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gic is the technology of deduction. Its business is to show how, from "given set of premisses, to derive conclusions that can be depended 'ri to be true if the premisses are true. Part of the technique, even iIi tiquity, was regimentation. Regimentation figured mainly, at first, in atching up clauses of the premisses. 1 Often a clause in one of the :remisses admits of recasting, without violence to the speaker's or the ... 'ter's purposes, in such a way as to match it with a clause of another 'eniiss. Each new duplication thus created is vital to the deductive ,'·'otential. i~'It is in symbolic logic that regimentation takes on modern efficiency: ~liat of prefabrication and mass production. A few basic and ubiquitous ,;idioms are singled out, each of which can accommodate a vast range :9i clauses when these are suitably paraphrased. These few forms stand "hpen in their symbolic rigidity waiting for content to be poured in at jthe user's pleasure. The fewer the forms, the greater the incidence of ,eventual duplication among the clauses of a set of premisses and hence ;:the richer the deductive yield. Such is the premium on economy of :primitive notation. tL: Symbolic logic in its neoclassical form is predicate logic. In its austerest form, it imposes just two idioms, or grammatical constructIons: ~truth function and the universal quantifier, together with variables for referring back to the quantifier. The mold is built up of these ';devices in iteration. The content to be poured into the mold consists of }predicates of one or more places. ""." In practice it is convenient and customary to relax this stark economy. : Symbols for five truth functions are admitted, though all can be reduced < to one by paraphrase. Existentialquantificatioil is added, though reduc,: ible to universal and negation. From the unlimited stock of predicates •to be drawn on for content, one in particular is appropriated as peculiarly logical: the two-place predicate '=' of identity. Finally, the gates .,' are opened to other ingredients besides predicates as admissible con, tent; namely, constant singular terms as well as functors such as 'plus', i 'times', and 'log' for forming complex singular terms. Each of th~e Synthese 98: 143-151, 1994.

© 1994 Kluwer Academic Publishers.

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could be reduced to a corresponding predicate, '" functions, quantification, and identity. The matching up of clauses. is no longer the main point of re' mentation. Equally important is the streamlining of canons of ded~' tion. In earlier times this scarcely mattered; the rules of the syllogi~': added little to the unimplemented light of pure reason. With the ri~, of symbolic logic, however, algorithms and complete proof procedui in rigorous formalization assumed vital importance, both for the p:. sophical understanding that they have afforded and for their practi¢: utility. Theburgeoning computer industry testifies to the latter. il On the philosophical side, the regimentation embodied in predic~ logic has also brought illumination quite apart from the technology.,,, deduction. It imposes a new and simple syntax on our whole languag~!~ insofar as our logic is to apply. Stripped down to the austere econolll~ that I first described for predicate logic, our simple new syntax is a~ follows. The parts of speech are: (1) the truth-functional connective;' (2) the universal quantifier, (3) variables, and (4) atomic predicatesQ!" one and more places. The syntactic constructions are: (1) application, of a predicate to the appropriate number of variables to form a sen~: tence; (2) prefixture of a quantifier, with its variable, to a sentence;,' and (3) joining sentences by the truth-functional connective an" the: adjusting parentheses. ., I h~sitate to claim that this syntax, so trim and clear, c~n accommo":1 date'in translation all cognitive discourse. I can say, however, that no,; theory is fully clear to me unless I can see how this syntax would}~ ac.commodate it. In particular, all of pure classical mathematics can be; thus accommodated. This is putting it Inildly. The work of Whitehead" and Russell and their predecessors and successors shows that the de.; scribed syntax together with a single two-place predicate by way of extra-logical vocabulary, namely the 'e' of class membership, suffices in principle for it all. Even '=' is not needed; it can be paraphrased in terms of 'e'. What makes for the surpassing clarity of theories couched in this syntax is their extensionality. This means, in part, that if within a true sentence we supplant a true component sentence by another truth, or a false component by a falsehood, the containing senten.ce will remain true. Furth~r, if we supplant a component open sentence by another that it fulfilled by just the same values of the variables, the containing sentence will still remain true.

