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is true iff p,
wh e r e“
”s h o ul dber e a da s“ t h epr o po s i t i o nt h a tp” .Ani n s t a n c eo f( E) here is one like <<snow is white> is true iff snow is white>, i.e., itself a proposition (1998a: 17f.). Horwich admits as a weakness of his theory that it cannot be finitely axiomatised, viz., that it contains infinitely many axioms, although, he argues, an inevitable one (1998a: 25 ff.). I argued in 1.5 that this lack of generality is unacceptable, and will not comment upon it here. Be s i de st h i st he o r ya bo ut“ t r u t hi t s e l f ” ,Ho r wi c ha l s oh o l d st h a to u ru n d e r s t a n d i ngo ft hewo r d“ t r u e ”“ c on s i s t si nt h ef a c tt h a tt h ee x pl a n a t o r i l yb a s i c regularity in our use of it is the inclination to accept instantiations of the s c he ma( E) ”( 19 9 8a :35 ) .It is reasonable that the widespread suspicion against dispositionalist theories of meaning is the reason that Horwich prefers the explication in terms of (MT). Another reason is that he wants a theory of “ t r u t hi t s e l f ”r a t he rt h a no neonl yo ft heme a n i n gof“ t r ue ”( 1 9 9 8 a :3 6 f . ) .Bu t , as I will argue in 3.5, it is difficult to sustain a theory that gives different accounts of truth itself and the meaning of “ t r u e ”i nt h i swa y wi t ho u t e n t a i l i n gc l a i mst h a tgoa g a i n s tt hede f l a t i o n a r ys pi r i t ,e . g . ,t h a t“ t r u e ”g e t si t s meaning by referring to the property of truth. Le tusf o c usnow o nt h ec l a i mt h a t“ ( MT)e xpl a i n sa l lf a c t sa b o u tt r u t h ” . Before the publishing of Truth, many philosophers had raised objections of t hef o r m“ s u c ha n ds u c hi saf a c ta b o utt r ut ht h a td e f l a t i o n i s mc a n n o t e xpl a i n ” .The (alleged) facts mentioned have included the fact that true beliefs facilitate successful behaviour, that meaning is truth-conditions, that it is the truth of theories that accounts for their empirical success, and many more. The method is described in 1.5, where we also saw an example of such an explanation –that of why true beliefs facilitate successful behaviour. Concerning certain theses that are not uncontroversially facts about truth, e.g., that truth is intrinsically valuable, Horwich goes on to argue that if it is a fact, then deflationism stands in no tension with it being so (1998a: 62f.). Thus, deflationism is quite neutral concerning this idea of intrinsic value, in
96
A Critical History of Deflationism
the sense that both proponents and opponents of this idea may both consistently be deflationists (cf. Soames 1999: 231). Whether this is always the case cannot, of course, be regarded as a settled ma t t e r ,b u tHo r wi c h ‟ s examples seem to indicate that deflationism is at large neutral concerning matters outside the theory of truth (1998a: 57f.). A well-known problem concerning the explanatory adequacy of (MT) is that general facts seem difficult to explain (cf. Gupta (1993b: 66) and Soames (1999: 247f.)). On (MT), it seems that all one can derive is every instance of ag e ne r a lf a c t ,e . g . ,t hei n s t a n c e so f“ I ft h ep r o po s i t i o nt h a tp and q is true then the proposition that p and the proposition that q are t r ue ” ,b u tno tt he general fact itself, i.e., that every true conjunction has true conjuncts. Horwich first proposed that an -rule would allow him to derive the general claim, but, as Panu Raatikainen has argued, Horwich seems to be precluded from using the -rule, since there are uncountably many propositions, wherefore the rule can never be followed by finite beings (2005: 176). Ho r wi c h‟ sl a t e s tpr o p o s a lf o rde a l i ngwi t ht hi sp r o bl e mi st oa d dar u l et ot he e f f e c tt h a t“ [ w] h e n e v e rs o me onec a ne s t a b l i s h ,for any F, that it is G, and recognizes that he can do this, then he will conclude that every F is G” (2002: 68, original emphasis). This was actually designed to explain our acceptance of the general propositions, but the fact-explaining is presumably taken to involve a corresponding claim with a consequent saying that one may conclude the universal claim. If this works, then, since the rule does not concern truth, the problem of explaining general facts is solved. We will see in 5.5, however, that there is a different problem concerning infinity that emerges in the context of explaining certain general facts. Ano t he ri mpo r t a n tf e a t u r eo fHo r wi c h ‟ sd e f e n c eo fd e f l a t i o n i s mi st h e e x pl a n a t i o no fs e ma n t i cc o n t r i but i on sof“ t r u e ”i n“ bl i n da s c r i p t i o n s ” ,s u c ha s “ Wh a t / Eve r y t h i ngSmi t hs a i di st r ue ” .OnHo r wi c h ‟ sa c c o un t ,“ Wh a tSmi t h s a i di st r ue ”c a nbee x pl a i ne ds i mpl ybys h owi n gt h a t ,g i v e na na p p r o p r i a t e i n s t a n c eof( E)a sap r e mi s e ,wec a nde d uc e ,e . g . ,“ Sn o wi swh i t e ”f r o m “ Wh a tSmi t hs a i di st r ue ”a nd“ Wh a t Smith said = <Snow is white>”( o r s i mpl y“ Wh a tSmi t hs a i di st h a ts now i swhi t e ” )bys i mpl er u l e so fl o g i c (1998a: 21).19 A similar account can clearly be given for universal truthascriptions. Instead of giving a paraphrase, the functioning of the blind truthascription is explained inferentially (though Horwich does not use this expression). We saw in 2.3 that the requirement to give paraphrases lacking 19
A seed to this idea may be found in Ayer (1963: 166).
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CHAPTER TWO
“ t r u e ”s e e me dt or e q ui r et h eus eo fpr o po s i t i on a lq ua n t i f i e r s ,wh i c h ,h o we v e r , was shown to yield an implausible grammatical account of the sentences paraphrased. With this inferentialist account, what has been accomplished is as o l u t i ono fFr e g e ‟ sc on und r um di s c us s e da bov e ,t h a tt h eo c c u r r e n c eo f “ t r u e ”i n“ Myc onj e c t ur ei st r ue ” ,a so p po s e dt h a ti n“ I ti s true that snow is wh i t e ”s e e mst oe xpr e s ss o me t hi ngi mpo r t a n ta n di r r e du n d a n t :we understand ineliminable occurrences of“t r u e ” by recourse to eliminable ones, viz., t ho s eo ft h ef o r m“ Th epr o po s i t i ont h a tp i st r u e ”( c f .So a me s1 9 9 9:2 3 0f . ) .
98
CHAPTER THREE: THE PROBLEM OF FORMULATION 3.1 INTRODUCTION This chapter will be of a slightly more technical character. It will deal with the question of how, in a specific sense, the deflationary theory of truth should be formulated. The question is not that of what is the primary type of truth-bearer (or which type of noun-phrases the truth-predicate primarily applies to), though this is also a major question (and the subject matter of Ch. 4). Rather, the problem here at issue is that of finding an acceptable generalization of the particular fact that it is true that snow is white iff snow is white, i.e., what was in 1.5 called the problem of formulation. In the same section, i nf i n i t et h e o r i e sl i k eHo r wi c h ‟ swe r ef o undu n t e n a bl eongeneral grounds concerning theory-preference, so we need a solution to this problem if deflationism is to remain a viable theory of truth. I here took the trutho pe r a t o r“ i ti st r uet h a t ”a sa ne xa mpl e ,a ndwi l lc o n t i n uet od os o ,b u t ,a g a i n , this is an arbitrary choice, since we are not concerned with what truth-bearer or truth-ascription is primary. I take there to be three possible solutions to this problem: (i) (ii) (iii)
Schematic solution, Solution by quantification, Linguistic solution.
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The formulation found mandatory in this chapter, namely (iii) will in the subsequent chapters be argued to yield a theory with considerable merits.1 The first type of solution, that we can dismiss right away, is that a sentence-schema like (ES), (PS) or (DS) may itself be the claim with which to explain all facts about truth. Though this has not (to my knowledge) been proposed by anyone as a correct theory, some non-deflationists have spoken as if such a schema is the theory itself. Although we are well accustomed to the use of sentence-schemata in the philosophy of language and logic, we must in this case look more critically to how they are used in order to see why this proposal will not work. To bring the problem to its head, we should note that, strictly speaking, a schema does not say anything, since it is not a sentence, but, precisely, a schema. It would not be correct to say that it is meaningless, of course, since it obviously partakes in meaningful sentences, sentences which say something. The claim, therefore, is rather that the production of a schema never non-elliptically amounts to an assertion. If it does so elliptically, we had better spell this out and see if the result provides a correct theory of truth. As will be argued below, the possible ways of spelling t h i so uta r e ,be s i de st hea bo vedi s mi s s e di n f i ni t et h e o r i e sl i k eHo r wi c h ‟ s , only (ii) and (iii). But, it may be countered, in logic one does derive claims from axiom schemata, so why not in a truth-theory? Well, first the practice in formal logic may perhaps be inadmissible, strictly speaking. But we can do better, and note two relevant differences: first, in such theories, the axiom schema can be substituted by the claim that the schema has true instances; second, the axioms do not necessarily have to be claims at all, whereas it seems clearly wrong to say that the theory of truth is not a claim –surely, it is supposed to tell us something about truth and say what truth is. I conclude that the schematic formulation fails. Though prima facie obvious, the idea that truth can be explained by declaring the schema true has still been questioned, so in 3. 2 I will spend some time refuting it. That refutation will then pave the way for a refutation 1
Discussions about this issue can be found in Tarski (1944), Pap (1952: 8, n. 2), Prior (1971: 22), Mackie (1973: 31, 60f.), Williams (1976: 6-10), Chisholm (1977: 138), Haack (1978: 40, 78f.), Platts (1979: 14f.), Blackburn (1984: 258), Forbes (1986), Baldwin (1989), Resnik (1990: 412f.), Kirkham (1992: 4.4, 5.7), Sosa (1993), David (1994: Ch. 4), Field (1994a: 267f.), Kalderon (1997), Kovach (1997), McGrath (1997b), Horwich (1998a: 25ff.), Soames (1999: 42, 86ff.), McGee (2000), Dodd (2000: 36ff.), van Inwagen (2002), Hill (2002: 17ff.).
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The Problem of Formulation
of the second type of solution, the solution by quantification. This solution consists in making a claim out of the preferred schema by adding propositional quantifiers. This, one might think, is possible, since the o c c u r r e nc e so f“ p”i n( ES)c o u l dbema d et of un c t i ona sv a r i a bl e s .Al lwe need to do, then, is toa d daun i ve r s a lq u a n t i f i e r“ ( p) ”( o bvi o us l yn o ta n existential one), and then say that the claim that results is the one which explains truth. As a kind of corollary of the refutation of this solution, de f l a t i o n a r yt he o r i e so ft h ef o r m“ Fo ra l lx, x is true iff ...x. . . ”wh i c hus e propositional quantifiers will also be found unacceptable on the same grounds. The final contender, which will be argued to be the only acceptable one, c o n s i s t si ng i vi n gac l a i ma bo utl i n g ui s t i ce xp r e s s i o n s ,h e n c e“ l i n g ui s t i c sol u t i o n ” .Th i sma yt a ket wof o r ms .I nt h ef i r s t ,o n ea s c r i b e ss o mep r o pe r t y (other than truth) to the instances of the preferred schema. It will be useful for our coming discussion to see that this kind of solution, where a predicate, call it F, is ascribed to the instances of, e.g., (ES), consists in giving a claim equivalent to (SA1) All sentences s a r es u c ht h a t“ I ti st r u et h a t ” s “ i f f ” s is F, whe r e“ ”i st het wo -place concatenation-function, which, applied to two expressions, refers to the expression obtained by juxtaposing in order the e x pr e s s i o n si ni t st wop l a c e s .( SA1)t h ush a st hef o r m“ Ev e r yx is such that F(f(f(f(a, x), b), x) ) ” .I nt h es e c on df o r mo ft hi ss ol ut i on ,t hec l a i mi st h a t some relation holds between the left- and right-hand sides of the instances of a schema, presumably some kind of equivalence. In analogy with the equivalence between the first form and (SA1), the second kind of linguistic solution, where a relation R is said to hold between the left- and right-hand sides of all instances of (ES), will involve giving a claim equivalent to (SA2) All sentences s a r es u c ht h a t“ I ti st r u et h a t ” s bears R to s, i . e . ,as e n t e n c eo ft hef o r m“ Eve r yx is such that R(f(a, x), x) ” . On the assumption that these three solutions exhaust the possibilities, it will be concluded that deflationism must be linguistically formulated. How can this assumption be justified? Well, if the criterion on the formulations is so weak as only requiring that they are attempts to generalize over the particular instances, then it seems difficult to give a deductive argument for
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it. Indeed, on that criterion, there seem to be an infinite number of ways to form a claim of the kind in question. But let us look closer at the de f l a t i o ni s t ‟ sb a s i ci d e a ,whi c hi st h a t ,e . g . ,“ I ti st r u et ha ts n o wi swhi t e ”i si n s omes e n s ee q ui v a l e n tt o“ Sn ow i swh i t e ” ,a n ds oo n ,a n dt h a ts o me statement of this fact is explanatorily exhaustive of truth. What is essential here is the structure of the sentences exemplifying the idea, whereas the pa r t i c u l a rs e n t e n c e“ Sn owi swhi t e ” ,us e di nt h ee x a mpl e ,i si n e s s e n t i a l .I ti s precisely this structure that is captured by the use of schematic sentenceletters. The point of introducing schemata when reasoning about logic, etc., is to enable us to make generalizations about certain classes of sentences (the instances of the schemata in question). If we are to generalize over the instances without using any additional notions in the generalization, it is difficult to imagine any other possibility than these three. (The solution by quantification may at first seem to go beyond this idea of what is the common denominator of the four solutions, but we will see in section 3.3 that this solution actually turns out to be essentially a disguised form of linguistic formulation on all reasonable interpretations of the quantifier.) Though it does not seem unimaginable that there is some further type of solution, I think it is improbable, and will take the burden of proof to be on the person who thinks there is. The argument of this chapter, then, aims at the conclusion that a linguistic solution of the problem of formulation is the only acceptable one. This means that a deflationary theory can only be properly formulated as a claim about the word “ t r u e ” .Mo re clearly, the only acceptable type of formulation is one wh e r e“ t r ue ”i snot used, but only mentioned. This was precisely how we r e g i me nt e dThe s i s( I V)o f1 . 4.I nas e n s e ,t h e n ,t h i st h e o r yi sn o ta b o u t“ t r u t h i t s e l f ” ,on l ya bo utt h ewo r d“ t r ue ” .I ti si mportant to distinguish this claim f r om t h emo r ec ommoni de at h a twes ho ul df oc u sont h ewo r d“ t r u e ”r a t h e r t h a n“ t r ut h ”i napr o pe rt r u t h -t h e o r y .Aus t i ns a y s ,f a mo u s l y ,“ Wh a tne e d s di s c u s s i n gr a t h e r[ t h a n„ t r ut h ‟ ]i st heus e ,o rc e r t a i nu s e s ,o ft h ewo r d„ t r u e ‟ . In vino,po s s i b l y ,„ veritas‟ ,b uti nas o be rs y mpo s i um„ verum‟ ”( 1 95 0 :1 17 ) .I agree with what is literally said here, but most, including Austin, seem, by c o n t r a s t i n g“ t r u t h ”wi t h“ t r ue ”t h i swa y ,t ome a npr i ma r i l ys o me t h i n ge l s e , n a me l y ,t h a t“ t r ue ” ,no t“ t r ut h ” ,s h o ul dbeus e d wh e nd i s c us s i ngt r u t h theories. The conclusion of this chapter, on the contrary, is that none of these words should be used, but that the only acceptable formulation (of deflationism) is one where the latter is only mentioned.
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The Problem of Formulation
Now, as a preparation for the dismissal of the quantificational solution, we need to look closer at the idea that truth could be explained by saying that such and such schema-instances are true. Recall that the problem of formulation was the problem of meeting simultaneously the constraints of finite formulation and non-circularity. The argument for the need to meet the first one was given in 1.5, and the argument concerning this second constraint will be given in the next section.
3.2 E XPLAINING THE SCHEMATA IN TERMS OF TRUTH As noted, the most natural and common way of understanding the use of sentence-schemata in logic and philosophy of language is to think in terms of their instances being true. This is the reading of schemata generally intended in textbooks of logic, as when the student is asked to say why we should e x pe c t“ I fp, then p”t of ol l owf r omag oo dt he o r y ,butn o t“ p and not-p” .Bu t there is obviously something suspicious about saying that the following sentence (the explication of Truth in terms of Truth): (TT) Eve r yi n s t a n c eo f“ I ti st r uet h a tp iff p”i st r ue can explain truth itself. (TT), of course, is of the linguistic form that will be argued to be the only acceptable, although (TT) itself, as we will see, fails. Now, although (TT) seems to be using the concept to be explained, we are not dealing with the usual case of circularity, as when a biconditional suffers from too apparent a triviality, as exemplified by an analysis of a concept F of t h ef o r m“ x is F iff x is G” ,whe r et h es y n o n y mybe t we e nF and G is too apparent for the analysis to be of any explanatory value. It may seem that one objection against such a formulation could be given by recourse to the inferential constraint on a successful deflationary theory of truth, i.e., the one which states that the theory must explain in virtue of what the valid inferences depending crucially on truth-ascriptions are valid. We can then follow Horwich in his objection to this type of theory that one cannot infer the instances from the claim that they are true (1998a: 26f.). If so, then one cannot infer the instances of (ES) from (TT), but only the claim that they are true. In order to infer the instances, we would need the instances
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of (DS). But, again, we cannot infer these from the claim that they are true. Thus, one would conclude, it is not circularity in its usual form that afflicts (TT), but rather one consisting in some type of presupposition that we are not allowed to make, i.e., that we have explained how to derive sentences from the claim that they are true. However, one could reply that all that is needed to licence the inferences is to define a valid inference as a Truth-Preserving one, thus: (TP) s1, s2, ..., sn s iffdef if s1, s2, ..., sn are true, then s is true. Then, one could assert the instances, because they are unconditionally true. Horwich mentions this reply, but dismisses it as circular (1998: 26). However, I do not see wherein the circularity is supposed to lie, since (TP) is not used to explain (TT), but only to be used in showing how to infer the instances from it. However, there are other problems with this move. This can be seen by looking closer at the status of (TP). First, if (TP) is regarded as a stipulative de f i ni t i onof“ ” ,t h e nwedoh a v eap r o b l e mo fs h o wi ngh owt ol i c e n s et he i n f e r e n c e s ,b e c a u s et h e n ,as e n t e n c e“ A B”i sj u s ta na bb r e v i a t i o no f“ I fA i st r ue ,t he nBi st r u e ” .Th e n ,( TP)wo ul dj us tb eac o n f u s i n gd e f i n i t i o no fa symbol which normally has a different use, namely as standing for derivability. More importantly, if (TP) is stipulative, then, with (TT), (TP) a n das e n t e n c e“ A B” ,wec a n n o ti n f e rB f r o m A,s i n c et h el a t t e rj us t a b b r e v i a t e s“ I fAi st r u e ,t h e nBi st r ue ” .Wec a nonl yi n f e r“ Bi st r u e ”f r o m “ Ai st r u e ” .Asas pe c i a lc a s e ,wec a nno ti n f e ras e n t e n c eAf r o m“ Ai st r u e ” . But this is the point of (TP), i.e., of giving a connection between truth and derivability such that with (TP), it can be shown how to infer the instances of a schema from the claim that all instances are true. For this to be made possible, we must thus not make (TP) true by stipulation, but prove it (and, to bea bl et odos o ,a s s umeapr i o rme a ni ngt o“ ” ) .Th u s ,i tmu s tb ea s s ume d that (TP) expresses, e.g., a material equivalence ,a“ c on c e p t u a la n a l y s i s ” ,o r something else other than a stipulative definition. But if (TT) is to give an exhaustive account of truth, then if (TP) is true, it must be proven true on (TT), together with claims not related to truth. Now, proving (TP) can be done only if one could derive the claim that if A is true, then B is true, on the (hypothetical) assumption that A B. This, i nt u r n ,c a nbedo n eo n l yi fo nec a nde r i ve“ Bi st r ue ”f r o m“ A B”a n d“ A i st r ue ”( a s s umi ngt h a t“ A B”me a n s“ Bc a nbed e r i ve df r o m A” ) .Th a ti s ,
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The Problem of Formulation
this is to be done only given (TT) together with non-truth claims. The claim ( TT)i st heon l yt h i ngt h a tma ybea s s ume da bo ut“ t r u e ” .I ti sc l e a rt h a tb o t h this, and the converse step, needed to establish (TP), cannot be done. The converse, in fact, is closely related to the very problem we began with, that of deriving a sentence from the claim that the sentence is true. For if it could be shown that B could be derived from A, on the assumption that B is true if A is true, it should also be possible to show the special case in which the set of premisses is empty. That is, it should be possible to show that if A is true, then A can be derived from the null set. This just means that A is categorically assertible. In response to this, one might, of course, say that (TT) and (TP) together are the axioms of the theory of truth. But such a theory would not be deflationary. It would rather be one where it is partly the notion of validity which explains truth. And since it seems hard to find any other way of deriving the instances without adding something like (TP), we have an argument against taking (TT) as the deflationary theory. Note that this is not the kind of fallacious argument considered by Lewis Carroll, assuming that in order to infer B from A, you always need the pr e mi s e“ I fA,t he nB” .I ft h a twe r er i gh t ,t he ny o uwo ul da l s on e e da n o t h e r pr e mi s e ,“ I f( I fA,t he nB)a n dA,t he nB” ,a n ds oon .Ia mn o tc l a i mi n gt h a t an instance of (DS) cannot be derived from the claim that those instances are true. In a sense, they can, but in order for the theory to meet the inferential constraint, and so be explanatorily exhaustive of truth, the validity of that step must be shown to be valid, in the sense that the conclusion must follow logically from the truth-theory together with the premise (and perhaps some claims not pertaining to truth). If this cannot be done, then the theory fails. If this were not required, then every argument depending for its validity on the truth-predicate would be trivially shown valid, just by assuming it being so. Wh a twewa n ti saun i f i e da c c o un to f“ t r ue ”t h a ti st oe x pl a i nwh ya l lk i n d s of inferences that are valid in virtue of it are indeed valid. In this way, it is of c o u r s ea s s ume dt h a t“ t r ue ”i sl e s sba s i ct h an such expressions as conditionals and quantifiers, because it seems that these expressions cannot be given the ki n do fe xh a us t i v ea c c o un tt h a twea s s ume dt obea v a i l a b l ef o r“ t r u e ” .I t seems impossible, for instance, to give a description of the semantics of “ Eve r y ”wh i c he n a b l e su st os h ow why ,e . g . ,un i ve r s a li n s t a n t i a t i o ni sv a l i d , without the explanation involving that very step. It may now be objected that Ih a v ea s s ume dwi t ho u ta r g ume n tt h a t“ t r ue ”i sn o ta sb a s i ca sq u a n t i f i e r s , etc. But it is reasonable, for any expression, to prefer an exhaustive account
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to a non-exhaustive one, if both alternatives are available. And whereas typically basic logical vocabulary does not seem to allow for such exhaustive accounts, it seems reasonable to believe that “ t r u e ”do e s . Now, surely, there is also something more directly circular about (TT). One case to be made, I believe, is that the circularity consists in the fact that someone not yet knowing what is meant by the claim that the instances of the schema are true cannot be taught that by being given (TT) as an explanation. Suc has e n t e n c ec a ne q u a l l ybet a ke nt oi mp l i c i t l yd e f i n e“ f a l s e ” ,s i n c e s ubs t i t u t i ng“ t r u e ”wi t h“ f a l s e ”wo ul dr e s ul ti na ne q ua l l yt r u ec l a i m( n a me l y “ Al li n s t a n c e sof“ I ti sf a l s et h a tp iff p”a r ef a l s e ” ) .I no r d e rt ol e a r nwh a t “ t r u e ”me a n sf r o m( TT) ,o n emus ta l r e a dyk nowwh a ti tme a n s ,wh i c hme a n s that (TT) is not explanatorily exhaustive. 2 Although one can give a certain piece of information about the semantic properties of expressions in a sentence by saying it is true (as (TT) does), how this is accomplished must be explained by the truth-theory. So, that (TT) gives some information about some semantic properties of the instances must be explained, but cannot be explained solely by (TT) itself. We would thus need a further claim about truth-ascriptions. But this would amount to a deflationary theory only if that further claim was a generalization of the equivalences. So either the appeal to (TT) is idle or one needs to give a non2
Ernest Sosa (1993) proposes as a truth-theory (FMT) For all propositions P, P is necessarily equivalent to the proposition that it is true,
which may at first look like a theory which is both perfectly general and non-linguistic ( s i nc e“ t r ue ”i su s e d,n o tme n t i o n e d ) .Ho we ve r , “ e q u i v a l e nc e ”i n( FMT)i se x p l a i n e dby (PE)
If
entails , then if p, then q.
Now, exactly the problems with taking (ES) to be a theory of truth can now be seen to afflict this combined account. Clearly, if (ES) by itself, or the claim that its instances are t r ue ,i sno tl e gi t i ma t e ,n e i t he ri s( PE) .Mc Gr a t h( 1 9 9 7 a )u s e sSo s a ‟ sp r i n c i p l e si no r d e rt o f o r mul a t ehi s“ we a kd e f l a t i o n i s m”( de f l a t i o ni s ma b o u tt r u t ho fp r o p o s i t i o n s ,b u tn o tf o r other bearers) and Kovach (1997) argues against it on grounds of circularity. In reply, McGrath (1997b) gives a putatively non-c i r c ul a ra c c o u n to f“ e nt a i l me n t ” ,wh i c hi n c l u de s “ Fo ra l lP, Q, P entails Q iff IF(P, Q)i sn e c e s s a r y . ” ,wh e r e“ I F( P, Q) ”r e f e r st ot h e proposition expressed by the conditional from P to Q.Ho we v e r ,“ n e c e s s a r y ”c a nme a n ma nyt hi ng s( “ n e c e s s a r yf ors u r v i v a l ” ,e t c . ) .Wha ti si n t e n de dh e r ei s ,o fc o u r s e , “ ne c e s s a r i l yt r ue ” .
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deflationary theory in order to make it work. I conclude that (TT) does not yield an acceptable deflationary theory.
