine Arbeit hier fortsetzen würde wie Sie. Es ist hier doch schon eine Tradition in wissenschaftlicher Philosophie geschaffen, mit ein paar sehr netten jungen Menschen; und ich würde sehr schweren Herzens weggehen wenn ich zusehen müßte, wie diese Stelle in die Hände eines Philosophen der üblichen Sorte fiele.” (HR 013-44-08. Letter from Reichenbach to Philipp Frank, dated 26 February 1938).
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The exile in Turkey also affected Reichenbach through the Turkish language. Although Reichenbach never learned to speak Turkish, he showed interest in its grammar and familiarized himself with it to some degree. In a chapter called “Analysis of Conversational Language” of his Elements of Symbolic Logic, Reichenbach analyzed the tenses of verbs and noted that Turkish has an extended tense which many other languages lack (Reichenbach 1947, p. 291). Later in the same book he also pointed out that Turkish was richer in moods than English. Thus, he wrote that in addition to subjunctive and conditional, Turkish possesses “a special mood expressing probability, i.e. a mood indicating that the truth of the sentence is none too well established; this mood is expressed by the suffix ‘mi¸s’. Thus ‘gitmi¸s’ means ‘he probably went away’ whereas ‘gitti’ means ‘he went away”’ (Reichenbach 1947, p. 338). While the translation of ‘gitmi¸s’ into English is not quite right, what Reichenbach says of ‘mi¸s’ in the rest of the quotation is accurate. Nevertheless, not having an adequate command of Turkish (possibly as a result of stopping studying Turkish to protest Istanbul University’s refusal to grant him leave for NYU), Reichenbach missed the use of ‘mi¸s’. ‘Mi¸s’ is used in contexts where one has no direct knowledge of something oneself, but knows of it by inference based on the evidence one has. That certain languages, such as Turkish, have a special mood for reflecting the inferential nature of at least some of our knowledge would have certainly pleased the author of Experience and Prediction, according to which our knowledge of both physical and psychical phenomena is essentially inferential. Finally, there is good reason to think that Experience and Prediction might not have been written at all under different circumstances. It was the first book Reichenbach wrote in English, and it seems that Reichenbach wrote it specifically for American readers, with the hope that it would help him get a job. In a letter to Kurt Lewin, he wrote: “As you know our direction is now popular in the US and you are right that Carnap’s appointment will further strengthen this. These days I am writing a book about general epistemological issues in English in order to get it published in Chicago with Morris’s help.”41 In a similar vein, he wrote perceptively in early 1935 as follows: Under these circumstances, it seems that America is a better option for me, now that Germany has dropped out of the ranks of Kulturländer…I have the impression that it is America with its sense of the concrete and the technical that should be better disposed for my natural scientific philosophy than Europe, where it is still the mystical-metaphysical speculations that are seen as true philosophy.42 This was the letter sent to Sydney Hook (dated 31.1.1935) in reply to his invitation to NYU. Toward the end of the letter Reichenbach wrote: 41 “Unsere Richtung ist ja jetzt in U.S.A beliebt und Sie haben ganz recht daß die Berufung Carnaps das noch vermehren wird. Ich schreib zur Zeit ein neues Buch über sehr allgemeine erkenntnistheoretische Dinge auf Englisch, um es dann mit Morris’ Hilfe in Chicago zu publizieren.” (HR 013-49-35. Letter from Reichenbach to Kurt Lewin, dated 24 September 1936). 42 “Unter diesen Umständen scheint mir Amerika eine günstigere Aussicht für mich, nachdem jetzt Deutschland ausgeschieden ist aus der Reihe der Kulturländer (…) Ich habe das Gefühl, daß gerade Amerika mit seinem Sinn für das konkrete und technische mehr Verständnis haben müßte für meine naturwissenschaftliche Philosophie als Europa, wo noch immer die mystisch-metaphysischen Spekulationen als die wahre Philosophie angesehen werden.” (HR 013-46-99. Letter from Reichenbach to Hook, dated 31 January 1935).
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I plan a book with less of a mathematical nature about the method of knowledge in natural sciences, in which I expose in more detail my theory on induction developed in the theory of probability. Should the plan with your university be realised already in the autumn of 1935, I could write this book in the form of lectures and could write directly in English. I would like this also because I would like very much to publish such a book in English.43 The Reichenbach of the 1930s was not the Reichenbach of 1918. He was no longer a young idealist and an aspiring philosopher but an internationally known scholar who was trying hard to distinguish his brand of scientific philosophy from that of the Vienna Circle. He needed to be at the frontier so that he could make his impact felt, and the newly emerging frontier was the US, as more and more philosophers and scientists were moving to this country. He thought that Experience and Prediction could be a pivotal stepping stone for securing a position in the US. And I believe not just the fact that it was written, but the very form it took was also due to his exile. In these respects there is a striking similarity between Reichenbach’s arguably most influential book Experience and Prediction and Auerbach’s masterpiece Mimesis, which is considered to be the founding text of comparative literature. Auerbach wrote his book in the same city in the early forties under similar conditions. In the closing paragraphs of his book he wrote: I may also mention that the book was written during the war and at Istanbul, where the libraries are not well equipped for European studies. International communications were impeded; I had to dispense with almost all periodicals, with almost all the more recent investigations, and in some cases with reliable critical editions of my texts. Hence it is possible and even probable that I overlooked things which I ought to have considered and that I occasionally assert something which modern research has disproved or modified. I trust that these probable errors include none which affect the core of my argument. The lack of technical literature and periodicals may also serve to explain that my book has no notes. Aside from the texts, I quote comparatively little, and that little it was easy to include in the body of the text. On the other hand it is quite possible that the book owes its existence to just this lack of a rich and specialized library. If it had been possible for me to acquaint myself with all the work that has been done on so many subjects, I might never have reached the point of writing. (Auerbach 1968, p. 557) I think this is largely true of Reichenbach and his Experience and Prediction as well.
43 “Ich plane ein Buch von weniger mathematischer Art über die Erkenntnismethode der Naturwissenschaft, in dem ich meine in der Wahrscheinlichkeitslehre entwickelte Theorie der Induktion in breiterer Form darlege. Sollte sich der Plan mit ihrer Universität schon zu Herbst 1935 verwirklichen, so könnte ich dieses Buch etwa in der Form von Vorlesungen ausarbeiten und sogleich in englischer Sprache schreiben. Das wäre mir auch deshalb angenehm, weil ich sehr gern ein derartiges Buch auf Englisch herausbringen möchte.” (HR 013-46-99. Letter from Reichenbach to Hook, dated 31 January 1935).
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Acknowledgements I thank Elliott Sober, Friedrich Stadler and especially Flavia Padovani for helpful comments and suggestions. I benefited also from Koray Karaca’s knowledge and insights about the topic at the initial stages of this research. I am grateful to Feza Günergün without whose help I would not be able to locate Hans Reichenbach’s file at the Istanbul University archives. I thank the Dean of the Faculty of Letters of Istanbul University for allowing me to use it. I owe thanks also to Çi˘gdem Yazıcıo˘glu for allowing me to use Eleanor Bisbee’s file at the Robert College archives. I am especially grateful to Brigitte Parakenings from the Konstanz University Archives for her guidance and supplying Hans Reichenbach’s letters, published by permission of the University of Pittsburgh. All rights are reserved. I thank Beril Sözmen for translating them and her comments on an earlier version of this paper. The research for this paper was partially supported by the Turkish Academy of Sciences. I thank them for their support.
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