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!The useful idioms of propositional attitude - 'x beli.eves th~t P': 'x . pes that p', 'x says that p', and the rest - are in conspICUOUS VIOlatIOn Jextensionality. We may well believe that p and not that q, though 'bth be true. ~IIWhat is worse, even scandalous, is that these idioms violate the i'bstitutivity of identity: the putting of equals for equals. How can >mething be true and false of the same ~hing ~nd~r differ~~t names? ;Yet these idioms are useful to the pomt of mdispensability. More" ~\;er, I think they are rooted in the earliest stages oflanguage. I picture he earliest idiom of propositional attitude as 'x perceives that p', where .. stands for an observation sentence such as 'It's raining', 'That's ''lk', 'That's a dog'. When the mother is monitoring. the chil~'s u~ter­ 'ce of such a sentence, she has to empathize with hIm. She Imagmes ~erself in his place, facing in the same direction, and then checks Whether she, thus oriented, feels moved to volunteer the senten.ce herself. In short, she checks, however inarticulately, whether the chIl.d ;teally perceives that it's raining, that .i~'s milk,. that it's a dog. Th~s much in the way of an idiom of propOSItIOnal attItude, all unspo~en, IS essential to the very handing down of language from generatIOn to .generation; for observation sentences are. t~e c~ild's en~ering wed~e to :language. And then, down the ages, the IdIOm x perceIves that p was 'extended to non-observational sentences, and, by analogy, the other idioms of propositional attitude emerged. .' . . . Gottlob Frege, confronted with the paradOXIcal faIlure o~ SUbStitUtIV'ity of identity, concluded that in those idioms the. recalcItrant terms . 'have changed their reference and taken to refemn~ to what ~ould ; normally be their meanings, or senses, rather than th~Ir normal ob~ect~. i' A better solution is suggested by the mother's relatIOn to the chIld m ; monitoring his observation sentence; namely, empat~y. When someone ascribes a propositional attitude to someone, he Impersonate~ th~t person to some degree. The subordinate clause of the co~structIon IS uttered from the subject's point of view, somewhat .as If from. the subject's mouth. No wonder sUbstitutivit~ of i~entity. falls.; the sUb~ect, , poor fellow,didn't know the things were IdentIcal. LIkeWIse for f~Ilure " of extensionality: the subject would have been unprepared to mter; change the two coextensive clauses in question, simply because he ,'. didn't know they were coextensive. . . . Along with the failure of extensionality and the failure of s~bstItut~v­ ity of identity, in clauses of propositional attitude, there IS a thIrd

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f~ilure: failure of quantifying in. A quantifier outside the clause cannot'!

bm.d a variab~e inside the clause, at least not without raising problem&~ of mterpretatIOn. The q u a n t i f i c a t i o n " (1)

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3x (Ralph believes that x is a spy)

raises an ontological problem of the value of 'x', since Ralph trust!!, Bernard J. Ortcutt but suspects a man in a brown hat who is in fact Ortcutt. The. difficulty, again, is just discrepancy between the rei world" to ~hICh. the outlying '3x' relates, and the empathized world';) "', Ralph ~ - .m w?Ich the recurrence of 'x' is trapped. ': , '. Clanty IS gamed by banishing propositions, as objects of belief and· other propositional attitudes, and settling somewhat unnaturally for the , sentences themselves, the mere strings of letters or phonemes. Thi!!, after all,. was where it all began, according to my conjecture: in th~ o~s~rvatIOn s~nt,ence~ that the mother felt moved to affirm when emp~~ .' thIzmg.t?echIld ~ attItude. Let us construe the conjunction 'that' of the proposItIOnal-attItude construction simply as a quotation mark. It does take an obvious bit of adjusting. 'He believes that he ill Napoleon' becomes He believes 'I am Napoleon', since the believed sentence is conceived as in the subject's mouth. In the cas.e of indirect ?isco~rse,. moreover, which is an idiom of propositional at~Itude, confusIOn wIth dIrect quotation would have to be avoided. We mIght agree to use 'say' for the indirect and 'utter' for the direct In taking the o~jects of the attitudes as sentences, I do not pr~sume that the creatllre m the attitude speaks the language of the sentence or ~ny language. The sentence is in the language of the ascriber of th~ attIt~de, but he frames it from what he takes to be the subject's point of VIew. The fail~re of extensi~nality, the failure of substitutivity of identity, and the faIlure of quantIfying in all become natural and obvious when the objects ~f the. attitudes ~re seen as sentences, set off in quotation. The quotatIOn SImply desIgnates the depicted string of letters or phonemes, unrelated syntactically to the outlying context. " We may, seem to have paid a price for this clarification. We may see~ to hav~ ~aken leave of the clear and simple syntax of predicate lOgIc b~ admIttmg a potential infinity of sprawling quotations as unanalyzed smgular terms. However" not so. Quotations can be reduced to