3.3 THE SOLUTION BY QUANTIFICATION The solution by quantification consists in giving as the fundamental claim of the truth-theory the preferred schema, prefixed by a universal quantifier, as in
(QES) (p)(It is true that p iff p). This solves the problem that the schemata are not sentences, and so do not say anything. However, there is here a serious problem concerning how to interpret this kind of quantification. We cannot treat the universal quantifier in (QES) as first-order, since (QES) would not be well-formed on such as r e a di n g ,t h el a s toc c u r r e n c eo f“ p”s t a n d i ngbyi t so wnwi t hnopr e d i c a t e attached to it, and the middle occurrence havi n gi n s t a n c e sl i k e ,e . g . ,“ I ti st r u e t h a tJ o h n ” .The r e f o r e ,( QES)c a n no ts i mpl ybet a ke na si n t e l l i g i bl ewi t h o u t further comment. Although philosophers often use propositional quantification quite freely, this cannot be granted the deflationist anymore than the sloppy appeal to schemata discussed above. Our problem is whether we can make sense of ( QES)i nawa yt h a tgi v e snoc i r c ul a r i t yc o n c e r n i n g“ t r u e ” .Toj ud g et he viability of the solution by quantification, I will devote this section to examining fourk i n d so fi n t e r p r e t a t i on so ft h ep r o po s i t i o n a lq ua n t i f i e r“ ( p) ” : (1) objectual, (2) substitutional, (3) infinitary, and (4) informal understandings of propositional quantification. A final subsection is devoted to truthanalyses of the (TA)-form which use propositional quantification. I will conclude that on all these interpretations, (QES) will not give an adequate account of truth. Therefore, the solution by quantification fails, but it does so in a telling way.
1. O BJECTUAL, SECOND - ORDER QUANTIFICATION Second-order quantification involves having quantifiers whose variables take positions in formulae other than term position, while still having an objectual
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interpretation. The semantics given for such sentences goes by taking the second-order variables tor a n geo ve ro bj e c t s( h e n c e“ o bj e c t ua l ” ) .Ho we v e r , these objects are of a different kind than those over which first-order variables range (wherefore the models in this type of semantics are called “ ma n y -s o r t e d ” ) .Th eo bj e c t sove rwh i c ht hes e c on d -order variables range are themselves assigned extensions in quite the same manner as are the predicates and sentences of first-order logic. These objects are intuitively thought of as properties or classes (for predicate-variables), or propositions or sentences (for propositional variables). Sentences with second-order quantifiers are then taken to be true depending on what is the case concerning such e xt e n s i o n s .Fo ri n s t a n c e ,as e n t e n c e“ ( F)(x)(F(x) ) ”i st y p i c a l l yd e f i n e da s true iff there is a class (in the second order domain), of which every object (in the first-order domain) is a member. There are now many obvious problems with giving the quantifier in (QES) the objectual interpretation while taking (QES) to be exhaustive of truth. First, the definition is meant to give the truth-conditions of sentences containing the quantifier. The quantifier in (QES) is thus supposed to be explained by the claim that (QES) is true in certain conditions. But if nothing i sp r e s upp o s e da bo utwh a ti n f e r e nc e si nv ol v i n g“ t r u e ”are correct, not much can be done with these truth-conditions. First, from (QES) and the claim giving its truth-conditions, those very truth-conditions cannot themselves be derived, since this would require that the claim that (QES) is true could be derived from (QES).3 If, per impossibile, this could be done, we would be able to infer that the open sentence (which is identical to (ES)) is satisfied by all objects in the range of the propositional quantifier. So much is required for the account to be objectual at all. But what is it for a sentence or proposition to satisfy (ES)? 3
Need the definition really state truth-conditions for the propositionally quantified sentence? A definition of, say, a predicate, need not give truth-conditions for sentences containing it, so why the quantifier? The answer is that a general account of a propositional quantifier, i.e., which interprets it in any possible occurrence, simply cannot avoid mention of truth-conditions without being schematic. More precisely, it would have to use as c he ma t i cl e t t e rs t a ndi ngp r o x yf o r“ o pe ns e n t e n c e s ” ,i . e . ,s e nt e n c e swi t hf r e es e n t e n c e variables. But the point of introducing the propositional quantifier was to avoid schemas. If one abandons this generality requirement, one can of course simply take the very sentence (QES) as definiendum, and give a definiens. But why not take that definiens itself to be the truth-theory? This manoeuvre simply consists in letting a certain undefined sentence be the truth-theory, and then defining the sentence by putting it as the left-hand side of a biconditional.
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If we assume that the relevant domain consists of sentences, then one is hard pressed to find any other way of defining satisfaction than by the claim that substituting the variable for the sentence yields a true sentence. At least, this should be a consequence of the definition, even if the definition itself may be more complex. It may, for instance, be recursive, giving the satisfaction conditions for every syntactic form of a sentence schema. But each such clause must clearly have the consequence that a sentence satisfies an open sentence iff replacing the variable with the sentence yields a true sentence. So, if the truth-conditions could be derived, we would still only come to know that the instances of (ES) are true. And we already know that this does not suffice for inferring the instances. I doubt taking the domain to consist instead of propositions would be of much help. To use an objectual semantics to explain (QES) would therefore require that these two problems are somehow solved. But it seems that a semantics along these lines that can also be granted the deflationist would have to be so different from those typically proposed that it seems misleading to call it “ o bj e c t u a l ”i nt h ef i r s tp l a c e .Al lwekn o wa bo uti ti st h a t ,b e i ng“ o bj e c t u a l ” , it is somehow supposed to explain the quantifier by an assignment of some kind of entity to the variables. But given how weak this description is, it seems gratuitous to think that any such semantics will solve the problem of formulation. There seems to be a more fundamental confusion in the idea that we should look for a way to assign objects to the propositional variables in order to make (QES) a non-circular theory of truth. Assume that the quantifier could be given an appropriately non-circular semantics that assigns a certain kind of objects to the variables. There still seems to be no reason first to formulate a sentence containing the new quantifier, namely (QES), and then give the semantics of the quantifier, so that we can derive something about (ES), instead of directly saying something about (ES) (or about its instances). The quantifier, after all, is to be accounted for by giving truth-conditions of sentences containing it in terms of properties of the rest of the given sentence, i.e., the open sentence following it, which in this case is (ES). (Just as the conjunction is explained by giving truth-conditions of sentences containing it in terms of the rest of the sentence, i.e., the conjuncts.) Being objectual, the account would require a specification of the objects in the range of the quantifier and some notion of satisfaction, as applied to the open sentence. But no matter how this could be accomplished, the resulting interpretation of (QES) could surely be reformulated as a claim about (ES) (or its instances).
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Why the indirect manoeuvre? I should stress that this has little to do with the objectual interpretation of first-order quantifiers. If Dummett (1959) was right that deflationary theories exclude a truth-theoretic semantics, then this account of first-order quantification is excluded (at least, as an account giving the meaning o f“ a l l ”a nd“ s ome ” ) .Bu tt h i si sawho l l yd i s t i n c tq ue s t i o n .I n a n yc a s e ,t hede f l a t i o n i s t ‟ sr i gh t to use first-order quantifiers is of course not touched by these considerations (pending some surprising argument to the contrary).
2. S UBSTITUTIONAL QUANTIFICATION This type of interpretation differs from our ordinary, objectual one, in that the truth-conditions of quantified sentences are given by recourse to the truth of sentences in which the variable is substituted for an expression of the a p p r o pr i a t es y n t a c t i cc a t e g o r y .Th us ,“ xFx”i se x p l a i n e da st r u ei f ft h e r ei sa term t s uc ht h a t“ Ft”i st r u e ,a nd“ ( x)Fx”i sd e f i ne da s“ n o t -x not-Fx” .Fo r any well-formed sentence ,f u r t h e r mo r e ,“ no t -”i sde f i ne da st r u ei f f is not true (for a detailed account, see Kripke (1976: 330)). In our case, we would need to speak of substitutions of sentences. In (QES), we would then interpret the quantifier as explained with the addition that the substituting expressions be sentences. But (QES), with the quantifier interpreted in that way, would be trivially equivalent to (TT), which we have already seen to be inadequate. Furthermore, if the quantifier is instead defined substitutionally by giving the conditions for the quantified sentence to be, say, assertible, rather than true, then (QES), together with that interpretation, would just be trivially equivalent to a linguistic solution (of the (SA1)-form), namely, the claim that every instance of (ES) is assertible. The same of course holds for any other property to be ascribed. But that only shows again that the route via (QES) and a definition of the propositional quantifier is idle. However, there are substitutional interpretations of propositional quantifiers that use the relational property of correct inference, rather than some monadic property like truth or assertibility. Such an account is examined but subsequently rejected by Horwich (1998a: 25f.), but advocated by Baldwin (1989: 101). What seems to be needed here is an Instantiation-rule like: (I)
(q)...q... – –– ––– –– ...p...
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Horwich (1998a: 26) expresses doubts about how this is to be ensured to allow any s e n t e n c eo ft hef o r m“ . . . p. . . ”t ob ei n f e r r e df r om“ ( q)...q. . . ” ,b u tt h e conventional way of reading symbolisms like (I) of course allow this by fiat. To avoid any misunderstanding, let us formulate the Disambiguated Instantiation-rule thus: (DI)
For any sentence s and formula , (q) (s/q).
He r e ,t h ev a r i a bl e“ q”i st ot a k eo nl ys e n t e n c e -po s i t i o na n d“ (s/q) ”r e f e r st o t h ee x pr e s s i o nr e s ul t i ngf r o mt her e pl a c e me n to fa l lf r e eo c c u r r e n c e so f“ q” by the sentence s. The problem with (QES) on this interpretation is, once again, that it does not yield a claim interestingly different from the claim that the instances of (ES) may unconditionally be inferred (or asserted). One could equally have said that the expression T is a (well-formed) sentence and that every instance o f( ES)c a nbed e r i ve df r om i t( a ndg i veTa so n e ‟ st r ut h -theory). One could also, and more naturally, just give a theory of the (SA2)-form and take the r e l a t i o nt obei n t e r d e r i v a bi l i t y( i . e . ,t h ec l a i mt h a ta n ys e n t e n c e“ I ti strue that p”a n dt hec o r r e s pon d i ng“ p”a r emu t ua l l yi nf e r r a b l e ) .Ic on c l udet h a ta l s oo n the substitutional interpretation, (QES) will either presuppose the notion of truth (such being the common interpretation of quantifiers generally), or (given the inferential definition), it will be equivalent to some form of the linguistic solution.
3. INFINITARY INTERPRETATION Hartry Field (1984) has proposed that we should understand substitutional quantification as a way of asserting infinite conjunctions or disjunctions. One idea would be to explain the meaning of (QES) by saying that it is equivalent t o“ ( I ti st r uet h a ts n o wi swh i t ei f fs nowi swh i t e )a nd( I ti st r uet h a tg r a s si s g r e e ni f fg r a s si sg r e e n )a n d. . . ” .Th i swi l ln o td oa si ts t a n d s ,h o we v e r ,s i n c e we need to ensure that all and only the intended instances are included in the conjunction. The claim would then have to be that (QES) is equivalent to the conjunction containing all and only instances of a certain schema. But as with the other interpretations, this one is such if it can really give a sensible explanation of the meaning of (QES) (which many will find doubtful), then, if (QES) explains truth, then the infinite conjunction should itself be able to explain truth, which has already been shown wrong. It may look as if we had
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a finite claim about truth, namely (QES), but if this is to be explained as e q ui v a l e n tt o ,o r“ e n c od i n g ”( c f .Da v i d( 19 9 4:89) )a ni n f i n i t ec o n j un c t i o n , then the infinitary nature of the theory is merely disguised. Again, the proposal is not relevantly different from (but only slightly more complex t h a n )at he o r yc o n s i s t i ngi nt hes e n t e n c e“ A” ,wh i c hi ss t i p ul a t e dt obe e q ui v a l e n tt o ,o ra bbr e vi a t i ng ,o r“ e n c o d i ng ” ,t hei n f i n i t ec o n j un c t i o ni n q ue s t i on .I ft he“ A-t h e o r y ”do e sn ot solve the formulation problem, it is hard to see why (QES) does. Thus, this idea violates the constraint of finite formulation, though the infinite character is disguised by the finitude of what i st a k e nt obe“ t het he o r y” .
4. INFORMAL UNDERSTANDINGS OF PROPOSITIONAL QUANTIFIERS
It might be insisted that we should not focus on formal accounts of (QES) such as the objectual or substitutional interpretation, but rather on possible informal understandings of the kinds of quantifications needed for (QES), viz., paraphrases into natural language. This does seem possible for other cases of quantification into non-term positions. For instance, it seems that “ ( F)(x)(F(x) ) ”c o ul dbep a r a p h r a s e di n t o“ Th e r ei ss ome t hi n gs u c ht h a t e v e r y t h i ngi si t ” .Th i si sp r o bl e ma t i ci nma nywa y s ,b u tac o r r e s p o n d i n g paraphrase of propositionally quantified sentences does not even seem possible. As Forbes (1986: 32) notes, contrary to the case of quantification into term- or predicate-position, when we quantify into sentence-positions, there is no copula available to make the claim into a sentence. He writes: Quantification into name and predicate position have this in common, that the copula is not absorbed by either kind of quantifier; the special difficulties we are encountering over the interpretation of quantification into sentence position seem to arise because the propositional quantifiers do not attach the variables of quantification to anything that can play an analogous role. (1986: 32)
The best way to clarify this idea, I think, is the following. Paraphrasing ordinary, first-order, quantifications into natural language in the way that most faithfully represents the structure of the sentence (in particular, the variables in all positions and connectives) is by using anaphoric pronouns. By “ mo s tf a i t h f ul l y” ,Ime a nt hewa yi nwh i c ht h e r ei s ,mo r et h a ne l s e wh e r e ,a one-to-one match between formal symbols and isolated expressions in the
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pa r a ph r a s e .Ane xa mp l ei s“ Eve r y t hi ngi ss u c ht h a ti fi ti sF, then it is G”a sa pa r a ph r a s eo f“ ( x)(F(x) (G(x) ) ” ,wh i c hi smo r ef a i t h f u lt h a n ,e . g . ,“ Al lF‟ s are G‟ s ” .Now,a c c o r d i n gt os u c has c h e mef o rp a r a ph r a s e ,t h er e a d i n go f (QES) into o r d i n a r yEng l i s hwo ul dy i e l dt heung r a mma t i c a l“ Ev e r y t h i n gi s such that it is true that it iff it. It is not inconceivable that resources enabling paraphrases of propositionally quantified sentences could be added to a natural language, however. Arthur Prior envisages such an addition, according to which the s e n t e n c e“ ( p)(p) ”i spa r a ph r a s e di n t o“ Fo rs ome wh e t he r ,t he t he r . ”( 19 7 1 : 37 ) .Th es e n t e n c e( QES)wo ul dt he nbe c ome“ Fo re v e r y wh e t h e r ,i ti st r u e t h a tt he t he ri f ft he t he r ” .Th epr o bl e m wi t ht h i sp a r a p h r a s ea sac o n t e n d e rt o an adequate truth-theory is that it is in as much need of explanation as the sentence paraphrased, (QES). I conclude that no informal paraphrase can yield an acceptable deflationary theory.
5. T RUTH - ANALYSES USING PROPOSITIONAL QUANTIFIERS It has been proposed by a number of authors that one could give a trutha n a l y s i so ft hef o r m“ Fo ra l lx, x is true iff ...x. . . ” ,wh e r et h eanalysans contains a propositional quantifier. These two variants of such analyses define truth for propositions and sentences, respectively: (TA3) For all x, x is true iff (p)(x is the proposition that p and p) (TA4) For all x, x is true iff (p)(x =“ p”a n dp).4 The question is now whether this use of propositional quantifiers escapes the objections raised against (QES). I argued at the outset that (QES) would need such an explanation, and there is no reason to think that the above analyses would not. The argument, further, against the original proposal was that, given the different ways of explaining the propositional quantifier, the resulting theory would be either circular (by using truth) or just an unnecessarily complex claim equivalent to a claim of the kind involving the
4
(TA3) is discussed in Baldwin (1989), Kalderon (1997: 491), van Inwagen (2002), and Hill (2002: 22), while David (1994: 74ff.) uses (TA4). McGee (2000) discusses analyzing „ xi st r ue ‟a s„ Fo ra l lp, if x =“ p” ,t he np‟ .The s ev a r i a t i o n swi l ln o tma t t e rt ot h ea r gu ment against taking these analyses to be acceptable theories of truth.
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linguistic solution. Therefore, the deflationist should opt for the latter kind of solution in the first place. A similar strategy can now be adopted to show that no truth-analysis using propositional quantification will yield an adequate account of truth. First, the definitions in terms of truth are obviously viciously circular in the same way as for (QES). We can also see that what was said about informal paraphrases above shows such an explanation to be impossible here too. The three remaining options are these: either (1) one e xpl a i n st heme a n i n go fas e n t e n c eo ft h ef o r m“ ( p)”b ya s s i g n i n go bj e c t st o the variables (the objectual interpretation), or (2) a sentence of the form “ ( p)”i se x pl a i ne di nt e r mso fv a l i di nf e r e n c e si nvo l v i ngi t( t h es u b s t i t u tional-inferential interpretation), or (3) such sentences are considered equivalent to infinite disjunctions of its substitution-instances (the infinitistic interpretation). Concerning the first proposal, we can see that given that the explication of the propositional quantifier must on pain of circularity be very unlike the known objectual accounts thereof, it again seems gratuitous to believe that some assignment of entities to the variables should somehow give a satisfactory explanation of the analysans. Further, imagining such an explanation to be presented, it seems likely that a more direct description of truth-ascriptions (i.e., the analysandum) should be possible to extrude from the explanation. In other words, whatever relation (like satisfaction) is supposed to hold between the entities in question and the variables, it seems that if the quantifier is appropriately explained that way, and the analysans of (TA3) or (TA4) indeed yields correct results for given truth-ascriptions, then the truthascriptions could just as well be explained by appeal to those entities and relations in some more direct manner. And then, the analyses just give an unnecessarily roundabout account. Similarly, on the second, inferential explanation of the propositional quantifier, it seems that whatever the way the analysantia are explained, if the explanation is adequate, and if the analysis is true, then one could instead explain the truth-ascriptions by appeal to these inference-rules appealed to in the explanation of the propositional quantifier. Hence, as with (QES), considering what is required by way of explanation of the propositional quantifier, it becomes apparent that only unnecessary complexity results from explaining truth in terms of propositional quantification, which in turn is explained some way. Finally, the infinitistic interpretation can again be charged with taking an infinite claim to do the explaining of truth-ascriptions while such infinite claims should be proven from the correct theory of truth-ascrip-
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t i on s .Fo r( TA3 ) ,t h ei n f i ni t ec o nj un c t i onmu s tb et h eo pe ns e n t e n c e“ ( i fx = the proposition that snow is white and snow is white) and (x = the proposition t h a tg r a s si sg r e e na ndg r a s si sg r e e n )a nds oon ” .I twa sa r g u e da g a i n s tt a k i n g (QES) together with the infinitistic interpretation of the quantifier as a trutht h e o r yt h a ti twa sno te s s e n t i a l l ydi f f e r e n tf r o mt a k i ngas e n t e n c e“ A”t obe the theory of truth, where this sentence is stipulated to be an abbreviation of the infinite conjunction. The proposal was therefore taken to be an infinitary solution in disguise. I see no reason the same could not be said concerning (TA3). The fact that it is an open sentence rather than a sentence proper s e e msi r r e l e v a n t ,f o ro n ec o ul ds t i pul a t et h eo pe ns e n t e n c e“ A( x) ”t oa bbreviate the needed infinite, conjunctive open sentence. That way, the variables would be ensured to be bound by the universal q ua n t i f i e r“ Fo ra l lx”o f t h ea n a l y s i s .Th a ti s ,t hea n a l y s i s( TA3)wo ul dt he nr e a d ,“ Fo ra l lx, x is true iff A(x) ” .Th i sdo e sno ts e e mr e l e v a n t l yd i f f e r e n tf r o m( TA3 ) .Bu tt h e n , (TA3) must be unacceptable, if this analysis is. And, surely, this analysis is also just a disguised infinitary claim.
3.4 THE LINGUISTIC C HARACTER OF DEFLATIONISM If the reasoning of this chapter so far is correct, the deflationary theory of truth has to be of the form (SA1) or (SA2), i.e., it has to be one about the semantic properties of the truth-predicate, rather than about, in some literal s e n s e ,“ t r ut hi t s e l f ” .This has been simply assumed by many in the literature, but the crucial argument, I take it, is that the other ways of generalizing the particular equivalences are either unacceptable or only disguisedly nonlinguistic. I nas e n s e ,Ta r s k i ‟ st h e o r yo ft r ut hc a na l s ob ec a l l e dl i n g ui s t i c ,i n t h a ti ta t t e mpt st o“ gi v et hee xt e n s i on ”o ft h et r ut h -predicate. But whereas it makes sense to say of that theory that it says what it is for something to be true, by giving necessary and sufficient conditions for a variable truth-bearer to be true, this is not so in the case of deflationism. While such truth-theories can be formulated so that they use, but do not mention, the truth-predicate (by giving a standard analysis), a correct deflationary theory cannot. It was suggested that Thesis (IV) of 1.4 should be interpreted precisely as the claim that a deflationary theory cannot be formulated so as to use, rather than men-
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t i on ,“ t r u e ” .Th us ,t hec o n c l u s i ono ft h i sc h a p t e r ,a g a i n ,i st h a tt hi st h e s i s under that interpretation is true. This conclusion raises some moot questions that I will discuss in this section. First, it may be thought that the above reasoning, if correct, shows that deflationists are committed to some type of anti-realism. In particular, it may be thought that if the theory needs to be linguistic in the sense made clear, truth will somehow be dependent on language. Presumably, the idea would be that whether something is true depends in general on facts about our language. I do not see how this would follow, however. Whether the proposition that snow is white is true depends wholly on whether snow is white, but whether snow is white need not be taken to be dependent on language, and the conclusion of this chapter does not seem to force the deflationist to say otherwise. Secondly, it could be argued that the above reasoning simply is a reductio of deflationism itself. More specifically, it could be held that the question the theory tried to answer was what truth is, but what is shown here is that a certain answer –deflationism –can only be appropriately formulated as an a n s we rt oad i s t i n c tq ue s t i o n ,n a me l y ,h o wt hewo r d“ t r u e ”wo r k s ,a n di s therefore inadequate. I believe there are two replies to this natural complaint. Fi r s t ,o n ec a na r g u et h a tt h e r ea r eo t he r“ t h i n g s ”o rp he n ome n at h a ta l s oc a n only be explained by describing the semantic functioning of the related l i ng ui s t i ce xp r e s s i o n s ,r a t h e rt h a nt he“ t hi n g s ” ,o rphenomena, themselves. Note that it would suffice to persuade the opponent of a single case of this kind to rebut the argument. For the argument, as stated, presupposes that any question about X can only be properly answered by speaking of X rather than th ewo r d“ X” .Wi t h o u tt hi sa s s ump t i on ,t h ea r g ume n ti si nc o mpl e t e ,s i n c ei t would require an argument that there is something about truth in particular which makes a linguistic theory inadequate. But I know of no such argument that a deflationist could accept. Someph i l o s o phe r sh a vef o undr e a s ont ot r e a ts uc h“ t h i n g s ”a sa v e r a g e persons, sakes and appearances in the same way I propose we treat truth. Perhaps existence provides an even better contender. Thus, it could be argued that we should not expect a true and exhaustive theory about existence to give necessary and sufficient conditions for something to exist or in any other way non-l i n g ui s t i c a l l ye xpl a i n“ wh a ti ti st oe xi s t ” .Thi sno t i o nj us td o e sn o t seem amenable to either form of explanation. Instead, one would argue, the no t i o no fe xi s t e n c ec a n n o tbee xpl a i ne d“ i nt h ema t e r i a lmo d e ”a ta l l ,b u th a s to be explained by a linguistic theory about the existential quantifier and/or
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t h epr e d i c a t e“ e xi s t s ” .Bu ti fnoc l a i mi nt hema t e r i a lmo ded o e sa n ye x pl a n atory work in the explanation of the notion, then it must be concluded that it can be exhaustively explained by a description of the related linguistic expressions, and that there is no meaningful further question about the nature of existence. Perhaps one could construct similar arguments concerning the universal quantifier vis-à-vis “ un i v e r s a l i t y ”o rn e g a t i v ee xi s t e n t i a l s / e xi s t e n t i a l quantifications vis-à-vis “ n o t hi n gne s s ” .Ag a i n ,i fa n yo ft h e s eno t i o n smus t be thus linguistically explained, the above argument against deflationism fails. The second reply is that if the deflationary theory of this linguistic kind gives the meaning o ft hewo r d“ t r ue ” ,a smo s td e f l a t i o ni s t sbe l i e ve ,t h e nt h e concept of truth will ipso facto have been explained. Next, one could appeal t oa ni n t u i t i v ed i f f e r e nc ebe t we e n“ t r ue ”a n dt h o s ewo r d swh e r et h e r ei sa n interesting question beyond the merely conceptual one, as seems to be the c a s ewi t hn a t u r a lk i ndt e r msl i ke“ wa t e r ”a n d“ r e d ” .I n t ui t i v e l y ,“ t r u e ”i sa non-observational ,“ l og i c a l ”e xp r e s s i on ,a n dt h e r e f o r e ,i tc o ul dbea r g u e d , there is no further question beyond the conceptual one. One can also compare t o ,e . g . ,“ b a c h e l o r ”o r“ d o c t o r ” ,a n da r g uet h a twh a ti ti st ob eab a c h e l o ro ra doctor can be exhaustively explained by describing the relevant concepts, and add that the question of truth is of the same kind. There is a more specific objection against this kind of deflationary theory, which is that if the theory of truth is linguistic in the sense made clear, then the th e o r yo ft r ut hi son ea bo u tt h es pe c i f i c a l l yEn gl i s hwo r d“ t r u e ” ,wh i c h seems to make it unacceptably provincial. This seems prima facie cogent. However, if it could be shown that the theory provides a means for characterizing translinguistically what it is to be a truth-predicate, then, it could be argued, the account is sufficiently general after all. I believe there is such an extrapolation. Suppose that the base-claim the deflationist opts for is that a certain (equivalence) relation E holds between ever ys e n t e n c e“ Th a tp i st r ue ”a n dt hec o r r e s pon d i ng“ p” .(I will henceforth take the truth-predicate pr i ma r i l yt oa pp l yt o“ t h a t ” -clauses, rather than quote-names of sentences. More on this in Chapter 4.) One could then generalize this idea thus: (T)
A language L contains a truth-predicate iff L contains a predicate F and a nominalising operator O such that, for any sentence s, O can be applied to s to form a nominalization O(s) and the sentence F(O(s)) bears E to s.
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The nominalising operator for Engl i s hi st h u st h ewo r d“ t h a t ” ,t h o ugha nominal may also be formed by changing the case of nouns and mode of verbs (as in Latin), or simply be identical to the sentence to be nominalised (as I have heard is the case in Chinese). Something like (T) could then be taken as the correct final account, and could be argued to solve the problem of language chauvinism. Finally, there are serious concerns about the use of semantic notions here, s uc ha st hea bo v eus eo f“ e q ui v a l e n t ” ,o r ,f o rt he o r i e so ft h e( SA1 )f o r m, the r e l e v a n tmo n a d i cpr o pe r t y( “ a s s e r t i bl e ” ,“ a n a l y t i c ” ,e t c . ) .On ea r g ume n tt obe made against this linguistic type of deflationary theory is that the semantic notion used will either presuppose the notion of truth in an inadmissibly circular way, or it will be such that the instances of the schema cannot be inferred. 5 The question is then, first, whether this is so, and, second, whether, if so, this is fatal to deflationism. In response to the first question, we may note that, assuming that Dummett (1959: 7) was right in deeming deflationism incompatible with taking truth as a central explanatory notion in logic and semantics, the deflationist is, independently of this issue, required to explain the relevant semantic notions by using some other concept. Thus, the possibility for the deflationist of eventually finding the required property stands and falls with the deflationary theory itself (lest we be meaning-sceptics). This means that there can be no objecting to the present use of semantic notions, like correct inference, without, by implication, begging the question against deflationism. The opponent must argue on independent grounds that no other concept than truth can help to explain the notions in question, which is to argue quite a lot. Suppose, then, that deflationism does not fail in this respect. That means that there is some alternative property that can legitimately be appealed to by the deflationist, which explains such ostensively defined notions such as equivalence, synonymy, derivability, etc. Of course, the relation of equivalence between two sentences must be such that if it holds between two sentences, then the proposition expressed by the first is true iff the proposition expressed by the other is. But this does not mean that the relation must be explained that way. Now, suppose we take the equivalence-relation appealed to by the deflationist to be a very strong one (this assumption will be supported in Chapter 4). Let us call it S-equivalence and define it for expressions of any syntactic category, as follows: expressions e and e‟are S5
I owe this point to Paul Horwich.
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equivalent iff for any sentence-context S(), S(e) and S(e‟ ) are mutually i n f e r r a b l e .Th ed ummye x pr e s s i on“ ”i st oma r kt hes l o ti nt h es e n t e n c e context. This slot of course always takes a position corresponding to the syntactic category of the expressions e and e‟ . If e is a sentence, then the slot takes sentence-po s i t i on .So ,t hec l a i mi st h a tf o ra n ys e n t e n c ei nwh i c h“ p”i s a subsentence, S( “ p” ) ,t hec o r r e s p ond i n gS( “ t h a tp i st r ue ” )c a nbei n f e r red from S( “ p” )a ndvice versa. As a special case (taking the sentence-context to bee mpt y ) ,s e n t e n c e so ft h ef o r m“ p”a n d“ Th a tp i st r u e ”a r et he ms e l v e s mutually inferrable. Given this S-equivalence, the biconditionals (the instances of (PS)) can themselves be derived simply by substituting in sent e n c e so ft h ef o r m“ p iff p” ,whi c hwea r ei nd e pe n de nt l ya l l o we dt oa s s ume . Thus, the dilemma is avoided. Personally, I do not accept the above solution, because I believe the notion of correct inference used in the explication of S-equivalence, and in semantics in general, should be an empirical notion. Thus, it cannot be taken as a regulative rule of inference as such rules are taken in formal systems. This should not be controversial. It is of course a contingent, empirical fact t h a ta c c o u n t sf o rt heme a n i ngo f“ t r ue ” .Fo ri n s t a n c e ,wemi g h ta swe l lh a v e us e d“ s c h r ue ”i n s t e a dof“ t r ue ” .Wh a t e ve ri ti st h a tgi v e s“ t r u e ”i t sme a n i n g , is a contingent, empirical fact. I happen to take it to be the S-equivalence fact just rehearsed. But if it is to be taken as meaning-giving, it must be an empirical notion, i.e., whether S-equivalence holds between two expressions must be an empirical question. Further, if Dummett was right in deeming truth-theoretic semantics incompatible with deflationism, this meaning-giving property must not be explained in terms of truth. But if so, it seems the premise of the objection is true after all, i.e., that the biconditionals themselves cannot be inferred without an illicit appeal to truth. That is, if the notion of inference is not truth-theoretic, then it is not such that the biconditionals can be derived given the S-equivalence. Rather, what can be derived i ss o me“ us e -t he o r e t i c ”f a c t ,e . g . ,t h a tt h ebi c on d i t i o na l sa r e( c a t e g o r i c a lly) a s s e r t i bl e ,o r“ a n a l y t i c ”( wh e r et h i si sno ts pe l l e do u ti nt e r mso ft r u t h ,b u t , e.g., as in Quine (1974: 78ff.)). Then, admittedly, the deflationist cannot explain facts about truth in the way this is normally taken to be done, by inferring them from the truth-theory together with other facts. However, it could be argued that it is sufficient for an adequate theory to e x pl a i no ur“ i n t ui t i on s ”c o n c e r ni ngt r ut h ,i nt hef o l l owi n gs e n s e .I fS-equivalence is assumed to hold, then, on a reasonable semantic theory, it should follow that, e.g., the instances of (PS) are assertible (or analytic). Then, it
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could be argued, one can explain an intuition about truth if the sentence e xp r e s s i ngt hei n t ui t i o n( e . g . ,“ I fwh a ts ome onebe l i e ve si st r u e ,t h e nh ewi l l bemo r el i k e l yt os u c c e e d ” )c o ul dbes howna s s e r t i bl e( o ra n a l y t i c ) .Th u s , whereas normally, one takes the task of the truth-theory to be to explain the fact that p byde r i vi n g“ p”f r om t het r u t h -theory together with sentences stating other facts, one here instead explains the intuition that p by seeing that the truth-t h e o r yi mpl i e st h a t“ p”i sa s s e r t i bl e( o ra n a l y t i c ) ,pe r h a p sbybe i n g an analytic inference from other assertible (or analytic) sentences. Here, one would presumably have to argue for a close connection between, on the one hand, having the intuition that p”a nd ,o nt h eo t h e r ,“ p”b e i n ga s s e r t i b l ei n on e ‟ sl a ng u a g eo ri di ol e c t .Suc hal i ng u i s t i cv i e wo fi n t ui t i o n s( a n dr e l a t e d notions like aprioricity) is a well-known philosophical standpoint, and is therefore motivated (whether rightly or not) by other considerations than for the sake of rescuing deflationary theories of truth. Even if many find this view unobvious when stated explicitly, we do not hesitate to accept an explanation to our intuition that, e.g., if blood is red, then it is coloured, on the g r o und st h a ti tme n t i on st h eme a ni ngoft hewo r d s“ r e d ”a n d“ c o l o u r e d ” . This conclusion may appear as a defeat, given that the deflationary theory was supposed to explain the facts about truth, whereas, now, all we can do is derive that various sentences we accept are assertible. But deflationists about t r ut ha r et y p i c a l l ya l s od e f l a t i o ni s t sa bo u t“ f a c t ” ;i na nyc a s e ,Ia m.Su c ha theory holds, sloppily, that all there is to the notion of fact is the schematic bi c on d i t i on a l“ Th a tp is a fact iff p” .Onad e f l a t i o n a r ya c c o un to f“ f a c t ” ,t he criterion of exhaustiveness comes to no more than this: for every p, if p, then the theory should entail that p (together with other claims). That is, it is a se n t e n c ege ne r a l i z i n gove ri n s t a n c e so ft hes c he ma“ I fp, then the theory should entail that p ( t og e t h e rwi t ho t h e rc l a i ms ) ” .A d e f l a t i o n a r yt h e o r yo f facts will of course also have to be linguistic, if the argument of this chapter is correct. From this perspective, there was never any non-linguistic issue to de a lwi t hi nt hef i r s tp l a c e .Ra t h e r ,t h epr oj e c to f“ e xpl a i n i n gf a c ta b o u tt r u t h ” becomes the project of showing, for every sentence that we accept (containi ng“ t r ue ” )t h a to u ra c c e pt a nc et he r e o fc a nbe explained by appeal to the Sequivalence and other facts. For instance, we are disposed to accept, e.g., “ Tr uebe l i e f sf a c i l i t a t es u c c e s s f ulbe h a vi o u r ” ,a n dt hi s ,wemu s ts h o w,i s because of the S-equivalence and a plethora of other things, such as the meaning of other words, past cognition involving relevant terms, perhaps various past perceptions, and so forth. A full explanation of a piece of behaviour is of course a gigantic and rather meaningless project. The important
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point is to make plausible tha tno t h i ngmo r ea b o ut“ t r u e ”i sn e e de di ns u c ha n explanation. To make it plausible, we can idealize, and simply derive the sentences from the truth-equivalences and other sentences we accept. If all goes well for the deflationist, what will have been achieved is the demons t r a t i o nt h a ta l la s p e c t so fo urus eo f“ t r ue ” ,a fortiori, our accepting various s e n t e n c e sc on t a i n i ngi t ,s u c ha s“ Tr uebe l i e f sf a c i l i t a t es u c c e s s f u lbe h a v i o u r ” , r e q ui r e sn omo r et h a nt h ede f l a t i on i s t ‟ sc l a i ma bo ut“ t r u e ” . We are now in position to close the case opened in 1.1, where the notion o f“ t hec o r r e c tt h e o r yo ft r ut h ”wa si n t r od uc e d .Wh y ,i npa r t i c u l a r ,s h o ul dwe regard the claim which, if taken as primitive, yields the simplest exhaustive overall account, to be the correct theory of truth, i.e., the theory which explains the concept of truth? This claim will be the simplest from which every fact about truth can be inferred. If indeed the S-e q ui v a l e n c ei n v o l v i n g“ t r u e ” accounts for all uses thereof in the simplest way, it will also be the simplest wa yofe xpl a i n i ngt h e“ f a c t sa bo utt r u t h ” ,s i n c e ,f o rt her e a s o n sj u s tg i v e n , t h i sc ome st on omo r et h a ne xpl a i n i ngo urov e r a l lus eo f“ t r u e ” .I nt h ee n d ,I be l i e v e ,t h ei mpl i c i tl e a r n i ngo f“ t r ue ” ,a c h i e ve dbyt r e a t i n gc e r t a i np a i r so f sentences as equivalent, is a feat of the brain, the emergence of a neural mechanism which, in interplay with other mechanisms, input stimuli, etc., is c a u s a l l yr e s po n s i bl ef o rt h eove r a l ll i ng ui s t i cbe h a v i o uri n v o l v i n g“ t r u e ” .I f t h e“ e x pl a n a t i o no ff a c t sa bo utt r u t h ”wi t ht h eS-equivalence works well, then, given the simplicity of the hypothesis, we are justified in holding that the function of the mechanism is to somehow tacitly substitute sentences of t h ef o r m“ Th a tp i st r ue ”wi t h“ p”a n dvice versa. Th i si swhyIt a ket h e“ o bj e c t i v i s t ”s t a n c e ,a n dt r e a tt h eq ue s t i ono ft h ec o r r e c tt he o r yo ft r u t ha smo r e than a question of which theory satisfies various desiderata optimally. The f a c t ua lq ue s t i oni swh i c hba s i cme c h a ni s mo r“ r u l e ”und e r l i e so u ro v e r a l luse o f“ t r u e ” .Th ep oi n tma dea tt hee ndo f1. 1,t h a t“ n o n -r e a l i s t ”t h e o r i e so fa c o nc e ptma ywe l lbe“ o bj e c t i v i s t ”i nt hi ss e n s eno wbe c ome sr e l e v a n t :wh i l e t h e r ei saf a c t u a lq ue s t i o no ft hes e ma n t i c so f“ t r u e ” ,t h e r ei sn ot h e o r yo f “ wh a tt r u t hr e a l l yi s ” . Finally, what can be said about the objection that typically semantic notions involve the notion of truth and therefore make trouble for the deflat i on i s t ?The“ t i g h tc o n ne c t i on s ”be t we e ns e ma n t i cno t i on sa n dt r u t ha r eo f t e n taken to indicate that the latter must partake in an explanation of the former, and that this is incompatible with deflationism (which I assume to be true). But if this type of argument is sound, we could likewise conclude that truth should be explained in terms of the various semantic notions, wherefore, of
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course, it is unsound. The connections pointed out are also easy to explain on a deflationary basis. That propositions have their truth-conditions necessarily f ol l o wsb yas i mp l ei n t e r s u bs t i t ut i ono f“ Th epr o po s i t i ont h a tp is t r u e ”f o r “ p”i ns e n t e n c e so ft h ef o r m“ Ne c e s s a r i l y ,p iff p” .Th et r u t h -conditions of propositions of course depend on what proposition it is, but so do, e.g., its verification conditions, so that is no reason to believe that the nature of propositions must be explained in terms of truth. Bar-On et al (2000) argue that since the meaning of a sentence determines its truth-conditions, deflationism is either false or compatible with truthconditional semantics after all. But this connection is also easily explained and does not indicate at all that meaning should be explained in terms of truth, or that truth must be used in a semantic theory. Meaning can plausibly be taken to determine what proposition is expressed by a sentence relative to a context. Taking a sentence to be true iff the proposition it expresses is, it follows trivially that meaning (plus context) determines the conditions in which the sentence is true (i.e., expresses a true proposition), given the intersubstitution claim. This is in no tension with deflationism, since it does not indicate any explanatory dependence. (The converse determination does not seem to hold, however, a notorious problem for truth-conditional semantics.) Fi n a l l y ,g i ve nmy( a n dma n yo t he rde f l a t i on i s t s ‟ )r e l i a n c eo ni n ferentialist explanations, something should be said here about the connection between correct inference and truth. Once again, we should not deny the connection; i nd e e d ,i ft h ei n f e r e n c ef r o m“ p”t o“q”i sv a l i d ,t h e ni f“ p”i st r ue ,t h e ns oi s “ q” .Th i si s explained by noting that if the inference is valid, then on any s o un ds e ma n t i ct he o r y ,“ I fp then q”i sa s s e r t i b l e .I fs o ,i tf o l l o wsbyt h eSe q ui v a l e n c et h a t“ I ft h epr o po s i t i ont h a tp is true then the proposition that q is t r ue ”i sa s s e r t i bl e .I fwewant to show this for sentences rather than propos i t i on s ,wen e e do n l ya s s umei n s t a n c e so f“ Th ep r o po s i t i o ne x p r e s s e dby„ p‟ is that p” ,a n da g a i nt a keas e n t e n c et obet r uei ft hepr o p o s i t i o ni te x p r e s s e s is. Gupta (1993b: 79f.) has argued that the truth-predicate must be used in e xpl a i ni n gt h eg e n e r a lf a c to fwhi c ha ni n s t a n c ei s :“ I f„ s n o wi swh i t e ‟c a nbe i n f e r r e df r o m„ e ve r y t hi ngi swhi t e ‟ ,t he ns n ow i swh i t ei fe v e r y t h i n gi s wh i t e ” .The r e f o r e ,hes a y s ,“ t hepr o s pe c t sf o ra ni nf e r e n t i a l i s ta p p r o a c ht othe me a ni ngo f„ t r u e ‟a r ebl e a ki n de e d ”( ibid.). Given the above claim about how to explain intuitions of this kind, we should take this instance to be explained byt h es e ma n t i ct he o r y ‟ sge ne r a lc on s e q ue n c et h a twh e n e v e ras e n t e n c e“ p”
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can be inferred from as e n t e nc e“ q” ,t h es e n t e n c e“ i fq, then p”i sa s s e r t i bl e (or analytic).
3.5 A FURTHER ARGUMENT FOR THE LINGUISTIC FORMULATION This section is devoted to giving an additional argument that a linguistic formulation is mandatory for a deflationist, insofar as s/he accepts thesis (VI), that the truth-predicate is merely a device for increasing the expressive strength of a language. It is crucial that everyone (as far as I know) agrees t h a t“ t r u e ”do e sh a v et h i sf un c t i on .Thei mpo r t a n ti s s u ei swh e t h e ri ti st he only function, or if it is a by-product of some underlying property. If this thesis is true, I will argue, one can only explain the equivalence between the s e n t e n c e s“ Th a tp i st r ue ”a nd“ p”b ys a y i n gt h a tt h e yh a v ebe e nc onv e n tionally stipulated to be equivalent, rather than being equivalent both because of a conventional stipulation and further facts. This, in turn, can only be done on a linguistic formulation. Th ed i f f e r e n c ebe t we e nt h e s e“ wa y so fbe i n ge q ui v a l e n t ”c a nbec l e a r l y explained by comparingt hef o l l o wi n gp a i r so fs e n t e nc e s :“ xi sab a c h e l o r ” -“ x i sa nu nma r r i e dma n ”a n d ,o nt heo t he rh a nd ,“ xi sar e n a t e ” -“ xi sac o r d a t e ” ( onQui ne ‟ sc o i n a g e ) .Thel a t t e rt wos e n t e n c e sa r ee q ui v a l e n tboth because of a conventional stipulation and an empirical matter of fact. The conventionality is not meant to come to anything more than the trivial fact t h a twemi gh ta swe l lh a v eu s e d“ s c hmo r d a t e ”a n d“ s c h me n a t e ” .Cl e a r l y ,t h i s linguistic convention does not by itself determine the (material) equivalence between the sentences in this case. The former two sentences, by contrast, are not equivalent due to any other fact than a linguistic convention to treat the e x pr e s s i o n sa ss yn on ymo u s .Thewo r d“ ba c h e l o r ”i sn o ti n t r o d uc e dbys o me kind of ostension to various objects, which we may or may not discover to be t h es a mea st h et h i ng swec a l l“ unma r r i e dme n” .Th e s ea r ei na n yc a s e assumptions that I find plausible, even if some old-school Quineans may want to disagree. 6 6
Quine would not –cf. inter alia his (1974: 78ff.) and (1991: 270). What might be argued, at most, is that he has consistently denied that there is a defensible notion of analyticity with the type of epistemological significance assumed by Carnap and others.
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One might want to object that this unduly presupposes that the introd uc t i o nof“ ba c h e l o r ”c o ul dno ti n s t e a dbee x pl a i n e da sac o n v e n t i o n a la s s o ciation between it and a meaning, which happens to be the very meaning with wh i c h“ u nma r r i e dma n ”i sc onve n t i o n a l l ya s s o c i a t e d .Bu t ,i nf a c t ,Ic o u l d allow this type of explanation. On such a view, the issue in question is wh e t h e r“ t r u e ”i si n t r od u c e dbyt hec o nve n t i ont oa s s o c i a t e“ t h a tp i st r u e ” with whatever meaning that is associated with the corresponding sentence “ p” .Suc ha na c c o un twi l ls e r v et hep oint I will make equally well. On such a vi e w,t heq ue s t i oni ss t i l lwhe t he rt hee q u i v a l e n c ebe t we e n“ Th a tp i st r u e ” a n d“ p”i sa ne f f e c tpu r e l yo fac o nve n t i on a ls t i pu l a t i on ,b u tt h es t i p ul a t i o ni s somewhat differently accounted for. The crucial common feature is that on this view, one cannot understand the expressions without taking the sentences in question to be equivalent. The same goes for the former account of conventional stipulation. Accordingly, on this view, the sentences are not equivalent because of facts that are independent in any way of what speakers need to know in order to use the expressions competently. The same goes for the former account of conventional stipulation. Th epoi n tn o wc ome st ot hi s :i f“ t r ue ”i si n t r o d uc e dmerely as a device of expressive strengthening (of the familiar kind), then the deflationary theory to be coupled with this claim must be linguistically formulated. A fortiori, it mus tbet hec l a i mt h a ts e n t e n c e s“ t h a tp i st r u e ”a n dt h ec o r r e s p o n d i n g“ p” are equivalent in virtue of a conventional stipulation and no more. I will argue that this cannot be made justice on a merely non-linguistic formulation, since such formulations, by our definition, do not essentially mention the wo r d“ t r u e ” ,bu tuse it. The remaining option is that of having a nonlinguistic theory of truth itself coupled with at h e o r yo f“ t r u e ” .Th i s ,h o we ve r , can accommodate the idea of expressive strengthening only with an impl a us i bl ec on s e q ue n c ec on c e r n i ngt her e l a t i o nbe t we e nt r u t ha n d“ t r u e ” .Or so I will argue. The argument is of course distinct from that which has mainly occupied us in this chapter. Beginning with a non-l i ng ui s t i cf o r mul a t i on ,s u c ha st h ei n f i n i t e“ Mi ni ma l Th e o r y”ofHo r wi c h ,t h epr o bl e mi st h a to ft a ki n gt h i st h e o r ya l o n et obe exh a us t i v eo ft r ut ha nds i mul t a ne o us l yh o l dt h a t“ t r ue ”i sme r e l yad e v i c eo f expressive strengthening. If such a theory is taken as exhaustive, then there ma yno tbea na dd i t i o n a lc l a i ma bo u t“ t r ue ”( a st h e r ei so nHo r wi c h ‟ s combined account). The propertie so f“ t r u e ”mu s tt h e nbeg i ve nbya na s s o ciation with the property of truth, as characterized by the non-linguistic theory. For instance, the word could be said to refer to the property in ana-
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logy with the way other adjectives refer to various properties. This is problematic as it is, but is not my main target here. Rather, the problem is t h a tont h i sa c c o un t ,t hee xp r e s s i ves t r e ng t he n i ngo f“ t r u e ”c a n n o tbes a i dt o be the only function. On this type of account, rather, this function is a byproduct of its referring to the property of truth, and the nature of this property. This account does not differ from correspondence theories (and other t h e o r i e s ) ,onwhi c h“ t r ue ”pl a y st hee xpr e s s i ver ol ei nq ue s t i o n ,b u ti sn o t introduced merely in order to play it, as deflationists hold. The equivalence be t we e ns e n t e n c e s“ Th a tp i st r ue ”a nd“ p” ,wh i c hr e s u l t si nt hee x p r e s s i ve strengthening, is not here merely conventionally stipulated, but is explained by appeal to the nature of truth, just as the equivalence bet we e n“ x is a r e n a t e ”a nd“ xi sac o r d a t e ”i se xpl a i ne dbya ppe a lt ot h en a t u r eo fc o r d a t e s a n dr e n a t e s .Suc ha na c c o un t ,a c c o r di ngl y ,wo ul dma kes pe a k e r s ‟k n o wl e d ge that the sentences are equivalent dependent not merely on their understanding t h ewo r d“ t r ue ”b uto nt h i stogether with their knowledge about the property of truth. It would not be able to take the equivalence between the sentences as basic, but would require further facts to explain it. I nt h ec a s ewi t h“ r e n a t e ”a n d“ c o r d a t e ” ,t h ee q ui v a l e nc eholds because of a contingent fact, of course, but I do not see that the modal difference between the cases is relevant. It is relevant only if necessity is treated, in logical positivist fashion, as a linguistic phenomenon. For then, one could say that whe r e a st hee q ui v a l e n c ei n v ol v i ng“ r e n a t e ”i sp a r t l yf a c t u a lwh i l et he truth-equivalences are merely linguistic. But on such an account of modality, together with the view that the equivalences are indeed necessary, one has already agreed with a wholly linguistic account of truth. Modality is not at issue, but only whether a certain concept can be explained merely by reference to intralinguistic relations, or if it also requires appeal to extralinguistic facts. If one denies the necessity of the truth-equivalences, on the o t he rh a n d ,on ec a n no t ,o fc o ur s e ,o bj e c tt ot h ea n a l og ywi t h“ c o r d a t e ”a n d “ r e n a t e ”onmod a lg r o un d s . The upshot is that a purely non-linguistic theory of truth cannot do justice t ot hei d e at h a t“ t r ue ”i si n t r od uc e d me r e l ya sade v i c eo fexpressive strengthening, but must agree with correspondence (and other inflationary) theories that this function is a by-pr o d u c to f“ t r u e ”r e f e r r i n gt ot r ut ha n dt he nature of the latter. In order to avoid such a non-deflationary consequence, one could perhaps say both that the equivalence is conventionally stipulated, and also that the nature of truth is explained by a non-linguistic theory. Specifically, the nature of truth might be explained by reference to the fact
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that the proposition that snow is truei f fs no wi swhi t e ,a n ds oon( Ho r wi c h ‟ s account). This we may call the dual account. The problem with this view is t h a ti tma ke st h epr o pe r t yo ft r ut ha ndt hewo r d“ t r u e ”i mpl a u s i b l yun r e l a t e d . The explanation of one does not make any reference to the other. But surely, i ft he r ei st obea nyme n t i o noft hepr o pe r t yo ft r ut h ,t h ee xpl a n a t i o no f“ t r u e ” had better be explained by reference to it.7 It may be thought that the dual account may be saved by the idea that a l t ho ug ht r ut hi t s e l fa n d“ t r u e ”a r ee xpl ained differently, they are still related in that the latter refers to the former in virtue of the conventionally establ i s he de q ui v a l e n c e .Thi si ss ome wh a tr e mi n i s c e n to fFr e g e ‟ si d e at h a twe g r a s pt h ec o n c e ptofd i r e c t i on by t a ki ng a sd e f i ni ng o f“ d i r e c t i o n”t he s e n t e n c e“ a and b h a vet h es a med i r e c t i o ni f ft h e ya r epa r a l l e l ”( Fr e g e( 188 4 : § 64)). But it is rather mysterious how a convention to treat two sentences as equivalent can enable the grasping of something external that was not previously grasped. Th i si so fc o ur s eu n p r o bl e ma t i ci ft he“ c on c e p t -g r a s p i n g ” is interpreted simply as the ability to correctly use the expression, and not something resembling Platonist quasi-perception. Thus, if the reference of “ t r u e ”t ot h epr o pe r t yoft r u t hi st a ke na sa long-winded way of saying that it means true, and this in turn is explained without reference to the property of truth, i.e., by a purely linguistic theory, then my only disagreement concerns the misleading terminology. But on the dual account here considered, the mention of the property of truth is precisely not irredundant in this way, and therefore, if the argument of this section is sound, the account either postul a t e samy s t e r i o u sc o n ne c t i o n ,o rc on f l i c t swi t ht h ec l a i mt h a t“ t r u e ”i sme r e ly a device of expressive strengthening. In summary, it is only a purely linguistic theory which can accommodate t hei d e at h a t“ t r ue ”i sme r e l yade vi c eo fe x pr e s s i v es t r e n g t h e n i n g .Th i si d e a is here (and generally) taken to exclude the view that the expressive function is a by-pr o d uc to f“ t r ue ”r e f e r r i n gt ot r ut h ,t o g e t h e rwi t hf a c t sa b o u t ,o rt h e 7
Thi sdi s uni t yofHo r wi c h‟ sc o mbi ne dv i e wi se a s i l yo v e r l o o ke d,a n dp r o b a b l yb e c a u s e of a three-f o l da mbi gui t yi nt h ewo r d“ e q u i v a l e n c e ” , wh i c hma yr e f e rt o( 1 )ac e r t a i nk i n d of proposition (e.g., the proposition that the proposition that snow is white iff snow is whi t e ,( 2)ac e r t a i nk i n dofs e n t e nc e( e . g. ,“ Th ep r o po s i t i o nt ha ts n o wi swh i t ei st r u ei f f s no wi swhi t e ” ,o rac e r t a i nr e l a t i o nbe t we e ns e n t e nc e s( t h eo net ha th o l d sb e t we e n“ Th a t s no wi swh i t ei st r u e ”a nd“ Sn o wi swhi t e ” ) .I fo ne slides between the first two of these, it may seem that the equivalences that explain truth are the same as those the categorical a c c e pt a nc eofwhi c hi sne c e s s a r ya nds uf f i c i e n tf o ru n d e r s t a n d i n g“ t r u e ” .On c eo nes e e s the difference, the question how the two facts are related create the problem here at issue.