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: the syntax of predicate logic by spelling them out. What we need ~re '; jU!!t names of the several signs or letters of our alphabet, togethe~ wIth : a term functor - analogous to 'plus' - to express the concatenatmg of ; one letter or string of letters with another to form a longer string. ; Given this much, we can define any quotation by spelling it out letter , by letter. When at last we are bent on reducing everything to the minimal syntax of predicate logic, we reduce the letter nam~s and t~e term functor to predicates, with help of '=', as noted earlIer. All m all, first by quotation and then by spelling, we digest the propositional t attitudes syntactically and logically. Extensionality prevails, as well as the substitutivity of identity and the syntax of predicate logic. Semantically, however, the propositional attitudes remain low grade. The objective criteria for whether x believes that p, regrets that p, etc., are heterogeneous, varying radically with 'p', and, as often as not, they are indecisive. This is something to put up with, pending progress of some sort or other; but the logical and the syntactical barriers are gone. In all this, however, I have been taking the propositional attitudes only dedicto. That is to say, I have be.en construing the ~on~ent ~lause a!! the ascriber's attempt to speak stnctly from the subject s pomt of view. The other interpretation, de re, permits the ascriber's own voice to intrude on his simulation of the subject's voice. If we recognize the de re alternative, the sentence (2)

Ralph believes that Ortcutt is a spy

becomes ambiguous. De dicto it is false, since Ralph denies the sentence 'Ortcutt is a spy', but de re it is true, because the subject in the brown hat is Ortcutt. More precisely, what may be taken de re or de dicto is not the whole ascription of the ,propositional attitude, nor yet the content clause, but only one or another place within that clause: one or another. place occupied by a singular term or a variable- thus the place occupIed ~y 'Ortcutt' in (2). A term in de re position, or what I have called refer~ntial position, is subject to substitutivity of identity after all, an? a va~~ble in that position can be quantified from outside. ReferentIal posItIOnS are where the ascriber's world has intruded. If the content clause of an ascription of a propositional, attitude contains referential positions, therefore, the content clause can no longer be represented in quotation. Accordingly, in 1956 I proPt:0sed

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analyzing such cases by means rather of quoted predicates, thus freeing:: the referential positions from quotation. 2 (2) becomes: ii,;; Ralph believes 'is a spy' of Ortcutt,

when taken de reo The referential position is thus exposed to sUbstitutiv~'\ ity and also to quantification, . 3x (Ralph believes 'is a spy' of x),

which captures (1). It seems important to make sense thus of (1) and to contrast it with the trivial Ralph believes '3x (x is a spy)'. (1) suggests that some trait or circumstance, some description, singles out the suspect in Ralph's mind. But this will not serve, as Robert Sleigh showed in his example of the shortest spy. 3 There is probably a unique shortest, and Ralph surely believes that the shortest spy is a spy; but this does not make for the political significance of (1). Nor should it matter that there might be more than one shortest spy. I now despair of a coherent theory of propositional attitudes de re, despite appearances. 4 When security agents are told (1), they are only given a lead and not a coherent message. Following the lead, they interrogate Ralph and record some straight de dicta beliefs, all nicely within the bounds of our extensional scientific framework. So I feel we have seen extensionalism safely through the perils of the propositional attitudes. But threats remain from other quarters, notably the modal logic of necessity and possibility. Modal logic differs from the propositional attitudes in that all term positions are referential, or potentially so. Quantification into modal contexts is unrestrained, but substitutivity of identity in modal contexts works for some terms and not for others. It is a question now not of position, not of where, but of what. Hence Dagfinn Fl1Illesdal's genuine singular terms, or Saul Kripke's rigid designators. These are the terms that obey substitutivity of identity even in modal contexts. These are the terms, also, that support inference by existential generalization, even in modal contexts; other terms do not. As we might say in a modal spirit, these are the terms that name their objects necessarily. They name them on the score of essential traits, not accidental ones.