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nature of, truth itself. Everyone agrees with this claim and therefore is not the de f l a t i o n a r yi de ao f“ t r ue ”a sme r e l ya ne x pr e s s i vede vi c e .Th er e a s o nwh y anything beyond a purely linguistic theory cannot accommodate the idea is, a g a i n ,t h a t“ t r u e ”mus te i t h e rbec h a r a c t e r i z e di nt e r mso fr e f e r r i n gt ot r u t h , whence the equivalence between truth-ascriptions and denominalized (or disquoted) sentences is partly explained by the nature of truth, or, that a dual a c c o un tc on s i s t i ngo fat he o r yoft r ut hpr o p e ra ndat h e o r ya b o u t“ t r u e ” ,wi l l not make the one relate to the other save by an inexplicable connection. A linguistic formulation, which holds that there is no theory about truth itself, but only about the semantic properties of truth-predicates, clearly avoids the dilemma.
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CHAPTER FOUR: THE PRIMARY TRUTH-ASCRIPTION 4.1 INTRODUCTION The foregoing chapter left us with the conclusion that the deflationary theory can only be properly formulated as a claim about linguistic expressions, more precisely, as a claim of the form (SA1) or (SA2) (cf. 3.1). As anticipated in 3.4, I will take the basic claim to be of the form (SA2), and to be: (D)
Ev e r ys e n t e nc eo ft hef o r m“ t h a tp i st r u e ”i sS-equivalent to the c o r r e s pond i ngs e n t e n c e“ p” .
To repeat, expressions e and e‟are S-equivalent iff for any sentence-context S( ), S(e) and S(e‟ ) are mutually inferrable. A sentence-context may simply be seen as a function from the expression in question to a sentence containing i t .So ,t h ec l a i m( D)ma ke si st h a tf o ra n ys e n t e nc ei nwh i c h“ p”i sa subsentence, S( “ p” ) ,t hec o r r e s po n di ngS( “ t h a tp i st r ue ” )c a nbei n f e r r e d from S( “ p” )a n dvice versa. As a special case (taking the sentence-context to bee mp t y ) ,s e n t e n c e so ft h ef o r m“ p”a nd“ Th a tp i st r u e ”a r et he ms e l v e s mutually inferrable. I will leave it open which view of inference should be adopted. This is a controversial issue, since it seems the deflationist is not allowed to give a truth-theoretic explanation of it. If this is so, and if a truththeoretic explanation is required, then deflationism fails. I will not discuss this issue here, but, rather, try to show that if this notion (and other semantic notions) can be explained in a way compatible with deflationism, then, whatever this explanation is, (D) enables us to explain a host of problematic f a c t sa bo u t“ t r ue ” .Th ee x pl a n a t i onmu s to fc o ur s eme e to bv i o u sc o n s t r a i n t s , such as validating the clai mt h a t“ p”c a nb ei n f e r r e df r o m“ p and q”( i n
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English), and so on. Thus, it is to justify our pre-theoretic intuitions about inference. This chapter will be devoted to defending (D), as well as showing how it avoids a number of problems that have afflicted other deflationary theories. These problems are those of: (1)
e xpl a i ni n gh o w“ t r u e ”c o n t r i but e st ot hes e ma n t i cme a n i n go fa n y sentence where it can occur, and doing it in a unified way (cf. the inferential constraint and the constraint of unification in 1.5)
(2)
explaining the problematic intuitions concerning sentence-truth,
(3)
steering between the Scylla of admitting propositions and the Charybdis of disquotationalism (the unacceptability of which was argued in 2.11),
(4)
enabling general facts about truth to be inferred, which is part of the explanatory constraint of 1.5.1
In this chapter, I will first defend (D) and then show how (1) and (2) can be accomplished, while (3)-(4) is left to Chapter 5. I should forewarn that I will somet i me sus e“ I ti st r uet h a tp”i n s t e a do f“ Th a tp i st r ue ”i nwh a tf o l l ows , to avoid certain awkward constructions. The switching between these forms wi l lbes ho wni n no c e n ti n4 . 3,whe r et he“ t r u t h -o pe r a t o r ”i sd i s c u s s e d . One might say that arguing that (D) i st h ec o r r e c ta c c o un to f“ t r u e ”i s simultaneously to argue that truth is a property primarily of propositions. The conclusion of the previous chapter requires this primacy claim to be metalinguistically formulated, however, as does the nominalist account of propositions that will be given in the next chapter. For simplicity, I will 1
For lack of time and space, I have had to omit a fifth problem here, namely that of explaining how the Liar paradoxes can be given a neat and simple (dis)solution, given a use-theoretic and linguistic account of truth. The idea was that natural languages are i nc o ns i s t e nti nv i r t u eo fc o nt r a di c t i ng r ul e sg o v e r n i n g“ t r u e ” ,n e g a t i o n ,a n do t h e r expressions, and that with the advertised kind of theory, this could itself be consistently and plausibly described (cf. Chihara (1979), (1984), and Burgess (2002)). That seems to be the only way to do justice to the ubiquitous intuition that the derivation of the contradiction, for all its troublesome consequences, is correct. It thus seems to be the only solution that does not violate intuitions, and so, the only one that is not in fact a nonsolution.
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o c c a s i o n a l l ys wi t c ht o“ t h ema t e r i a lmod e ”i ndi s c u s s i n gt h i si s s ue ,t h a ti s , arguing more straightforwardly that propositions should be considered the primary bearers of truth, rather than discussing what is the primary grammatical object of the truth-predicate. This switch will be discussed and defended in the next chapter.
4.2 A DEFENCE OF INTERSUBSTITUTABILITY There are first a number of alleged counter-examples to the substitution claim that should be considered. First, in making intersubstitutability-claims, it is commonplace to state exceptions pertaining to quote-contexts. However venerable, I will argue that this is not mandatory, but that there is a view about quote-names with the consequence that this exception need not be added, and which, in fact, is to be preferred. When claiming that an expression e of a certain grammatical category can substitute another, e‟ , one does not mean that any string of letters or phonemes which constitutes e can substitute any string of letters or phonemes which constitutes e‟ . Borrowing an example from Quine (1953: 140), someone who claims that synonyms are s ubs t i t u t a bl ed oe sno tme a nt h a to nec a ns u b s t i t u t ei n“ c a t t l ei se x pe n s i v e ”s o ast og e t* “ f e l i n e t l ei se x pe n s i ve ” ,a l t h o ug h“ c a t ”a n d“ f e l i n e ”a r es y n o nymous. But surely, the adherent of this substitution view is not required to s pe c i f yt h a tt h es t r i n go fl e t t e r s“ c a t ”mus toc c u ra san o uni no r d e rt obe substitutable. What I shall now argue is that what comes inside the quotemarks in a quote-name of a sentence does not occur as a sentence anymore t h a nt hes t r i n go fl e t t e r s“ c a t ”o c c ur sas an o u ni nt h ewo r d“ c a t t l e ” .Th i si sa consequence of a certain principle of compositionality, namely, that if an expression e of category C occurs as an instance of C in a sentence, then the semantic content of e will contribute to that of the sentence. But clearly, the s e ma n t i cc o n t e n to f“ Sno wi swh i t e ”d oe sno tc ont r i b u t et ot h a to ft h e sentence “ Sn owi swh i t e ”c on t a i n st h r e ewo r d s . If a linguistic theory satisfies this principle, I believe, then it is ceteris paribus to be preferred over one that does not. If so, quote-names should be seen as referring to a type or token string of letter/phonemes determined by
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the marks that occur inside the quote-marks, but that what comes inside the quote-marks is not a sentence. This view is further evidenced by the fact that quote-names of signs that have never been used before (or of ill-formed strings li k e“ kk r q 7” )a r ep e r f e c t l yi n t e l l i gi b l e ,a n dr e f e rt ot o ke n so ft h es a me shape or that type of shape. What occurs in the quote-name above is of course a string of letters belonging to a type of strings some of whose tokens occur as sentence-tokens, but it does not itself so occur. Likewise, the string “ c a t ”o c c ur si n“ c a t t l e ” ,b utno ta san o un ,b uta sas t r i n gbe l o n g i n gt oat y pe some of whose tokens occur as nouns. Thus, since what (D) claims is that certain sentences can be substituted for others, it need not be supplemented with exceptions for quote-contexts. One may wonder whether this is cons i s t e n twi t ht h ea p po s i t i o n“ Thesentence „ s n owi swh i t e ‟ ” .I ti s .Onec a n( a nd should) say that quote-names can refer to sentences without claiming that what comes between the quote-marks is ever a sentence. So, quote-names do not refer to what is within the quote-marks, on this view. But it does say that they can refer to types of strings some of whose instances are sentencetokens. This is no more surprising than the claim that the string-t y pe“ c a t ” can be tokened either as a noun-t o ke n ,o r ,e . g . ,i nt h en o un“ c a t t l e ” ,whe r ei t is not a noun-token. In summary, if the compositionality principle is to be satisfied, we should say that in a token quote-name of a sentence, what comes inside the quote-marks is not a sentence-token. Therefore, (D) need no exception. (Those in doubt may of course read in an exception to (D).) Another common objection against an unrestricted intersubstitutability claim is that whereas the truth-a s c r i bi n gs e n t e n c ec o nt a i n i n ga“ t h a t ” -clause always commits itself to the existence of something which is true, the s e n t e n c ei nt h e“ t h a t ” -clause need not (cf. Field (1994a: 250)). Thus, one mi g h ta r g ue ,i nt h es e n t e n c e“ Th a ts n owi swhi t ei st r ue ;t herefore, something i st r ue ” ,on ec a n n o tr e pl a c e“ Th a ts n ow i swh i t ei st r u e ”wi t h“ Sn o wi s whi t e ” .Bu tt h i sc a nber e s i s t e d .Suppo s es o me o ne ,i n s p i r e dbyNi e t z s c h e , claims that nothing is true, and that a more analytically-minded philosopher tries to trap h i mbya s ki ng ,i nno c e n t l y ,“ Buti ss n owwhi t e ? ” .Hema yt h e n ,i f t h eNi e t z s c he a ns a y s“ Ye s ” ,g oont os a y ,“ Buti fs no wi swh i t e ,t h e ns o me t h i n gi st r ue ! ” .Th i si saf ul l yr e a s on a bl er e s po n s e .Mo r ei mpo r t a n t l y ,wed o not take it to be assertible only on the assumption of other sentences. It is simply one that a competent speaker will assent to (absent semantically irrelevant inhibiting factors, like the occasional obstinacy of a Nietzschean). The e x pl a n a t i o no ft h i si st h a to urunde r s t a n di n g“ t r u e ”s i mpl y consists in our speaking in conformity with (D).
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But, the objection might continue, one cannot similarly substitute in the s e n t e n c e“ I ti slogically true that if that snow is white is true, then something i st r ue ” .Th i sc h a r g ef a i l sbe c a us et hede f i n i t i o ns of logical truth typically make it a property of sentences, e.g., so that sentences are logically true iff true for all variations of the non-logical vocabulary, or true under all interpr e t a t i o n s ,o ri na l lmo de l s ,e t c .Buto ns uc ha ne x pl a n a t i o no f“ l ogically t r ue ” ,t h es e n t e n c ei nq ue s t i oni ss t r i c t l ys pe a k i ngun i n t e l l i g i bl e .Si n c e“ c o n t a i n st h r e ewo r d s ”i sap r o p e r t yo fs e n t e n c e s ,t h es e n t e n c e“ I ti sl o g i c a l l yt r u e t h a ts now i swhi t e ”i sl i k e“ I tc on t a i n st h r e ewo r d st ha ts n o wi swh i t e ” .Of course, wedo ,i nph i l o s o ph y ,s a yt h i n g sl i k e“ I ti sl o gi c a l l yt r u et h a ti fp, then p” ,bu ti fl o g i c a lt r u t hi sap r o pe r t yo fs e n t e n c e s ,t h i smu s tb et a k e nas l o p py a n dmi s l e a d i n gwa yo fs a y i ngt h a t“ I fp, then p”i sl o g i c a l l yt r u e .Bu tt h e n , the above point about quote-contexts can be made anew, and the alleged counter-example fails. Could one not define logical truth instead for propositions in such a way that a counter-example to (D) could be formulated on the lines above? Note first that, by (D), we easily obtain all instances of The proposition that the proposition that p is true = the proposition that p, by applying (D) to the left hand side of a self-identity sentence The proposition that p = the proposition that p. (By the same token, we easily deri vet h ei n s t a n c e so f“ Tos a yt h a ti ti st r ue that p is just to say p” ) .Th us ,( D)e n t a i l st h a tt he r ec a nben od e f i ni t i o no fa property with the consequence that a proposition P may have (lack) it while the proposition that P is true does not. To get a counter-example to (D) one thus only needs to show that these pairs of propositions are distinct, but not ne c e s s a r i l yb yd e f i n i n g“ l og i c a l l yt r u e ” .Pr o b a bl y ,o ppo n e n t st o( D)wi l l mainly argue that they have different structure. I cannot here provide a rebuttal of this view, of course; suffice it to anticipate that the nominalist account of propositions to be proposed in Chapter 5 entails that the idea that propositions have structure is wrongheaded. It is crucial that the equivalence expressed in (D) is a semantic notion, in the sense that it does not concern various pragmatic effects, poetic value, or connotation, that utterances of the relevant sentences may have. The distinction between pragmatic and semantic becomes especially relevant as
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concerns the putative counter-examples pertaining to propositional attitude c o n t e x t sl i k e“ x be l i e ve s / k n ows / s a y s / me a n st h a t. . . ” ,“ Se n t e n c es means that . . . ” ,e t c .Towi t ,wef i n dt hef o l l owi ngt obepo s s i bl yt r u e : X believes that snow is white but not that it is true that snow is white. First, this intuition is apparently not shared by everyone, since Frege, for one, said, on the contrary, that always when one judges something to be thus or so, one judges a thought to be true (cf. 2.2). Unlike me, he could not be accused of adapting his intuitions to fit his theory, since he had no theory which entailed it, but simply found it intuitive. But many do have the intuition and this must be accounted for. The sentence above seems to say that X believes that snow is white, but no tt h a t“ t r u e ”a p pl i e st ot h i sp r o po sition, or some such. But this can plausibly be taken to be pragmatically, not semantically, expressed. What is semantically expressed is a contradiction, given (D). The pragmatic effect can then be taken to arise because of the following facts: Firstly, the semantic content is a contradiction, wherefore this interpretation is automatically avoided (hence, what is saliently expressed is only a pragmatic effect). That we should avoid interpreting utterances as communicating contradictions is common to all pragmatic theories. Secondly, the second conjunct contains a semantically redund a n tp h r a s e ,“ i t i st r u et h a t ” ,wh e r e f o r ea ni n t e r pr e t a t i oni sma dewh i c hs a t i s f i e st h ea s s ump tion that the apparent violation of a maxim (under the category of Manner – “ Bebr i e f ! ” )c a nbee x pl a i ne d .Si mi l a r l y ,ont heRe l e v a n c eTh e o r yo fSpe r b e r and Wilson (1986), it should be assumed that the utterance is the least effortrequiring way of communicating the message. Therefore, the semantically redundant phrase will be taken to have a point. Thus, something more than what is semantically expressed will be taken to be communicated. Thirdly, since this phrase is semantically redundant, it must be either a non-semantic property of the phrase (like its poetic value) or (a part of) the very phrase itself, which guides the audience (us) to the right interpretation. Fourthly, the interpretation which both stays closest to the semantic content of the sentence and satisfies the assumption that there is a point with the semantically redundant phrase is something like the above interpretation, on which what is communicated is that X believes t h a ts n ow i swh i t eb utn o tt h a t“ t r ue ”a ppl i e st ot h ep r o po s i t i o nt h a ts n o wi s white (perhaps because X knows no English). Note that the interpretation is he l pe dbyt h es t r e s so n“ t r u e ” .Wi t ho uti t ,t h ei n t ui t i oni sl e s sc l e a r .Bu tt h i si s
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also in line with modern pragmatics, according to which stress on a word indicates that it is to be taken to inform the interpretation in a way it would no td oo t he r wi s e .Co n s i d e rt hes e n t e nc e“ X believes that blood is red, but not that it is true that blood is red” .Th i si sa l mos tu ni n t e l l i gi bl e ,b u tmi g h tbe interpreted as communicating (if anything) that X believes that blood is close to paradigmatic red but not quite paradigmatic red (or some such). The point i st h a ti ti st hewo r d“ r e d ”t h a tg ui de st h ei n t e r pr e t a t i o n ,r a t h e rt h a n“ t r u e ”i n this case. In any case, I take it the above is a proper application of uncontroversial pragmatic principles that explain why the intersubstitution seems to fail in the relevant contexts.
4.3 THE VARIOUS OCCURRENCES OF “ TRUE” This section is devoted to arguing that (D), with a minor and similar-spirited extension, suffices for explaining t hes e ma n t i cc o n t r i b u t i ono f“ t r ue ”a si t o c c ur si na n yc o n t e xt .Si n c e( D)i st a ke nt og i vet heme a n i n go f“ t r u e ” e n t i r e l y ,t hec l a i mi st h a tt h es e ma n t i cc o n t r i but i o no f“ t r ue ”i se n t i r e l yg i v e n by( D) .Wh a twi l lbed on ehe r ei st h usn o tt os a yh o w“ t r u e ”c o n t r i bu t e st o the meaning of sentences containing it. Its contribution is its figuring in the equivalence described in (D). The point of this section, rather, is to show how one with (D) and other, independent facts about meaning and logic can explain how intuitively meaning-r e l a t e df a c t sa bo uts e nt e n c e swi t h“ t r ue ”c a n be explained. These facts consist mainly of intuitions about valid inferences a n da b o ut“ wh a th a sb e e ns a i d”byv a r i o uss e n t e n c e sc on t a i n i n g“ t r u e ” .We wi l lt h usno ts a yt h a tt he“ me a ni ng ”o f ,e . g . ,“ Ev e r y t h i ngh es a i di st r ue ” somehow consists in, or is given by, its inferential relations to other sentences. Rather, these inferential facts are taken as consequences of the s e ma n t i cpr o pe r t yo f“ t r u e ” ,g i ve nby( D) ,a n dt h es e ma n t i cp r o pe r t ies of the other expressions in the sentence. What follows, then, is evidence for the c l a i mt h a t( D)g i ve sa ne xh a us t i ves e ma n t i cc h a r a c t e r i z a t i ono f“ t r u e ” . Recall that the inferential constraint required that every argument depending for its validity on “ t r ue ”bes h ownv a l i d .Th a ti s ,t h ec o n c l us i o ns h o ul d follow logically from the premises and the theory of truth. This will be shown for a number of such arguments, and these demonstrations are intended to make it plausible that any such argument can be explained on the basis of (D). To repeat, the explanations are meant to be neutral towards possible
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explanations of the notion of inference (insofar as it is not explained in terms of truth, if this is indeed incompatible with deflationism). An important feature of this semantic account is that we do not give paraphrases or a n a l y s e sl a c ki ng“ t r u e ”o fs e n t e nc e sc on t a i ni n gi t .The r ei sn or e a s o nwh y this should be required, however, and we saw in 2.3 that imposing this requirement has caused much unnecessary confusion and disillusionment. In the preceding section, occurrences in various problematic contexts like those created by propositions attitude verbs were treated on the basis of (D) and other independent (pragmatic) facts. The claim that (D) suffices for e n t i r e l yc a p t ur i n gt hes e ma n t i c so f“ t r ue ”wi l lno w bef u r t h e re v i d e n c e dby treating six other types of occurrence, in this order: (i)
in modified truth-ascriptions,
(ii)
i nt he“ t r u t h -o pe r a t o r ” ,
(iii)
in quantified truth-ascriptions,
(iv)
in application of the truth-predicate to definite descriptions,
(v)
i nde mo ns t r a t i veu s e sl i ke“ Th a ti st r ue ” ,a n d
(vi)
i nde r i v a t i v eus e sl i k e“ t r uer e be l ” ,“ t r uef r i e n d ” .
The next section is devoted to explaining what looks like truth-ascriptions to sentences. Except, perhaps, for case (vi), these explanations will more or less suggest themselves, in that it will be rather obvious which further facts about language to appeal to and how to exploit them in the explanations. What is important is that it is so obvious, and, therefore, how much more plausible (D) is than other deflationary theories, especially those that take sentences as primary truth-bearers. It is crucial to the explanation of occurrences (ii)-( v )t on o t et h a t“ t h a t ” clauses work in important respects like paradigmatic singular terms. In my view, they are singular terms, as will be argued at length in 5.4. In what f ol l ows ,ho we ve r ,wene e do nl ya s s umet h a tu n c on t r o ve r s i a lv i e wt h a t“ t h a t ” clauses behave in certain respects in a term-like way.
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1. M ODIFIED TRUTH - ASCRIPTIONS Not many deflationists have addressed the question of how to deal with modified truth-a s c r i pt i o n s ,s uc ha s“ I tmi g h tb et r uet h a ts n o wi swh i t e ” ,t h e e xc e p t i on sbe i ngt hep r o s e n t e n t i a l i s t sa ndHa r t r yFi e l d .Th ef o r me r s ‟account, however, has been the target of severe criticism by Kirkham (1992: 327f.)), and for Field, the case of modified truth-ascriptions constitute the typical kind of impediment to the pure disquotationalist theory (as we will see in 4.4). In showing how to treat modified truth-ascriptions, we may take i n t u i t i ve l yv a l i di nf e r e n c e sa so urpr i ma r yd a t u m,f o ri n s t a n c e ,t h a tf r o m“ I t mi g h tbet r uet h a ts n ow i swhi t e ”t o“ Sn ow mi g h tbewh i t e ”a n db a c k .By “ modi f i c a t i on ” ,Iwi l la l s oi n c l udes uc hs e n t e n t i a loperators as negation and a d ve r b i a lmodi f i e r sl i k e“ ne c e s s a r i l y” ,“ pr e s uma b l y ” ,“ a p p r o x i ma t e l y ” ,a n d so on. To see how the account will work, recall first (from 3.1) that (D) can be equivalently reformulated by quote-names of expressions and the Concatenation-function: ( D‟ ) Every sentence s i ss u c ht h a t“ t h a t ” s “ i st r ue ”i sS-equivalent to s. Next, we introduce the notion of a modifier-function by these examples: the function Neg(x) takes sentences to their negations; Might(x), similarly, takes the sente n c e“ Sn ow i swhi t e ”t o“ Sno w mi gh tbe wh i t e ” ,a n ds oo n ; Presum(x)t a k e s“ Sn owi swhi t e ”t o“ Sno wi sp r e s uma bl ywhi t e ” ,a n ds oo n . Finally, we must also include functions whose values can only occur in wider contexts, such as More(x), one of whose values is the first subsentence of “ Hei smo r es wi f tt h a nh ei ss t r o ng ” .Th el a s tk i ndi sa l s on e c e s s a r yf o r dealing with subjunctive and counterfactual conditionals. We could now account for all these modified truth-ascriptions by the following extension of (D): (MD) For every sentence s and modifier-function f, f( “ t h a t ” s “ i st r ue ” )i s S-equivalent to f(s).2 2
Some adverbs, however, do not allow exportation from an ordinary sentence to the corresponding truth-c l a i m.Th a ti s ,y o uc a n n o ti n f e r ,e . g . ,“ Tha th er a ni squ i c k l yt r u e ” f r o m“ Her a nqu i c k l y ” ,f o rt hef o r me rdo e sno tma k es e n s ea ta l l .I ts e e ms ,t h e n ,t h a twe must exclude those adverbs which, intuitively, are applied to the verb and not the whole s e nt e nc e .I nt h ec a s eof“ a ppr o x i ma t e l y ” ,t hes t e ps e e mst ob ea l l owed in virtue of the
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Now,as i mpl ei n s t a n c eo f( MD)i spr e c i s e l yt h a tt h es e n t e n c e s“ Sn o wmi g h t bewhi t e ”a nd“ Th a ts n owi swh i t emi gh tbet r ue ”a r eS-equivalent. Since the identity function is in the range of the quantifier, (D) is entailed by (MD). It is thus a stronger claim that (D), but a natural extension of it. The claim (MD) actually has some wider implications, which deserve comment. Peter Smith (1998) has proposed at r e a t me nto f“ i sa p pr o x i ma t e l y t r u e ”o nt he s el i ne s ,s oa st os how de f l a t i on i s mc o mpa t i b l ewi t ht h ei d e ai n the philosophy of science, that scientific theories are only approximately true. Mutatis mutandis for propositions, to say that the proposition that Sicily is triangular is approximately true is to say that Sicily is approximately triangular, and so on for all other approximate truths. Could we also make sense of the idea that some theories are more true than others, thus explaining problematic aspects of the progress of science? To say that it is more true that Einstein was right than that Newton was, is, as follows from (MD), to say that Einstein was more right than Newton was, which seems intelligible. But we would also have to admit the intelligi b i l i t yo fs e n t e n c e sl i k e“ Spa c ei s mo r er e l a t i vet h a na bs o l u t e ”a n d“ El e c t r on se xi s tmo r et h a nt h ee t h e r ” .I f these are unintelligible, then, the Deflationist should simply say, so is the claim that the one proposition is truer than the other. A similar situation holds for numeric degrees of truth. If it is true to degree 0.1 that phlogiston exists, then phlogiston exists to degree 0.1. It may be objected, however, that whereas we can make sense of the claim t h a tEi n s t e i n ‟ st h e o r yi smo r et r uet h a nNe wt o n ‟ s ,i tdo e sn o tma k es e n s et o say that space is more relative than absolute. In any case, the claims seem different, and therefore, a counter-example to (MD). Of course, we must here focus on the claim that the proposition that space is relative is more true than the proposition that space is absolute. A theory can derivatively be said to be more true if it contains a greater ratio of true claims, which is not a problem for (MD). First, if space is relative and not absolute, then it should not be unreasonable to say that space is more relative than absolute. If this is what is meant, then (MD) is not refuted. Insofar as the implication of gradualness is to be made greater justice, however, I believe a deflationist must say that the claim that the proposition that space is relative is more true than the proposition that space is absolute, is strictly speaking as nonsensical as the claim sensibleness of treating the adverb as somehow modifying the claim made by the s e nt e nc e ,r a t he rt ha nt h ea c t i v i t yde s c r i be dbyt hev e r b ,a swi t h“ q u i c k l y ” .Th e r emu s tb e some explanation to this difference between adverbial phrases even if Deflationism is false, and it therefore poses no problem for Deflationism specifically.
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that space is more relative than absolute. The sensible gradualness cannot, strictly speaking, concern truth simpliciter, but something like truth-likeliness or truth-obviousness (i.e., how likely or obvious it is that something is true). I ti st e l l i ngt h a tt h ebe s te x a mpl e so fpl a u s i bl ec l a i msma d eby“ mo r et r ue ” concern theories for which there is only very indirect evidence, or involve v a g ue ne s s .I ns u c he xa mpl e s ,i ti se a s i e rt o“ r e a di n ”s o me t h i n go t h e rt h a n truth, like likeliness or obviousness, which may nevertheless be intimately and relevantly related to truth. In finding out which physical theory is true, we have only indirect evidence to go on, which may make a theory more or less likely to be true. Concerning vagueness, it is more or less clear that an o bj e c ti si nt het e r m‟ se x t e n s i on ,a nds o ,mo r eo rl e s sc l e a rt h a tt h ec l a i m made by the sentence containing the vague term is true. We may here repeat part of the explanation to the alleged counter-example to substituting in propositional attitude contexts, that given the non-sensicalness of what is literally said, we add something to this content to make sense of the sentences i nv o l vi n g“ mo r et r ue ” .Th i sk i ndof“ e n r i c hme nt ”i so fc o u r s eu b i q ui t o u si n language use. For most cases of modified truth-ascriptions, however, (MD) seems correct. That the equivalence between truth-claims and denominalized sentences is so strong is in itself remarkable. The more modifiers one examines, modal and evaluative modifiers, intensional contexts, occurrences in counterfactuals and subjunctive conditionals, the more it seems that the general claim must be right, its audacity notwithstanding. 3 This is something that should make anyone hesitate to take sentences as primary truth-bearers, given that T-biconditionals must be supplemented with separate clauses for every modification.
2. T HE ( SO - CALLED ) TRUTH - OPERATOR Sentences prefixed by thee xpr e s s i o n“ I ti st r uet h a t ”c a ne a s i l ybee xp l a i ne d by recourse to explanation of truth-a s c r i p t i o n st o“ t h a t ” -clauses. It is a general fact that when a predicate or verb-ph r a s e“ : s ” ,wh i c hi sa p p l i c a b l e wi t h o uts e ma n t i ca n o ma l yt o“ t h a t ” -clauses (as op po s e d ,e . g . ,t o“ i sg r e e n ” ) o c c ur si nas e n t e n c e ,“ Th a tp : s ” ,t h e nthere is always a trivially equivalent s e n t e n c eo ft hef o r m“ I t:s that p” .Fo re x a mp l e ,“ Th a tp i sg oo d ”a n d“ I ti s good that p”h a vee q ui v a l e n ti n s t a n c e s ,a n dt h es a meh ol d sa l s of o rmore 3
This transparency of truth-ascriptions has also been noted by Brandom (2000: 162f.).
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c o mpl e xe xp r e s s i o n s ,e . g . ,“ Th a tp wa sno td i s c ov e r e dun t i l1 8 3 0”a n d“ I t was not discovered until 1830 that p” .Th ebe s twa yt oe xpl a i nt h i si st o r e g a r dt h e“ I t ”i nt hel a t t e rt y peofs e n t e n c ea sa n a p h o r i c a l l y( a c t u a l l y , cataphorically) referring to t he “ t h a t ” -clause. These sentences are thus g r a mma t i c a l l yonapa rwi t h“ Hei sni c eyo urh u s ba nd ” ,wh i c h ,o fc o u r s e ,i s 4 e q ui v a l e n tt o“ Yo urh u s ba ndi sn i c e ” . As Horwich (1998a: 16, n. 1) notes, t h eg r a mma t i c a l i t yo ft hes e n t e nc e“ I ti st r uewh a tOs c a rs a i d ”i sf ur t he r evidence for this view. Thus, (D) stands in no need of further addition. It s ho u l dno wbee v i de n twh ye xpr e s s i on so ft hef o r m“ I t: st h a t ”s h o ul dn o t be called operators:i ts ug ge s t st h a tas e n t e n c e“ I t:s that p”i spr i ma r i l y f o r me dby“ I t: st h a t ”a n dt h es e n t e n c ef o l l owi n gi t .Th i sa n a l y s i sc l a s he s wi t ht hes t r on ge vi d e n c et h a t“ t h a t ” -clauses are singular terms, and so separate syntactic units (cf. 5.4).
3. Q UANTIFIED TRUTH - ASCRIPTIONS To see how to explain quantified truth-ascriptions, consider the argument we looked at in 1.5: (B)
Nothing Descartes believed is true. Descartes believed that he existed. Therefore, Descartes did not exist.
4
Mc Gr a t h( 20 03 :6 68,n .9 )n o t e st ha tma nys e n t e n c e se mbe dd i ng“ t h a tp is t r u e ”a r e a wkwa r d,a n dt ha twet h e r e f o r eof t e npr e f e r“ i ti st r u et h a tp” .Fo ri n s t a n c e ,“ Hebe l i e v e s that it is true that p”i sc l e a r l yt obep r e f e r r e do v e r“ Heb e l i e v e st h a tt h a tp i st r u e ” .Th e r e c a nbenoqu e s t i o nt ha t“ t h a tp i st r u e ”i sg r a mma t i c a l ,however, and so it must also be correct to embed such a sentence in sentential contexts. I believe some of these e mbe ddi ng ss e e m un gr a mma t i c a lbe c a us et he yha v e“ c e n t r e -b r a n c h i n g ”t r e e s( c f .Yn g v e (1960)). Such sentences are relevant for linguists because they seem clearly dictated to be grammatical but nevertheless appear unintelligible. This is taken to be because of the amount, or kind, of cognitive processing that is required to parse them. An example is “ Thema nt heb oyt h egi r lki s s e dme tr a n ” ,whi c h“ s h o u l d ”j u s tme a na p p r o x i ma t e l y , “ Thegi r lki s s e dt heboywh ome tama nwhor a n. ” .Asc a ne a s i l yb et e s t e d ,t h es e n t e n c e f o r m“ x be l i e ve st ha ti ti st r u et h a ts no wi swhi t e ”i sl e s sc e n t r e -branching even on the grammatical analysis which suits this explanation worst (within reasonable bounds). This is plausibly the explanation to why such sentences are preferred to the former type, and why the former type appears awkward.
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Toe xp l a i nt hi s ,weo nl yn e e dt ol ooka ta na r g ume n twi t ho u t“ t r u e ”b u to ft h e same f o r m:“ No t h i ngi nt h er oo mi smi ne ,t hedi c t i o n a r yi si nt h er o o m; t he r e f o r et hed i c t i o n a r yi sn o tmi ne ” .Si mi l a r l y ,wec a ni n f e rf r o mt h et wo pr e mi s e si n( B)“ Th a tDe s c a r t e se xi s t e di sno tt r u e ” ,a n d ,t h e n ,by( D) , “ De s c a r t e sdi dn o te xi s t ” .Th i st r e a t me nt explains how we derive, from s e n t e n c e sc o n t a i n i ng“ t r u e ” ,s e n t e n c e sl a c ki n gt h e m,a si nt h ee x a mpl e st h a t showed the truth-predicate to increase the expressive power of a language ( t he s i sVI ,1 . 4) .Su c hs t r e ng t he ni ngi se xe mpl i f i e dby“ No t h i n gDe s c a r t e s be l i e v e di st r u e ”i nt h a ti ti mpl i e sa l ls e n t e n c e so ft hef o r m“ I fDe s c a r t e s believed that p, then not-p” .
4. APPLICATION OF “ TRUE ”TO DEFINITE DESCRIPTIONS Another kind of truth-ascription considered as an example of the fact that “ t r u e ”i n c r e a s e dt hee xpr e s s i v epowe ro fEn gl i s hwa s“ Wh a tPe r c ys a i di s t r ue ” .As wi t hq ua n t i f i e dt r ut h -ascriptions, this will be dealt with by comparison to a sentence containing neither reference to propositions or t r ut h ,e . g . ,“ Wh a th ebo ug h ti se xpe n s i v e ” .No w,j u s ta st h ea r g ume n t“ Wh a t he bought is expensive, what he bought is (=) the last umbrella; therefore, the l a s tumb r e l l ai se xpe n s i ve ”i sv a l i d ,s oi st h i so n e :“ Wh a tPe r c ys a i di st r u e , wh a tPe r c ys a i di st h a ts now i swhi t e ;t h e r e f o r e ,t h a ts n o wi swh i t ei st r u e ” . Both of these argument have the following form: F(a) and a = b; therefore, F(b) .Fr om t h ec o n c l u s i ono ft h el a t t e r ,wege t“ Sn o wi swh i t e ” ,a n dt h i s shows why the original truth-a s c r i pt i o nh a sa l li n s t a n c e so f“ I fwh a tPe r c y said is that p, then p”a sc o n s e q uences (Horwich (1998: 3)).
5. APPLICATION OF “ TRUE ”TO DEMONSTRATIVES Th es i mpl eph r a s e“ Th a ti st r ue ” ,a sut t e r e di nr e s po ns et os o me o n e ‟ su t t e r ance of a sentence is plausibly explained in a similar way. In the previous example, one might say that, given a sentence identifying the thing said (or, for other cases, believed, assumed, feared, etc.), that is, a sentence of the f o r m“ Wh a tx said is that p” ,wec a n ,wi t ht h et r u t h -ascription, infer a corresponding denominalised sentence. When we say in response to some ut t e r a n c e ,“ Th a ti st r ue ” ,t h i ss ho ul dbet a k e na ss h or t -h a n df o r“ Wh a th a s be e ns a i di st r u e ” .Gi ve nt h a ti ti sno r ma l l yo bv i o uswha th a sb e e ns a i d ,t h e r e i sas e n t e n c eo ft hef o r m“ Wh a th a sbe e ns a i di st h a tp” ,s u c ht h a tb o t h speaker and audience can infer, together with the truth-ascription, the sen-
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t e n c e“ p” .I ti spr o b a bl ybe c a us ei ti sno r ma l l ye v i d e n tt obo t hs pe a k e ra n d a ud i e n c ewh i c hde no mi n a l i z e ds e n t e nc et oi n f e rf r o m“ Th a ti st r u e ” ,t h a t some philosophers have explained utterances of “ Th a ti st r ue ”a ss i mp l y being equivalent to the foregoing sentence (especially Strawson and the prosententialists –cf. 2.5 and 2.8). But this obscures the fact that two steps have been taken and, crucially, it does not explain this equivalence from a unified theory on which other truth-ascriptions can be explained. When the utterance preceding this type of truth-ascription contains context-sensitive expressions, the sentence the audience will infer from the truth-ascription will not always be identical to that uttered. If the foregoing ut t e r a n c ei s ,e . g . ,“ Ia mh ung r y” ,Iwi l ln o ti n f e r“ Ia mh un g r y ”f r o m my ut t e r a n c e ,“ Th a ti st r u e ” .Butt h i sphe nome n oni sge n e r a l .I fy o uu t t e r“ Ia m h ung r y ” ,a n dIr e s pon d ,“ Ib e l i e vet h a t ,t o o ” ,i ti si n c or r e c tt os a y“ I believe t h a tIa mh ung r y ”i sa na p pr o pr i a t ei n f e r e n c ef r om t h e s eu t t e r a n c e s .Th i si s naturally taken to be explained by reference to the propositions expressed, of course, but on the theory of propositions to be sketched in the next chapter, such explanatory appeal to propositions is forbidden. We therefore have to assume that speakers accomplish something like a tacit translation of contextsensitive expressions when they occur in utterances other than their own present ones, into sentences that, intuitively, say the same thing as uttered in the present context. Whether the view of propositions is correct or not, the phenomenon is general and not produced by the truth-theory, and so we may assume there to be a solution to it, which, together with (D), will entail that f r om myut t e r a n c e“ Th a ti st r ue ” ,a sar e s po n s et oyo u ru t t e r a n c e“ Ia m h ung r y ” ,o nec a ni n f e r“ Yo ua r eh ung r y ” ,a sut t e r e db ymei nt h es a mec o n text. What has to be done here is to take the notion of inference to hold relative to contexts ins uc hawa yt h a tt hes e n t e n c e“ Ia r eh ung r y ”c a nbe i n f e r r e df r o m“ Yo ua r eh ung r y ”r e l a t i vet oac o n t e x ti nwh i c ht h es pe a k e r uttering the first is the same as the one to whom the second is uttered. That is, for some sentence-pairs, the one can be inferred from the other only relative some contexts. For the above pair, this will hold only in contexts where the personal pronouns are assigned the same values. With this notion of inference, (D) can be taken as it stands and yield the desired result: from “ Th a ti st r ue ” ,a sut t e r e di nr e s po n s et o“ Ia mh ung r y ” ,“ Yo ua r eh u n g r y ”c a n be inferred.
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6. D ERIVATIVE APPLICATIONS OF “ TRUE ” Finally, we will see that (D) even enables a promising account of such de r i v a t i veu s e so f“ t r u e ”a si n“ Hei sat r u er e be l ” .Fi r s t ,what are the intuitions about this sentence that an explanation should do justice? It seems r e a s on a bl et ot a k et h i st obes e ma n t i c a l l ye q ui v a l e n tt o ,“ Hei sar e be l ” .Fo r one thing, they intuitively have the same truth-conditions. It would not be true to say that he is a rebel, unless he were a true rebel. However, the former c l e a r l yi mpl i e ss o me t h i ngmo r e .Tome ,t h i su s eo f“ t r u e ”s e e mst obeu s e dt o refer to things that do not merely claim to be such and such, but really are. To see how to account for the semantic intuition, we can treat the former s e n t e n c ea sonap a rwi t h“ Hei sa no bvi o u sc r i mi n a l ” .Th i sc a n n o tbe a n a l y z e da s“ Hei saDa n i s hpr i n c e ” ,be c a us ewh a ti ss a i di sn o tt h a th ei s o bv i o usa n dc r i mi n a l .Ra t h e r ,i ti se l l i p t i cf o r“ Th a th ei sacriminal is o bv i o us ” .Li ke wi s e ,“ Hei sat r uer e be l ”d oe sn o ts a yt h a th ei st r u ea n da r e be l ,b uts ho ul dbes e e na se l l i pt i cf o r“ Th a th ei sar e be li st r ue ” .Th e pragmatic difference is due, in the first instance, to the semantic redundancy o f“ t r ue ” ,wh ich violates conversational maxims (cf. the argument in 4.2 on applying (D) to propositional attitude contexts). As suggested to me by Peter Pa g i n ,t hep r a gma t i ce f f e c to f“ t r uex”mi g h tbee xpl a i ne dbyc o n t r a s t i n gi t wi t h“ f a l s ex” .Now,“ f a l s ex”i sno tused to say simply that something or other is not an x, but to say in addition that the object is falsely indicated or said to be an x. A false coin is falsely indicated to be a coin, and a false friend is falsely indicated (by himself) to be a friend. The question is then how this e f f e c ti spr o d u c e d .I ft hi sc a nbee xpl a i ne d ,t h e n“ t r uex”ma ys i mpl ybe explained as communicating the negation of what is communicated with “ f a l s ex” .Wh a ti sne g a t e di spl a us i b l yac o nj un c t i on :t ha tt h et h i ngi sn o ta nx and that it is indicated or said to be an x” .Th i s ,t o g e t he rwi t ht h es e ma n t i c c o n t e n t ,s q ua r e sn i c e l ywi t ht hei n t ui t i o nt h a tt h ee x pr e s s i o n“ t r u ex”i sus e d to say that the thing is not merely indicated or said to be an x, but really is. Let us now take falsity simply to be lack of truth (deflationism is wellkn ownt ol e a v ef e wo pt i o n she r e ) .Now,wec a ns e et h a tt hee x p r e s s i o n“ f a l s e x”do e st wot h i n g s .Fi r s t l y ,a sn o t e da bo ve ,as e n t e n c e“ y is a false x”i s e l l i p t i cf o r“ Th a ty is an x i sf a l s e ” .Ont hes e ma n t i cs i d e ,t he r e f o r e ,“ f a l s ex” contributes to communicating that y is not an x, by (D). Secondly, on the pragmatic side, it contributes to communicating that the object is said or indicated to be an x (which, by the semantic content, is false). We may next note that when propositional properties are superficially ascribed to non-
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propositions, the interpretation is that it is something said or indicated which h a st h epr o pe r t y .Whe n wes a y ,“ Ibe l i e v eher” ,i ti s ,n o n -elliptically speaking, what she said or indicated that is said to be believed. A person c a n n o t ,s t r i c t l ys pe a k i ng ,bebe l i e ve d .Si n c e ,i n“ yi saf a l s ef r i e nd ” ,ap e r s on is ascribed the propositional property of falsity, the interpretation is that what the person says or indicates is false. What is it, that is said or indicated? Since t h es e n t e n c e“ yi saf a l s ef r i e nd ”i s ,i nt hef i r s ti n s t a n c e ,a ne l l i ps i sf o r“ Th a ty i saf r i e ndi sf a l s e ” ,t h ep r o po s i t i oni nq ue s t i o ni sp l a u s i bl yp r e c i s e l yt h a ty is a friend. And so it is that the conjunction mentioned above is communicated. A wo r do fc a ut i o ni st h a tt h i su s eo f“ t r u e ”ma yh a vebe c o mel e x i c a l l y distinct, at least for some speakers, though once originated in the pragmatic way here envisaged. This is of course the case with many expressions, e.g., dead metaphors. In that case, (D) would not entirely exhaust the semantic me a n i ngof“ t r ue ” ,t h o ug hi two ul df i g ur ee s s e n t i a l l yi nt h ec a u s a l -historical explanation of the additional sense.
4.4 THE TRUTH OF SENTENCES AND UTTERANCES We have seen that deflationary theories taking sentences as primary truthbearers fails in accounting for ordinary intuitions and use. The approach t a k i ng“ t r ue ”t obea pp l i e dpr i ma r i l yt o“ t h a t ” -clauses, by contrast, need only be supplemented with more or less truistic claims about language in order to account for sentences containing it. One type of occurrence that will naturally attract special attention, is where truth seems to be ascribed to sentences. I take these occurrences to be elliptic variants of the type of truth-ascription e xe mpl i f i e dby“ Wh a tPe r c ys a i di st r ue ” .Towi t ,Se n t e n c e -Truth is to be explained on the basis of, (ST) “ ( Th es e n t e n c e )s i st r ue ”i se l l i p t i cf o r“ Wh a ts s a y si st r u e ” . This may be contrasted with a different deflationary account of sentencetruth, ( ST‟ )If s means [i.e., says] that p, then s is true iff p,
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wh i c hh a sbe e ndi s c us s e d ,e . g . ,bySo a me s( 1 999:2 3 8) .No w,( ST‟ )i sc l e a r l y a consequence of (ST), but, since it only gives a sufficient condition for a sentence to have certain truth-conditions, it is not obvious how to explain various truth-ascriptions to sentences on its basis. It therefore seems plausible t oa g r e ewi t h( ST‟ )b u tt a k ei tt obee xpl a i ne dby( ST) . It is plausible that all so-c a l l e d“ de r i v a t i v e ”u s e so fap r e di c a t e ,i . e., a use for something that is not of the right category for the word, is elliptic. Thus, on es a y st h a to neh a sar e dvi s ua le xpe r i e n c e ,t hi si se l l i p t i cf o r“ On eh a sa vi s ua le xpe r i e nc eo fs o me t hi ngr e d” ,o rs o mes u c h .Cl o s e rt o( TS)i st he ph r a s e“ be l i e veape r s on ” ,whi c hi se l l i p t i cf o r“ be l i e vewh a tap e r s o ns a y s ” . Asno t e di n2 . 1 1,s a y i n gt h a ts e n t e n c e sa r e“ d e r i va t i v e l yt r u e ” ,e t c . ,i s misleading because it implies that sentences are true, though in a special way. But if something else than sentences are taken as primary truth-bearers, then sentences should not, strictly speaking, be taken as true at all, just as experiences should not in any way be taken to be red. Ellipses like these work because of pragmatic inferences: since it is absurd to say literally that an experience is red, the audience finds a pragmatically sound interpretation as close as possible to what is literally said. It seems plausible that there is only one primary truth-bearer. If not, then we have two different truth-concepts, which seems gratuitous, since truth for different entities are more or less straightforwardly interdefinable. However, defining sentence-truth in terms of propositional ditto is remarkably simpler than the converse, which is of course one of the main arguments for the present standpoint. It is not reasonably considered unimportant what we take as primary truth-bearers, given how central truth and meaning are to analytic philosophy. Indeed, this choice seems pivotal in that taking propositional truth to be primary seems to exclude a truth-conditional theory of meaning. If propositions are primary, then what it is for a sentence to have certain truthconditions (in a context) is for the proposition it expresses (in that context) to be true under those conditions. But one way of saying what a theory of meaning is, is by saying that it is to explain what it is for a sentence to express a proposition (relative to a context). So, in order to explain what it is for a sentence to be true (and thus have certain truth-conditions), we must explain what it is for it to express the proposition it expresses (relative to a context). The concept in terms of which meaning was to be explained thus involves the concept to be explained in an immediate way, and so the theory moves in a narrow circle. Taking propositional truth to be primary therefore excludes explaining sentence-meaning in terms of truth-conditions (cf.
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Dummett (2003: 5) and Soames (1999: 244), whose reflections on these matters come very close to this conclusion). Th ee xpr e s s i on“ s a y ”i n( TS) ,i sp l a u s i bl ya l s ot a k e nt obed e r i v a t i v e . Sentences do not say anything, people say things in uttering them. Furthermore, what people say in uttering a sentence depends on the context. But precisely because what is said by a sentence depends on the context, truth itself need not be relativized to contexts, if we take propositions as primary truth-bearers. On such an account, the context-dependence of sentence-truth derives from the context-dependence of saying. Theories taking truth to be a property of sentences, by contrast, must take truth itself to be relative to contexts. Taking propositions or utterances to be primary therefore has the advantage over primary sentence-truth of leaving truth absolute. (True, not all relativizations of truth are equally counter-intuitive; so-c a l l e d“ t e mpo r a l i s t s ” intuit that the truth of propositions is relative to times. My point is that sentence-truth entails certain counter-intuitive types of relativity.) Truth for sentences must also be relativized to languages (the awkwardness of which was urged by Black (1948)). Clearly, a sentence may be true in one language and false in another. This phenomenon is of course also obvious for the propositionalist: sentences express different propositions in different languages. Propositional truth should also be favoured over utterance-truth in that truth is not plausibly taken to be a property of an event (many, of course, also think it is confused to say that a string of letters or phonemes, i.e., a sentence, can be primarily true). Further, defining propositional truth in terms of utterance-truth is unnatural and requires nonactual utterances, whereas the converse is simple and obvious. It is also hard to see what a theory of utterance-truth would look like. One is rather tempted to say that an utterance is true iff something true is said by the utterance. Indeed, in some cases, those favouring utterance-truth have just conflated the thing said by an utterance with the utterance itself. It is clear that Austin (1950: 113f.), Strawson (1952: 2ff.) and other similar-minded philosophers at the time were analogously unclear about the difference between the act of s t a t i n gs o me t hi n ga ndt h et h i ngs t a t e d ,bo t hp r o pe r l yc a l l e d“ s t a t e me n t s ” ,a conflation which con s i de r a b l ywe a k e n e dt h e i rc a s ea g a i n s tTa r s k i ‟ ss e n t e ntialism. We will now look at a few further cases of truth-ascriptions to sentences which meant trouble for disquotationalism, but which are easily treated on the present account. The cases of context-se n s i t i v i t yi so bv i o u s :“ Ia m h ung r y ”e x pr e s s e sdi f f e r e n tpr o po s i t i on sde pe n di n go ni t ss p e a k e r ,a n d
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therefore has different, corresponding truth-conditions. Further, certain types of modal and counterfactual truth-ascriptions have been discussed at length in relation to disquotationalism5, in particular, (M1) I fweh a du s e dt hewo r d“ whi t e ”d i f f e r e n t l y ,“ Gr a s si swh i t e ” might have been true, (M2) I fweh a dus e dt hewo r d“ whi t e ”d i f f e r e n t l y ,g r a s smi g h th a v ebe e n white, (M3) “ 1 +1=2”mi gh tno th a vebeen true. On Fi e l d‟ so r i gi n a l ,“ pur e di s q uo t a t i on a l i s m” ,( M1)wa st a k e nt o be equivalent to (M2), though, as we saw in 2.11?, he later proposed a truththeory quantifying over meanings to give a more intuitive account. With (D), (MD) and (TS), we can avoid the dilemma by noting that there are two ways of spelling out the ellipsis referred to in (TS). Depending on the reading, the Consequent of (M1) is one of the following: (C1) Wh a t“ Gr a s si swhi t e ”( a c t u a l l y )s a y smi gh th a vebe e nt r u e , ( C1 ‟ )Wh a t“ Gr a s si swhi t e ”wo u l d( t h e n )h a v es a i dmi g h tno th a vebe e n true. As s umi ngs o meo bv i o usf a c t sa bo utwh a t“ Gr a s si swhi t e ”a c t u a l l ys a y s ,we see that, on the first reading, (M1) entails (M2), but is not true, and on the second, it is true, but does not entail (M2). Concerning (M3), Field notes that there are two readings here, one on which, intuitively, it says that what “ 1 +1 =2”( a c t u a l l y )s a y smi g h tno th a vebe e nt r ue( a bs u r d ) ,a n do n eo nwh i c h i ts a y st h a twh a t“ 1 +1=2”mi gh th a ves a i d( i nc e r t a i nc i r c ums tances) is not true (plausible). So, whereas simple truth-ascriptions to sentences are given by (TS), modified ones allow readings with different scopes of modal and subjunctive expressions. It is of course the former reading of (M3), and (C1) which Field was after when spelling his truth-p r e d i c a t e“ t r u e -as-we-understand-i t ”( 1 994 a :2 65f . ) . Th i si n t ui t i vewa yo fs p e c i f y i n gt h ei n t e n d e dr e a d i n g 5
See, e.g., Etchemendy (1988: 63f.), Field (1986: 58) and (1994a: §§ 5, 9), GarcíaCarpintero (1998: 50ff.), Halbach (2001) and (2002).