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.. Modal logic fails of extensionality, and up to a point it fa.ils of ; substitutivity of identity. Must I curb and compromise my extenslOnal, ism after all? My answer this time is that I have not been sold on the notion of necessity, the distinction between necessity and contingency, which is what modal logic in its standard interpretation and primary motivation is about. The adverb 'necessarily' in its everyday use is another matter. Typi, cally it serves merely to mark a statement that one's interlocutor is .", presumed to agree with, in contrast to whatever matters are u~der ; discussion or investigation at the time. This use is clear and convement, . but it has no place in logically regimented science, any more than other occasion-dependent locutions such as'!', 'you', 'here', 'now', and the tenses of verbs. The pioneer ventures in modal logic undertaken a century ago by r Hugh MacColl and more economically in 1918 by C. I. Lewis were . motivated by dissatisfaction with the truth-functional conditional. They wanted a stronger connective: 'necessarily if'. What was lurking in the background was the subjunctive conditional, and there is no denying that it pervades scientific thinking. It is implicit in the design of every experiment: 'If this and this were set up, such and such would occur'. However, the universally quantified truth-functional conditional covers such cases. The experimenter's conjecture is a general one: 'Whatever this and this obtain, such and such occurs'. Then he tests this general conjecture by setting this and this up and watching for such and such. The contrafactual case of the subjunctive conditional, however, must be treated as elliptical and occasion-dependent. A universally quantified truth-functional conditional is again implicit, I think, but with a complex antecedent some of whose clauses are left tacit, to be divined from the context and circumstances. It is along such lines that I would make sense of subjunctive conditionals, contrafactual and otherwise, without compromising extensionality. . . Disposition terms such as 'soluble' are naturally associated WIth the contrafactual conditional; thus, 'If this were in water, it would dissolve'. My view of disposition terms, however, is that they do not ascr~be a special sort of property, a potentiality, but that they just name ordInary properties in a special way, namely, by alluding to a fairly dependable and convenient symptom or test. Solubility in water is a physical property analyzable, like others, in microphysical terms, but an easy and

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generally reliable test of it is immersion in water to see if the stuff dissolves. Again, fragility is explicable microphysically, but a fairly reliable test is to drop the object and see if it breaks. The relation of cause and effect has been seen as a challenge to extensionality, but again I think I see a reconciliation. I see the relation as relating events, and I see events as physical objects in my broad sense. Each event, each physical object, is just the total content of some portion of space-time. If someone whistled a certain tune all the way to the bus, and only then, I am prepared to identify his whistling that tune with his walking to the bus; they are the same event. So, if his walking caused his arrival at the bus stop, his whistling ,caused it. This is odd usage, but harmless, for I do not generalize on it. Causal laws relate classes of events, as usual, and whistling, a tune does not usually cause an arrival. Finally, how does probability fare under extensionality? Where the probability is statistical, we can settle for a statement of the statistical basis itself as the ratio of sizes of classes of cases. Where the probability is subjective, Le. the degree of expectation, we are up against issues of behavioral or physiological analysis of mental phenomena, irrespective of extensionality. The ,neat behavioral measure of a subjective probability is the minimum acceptable odds at a wager. Enigmatic as subjective probability may be, the crucially enigmatic locus of probability is quantum mechanics. It seems that something like probability invests the behavior of elementary particles irreducibly. This problem I leave to the scientists, eagerly awaiting further progress on their part and enlightenment on mine. There has long been discussion of revisions even of logic for the simplification and clarification of quantum theory, and I can conceive that extensionality might not remain immune. I can only hope, and leave it to the future to speak for itself.

NOTES

I was alerted to this central but largely neglected aspect by Sherry (1991). Quine (1956). 3 Sleigh (1968). 4 But see Burdick (1982). He accommodates them extensionally by citing additional open sentences as tacit parameters. 1

2

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REFERENCES

. d' 1982 'A LoO'ical Form for the Propositional Attitudes', Synthese 52, 0" BurdIck, Howar . , 1.85-2W30. V . 1956 'Quantifiers and Propositional Attitudes', Journal of Philosophy 53, , QUlne, ..0 177-87. h ' H' tory and Philosophy of 'd' 1991 , 'The Conspicuous Role of Parap rase, IS Sherry, D aVI. Logic 12, 151-66. . . Lo . , N CIs 2 391-89 Sleigh, Robert: 1968, 'On a Proposed System of EplstemIc glC, 0 , . Department of Philosophy Harvard University 208 Emerson HaIl Cambridge, MA 02138 U.S.A.