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is of course easy to explain: we understand it as saying that grass is white. With this in mind, the derivation of the disquoted sentence is unequivocally valid, since the other interpretation is explicitly ruled out. We will end this section by discussing how (ST) fares with sentences that do not intuitively say anything, or say more than one thing. We should first note that ellipsis is a pragmatic phenomenon, and therefore does not obey strict rules that are to apply in every case. However, (ST) does seem to work also for most problematic cases. Take, to begin with, a sentence which does not seem to say anything because of non-e xi s t i n gwor d s ,s uc ha s“ Gwe e k s t h wa r t l e ”( a s s u mi ngt h i st obeas e n t e nc ea ta l l ) .On ema yh a v et h ei d e at h a t the claim that this sentence is not true is itself true. Since nothing is said, there is nothing than can be true. This seems to me to be primarily a philos o phe r ‟ sr e a c t i o n ,ho we ve r .A no r ma ls pe a k e rwo ul df i n dt h i sme r e l yc o n f us i n g .On emi gh tbepr e pa r e dt os a yt h a t“ Sn o wi sbl a c k”i si n d e e dn o tt r u e , bu ts i n c e“ Gwe e k st hwa r t l e ”i sme a ni ngl e s s ,i ti ss i mpl yc o n f u s i n gt os a yt h a t it is n o tt r ue .Onema yo fc o u r s ec h a ng eon e ‟ smi ndi fi ti se x p l a i n e dt h a t since it is meaningless, it cannot very well be true. But such a claim would e n f o r c ead i f f e r e n ti n t e r p r e t a t i on ,n a me l yt hei n t e r p r e t a t i ono nwh i c h“ s is not t r u e ”i si n t e r p r e t e da ss a y i ng that s does not say something true, rather than (by (ST)) saying that what s says is not true. That such opposing reactions are manifested is rather natural given that it takes pragmatic interpretation to make sense of ascriptions of sentence-truth in the first place. (ST) registers a default type of interpretation. This is why a speaker will at f i r s te xpe r i e n c ea sa wkwa r dt hec l a i mt h a t“ Gwe e kst hwa r t l e ”i sn o tt r u e .I f (ST) is applied here, then, since nothing is said by the sentence, the claim will be taken as a supposition failure. 6 When a string of letters is said to be true or not true, it is presupposed that it says something. The opposing interpretation, which is intended when it is explained that the sentence is 6
Ana dhe r e ntofRus s e l l ‟ sa n a l y s i sofde f i ni t ede s c r i p t i o n swo u l ds a yt h a tt h ec o nf u s i o n in this case is caused by a scope ambiguity of the negation. I will not here discuss this disagreement at length here, since the differences for this case are only special cases of the general, well-known differences between these competing analyses of definite des c r i pt i o ns .I nmyv i e w,Rus s e l l ‟ sa na l y s i sgi v e st h ewr o n gp r e di c t i o n sf o rs e n t e nc e swi t h empty descriptio nsa nda ne x t e r na ln e g a t i o n ,e . g. ,“ I ti sno tt h ec a s et ha tt h ek i n do f Fr a nc ei sba l d ” .Onhi sa na l y s i s ,t hi ss ho ul dbeun p r o b l e ma t i c a l l yt r ue ,s i n c et h e r ei sn o possibility of scope ambiguity for the negation. But this sentence appears just as “ i na p pr o pr i a t e ”o r“ f a i l e d”a s“ Th eki ngo fFr a nc ei sb a l d ” .I na nyc a s e ,Iwi l la s s u met h e presupposition view to be correct.
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untrue since it does not say anything, is special, since it is usually trivial and irrelevant that meaningless sentences do not say something true (since they do not say anything at all). As always, such pragmatic considerations of relevance govern interpretation, whence the possible confusion upon e n c o u n t e r i ngt h ec l a i mt h a t“ Gwe e k st hwa r t l e ”i sn o tt r u e .I fap h i l o s o ph e r for some reason wants to say that meaningless sentences are untrue, he is entirely free to do so. He will then just make clear that when calling a sentence true, he means to be saying that it expresses a true proposition. The c l a i m( ST)i sn o tl e g i s l a t i v e ,butr e c o r d saf a c ta b o utno r ma ls pe a k e r s ‟i n t e r pr e t a t i o n ,whi c ha l s ot e n d st obeph i l o s o ph e r s ‟i n t e r p r e t a t i o n ,a b s e n tv a r i o u s theoretical involvements that enforce a different interpretation. We have already seen that though (ST) works for most normal cases, it does not determine the interpretation for any possible case, as a semantic principle should. The modal truth-ascriptions were a case in point. The deviating cases are explained by reference to ordinary pragmatic principles. Sentences which do not say only one thing are treated similarly. With c a s e so fa mbi g u i t y ,a si n“ Ba n k sa r ema n -ma d e ” ,t r u t h -ascriptions are judged r e l a t i vet ot hei n t e r p r e t a t i onof“ ba n k ” .I fa particular interpretation is salient, (ST) might be directly applied. Then, what is said is that what the sentence s a y sun de rt h a ti n t e r p r e t a t i ono f“ ba n k ”i st r ue( o rno t ) .I fn op a r t i c u l a r interpretation is salient, the truth-ascription will raise the kind of confusion as di d“ Gwe e k st h wa r t l e ” .I st het r ut h -ascription taken to be a supposition f a i l ur e ,o ri si tt obet a ke na st r ue ,s i n c eo nonei n t e r pr e t a t i o no f“ b a n k ” ,t he sentence says something true, or is it false, since on one interpretation of “ b ank, what is said is false? What is meant in a real situation, if that can be worked out, is of course determined by contextual features, but taken in isolation, there is no real question here, since there is no determinate interpretation. That we normally interpret truth-ascriptions in accordance with (ST) is evidenced, however, by the fact that we tend to ask for a specif i c a t i on ,r a t h e rt h a na n s we r i n g“ Ye s ”o r“ No ” .I fIa s k“ I st h es e n t e n c e„ Ia m t a l l ‟t r u e ? ” ,t hea u di e nc ewi l le i t he rp r e s u ppo s ear e f e r e n c ef o r“ I ” ,e . g . , my s e l f ,a n da n s we r“ Ye s ”o r“ No ” ,o rt h ea udi e nc ewi l lo b j e c t ,“ I td e pe n d s onwh out t e r si t ” .I ti si mp r o ba bl et h a tas pe a ke rs a y s“ Ye s ”f o rt h er e a s o n that something that could be said by the sentence (namely if uttered by a tall person) would be true. Thus, (ST) works most of the time, but because this is a pragmatic issue, we need not, and should not, say anything more specific. As long as there is some pragmatic explanation of every piece of linguistic
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behaviour with respect to truth-ascriptions to sentences which takes speakers t oi n t e r pr e t“ t r u e ”a sp r i ma r i l ya s c r i be dt opr o p o s i t i o n s ,wea r ei nt h ec l e a r .
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CHAPTER FIVE: THE SEMANTICS OF “ THAT” -CLAUSES 5.1 INTRODUCTION It is often because of nominalist scruples that philosophers have spoken of truth for sentences rather than propositions, despite the counter-intuitive consequences noted in 4.4. For a deflationist, the choice is quite different, since deflationism coupled with the view that sentences are primarily true – that is, disquotationalism –fares especially bad in accounting for our ordinary us eo f“ t r u e ”a n di si ng e n e r a lq ui t ec o un t e r -intuitive, as we saw in 2.11. I am myself sympathetic to a nominalist stance, why I take comfort in the fact that (D) is not committed to propositions. It only claims an equivalence relation be t we e nc e r t a i nf o r mso fs e n t e nc e s .Si n c e“ t h a t ” -clauses uncontroversially exist and must have some semantic functioning to be accounted for, nominalists should have no ontological qualms about (D). The aim of this chapter is thus to argue that the deflationary theory defended in the last chapter can plausibly be combined with a nominalist view o f“ t h a t ” -clauses, thus solving problem (3) of 4.1, i.e., the problem of “ steering between the Scylla of admitting propositions and the Charybdis of di s q uo t a t i on a l i s m” .Ofc o ur s e ,t hi sr e q ui r e st h a ton egi veal i n g u i s t i ck i n do f deflationary theory, like (D), but this was found mandatory in Chapter 3 in any case. Given the argument of Chapter 3, then, nominalist deflationists are free to adopt any view of the primary bearers of truth. Given the many advant a g e so fd e f l a t i on i s tpr o po s i t i o n a l i s m,a ndg i v e nt h a t“ t h a t ” -clauses are there to be accounted for in any case, the choice should be obvious. Some space will be devoted to the formulation of a nominalist constraint, which is to guide us in making sense of ordinary speech (and those of its features that engender realist metaphysics) without admitting propositions through the back-door. In
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Be r k l e y ‟ swo r d s ,wewi l ls howhowt o“ t hi n kwi t ht h el e a r n e d ,a n ds pe a kwi t h t h ev ul g a r ” . I will first provide a clearer statement of the nominalist constraint I will adopt, and defend this particular formulation of nominalism. Then, I will argue that the views of truth and semantics advertised in this work are in be t t e rs h a pe f o rc o n s t r ui n ga na c c o un to f“ t h a t ” -clauses meeting the nominalist constraint than does ordinary, truth-theoretic semantics. It will also be seen that the conclusion of Chapter 3 about how a deflationary theory must be formulated is not happily combined with a non-nominalist view of propositions, which is thus a converse case of motivation. This mutual support is taken to display an attractive coherence of the deflationist-nominalist view. We will then discuss various more specific syntactic and semantic questions a bo u t“ t h a t ” -clauses, such as the question whether they are singular terms, and their role in propositional attitude ascriptions and quantifications. As a corollary,as o l u t i ont opr o bl e m( 4)o f4 . 1wi l lbepr e s e n t e d ,i . e . ,Gu p t a ‟ s problem of explaining general facts about truth. It will also be seen that this avoids a problem that arises for Horwich. After that, we will briefly discuss t h et e r m“ p r o po s i t i o n ”a n di t sr e l a t i o nt o“ t h a t ” -clauses. Finally, I will say something about what I think a correct semantics should be like, given the deflationist and nominalist theories presented. The main contribution this chapter makes to the preceding discussion, however, is showing how to get the good from propositional deflationism while avoiding commitment to propositions, the latter being the main motivation for disquotationalism.
5.2 THE NOMINALIST C ONSTRAINT In view of what was said in the previous chapter, that one must take propositions as the primary truth-bearers, it may be surprising that a nominali s tv i e wo fp r o po s i t i o n swi l lnowbede f e nde d .Ad mi t t e d l y ,Ih a v es po k e n“ o f pr o po s i t i o n s ”a b ov ei nt hes e n s et h a tIh a vebe e nu s i n gt het e r m“ p r o p o s i t i o n” in an obviously committive way, i.e., as entailing by existential generalization that there are propositions. The nominalist theory that will here be sketched, however, takes such commitment to be forgivable, or even mandatory, in casual speech and in many fields of philosophy, but holds that this usage is to be treated as a datum that should be explained in a nominalist way, rather than something that must be eliminated. Some might not want to call such a view
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“ n omi n a l i s t ” ,b utIt a k ei tt obes uf f i c i e n tf o rde s e r v i n gt he label that it is motivated by the common nominalist grounds, and that it is in opposition to non-no mi n a l i s tt he o r i e s( e x c e p t ,po s s i bl y ,t os uc h“ t wo-dimens i on a l ”v i e wso f on t o l og ya sCa r n a p ‟ s( 195 6 ) ) . At one level, the type of ontological commitments made in the previous chapter must be done away with. A beginning of such a regimentation was the alternative phrasing of the view that it truth is primarily a property of propositions, namely, “t r u e ”ap pl i e sp r i ma r i l yt o“t ha t ”-clauses. Rephrasing the claims and arguments of the previous chapter should not seem anymore worrying than the general requirement to give a nominalist treatment of all us e sof“ t h a t ” -clauses and what appears superficially to be quantification over, and reference to, propositions, which is ubiquitous in natural language. (The wo r d“ pr o po s i t i o n ”i sno tu s e di nn a t u r a lEng l i s ha si ti si np h i l o s o p h y ,o f c o u r s e ,b utwe l le x pr e s s i o n sl i ke“ t h i ng swebe l i e v e ,s a y ,e t c . ” . )Wema ys a y t h a tmya bov er e a s o ni ngus i n g“ pr o po s i t i o n ” ,e t c . ,i sa ninstance of semantics in the material mode, which is to be regarded as a preliminary to the final, nominalistically kosher semantics. It is a convenient way of displaying linguistic intuitions and inferential relations by using, rather than mentioning, various sentences. The final semantics is to explain the facts about our linguistic use so displayed, but may not use the committive expressions, but on l yme n t i o nt h e m.Ther e a s ont h a tno“ t h a t ” -clause may be used is that a sentence containing it entails a corresponding existential sentence. For i n s t a n c e ,“ Ibe l i e vet h a ts now i swhi t e ”e n t a i l s“ Ibe l i e v es o me t h i ng ” .The wo r d“ pr o po s i t i o n ”i ss i mpl yus e d( byph i l o s o phe r s )i ns u c hawa yt h a ta s e n t e n c el i k e“ Ibe l i e ves o me t h i ng ”i sad i r e c tc ommi t me n tt op r o positions, since propositions just are the things believed, known, etc. (More on the philosophical use of this word in 5.6.) We may now more explicitly formulate the Nominalist Constraint: (NC) There must be no quantifying over, or referring to, propositions and no use of notions primarily defined for propositions. The nominalist claim that I will here argue for is that we can give an exhaustive account of all uncontroversial facts while still obeying (NC). By “ u n c o n t r ov e r s i a lf a c t ” ,Ime a nt oe xc l udesuch alleged facts as that there really are things we believe, assert, etc., with some nature to describe. It is of course question-begging to require a nominalist to explain this alleged fact. Th e“ un c o n t r ove r s i a lf a c t s ”i n c l ude ,r a t he r ,t h o s ea bo u to u rl inguistic behav-
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iour and cognition in general that can be expressed in a nominalistically tolerable way. Particularly relevant for the present study, then is the question whe t he rt h es e ma n t i c sf o r“ t h a t ” -c l a us e s ,q u a n t i f i c a t i on sl i ke“ Ev e r y t hi n gh e believes . . . ” ,a n dwo r d st h a ta ppl yp r i ma r i l yt o“ t h a t ” -c l a us e s ,l i ke“ t r u e ”a nd “ be l i e ve s ” ,c a nbeg i ve ni name t a l a ng ua gewh i c ho be y s( NC) . Byd i s a l l owi ng“ q ua n t i f yi ngov e r ”p r o po s i t i o n si n( NC) ,Ime a nt h a tn o q ua n t i f i e ds e n t e n c ewh o s ei n s t a n c e sc on t a i n“ t h a t ” -clauses may be used in the s e ma n t i c s .Fo ri n s t a n c e ,“ Hebe l i e ve se ve r y t hi n gh ekn ows ”h a si n s t a n c e sl i ke “ I fh ekn owsthat snow is white, then he believes that snow is white” .I ts e e ms a pp r o p r i a t et oe x pl a i nt hec ommonl yus e d“ q u a n t i f yov e rx‟ s ”i nt h i sway, since the latter seems to entail that there are things, namely propositions, that we must not quantify over. This would make the constraint violate itself. Reference to propositions, similarly, is to be understood simply as the use of a “ t h a t ” -clause, o rad e s c r i pt i onl i ke“ Wh a th es a i d ” ,wh i c hc a ni n t e l ligibly be i n s e r t e dt o g e t h e rwi t ha“ t h a t ” -clause in an identity-s e n t e n c e( “ Wh a th es a i di s ( =)t h a ts n o wi swh i t e ” ) .Fi n a l l y ,i ti son l yn a t u r a lt h a tan o mi n a l i s t i c a l l y acceptable semantics not includei ni t sc on c e p t u a le q ui pme n t( o r“ i de ol og y ” , i nQui ne ‟ ss e n s e )a n y“ no t i on sde f i ne dpr i ma r i l yf o rpr o p o s i t i o n s ” ,t h a ti s , wo r d st h a ta p pl ypr i ma r i l yt o“ t h a t ” -c l a us e s .Th e“ pr i ma c y ”h e r ec o ul dbe explained in terms of learning the word or introducing it in the language. If a word can only be learnt or introduced by figuring in sentences that also c o n t a i na“ t h a t ” -c l a us e ,t he ni ti spr i ma r i l ya p p l i e dt o“ t h a t ” -clauses, on this terminology. According to the above deflationary theory, where (D) plays an essen t i a lr ol e ,“ t r u e ”c l e a r l ya p pl i e spr i ma r i l yt o“ t h a t ” -clauses in the relevant sense, and it is rather obvious that propositional attitude verbs do as well. This type of nominalism should be distinguished from what may be called traditional nominalism, the simple claim that there are no propositions. I have avoided this formulation because I think it misleading in important ways. In my view, this claim may be regarded from two different perspectives (not whol l yu n r e l a t e dt o Ca r n a p‟ s di s t i n c t i on be t we e ni n t ernal and external questions (1956: suppl. A)). As expressed by (NC), we may not, when c o n s t r uc t i n gt hes e ma n t i ct he o r y ,us e“ t h a t ” -clauses, quantified sentences with “ t h a t ” -clauses as instance-terms, or expressions which are primarily applied to “ t h a t ” -cl a u s e s( l i k e“ t r ue ” ) .Th i spl a us i bl yme a n st h a tt he“ p r o po s i t i o n ”wi l l no tb ei nt h es e ma n t i c se i t h e r . Thes e n t e nc e“ Th e r eare p r o po s i t i o n s ”wi l lt h u s be compatible with the semantic theory, but I believe this is less of a problem and that adhering to (NC) is anyway a recognizably nominalistic standpoint. The reason for this roundabout formulation of nominalism has to do with the
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s e c o nd“ pe r s p e c t i v e ”f r om whi c ht hed e n i a lo fp r o po s i t i o n sma ybet a k e n . Th i si sr e l a t e dt owh a tIc a l l e d“ s e ma n t i c si nt hema t e r i a lmo de ” .Th i si st he activity of uttering those sentences that are assertible and drawing the correct inferences in order to see which intuitions a final semantics should account for. Otherwise put, one hereby displays facts about meaning that the semantics is to explain. It is simply much more convenient, and, more importantly, a safer way to avoid confusion, thus getting unreliable data, than by d i s c us s i n gs pe a k e r s ‟u s ei n a mo r et he o r e t i c a l( a n dn o mi n a l i s t i c a l l y acceptable) way. For instance, asking as pe a k e r ,“ Do e ss o me o n ewh obe l i e ve s t h a ts now i swh i t ea l wa y sbe l i e ves ome t hi ng ? ”wi l lg i v ec l e a r e rr e s u l t st h a n asking him to answer metalinguistic questions about the relevant sentences. The semantics, of whatever kind, should simply explain ordinary linguistic use, not high-level philosophical discussions about semantics. It was mainly byt he“ me t h od ”o fs e ma n t i c si nt hema t e r i a lmod et h a twei nt h ep r e v i o u s c h a pt e rf o undt h a ti ti smo r ec onve ni e n tt ot a ke“ t r ue ”t obep r i ma r i l ya p p l i e d t o“ t h a t ” -clauses, rather than quote-names of sentences. But this result was reached mainly by asking whether propositions were more plausibly taken as the primary truth-bearers than sentences, not exclusively by asking metalinguistic questions. When doing semantics in the material mode, it is of course necessary to a s s e n tt os e n t e n c e swi t h“ t h a t ” -clauses and propositional quantifications. We are here simply to act as normal speakers, these being (by definition) the object of the semantic study. The semanticist is included in the subject-class, and, in practice, typically the only subject. Hence, it is clearly incorrect to assert traditional nominalism if we are doing semantics in the material mode. I nf a c t ,i fweu s e“ t r ue ”i na c c o r d a n c ewi t h( D) ,a sIh a v ea r g ue di swhat un de r l i e se v e r yu s eo ft h ewo r d ,t he na n ys e n t e nc e“ p”e n t a i l st h ec o r r e s pon d i ng“ Th a tp i st r ue ” .Butt he n ,gi ve nt h a t“ t h a t ” -clauses admit of existential generalisation, any sentence whatsoever entails that there are propositions. Any sentence thus contradicts traditional nominalism. This does not mean that we have to admit propositions after all, only that we should be careful with the claim that there are no propositions. The analogy with Ca r n a p‟ sd i s t i nc t i oni so bv i o us ,butIwo u l dl i k et oe mp h a sise that the two “ p e r s pe c t i ve s ”t h a tIa p pe a lt odono tc o r r e s p ondt oa l l e g e dd i s t i n c ti n t e r pr e t a t i o n sof“ t he r ei s ”o r“ e xi s t ” .Th i sa l l e g e da mb i gui t yi sn o te mp i r i c a l l y supported and does not have intuitive support, but is suspiciously handy for eating the ontological cake and having it.
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Another obvious reason that care must be taken with this claim is that when doing other kinds of philosophy, it will be practically inappropriate to follow (NC). For instance, when doing epistemology, these ontological questions are irrelevant and should therefore not encroach by requiring cumbersome reformulations. For instance, instead of saying that one believes what on ek no ws ,( NC)wo ul dh a veuss a yt h a ta n ys e n t e n c e“ x knows that p” (analytically) entails the corre s pond i n g“ x believes that p”( o rs omes u c h ) ,b ut no nominalist will be able to follow the requirements on her semantic theory in this way. Thirdly, of course, no one will be able to obey (NC) in ordinary life. Therefore, we might as well anticipate possible criticisms by separating what is acceptable in a nominalist semantics from what may be accepted in more informal circumstances. One might say that the above formulation of nominalism is intended (partly) to avoid typical charges of self-defeat. However consistent, this may appear as some kind of fiddling. Some will pr o ba bl ye x c l a i m,“ Buta r et he r epr o po s i t i o n so rn o t ? ” .Myi n s t a n ta s c e n tt oa metadiscursive level may seem dishonest or evasive, but, in my opinion, it is really only a move necessitated by the fact that every philosopher and nominalist is also a normal speaker, who is not always, not even always when philosophizing, doing semantics. There is no theoretical problem with the ki n do fwi d e“ i nc on s i s t e n c y”a l l owe dhe r e–t h a ti s ,i ti sn o ta n“ i ncons i s t e nc y ”t h a ti n d i c a t e st h a tt hen omi n a l i s t i cv i e wi sf a l s eo ru n wo r k a b l e ,i . e . , that we need to posit propositions in order to account for the uncontroversial facts. Should we, when doing semantics, say that there are no propositions? Well, it is ruled out by (NC), since any use of a word introduced together with a“ t h a t ” -clause is disallowed. And I think this is correct. When doing nominalist semantics, one should act as an observer and commentator of what has been called the uncontroversial facts, among which is the fact that speake r su t t e r“ t h a t ” -c l a u s e sa nd“ t hi n g ss a i d / be l i e ve d / kn o wn ” ,e t c . ,i nc e r t a i nc o n ditions, and try to find a systematic explanation of this behaviour. He will thus mention all the words that are ruled out by (NC), and explain our use thereof, but it is question-begging to object that he must use these expressions in the explanations. That he need not is precisely the nominalist claim. If one engages in conversation with a speaker in order to display fact about usage, or, as is more common, if one tests what intuitions one has oneself, one must temporarily abandon the role as semanticist. As long as the (somewhat imaginary) orthodox nominalist can be seen not to end up in contradictions
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himself, it should not be unproblematic to allow him to use the expressions in o r de rt o“ e x pe r i me n t ”wi t ho t he rs pe a ke r so rhi ms e l f . It may seem as if a traditional nominalist must say that we ordinary speake r ss o me howgowr on ge ve r yt i meweus eas e n t e n c ewi t ha“ t h a t ” -clause. But this would surely go counter to a plausible principle of common sense. Like Cartesian scepticism, it seems to set the standards too high. This is not the type of argument that will persuade a real sceptic, of course, but there are very few sceptics, and precisely because of its clash with common sense. The issue concerns not how to persuade someone with radical views but the fact that most of us do accept the constraint on philosophical theories that they accord with common sense. Traditional nominalists therefore usually do try to account for ordinary judgments, by taking the commitment to propositions to be only an illusion created by the superficial form of the relevant sentences. The real meaning of the relevant sentences is then thought to be given by various paraphrases which lack commitments, and the view is often called “ p a r a ph r a s en omi n a l i s m” .The s ea n a l y s e sh a vebe e nmuc hc r i t i c i z e d ,h o wever, and widely abandoned (below, I will myself explain why I do not accept them). If paraphrase nominalism fails, the clash with common sense is another r e a s onf o ra d o pt i ngt hemo r e“ r o und a bo ut ”n omi n a l i s m. But if we adopt (NC), do we not still somehow have to say that people are massively wrong? One idea may be that we have to say that people all say false things when ut t e r i ng“ t h a t ” -clauses. But falsity, like truth, is a property of propositions, and is therefore not to be used to characterize ordinary language at all in the nominalist semantics. Any sound semantics should make pe o pl ec omeo utmo s t l yr i gh t ,but“ r i g h t ”mu s tn o tbei n t e r p r e t e da s“ t r ue ” ,i f (NC) is to be respected. According to the semantics that will be defended (and wh i c hi si na n yc a s ema n d a t e dbyde f l a t i o n i s m) ,u t t e r i ng“ Ibe l i e v et h a ts n o w i swhi t e ”i sc o r r e c ti np r e c i s e l yt hes a mes e n s ea si ti sc o r r e c tt ou t t e r“ Sno wi s wh i t e ” .The yon l yh a v ed i f f e r e n tt y pe so fc o r r e c t n e s sc o nd i t i o n s :wh e ns t a t i n g the correctness conditions for the latter we may (and should, I believe) use “ s n o w” ,b uti ns t a t i n gt h o s eoft hef o r me r ,wema yno tu s e“ t h ep r o po s i t i o n t h a ts n o wi swh i t e ” . Even if the present nominalism does not clash so obviously with common sense as does the traditional variety, there may still linger an initial doubt that such a linguistic take on the phenomenon of proposition can be right. Here, we could repeat the line of reasoning in 3.4, and appeal to those issues where on l yal i ng ui s t i ca n s we rs e e mspo s s i bl e ,i . e . ,c o n c e r n i n g“ wh a ti ti st oe xi s t ” , “ t h ea ve r a gepe r s o n ”a n d“ s a ke s ” .Eve ng i ve naf ul la c c o un to ft h ee xi s t e n t i a l
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quantifier and the existence-pr e di c a t e ,s ome o nema ya s k ,“ Butwh a ti si tt o e xi s t ?Yo uh a v eon l yde s c r i be dt her e l a t e dl i ng ui s t i ce xp r e s s i o n s ! ” .Th i st y pe of charge should not without further argument seem more pressing for the pr e s e n tpr o po s a lt h a ti tdo e sf o ra“ l i ng ui s t i cv iew of existence or the average pe r s o n” .Th a ti s ,wes ho ul dr e q ui r ef ur t he ra r g ume n tf o rt h ec l a i mt h a tt he notion of proposition in particular requires more than a merely linguistic account. It is not obvious an argument to that effect, which does not beg the question against nominalism, can be construed.
5.3 THE C OHERENCE OF A NOMINALISTDEFLATIONIST V IEW In order to do justice to ordinary linguistic intuitions and use, a positive semantic value must be ascribed to all or most sentences that we unconditionally assent to. In a non-alethic semantics, one can take this value to be the very assent itself, or one may take it to be some notion of (unconditional) assertibility or analyticity (cashed out in non-alethic terms). An ordinary truth-theoretic semantics will typically take it to be truth proper. We may for simplicity disregard such notions as supervaluationist truth, high degree of truth and other such variations. First, they seem to get similar results for the cases that will be discussed, at least if these truth-notions are even remotely similar to ordinary truth. Secondly, they are dialectically rather peripheral and have cogently been objected to on more principal grounds. We will first see that a truth-theoretic semantics that satisfies (NC), while accounting for uncontroversial facts about usage, will have rather implausible consequences, and therefore seems unsuitable for being coupled with nominalism. It will next be argued that a use-theoretic type of semantics does not seem to be in danger in these respects. There might be other reasons yet to be given why such a semantics cannot be both adequate and satisfy (NC), but, prima facie, it is particularly truth-theoretic semantics that seems unfit for nominalism. It will emerge after this discussion that the preferred alternative semantics will in important respects play a polemic role, in that its potential s uc c e s si na c c o un t i ngf o rr e a l i s t ‟ si n t ui t i on si ss i mul t a n e o u s l yawe a k e n i n go f t h er e a l i s t ‟ sc a s e .Fi n a l l y ,wewi l ls e et h a tgi v e nt h ewa yad e flationary theory must be formulated, as concluded in Chapter 3, there is a reason why no deflationist ought to admit propositions. So, while the first consideration
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shows why nominalists should love deflationism (or at least the kind of semantics it requires), the second shows why deflationists should love nominalism (whether they like it or not). There is thus a mutual coherence in the combination of deflationism and nominalism. That truth-theoretic semantics does not fit well with nominalism should not be surprising, since it has been common to argue for Platonism precisely by considering what follows from the truth of various sentences. The most c o mmo na r g ume n ti st h a ts i n c e“ t h a t ” -clauses are singular terms, one must posit objects as referents in order to explain how sentences containing them can be true. The form of this argument is age-old, and can be found in various writings of Plato and Frege (e.g., Frege (1884: § 60)), though they mainly s pe a ko fn umbe r sa n dn ume r a l s .I nFr e ge ‟ s( 1 892 )a n d( 1 9 1 8 ) ,however, the argument for propositions are given a clear statement. The argument, then, is t h a t“ t h a t ” -c l a us e sa nde x pr e s s i o n sl i ke“ t hebe l i e f( t h o ug h t ,f a c t ,e t c . )t h a t s now i swh i t e ”a r es i n g ul a rt e r msa n da l ls i ng ul a rt e r msf i g u r i n gi nt r u e sentences ha ver e f e r e n t s .Be l ow,Iwi l lde f e ndt hec l a i mt h a t“ t h a t ” -clauses are singular terms, so the question is how to block the commitment to pr o p o s i t i on s .Th ea n s we ri ss i mpl e :“ t r ue ”mus tn o tbeu s e di nt h es e ma n t i c s at all, since (NC) requires that no expressi o n sp r i ma r i l ya p pl i e dt o“ t h a t ” clauses be used. Therefore, this argument does not create a problem. Of course, we intuit t h a t“ Ib e l i e v et h a ts n ow i swh i t e ”i st r ue ,s oIb e l i e vet h a t snow is white, so there is something that I believe. But in saying this, we are only doing semantics in the material mode, i.e., displaying what facts about o urus eo f“ t h a t ” -clauses that the semantics is to explain. (This kind of response will be more thoroughly discussed below.) The present point is that an adherent of truth-theoretic semantics cannot make this move, and that it is not obvious how he should respond to the a r g ume n t .Hec a nno tde ny t het r ut hofa l ls e n t e n c e swi t h“ t h a t ” -clauses without being unable to account for linguistic practice. To say this does not beg the question against such eliminativists who want to deny the truth of all these sentences, for I am only making the more uncontroversial claim that such an eliminativist cannot, or at least, cannot reasonably, adopt a truthconditional semantics. How, then, can one admit the truth of sentences cont a i n i ng“ t h a t ” -clauses without admitting propositions, i.e., things believed, etc.? De ny i ngt h a t“ t h a t ” -clauses are singular terms is a possible move here, but there is a related argument that cannot be thus blocked. The truthc o ndi t i o n a l i s tn o mi n a l i s tmu s tt a kea tl e a s ts o mes e n t e n c e so ft h ef o r m“ x Vs
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that p”t ob et r ue ,i no r de rt oa c c o un tf o ro url i n g ui s t i cp r a c t i c e .Ev e nt h o ug h hec a nde nyt h a t“ t h a t ” -clauses are singular terms, it is very implausible to denyt h a ta ne xi s t e n t i a ls e n t e n c e ,“ x Vss o me t h i n g”c a nb ei n f e r r e df r o ma s e n t e n c eo ft h ef o r m“ x Vs that p” .Buto nat r u t h -theoretic semantics, valid inferences should be truth-preserving, so the existential sentence must be true. In order to avoid commitment to propositions, i.e., that there is something that someone believes, knows, says, etc., the truth-conditionalist must then deny the homophonic T-bi c o n di t i o n a l sf o rs e n t e n c e so ft h ef o r m“ x Vss o me t hi n g ” . And this, rather than denying existential generalisation, has indeed been the common reaction to the dilemma. This respects (NC), which is typically a c c e pt e dbyn omi n a l i s t s ,b uti tf o r c e sonet oh o l dt h a t ,e . g . ,“ Kr i p k ebe l i e v e s s ome t hi ng ”i st r u ewh i l ede nyi ngt h a tKr i pk ebe l i e v e ss o me t h i n g ,a n ds oo n, which is of course rather counter-intuitive. The alternative semantics coupled wi t ht h i sc l a i mc on s i s t si na n a l yz i ngt he“ l og i c a lf o r m”o r“ de e ps t r u c t u r e ”o f the problematic sentences so as to give them truth-conditions different from those given by homophonic T-sentences. Truth-conditionalist nominalists thus typically respond to the realist arguments from the truth of sentences with “ t h a t ” -c l a u s e sby de ny i n gt h a t“ t h a t ” -clauses are singular terms, and by denying T-sentences for what looks like quantifications over propositions. It may seem, however, that the nominalist need not make the unattractive move of denying T-sentences. After all, if the analyses show how sentences l i ke “ Some t hi n gi s be l i e v e d” a nd “ The r ea r et h i n g s be l i e v e d( k n o wn , assumed, e t c . ) ”c a nbet r u ewi t h o utc o mmi t me n tt op r o po s i t i o n s ,wh ys h o u l d it not be possible to endorse such sentences in the semantics, thus abandoning ( NC) ?Bu tgi v e nho w“ p r o po s i t i on ”i sus e di ni t sphi l o s o ph i c a ls e n s e ,t h e s e n t e n c e“ The r ea r ep r o po s i t i on s ”j us t follows from such sentences. So, this no mi n a l i s th a sa l s ot oa dmi tt h a t“ Th e r ea r epr o p o s i t i o n s ”i st r u e .Si n c et r u e s e n t e n c e sa r ee n do r s e do nt hi ss t r a t e gy ,t h er e a l i s t ‟ so wn c l a i m wi l lbe explicitly asserted. It therefore seems that the truth-conditionalist nominalist must either deny the T-sentences after all, or find some way of distinguishing s e n t e n c e sl i ke“ Th e r ea r et hi n g sbe l i e ve d( kn own ,a s s u me d ,e t c . ) ”f r om “ The r ea r epr o po s i t i on s ” .Bu tt hei n t e n to ft hel a t t e rs i mpl yi st os a yt h es a me as the former. So, if, as seems plausible, they cannot be distinguished in the relevant way, the nominalist must deny the T-sentences after all. But there is a f ur t h e ri mpl a u s i bl ec o n s e q ue nc eoft hi s .Si n c e“ Th e r ea r et h i n g sbe l i e v e d ( kn own ,a s s ume d ,e t c . ) ”a n d“ Th e r ea r ep r o po s i t i o n s ”c a n n o tbed i s t i nguished in the relevant way, the latter must be held to follow from the former. But t h e n ,“ Th e r ea r ep r o po s i t i o n s ”mus tbehe l dt r ue .Howe ve r ,i tc a n n o tbeg i v e n
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a homophonic T-sentence. When giving the semantics for this sentence, then, i tmus tbehe l dt od i v e r ger a d i c a l l yf r om,e . g . ,“ Th e r ea r es t o n e s ” . What, then, is the positive account of paraphrase nominalists? Rudimentary varieties of this idea were vented in the middle ages, e.g., in Oc kh a m‟ s“ t he o r yofe xpo s i t i on ”( s e e ,e . g . ,Fr e d do s oa n dSc h u ur ma n( 19 8 0: II.11)). Modern paraphrase nominalism may be seen as a syntactico-semantic analysis for a certain range of expressions in natural languages, which exploits various formal methods in support of their ontological view. On these t he o r i e s ,“ t h a t ” -clauses are typically not regarded as proper syntactic units e v e nonas upe r f i c i a ll e ve l( l e ta l onea ss i n g ul a rt e r ms ) .Ra t h e r ,as e n t e n c e“ x Vs that p”i sa n a l y z e da sc o n s i s t i ngo fal e f t -most noun-phrase left, a rightmo s ts e n t e n c e ,a n dt h ee xp r e s s i on“ Vst h a t ” ,t ober e g a r d e ds y n t a c t i c a l l y 1 rather as a function from a sentence to a predicate. Prior also proposed that wh a tl o ok sl i keq ua n t i f i c a t i onove rpr o p o s i t i o n s ,e . g . ,“ Hes a y se v e r y t h i n gI be l i e v e ”i st obet r e a t e da sh a v i nga si t s“ l o gi c a lf o r m”apr o p o sitionally q ua n t i f i e ds e n t e nc e ,“ ( p)(If I believe that p, then he says that p” .The s ec l a i ms mus tbet a ke nt oc on c e r ns yn t a c t i c“ d e e ps t r u c t ur e ”o r“ l o g i c a lf o r m” ,f o r clearly, this natural language sentence has the same superficial form as, e.g., “ Hes t o l ee ve r y t h i ngIown ” .Pr i o r ‟ sp r o p o s i t i o n a l l yq ua n t i f i e dp a r a p h r a s e does not obviously give the wrong meaning to the target sentence. But one may wonder why the similarity (or identity, if you will) of meaning should give any evidence for a syntactic claim. The very idea of deep structure or logical forms has been hotly debated, and what is known for sure is only that it will be long before there is agreement on the number, meaning and existence of syntactic and semantic levels. It is thus far from a firm ground on which to base a nominalistic project. Nominalists who distinguish syntactic levels do so for merely semantic reasons, why it may be difficult to see why syntax is brought up at all. Let me clarify this point by an example. A common argument against various propo s a l so fpa r a ph r a s en o mi n a l i s t si st h a t ,e . g . ,t hee xpr e s s i o n“ t h ea v e r a g ex” s e e msmo r ea p tf o r“ p a r a ph r a s i n ga wa y ”t h a nt heno mi n a l i s t ‟ st a r g e to f paraphrase. For instance, when giving, as a paraphras eo f“ Thea v e r a g eAme r i c a nh a s2. 3c hi l d r e n ” ,t h es e n t e n c e“ Ame r i c a n s ,o na v e r a g e ,h a v e2 . 3 c h i l d r e n ” ,o nes e e mst og i veapl a us i bl ea c c o un to fwh a twemean by the l a t t e r .Th e n ,t hi si sc on t r a s t e dt ot heno mi n a l i s tp r o p os a l ,wh e r e ,e . g . ,“ 3i sa 1
This view is endorsed, more or less explicitly, by Russell (1910), (1912: XII), Quine (1960: 216), Prior (1971: 16ff.), Tye (1989), and Matthews (1994), and it receives a very elaborated treatment in Moltmann (2003).
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pr i me ”i spa r a ph r a s e da s“ Th es e n t e n c e„ 3i sp r i me ‟f o l l owsf r o mt he a xi oms ” ,whi c hs e e mst oa s c r i bet hewr ongme a ni n gt ot h es e n t e n c e .Th e s e observations are often fine as far as they go. But it may be surprising that one t a k e st hi st os h ow t h a tt h ea n a l y s i sof“ t h ea v e r a g eAme r i c a n ”i sabe t t e r syntactic a n a l y s i s .Ev e ngi ve nt h a tt hepa r a p h r a s er e a l l ydo e sgi v et h e“ r e a l me a n i ng ”o ft hes e n t e n c ec on t a i ni ng“ t h ea ve r a g eAme r i c a n ”( wh a t e v e rt h a ti s supposed to mean), some further argument is needed in order to show that this has any relevance for syntax. Nominalists in general, including myself, are sympathetic to the idea that it is superficial grammar that lures people into realism. But one is not required to elaborate this idea by distinguishing different syntactic layers. A fortiori, on ene e dno tma k et heq ui xo t i cc l a i mt h a t“ t h a t ” -clauses are not syntactic un i t s .On ec a nt a ke“ t h a t ” -clauses to be singular terms, and simply say that not all of these refer to objects, and that realism is the result of overgeneralising from referring singular terms. Propositions are avoided, and without exotic linguistic analysis, by taking certain syntactically cotypical expressions to have radically different types of semantic functioning. We know that, e.g., noun-phrases, like quantifiers and names, have radically different semantic functioning, so why not singular terms? In section 5.4, we wi l ls e eh owt ot r e a t“ t h a t ” -clauses as singular terms without commitment to propositions. It would also be better, and more in line with current linguistics, to treat all superficially similar quantifications the same way, contrary to Pr i o r ‟ sa n a l y s i s .I ns e c t i o n5. 5,wewi l ls ho wt od ot h i si no be d i e n c eo f( NC) . The important lesson of these sections is that this can only be done with a non-alethic semantics, if we are to avoid the consequences here highlighted: the counter-intuitive truth-conditions of various sentences, the unnatural s yn t a c t i ca n a l y s e sa n dt h er e s ul tt h a t“ Th e r ea r ep r o po s i t i o n s ”i sj ud g e dt r u e . Paraphrase nominalism has been somewhat replaced by fictionalist strategies for nominalists who endorse truth-theoretic semantics (e.g., Field (1980), (1989)). On this view, ordinary intuitions and use are supposed to be accounted for by the positive value of truth in a fiction. Thus, the sentence “ 1+1=2 ”i sn o tl i t e r a l l yt r u e ,buto nl yt r uei nt h eus e f ulf i c t i o no fma t h e matics, j us ta s“ Sh e r l oc kHo l me si sade t e c t i ve ”i sno tl i t e r a l l yt r u e ,b u tt r u ei nt h e novels by Conan A. Doyle. This is supposed to avoid both the syntactic claims of paraphrase nominalism and the strange consequences of nonf a c t ua l i s tt he o r i e ss uc ha se xpr e s s i vi s m.I ti sn o to bv i o u sj u s th o w“ t r u t h t h e o r e t i c ”s u c hs e ma n t i c si s ,howe ve r .I np a r t i c ul a r ,o nema ywo n d e rh o w mu c hwo ul dbel o s tb yr e p h r a s i n ga wa y“ t r ue ” .From the claim that a sentence
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is true in the fiction (as opposed to just true), the sentence should not itself f ol l o w,i fno mi n a l i s mi st obede f e nde d .Wh a ti n t u i t i ve l yf o l l o wsf r o m“ „ p‟i s t r uei nt h ef i c t i o n ” ,h owe v e r ,i s“ I nt hef i c t i on ,p” .Co ul do n enot then simply r e pl a c e“ si st r u ei nt hef i c t i on”wi t h ,“ si sa f f i r me db yt h ef i c t i o n ” ,o rs o me s uc h ?I tma ybea l s ot h a t“ t r ue ”onl ypl a y sap u r e l ydi s quotational role here, i . e . ,t h a ti ti sus e do n l yt oe xpr e s st hei n f i n i t e l yma nyi n s t a n c e so f“ I nt h e fiction, p” ,whe r e“ p”i st ober e pl a c e dbya p pr o p r i a t ema t he ma t i c a l s e n t e nc e s . If so, then the semantics will not be truth-theoretic. The fictionalist will then rather explain mathematics by providing a theory of how mathematicians create a fiction and how things can be or become the case in this fiction. It is not obvious how much similarity can plausibly be claimed between mathematics and the paradigmatic cases of fictional truth besides the negative property of not being literally true. Proving mathematical theorems is quite unlike creating or consuming narratives (writing or reading novels, etc.), which are the known ways of determining what is true in a fiction. What is true in a fiction is determined by fiat and with complete freedom by an individual author or artist, while mathematicians are obliged to operate within certain bounds, e.g., respecting the law of non-contradiction (Katz (1998: 12ff.)) and requiring evidence of some kind (Resnik (1997: 188f.)). I think such considerations shows that the appeal to fiction is more charitably interpreted as a gesture toward the view that the acceptance of the sentences in question are not to be accounted for in terms of their truth proper, but some other way. The positive theory in terms of fiction seems possible to replace for an explicitly non-alethic theory without great loss for a nominalist. In the actual positive accounts given by fictionalists, acceptable mathematical s e n t e n c e ss e e m mu c ht obec a l l e d“ t r uei nf i c t i on ”i nn a meo n l y ,a n dt he positive similarities with paradigmatic cases of truth in fiction are downplayed. It is of course necessary to deny many similarities for the theory to avoid gross implausibility. But when the obvious differences between paradigmatic fiction and mathematics have been dealt with, mostly negative features remain. Therefore, I do not see that there should be any loss at all, gi v e nt hef i c t i o n a l i s t s ‟g e n e r a l( pr e -semantic) desiderata, if one were to r e pl a c e“ si st r u ei nt h ef i c t i o no fma t h e ma t i c s ”wi t hs ome t h i n gl i k e“ t h erules of mathematics legitimate (or mandate) the acceptance of s” .Th e ys e e m equally well suited to explain linguistic behaviour, and differ only in that the fictionalist account claims some connection to paradigmatic fiction. If so, then this goes to support the original point: that from a nominalist perspective, some non-alethic property is better suited to account for the discourse.
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As concerns propositions specifically, the fictionalist would presumably s pe a ko fs e n t e nc e swi t h“ t h a t ” -clauses being true in the fiction of folkpsychology and folk-semantics. Here, there is an element that does not arise in t h ec a s eo fma t he ma t i c s :s pe a ke r s ‟c o r r e c tj ud gme nt sv a r yd e pe n d i n go n empirical circumstances. Presumably, folk-psychology is here taken to be a theory which states relations between behaviour and propositional attitudes. Here, there seems again to be no obvious reason why we should claim that the sentences licensed by this theory (given empirical evidence about behaviour) s ho u l d be c a l l e d“ t r ue ( gi ve n the behaviour) in the fiction of folkps y c ho l og y” ,r a t h e rt h a nme r e l y“ l i c e n s e d( g i v e nt hebe h a v i o u r )byt h er u l e s of folk-p s y c hol og y ” .Fu r t h e r ,af i c t i o n a l i s ta bo utpr o po s i t i on swi l ln o t ,o f course, believe that there is a reduction of propositional attitudes to behaviour, i.e., necessary equivalences relating them. Rather, it should be possible for one ascription of propositional attitudes to be licensed by the facts about behaviour at one moment, and an incompatible sentence to be licensed later, as new facts about behaviour have emerged. Either, then, contradictions are taken as true in this fiction, or what is true is taken to change over time. This predicament is common for justification, of course, but one hesitates to say that the truth-value changes, or that the sentence in such a situation is both true and false. If so, then a normative, non-alethic positive property of sentences would be better to appeal to than truth in a fiction. We will now look closer at the nominalist response to the realist‟ s argument from intuition, which is that the intuition itself is simply a fact of usage, which is to be explained by a nominalist semantics. (A truthconditionalist can also make this move, but, as we have seen, this entails paraphrase nominalism.) The final, nominalist semantics must ascribe a positive semantic value to the sentences that speakers assent to (and that nominalists assent to when doing semantics in the material mode), but which (NC) forbids us to use in the semantics. A fortiori, it will claim that the s e n t e n c e“ The r ea r ep r o po s i t i on s( i . e . ,t hi n g so nema ybe l i e v e ,k n o w,e t c . ) ”i s a n a l y t i c ,be c a us ei ti sa ni nf e r e nc ef r om a n a l y t i cs e n t e n c e sl i k e“ Th a tb a c h e l o r sa r eu nma r r i e di st r ue ” .How,t he n ,i s“ a n a l y t i c ”t obeun d e r s t o o d ?Ii n t e n d to use it, in a use-theoretic spirit, as cognate to the notion of inference that has been used throughout. Intuitively, if B can be inferred from A, then the assertibility of A guarantees that of B. That is, if A is assertible, no further sentence needs to be assertible for B to be. This much simply lies in the notion of inference. Also the truth-conditionalist grants a corresponding guarantee, bu ts pe a k si n s t e a do fas e n t e nc e ‟ st r ut hg ua r a n t e e i n gt h a to fa n o t h e r .Ont he
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present account, an analytic sentence is then just a sentence which is guaranteed to be assertible independently of what other sentences are a s s e r t i b l e .Fo rt h i sus eo f“ a n a l y t i c ”t ode f e a tt hes t r a t e g y ,i tmu s ts o me h ow bes ho wnt h a tt hec l a i mt h a t“ p”i sa n a l y t i ce n t a i l st h a tp. For then, the claim t h a t“ The r ea r epr o po s i t i on s ”i sa n a l y t i c( a n dt h a tv a r i o u ss e n t e n c e swi t h “ t h a t ” -clauses are analytic) entails that there are propositions. To show that this holds, one must show that any elucidation of analyticity or inference available to the deflationist must have this consequence. But this does not ho l df o rt hec a nd i d a t e sa c t ua l l ya do pt e dbyv a r i o u sde f l a t i o n i s t sa n d“ u s e t he o r i s t s ” .Fo ri n s t a n c e ,t h ec l a i mt h a ts pe a k e r sun c on d i t i o n a l l ya s s e n tt o“ p” does not entail that p, nor does the claim that as e n t e nc e“ p”i sa s s e r t i bl e ,on many elucidations of this notion. For instance, that speakers reinforce the ut t e r a n c eo fo ra s s e n tt o“ p”( c f .5. 7)do e sn o th a v et hec on s e q ue n c et h a tp, no rd oe st h ec l a i mt h a tt he r ei save r i f i c a t i onf o r“ p” .Si n c et y pi c a l usetheoretic proposals for elucidating analyticity do not have this feature, I do not s e et h a tt h e r ei sa n yr i s kt h a tc a l l i ng“ Th e r ea r epr opo s i t i o n s ”a n a l y t i cwi l l vi o l a t e( NC) .I np a r t i c ul a r ,g i ve nt h a tt h es t e pf r om “ p”t o“ Th a tp i st r ue ”i s merely stipulated as unconditionally assertibility-preserving, the consequences of the claim that the latter is assertible will be identical with the consequences of the claim that the former is. So, the assertibility conditions of “ Sn ow i swhi t e ”a r ei de n t i c a lt ot ho s eo f“ Th a ts n o wi swh i t ei st r ue ” .I ft he claim that the former is assertible does not entail the existence of abstract objects, nor will the claim that the latter is assertible. Similarly, as we will see i n 5. 6 ,t he de r i v a t i on o f“ The r ea r ep r o po s i t i o n s ”f r o m a n ys e n t e n c e c o n t a i ni n ga“ t h a t ” -clause is taken as unconditionally assertibility-preserving byt h es t i p ul a t i ono f“ p r o p o s i t i on” . Ac c e pt i n gt h a ts e n t e n c e swi t h“ t h a t ” -clauses entail existential sentences is similarly to be explained as consisting in the fact that the assertibility of any s e n t e n c eo ft hef o r m“ F(that p) ”g u a r a n t e e st h ea s s e r t i bi l i t yo ft h ec o r r e s po ndi ng“ F( s ome t h i ng) ” ,wh i c hi sac o n s e q ue nc eo ft hef a c tt h a t“ t h a t ” clauses are introduced as singular terms. The apparent connection between truth and validity is again taken as fact of usage, as in 3.4, where this intuition wa se xpl a i ne dbyr e f e r e n c et ot hede f l a t i on a r yt h e o r yo f“ t r u e ” .Si mi l a r l y ,o u r i n t u i t i ont h a tt hes e n t e n c e“ Webe l i e vet h i n g s ”i strue, is to be treated as a fact of usage, namely the fact that we are strongly disposed to assent to the s e n t e n c e“ „ Webe l i e v et hi ng s ‟i st r ue ” ,whi c hi nt u r ni st obeun d e r s t o o dby (D), (ST), and other linguistic facts. The same move is made in response to the realist argument from si ng ul a rt e r ms ,t h a t“ Kr i p k ebe l i e ve st h a ts now i s
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whi t e ”i st r ue ,s ot he r emus tbes omet hi ngr e f e r r e dt obyt h et e r m,wh i c hi s what Kripke believes. To object that there is more to account for than the correct assent to these sentences, namely that we really seem to believe things, and that it the sentence about Kripke really is true and entails that there are propositions, is to require, unreasonably, that the nominalist is to take the existence of propositions as a datum. Our (unconditional) assent to the relevant sentences is the only uncontroversial fact, and so, the only one that needs explaining. A successful semantics which satisfies (NC) may be regarded as required by nominalism, but not something that furthers its case positively. But I believe a successful nominalist semantics also has the effect of neutralizing realist intuitions which would tip the balance in favour of nominalism. For if the semantic theory succeeds in explaining the uncontroversial facts about our us eo f“ t h a t ” -clauses and expressions that take them as objects (attitude verbs, “ t r ue ” ,e t c . ) ,t he ni twi l la l s oe xpl a i nwhyt h er e a l i s t s ‟v e r yn a t u r a lq ue s t i o n s and objections make sense in the first place. Among the explanantia here will be such facts as the validity of existential generalisation and that we have a t e nde n c yt oa s k ,q ue s t i on so ft hef o r m“ Wh a ta r eFs ? ”wh e nweh a v ea meaningful general term, and so on. We can see already that relevant q ue s t i on sl i ke“ Wh a ta r et h e s et hi ng swebe l i e ve ? ”a n d“ Dot h e ye xi s t ? ”a r e clearly well-formed, and that they are of the same form as various questions which do h a vei n t e r e s t i nga n di n f o r ma t i vea n s we r s ,f o ri n s t a n c e ,“ Wh a ta r e s t a r s ? ” ,“ Do e sph l o gi s t o ne x i s to rno t ? ” .So ,if the semantic theory succeeds, we will also have explained why these questions seem fair and legitimate in the first place, since it is simply a linguistic datum that they are. However, t h e s eq ue s t i o n swi l li nt h ee ndbee xpl a i ne da so napa rwi t h ,“ Bu twh oi st h i s a ve r a g epe r s on ? ” ,o nl yl e s so bv i o us l ys o .Th u s ,i fawell-formed question cannot be straightforwardly answered, this fact should itself be satisfyingly explained by the theory. The most important linguistic account of realist i n t u i t i on s ,h owe v e r ,wi l lde r i vef r omt hec l a i mt h a t“ t h a t ” -clauses are singular terms, and the intralinguistic, inferential characterization of this notion. Singular terms are essentially such as to make it prima facie reasonable to take them to refer. Existential generalisation, for instance, must be taken either as a criterion or a symptom of being a singular term, and this inference step is also a reason why we should wonder what thing is it that is said to be believed, known, etc. That way, the execution of the nominalistic semantic project will also be a polemic move in the ontological debate. The intuition that there clearly seem
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to be propositions, and that they are sometimes true, is the kind of thing realists will take to be arguments in their favour. But if these phenomena are regarded as pieces of linguistic data that can be explained in obedience of (NC), then the rug is in a way pulled from under the realist. We agree that wh a tt her e a l i s t sa c c e pt s ,l i k e“ The r ea r et r uep r o po s i t i o n s ” ,i sa n a l y t i c .Bu t since analyticity does not entail truth, we are not defeated by the obvious pl a us i bi l i t yo ft h er e a l i s t ‟ sa s s e r t i o n s .Co mmons e n s ei sn o tv i o l a t e d ,s i n c et he utterances are counted as correct in the same sense as other unproblematic ut t e r a n c e s ,e . g . ,o f“ Sn owi swhi t e ” ,s i n c et hes e n s eo f“ c o r r e c t ”t h a ti su s e di n the semantics is plausibly the same for all sentences. The difference, as noted above, will only concern the type of conditions for the utterance to be correct. Wi t h“ Sn ow i swhi t e ” ,t her e f e r e n tof“ s now”( na me l y ,s n o w)ma y be appealed to in stating the correctness condit i o n so f“ Sn ow i swh i t e ” ,b ut no t h i ngt h a tc a nbet a ke na st her e f e r e n to fa“ t h a t ” -clause will be appealed to in stating the correctness conditions for sentences containing it. Likewise, the correctness-c on d i t i o n so fs e n t e n c e sc o n t a i n i ng“ wh i t e ”( a so p po s e dt o“ t r u e ” ) ma ybes t a t e dbyu s i ng“ whi t e ”( mo r eo nt hi si n5 . 7 ) .Ev e ni ft h es e ma n t i c c o n t e n tof“ wh i t e ”we r eg i ve ne n t i r e l ywi t h o uts u c hme n t i o n ,b u t ,e . g . ,b y reference to a private quale (which I find very implausible), there will still be a causal story relating the word to white things (via the quale). But there will benoc a u s a ls t o r yr e l a t i n g“ t r ue ”t ot r u et h i n g so r“ t h a t ” -clauses to their a l l e ge dr e f e r e n t s .Ev e no ns uc hat he o r y ,“ t r u e ”wo ul db ed i s t i n g ui s h e df r om “ whi t e ”i nt h a tt hes e ma n t i ca c c o un to f“ wh i t e ”wo ul dn o tbee xh a us t i veo f wh i t e n e s s .Th ei de a ,t h e n ,i st h a ti ft her e a l i s t ‟ sut t e r a n c e sc a nbee x pl a i n e d consistently with the denial of propositions, then they no longer constitute an argument for realism. The trick is to explain linguistic behaviour in nonr e pr e s e n t a t i on a lt e r ms ,a ndt ot a ket hepl a us i bi l i t yo ft her e a l i s t ‟ sa s s e r t i o n sa s just another fact of usage. The final arbiter, here as everywhere, should be the dispersion of mystery, but the impossibility of giving a straight answer to a question is no mystery if it can be predicted by an otherwise satisfactory theory. The only possible refutation of this view, as far as I can see, would consist in showing that there is some uncontroversial datum that cannot be explained without commitment to propositions. But this argument cannot be a n y t hi n gl i ke“ Pr o po s i t i on se xi s t ,s i nc ei ti sat r ui s mt h a tpe o p l ebe l i e ve t h i n g s ,e t c . ” . Above, I intended to show that nominalism can be made more plausible by combining it with a non-alethic semantics, which, in turn, is mandated by deflationism. But it also seems that the kind of deflationism defended above
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requires nominalism. Or, at least, it is not plausibly combined with the view t h a t“ t h a t ” -clauses refer to objects (i.e., propositions), even if it may be difficult to find a conclusive argument that it excludes it. Consider (D), which i sme a n tt ogi v ea ne xh a u s t i ves e ma n t i ca c c o un to f“ t r u e ” .No ws u p p o s et h a t “ t h a t ” -clauses refer to propositions. It seems reasonable that when a predicate applies primarily to a certain type of term, and these terms refer to a certain kind of object, the semantic account of the predicate should somehow mention t h e s eo bj e c t s .Fo rp r e s e n tpur po s e s ,i f“ t h a t ” -clauses refer to propositions, t h e n“ t r ue ”s h o ul dbet a k e nto describe these objects. But since (D) is meant to give an exhaustive s e ma n t i cc h a r a c t e r i z a t i o no f“ t r u e ” ,i ti sh a r dt os e eh ow i tc a ne xp l a i nwh a tc on ne c t i on“ t r ue ”h a swi t hp r o pos i t i o n sa ta l l .Pr i n c i pl e (D) is wholly intralinguistic, so any alleged re f e r e n to fa“ t h a t ” -clause would pl a yn or o l ei na c c o un t i n gf o rs e n t e n c e soft h ef o r m“ Th a tp i st r u e ” .Fo rt h e s e a r ej u s tt obec o n s i de r e da se q ui v a l e n tt ot hec o r r e s p on d i n g“ p” ,a n dt h a t , together with facts about other expressions, is meant to explain all ( s e ma n t i c a l l yr e l e v a n t )f a c t sa bo uto uru s eo f“ t r ue ” .I na l lo t h e rc a s e so f referring terms, one takes sentences containing them to say something about the object, to have truth- or assertibility-conditions depending on what is the case concerning the object, or some other way make essential use of the referent. Even when the predicate is given a non-factualist analysis, as pe r h a p st hepr e d i c a t ei n“ a i sbe a ut i f ul ” ,t h es e ma n t i ca c c o un twi l ls t i l l mention the object. One might hold, for instance, that this sentence is used to a e s t he t i c a l l yc o mme ndt h er e f e r e n to ft het e r m“ a” ,o rs omes u c h .I f“ t h a t ” c l a us e sh a ver e f e r e n t s ,ho l d i ngt h a t( D)i se xh a u s t i veo f“ t r u e ”wo ul dma k e s e n t e n c e so ft hef o r m“ Th a tp i st r ue ”as ome wh a tmy s t e r i o u se xc e pt i o n . The idea ma y bec l a r i f i e d by f o c u s s i n g mo r eo ns p e a k e r s ‟s e ma n t i c c o mpe t e n c e .I f“ t h a t ” -c l a us e sr e f e rt op r o po s i t i o n s ,c ompe t e n tu s e r sof“ t h a t ” c l a us e smu s th a v es o meg r a s po fpr o po s i t i on s .Buti f“ t r u e ”p r i ma r i l ya p p l i e s t o“ t h a t ” -clauses, then competent users o f“ t r u e ” ,i ts e e ms ,mu s ta l s oh a ve some grasp of what is said about a proposition when a sentence of the form “ Th a tp i st r u e ”i sut t e r e d .Th i ss e e mst r i v i a l l yt obet r u ei nu nc on troversial c a s e so fr e f e r r i ngt e r ms .Co mpe t e n tus e r so f“ r e d ”o bvi o u s l yh a v e some grasp of what an object, referred to by a term t,mus tb el i k ewh e n“ ti sr e d”i st obe accepted, or is true. They know what the sentence says about the object, and so on. But the claim that (D) gives an exhaustive semantic acc o un tof“ t r u e ” leaves nor o omf o ra n ye xpl a n a t i o no fhow“ t r ue ”r e l a t e st opr o po s i t i o n s .Th i s i sr e a s on a bl ys ome t hi n gc o mpe t e n tus e r so f“ t r u e ”s ho u l dk n o ws o me t h i n g a bo u t ,i f“ t h a t ” -clauses refer to propositions. Since it was shown in Chapter 3
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that no deflationary theory can be properly formulated unless it gives a purely metalinguistic claim, it seems that any properly formulated deflationism will bei nt e n s i onwi t ht h ev i e wt h a tt het e r mst owh i c h“ i st r ue ”p r i ma r i l ya p p l i e s refer to objects. Any such theory must be wholly intralinguistic, and is supposed to give an exhaustive semantic account, so how can it possibly do j us t i c et ot hei de at h a t“ i st r ue ”r e l a t e si ns omes e ma nt i c a l l ye s s e n t i a lwa yt o the objects? I f“ t h a t ” -clauses are not taken to refer to anything, however, the mystery di s a ppe a r s .“ Th a t ” -clauses are regarded as term-like expressions, following the subject-predicate form that natural languages love so much, which must be coupled with predicates in order that proper sentences be formed. Given a semantic account like (D), further, it can be shown to enable the expressive strengthening witnessed in 1.4, and the rest of the story was given in Chapter 4. This story may be doubted, of course, but the present point is only that no mi n a l i s m wi t hr e s pe c tt o“ t h a t ” -clauses avoids a mystery that deflationists wo ul dh a vet oe x pl a i ni f“ t h a t ” -clauses are taken to be referring expressions.
5.4 THE INTRALINGUISTIC NOTION OF S INGULAR TERM I nt hi ss e c t i o n ,Iwi l la r g u et h a t“ t h a t ” -clauses are to be seen as syntactic units, and, more precisely, as singular terms. We may cautiously note, though, that mo s to ft hes e ma n t i ca c c o un t sofv a r i o uso c c u r r e n c e so f“ t r u e ”i n4 . 3d on o t ne e dt h ec h a r a c t e r i z a t i ono f“ t h a t ” -clauses as singular terms, but only the uncontroversial observation that“ t h a t ” -clauses behave in some important ways as paradigmatic singular terms. Those resemblances were exploited in that section, but one need not agree that there are any further common denominators in order to accept those explanations. But fair is fair. We will here also see that the notion of singular term is a bipartite notion with a syntactic component and a logico-semantic one. The discussion of the claim t h a t“ t h a t ” -clauses are singular terms will accordingly be split in two, and we will begin with the syntactic part. Th es yn t a c t i c“ c o mpo n e n t ”o ft hen o t i ono fs i n g ul a rt e r mi st h ec o n d i t i on that any singular term is a syntactic unit, and, more precisely, a noun-phrase. We may give an intuitive explanation of the notion of a unit by giving examples of what is reasonably not a syntactic unit. In the sentence preceding
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t h i sone ,t h es e q ue n c e“ n o t i onbygi vi ng ”i sno tr e a s o n a b l yt a k e na sau n i t . How exactly to define the notion may be debatable, but it seems fairly clear that it has to do with which categories to use when stating grammatical rules o rge ne r a l i s a t i o n s .I tma ybet h a ti naf i n a l ,“ i d e a l ”t h e o r yo fg r a mma r , o r d i n a r yg r a mma t i c a lc a t e g o r i e sl i ke“ no unph r a s e ”wi l ln o tbeu s e d ,j u s ta sa final physics will probably not use the category of cups, teeth, wood, etc. But traditional syntactic notions will still be seen, from the perspective of the final t h e o r y ,t oowns omer e a l i t y ,whi c hwi l lj us t i f yt heu s eo ft h e s e“ h i g h e r -l e v e l ” , vaguer but pragmatically indispensable, categories. That is, the idea that s t a t i n gge ne r a l i s a t i on sus i n g“ no unph r a s e ” ,r a t h e rt ha ns o met e r mc o v e r i n g “ n o t i o nbyg i v i n g” ,a su s e di nt hea boves e n t e n c e ,wi l ls u r e l ybej u s t i f i e dby the ideal final theory of grammar in that it yields better generalisations, even if they are not perfect like those in the ideal, final theory. Now,t he r ei spl e n t yo fi n t ui t i v ea nd“ n a ï ve ”e vi d e nc et h a t“ t h a t ” -clauses a r es y n t a c t i cun i t s ,a n dt r a d i t i on a l“ s c h oolg r a mma r s ”a c c o r d i n g l yc a t e g o r i z e t h e ma n do t h e r“ s e n t e n t i a l ”e xpr e s s i on t h a tbe h a v ea snoun phrases as nominal clauses. For instance, the simplest and most typical kind of occ u r r e n c eo fa“ t h a t ” -clause is in a sentence which seems superficially to combine it with a one-place predicate. This may be a copula and an adjective ( “ i st r u e ” ) ,ano unph r a s ea ndat r a n s i t i v ev e r b( “ Hebe l i e v e s ” ) ,a n ds oo n . School grammars usually do not say that they are noun phrases, however, since these are defined as having a noun as its head. However, this seems like an unmotivated complication. Instead, cotypicality should be determined by external relations to other expressions, and having a noun as head should be considered just as irrelevant for syntax as, e.g., containing a certain number of words. Ta k i n g“ t h a t ” -clauses as noun-phrases will license sentences l i k e“ He be l i e v e st h eEi f f e lTo we r ”a sg r a mma t i c a l ,o fc o ur s e ,b u tt r a d i t i o n a lg r a mma r sa l s ol i c e n s e“ He d r a nk pr o c r a s t i n a t i on ” ,e t c .Th e s es e n t e n c e sa r e semantically anomalous, not ungrammatical. The idea that they are ungrammatical seems to stem from two further ideas. First, the common but dubious idea that synonymous sentences must somehow share syntactic structure (and vice versa). Secondly, the idea that these semantically a n oma l o u ss e n t e n c e sa r e“ me a ni ng l e s s ” .I ti sn o to bv i o u st h a tt h e ya r e , however. They might simply be taken as (trivially) false, hence meaningful. Th ema i npr o bl e m wi t ht h i si de a ,howe ve r ,i st h a t“ me a n i n g ”a n d“ me a n i n g f u l ne s s ”a r et o oc o a r s e -grained to be applied thus uncritically. There is an o bv i o usdi f f e r e n c ebe t we e n“ Hebe l i e ve st heEi f f e lTo we r ”a nd“ Ga gr a t h
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bl a y t ”o r“ Runwi t hs i t st h e r e ” .Then a r r o we rno t i o no fs e ma n t i ca n o ma l y be t t e rc h a r a c t e r i z e s“ Hebe l i e ve st heEi f f e lTowe r ” ,a n dt h ec o n t r a s tb e t we e n this sentence and the other incorrect sentences should make it clearer that it should not be called ungrammatical. What may seem worse, however, is that this account also has to allow as grammatical (?)
John is to the left of that snow is white.2
Intuitions are unreliable here, however. As explained in note 4, Chapter 4, t he r ea r e“ c e n t r e -br a n c hi n g ”s e n t e n c e swh i c ha p pe a ru n g r a mma t i c a l ,l i ke “ Th ema nt hebo yt heg i r lk i s s e dme tr a n ” ,whi c ha r eg r a mma t i c a l ,b u ta r e constructed according to the rules in such a way that we are unable to parse them correctly. Given that (?) is so obviously semantically anomalous, it is not clear how to classify its incorrectness. A positive argument for taking (?) as grammatical, however, might be the intelligibility of the following. There are things believed, e.g., that snow is white, and so on. These things may, strange as it seems, be to the left or right of people. For instance, the thing I most firmly believe, that snow is white, is to the right of John. So, that snow is white is to the right of John. That is, John is to the left of that snow is white. Try pronouncing the last sentence with appropriate pauses and stresses. Well, it still feels a bit wrong, but the penultimate sentence does not, and this seems to force us to take (?) as grammatical after all, and explain its awkwardness in terms of the specific order of phrases. I nt hee nd ,t he r ei sa l wa y st h er e t r e a tpo s i t i o noft a k i n g“ t h a t ” -clauses to be me r e l ynomi n a lc l a us e s .Un t i lpr ove nwr o n g ,ho we v e r ,wet a k e“ t h a t ” -clauses t obeno unph r a s e s ,ont h epr e s e n tus eoft h et e r m“ n o unph r a s e ” .Ont he t r a d i t i on a ld e f i ni t i ono f“ no unph r a s e ” ,myc l a i mi st h a tn o unph r a s e sa n d “ t h a t ” -clauses belong to the same category, and that a further division between them will be syntactically superfluous. The point of showing that “ t h a t ” -clauses are noun-phrases is that it makes it easier to defend the claim that realists err in linguistic over-generalisation. Together with the fact that “ t h a t ” -clauses are also logico-semantically singular terms, it is only understandable that one should take them to be like singular terms that are also typical traditional noun phrases, i.e., referring expressions. The more reasona b l eo nec a nma k et h evi e wt h a t“ t h a t ” -clauses refer, consistently with the denial with this claim, the better the chances of neutralizing realist intuitions. 2
I owe this example to Peter Pagin.
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Wh a ti st hepo s i t i v ee vi de n c e ,t h e n ,f o rt hec l a i mt h a t“ t h a t ” -clauses, pace Prior, are syntactic units? There is too much of it to rehearse here, but we may here provide a sample for the uninitiated. One piece of evidence comes from spl i t t i n g .Wed on o ts a y ,* “ I ti st r uet h a t ,Ipr e s ume ,p” ,b u t ,“ I ti st r u e ,I presume, that p” .Th i s ,a smo s ta r g ume n t so nt h e s ei s s ue s ,i sago o di nd i cation bu tn o tc on c l us i v ee v i de n c e .Si nc ema ny be l i e vet h a t“ t h a t ” -clauses are singular terms, indeed, referring expressions, it is to be expected that there is more to their behaviour that indicates that they are syntactic units. There is thus the case of existential generalisation, noted above, the fact that we say “ Th a ts n o wi swh i t ei st h emo s to r d i n a r yt h i ngt os a y ” ,a n dma n yf ur t h e rmo r e or less hackneyed examples that need not be listed here.3 The syntactic condition upon singular terms should now be supplemented with a logico-semantic one, which it is more difficult to state.4 One can provide various specific criteria, pertaining to inferential relations between sentences containing the expressions and others, but it is not clear which should be regarded as symptoms of the correct constraint, and which are to be regarded as parts of the constraint itself. One thing that intuitively indicates t h a t“ t h a t ” -c l a u s e sa r es i n g ul a rt e r msi st h a twec a nde r i vef r om “ Kr i p k e be l i e v e st h a ts no wi swhi t e ” ,t hes e n t e nc e“ Th ething Kripke believes is that s no wi swhi t e ” .Butt h i ss h o ul dpl a us i bl ybet a k e na sac o n s e q uence of the de f i ni t i o no f“ s i n g ul a rt e r m” ,t oge t he rwi t ht h es e ma n t i c so f“ t h i n g ” ,r a t h e r than being in the condition itself. What is important is that the constraints be intralinguistic, more precisely, inferential, rather than one that requires an extralinguistic property. Those insisting on an extralinguistic criterion will typically take this to be reference to an object. One cannot deny that some singular terms refer to objects. This reveals a potential terminological confusion. For even a nominalist that agrees with what I have said may want to call singular terms t h a tr e f e rge n ui n es i ng ul a rt e r ms ,a ndho l d“ t h a t ” -c l a us e st obe“ me r e l y
3
For more interesting examples of evidence, see, e.g., Bealer (1982), (1998), Bealer and Mönnich (1989), Schiffer (1992), (1996) and Parsons (1993). 4 There is no tension here with the above expressed view that syntax and semantics come apart. The claim was that syntactically cotypical expressions need not be semantically c o t y pi c a l .Ide f i ne“ s i n gu l a rt e r m”a ss o me t hi ngt h a tme e t sb o t hs y n t actic and semantic conditions, so it is not a syntactic category. This should be obvious, but confusion may be caused by the fact that I above reasoned on the assumption that if something is a singular term, it is a syntactic unit. This is of course consistent with (and in fact follows from) the claim that if something is a singular term, it is a noun-phrase.
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s upe r f i c i a l ”s i ng ul a rt e r ms .He ma yt h e nj o i nt h epr o j e c to fg i v i n ga n inferential account of the notion of (superficial) singular term. But I think this terminology is flawed. One reason not to make a distinction between genuine (i.e., referring) and superficial singular terms is that the question which category an expression belongs should not depend on a posteriori, unknown, and linguistically irrelevant facts. A linguistic theory should not require knowledge of, say, physics or history in order to be able to classify expressions (knowledge that physicists or historians may not have themselves). One may want to avoid this consequence by defining genuine singular terms as those which purport to refer to objects. But this will create the problem that realists will say that various expressions purport to refer (and succeed) where the nominalist denies this. Just as linguistic classification should not depend on knowledge of physics, it should not depend on ph i l o s o phi c a lo pi n i on .De f i ni ng“ s i ng ul a rt e r m”i nt e r mso fr e f e r e n c es i mp l y does not seem appropriate. Since we have an intuitive notion of singular term, and since it seems relevant to metaphysical issues, it is still an important question how it should be defined. But it should then be made uncontroversially applicable. That is, we should find criteria that satisfy our intuition that there is something in common among pr o pe rn a me s ,n ume r a l s ,“ t h a t ” -clauses, and so on, the application of which does not turn on any opinion at stake in metaphysical disputes. A good candidate is precisely a definition in terms of inferential properties. The relevant metaphysical questions, properly formulated, are t h us ,“ Wh a tma ke sa ne xpr e s s i onas i ng ul a rt e r m? ” ,“ Dot h e s en e c e s s a r i l y r e f e rt oo bj e c t s ? ” ,a n d“ Wh i c ho ft he m doa n dwh i c hd ono tr e f e r ? ” . Incidentally, this has some relevance for the polemical situation concerning realism. Crispin Wright has argued cogently (1983: v and vii), and that there is no non-a r bi t r a r ywa yo fdi s t i n g ui s h i ng“ r e a l ”( i . e . ,r e f e r r i n g) s i n g ul a rt e r msf r o m me r e l y“ s t yl i s t i c ”( i . e . ,u n c o n t r o ve r s i a l l yn o n -referring) ones, save by appeal to foresworn referential notions. But most realists will probably follow me in not taking all singular terms, inferentially defined, to refer, since they would otherwise have to admit more objects than desired, such as the average American, and so on. But if there is only one legitimate notion of singular term, and the expressions falling under this notion do not all refer, then the argument that there are true sentences with singular terms does not establish that there are propositions (or other abstracta). But if one defines “ s i n g ul a rt e r m”i ns u c hawa yt h a ti tf o l l o wst h a ta n ys i n g u l a rt e r mr e f e r s , then since there uncontroversially are other notions of singular term, e.g., the
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notion of a superficial singular term, the argument will be question-begging in a s s u mi ngt h a t“ t h a t ” -clauses belong to the referring kind. It is a moot question exactly what inferential constraints should be set on singular terms. Clearly, more than the licensing of existential generalisation is ne e d e ds i n c e“ s ome t h i n g”wo ul do t he r wi s ec o u n ta sas i ng u lar term. I will not he r ec on t r i b ut et ot h el i t e r a t ur eonde f i ni ng“ s i ng ul a rt e r m”i n t r a l i n g uistically. There are several attempts at intralinguistic accounts of singular terms which may serve as starting points for the present nominalistic project.5 It should be noted, however, that while this at base Fregean enterprise has mainly been intended to reveal the nature of various types of entities via logico-syntactic analysis, this is of course contrary to my intentions. To me, it seems too idealistic to say that the notion of object should be characterized by reference to languages (if they can be characterized at all, rather than being primitively understood). By the same token, if we are to countenance abstract objects after all, we should follow intuition and linguistic practice and take them to be eternal and wholly objective, and to explain our knowledge of and reference to them on the basis of what they are like, not the other way around. Now that we do away with them, our intuition of eternality and objectivity are instead taken as a further linguistic datum to be accommodated by the nominalist theory. This objectivity could perhaps be inferentially explained. For instance, there seem not to be any non-trivial correct inferences between sentences describing our language use and sentences containing abstract singular terms, l i ke“ 1+1 =2”o r“ Th a t1=1e n t a i l st h a t1=s ome t h i n g ” .Th eFr e g e -Dummettian middle way between Platonism and nominalism seems to me to unite the worst from both views in admitting abstract object but make them dependent on us. Although I believe the definition of singular term should be entirely intralinguistic, a theory about singular terms need not completely lack mention of reference to objects. In biology, a phenomenon often requires a diachronic explanation to be exhaustively explained, e.g., the appendix in humans. It may be, likewise, that the category of singular term emerged, in the wake of human language, essentially as a category of expressions referring to material objects, but that non-referring expressions were subsequently introduced as singular terms, i.e., as having the same inferential properties. Pe r h a p ss ome t hi n gs i mi l a ri st r ueo fe a c hs pe a k e r ‟ si nd i v i d u a ll e a r n i n gp r o 5
See, e.g., Frege (1884: §§ 26, 60-62), Dummett (1973: 57ff.), Geach (1975), Wright (1983: ix), Hale (1987: Ch. 2), Hale and Wright (2001: Chs. 1 and 2), Brandom (1994: Ch. 6), Heck (unpublished).
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cess (perhaps, to some extent, idiolectogeny (if I may) recapitulates glossogeny). This, in any case, could do justice to the intuitive connection between singular terms and reference.
5.5 OUTLINES OF A NOMINALIST SEMANTICS We will now look at a few more specific questions about how a nominalist treatment on the above lines should deal with various sentences that superf i c i a l l yr e f e rt oo rq u a n t i f yo ve rpr o po s i t i on s .Si mpl es e n t e n c e swi t ha“ t h a t ” clause, to begin with, are given a standard (i.e., relational) syntactic analysis, but what can be said about their semantics? I believe that the semantic c h a r a c t e ro fas e n t e nc el i ke“ Kr i pkebe l i e ve st h a ts n o wi swh i t e ”i saf u n c t i o n f r om t h es e ma n t i cc h a r a c t e r so f“ Kr i pke ” ,“ b e l i e ve s ” ,a n dt h ee mbe d d e d s e n t e n c e“ Sn ow i swh i t e ” .Somes e e mt ot a k et hi sv i e wto motivate the synt a c t i ca n a l y s i sonwh i c h“ t h a t ” -clauses are not syntactic units. But besides resting on the above-criticized idea that syntax should mirror semantics, the semantic claim in this case does not even seem to motivate the syntactic claim, ev e ng r a n t e ds uc hac o nne c t i on .Fo rwhys ho ul dt he“ t h a t ”g owi t h “ b e l i e ve s ” ,r a t h e rt h a nwi t ht hes e n t e n c e ?I tt h e r e f o r es e e msmo r epl a u s i b l et o a c c e p tt h es e ma n t i cc l a i ma ndr e g a r d“ t h a t ” -clauses as syntactic units, and, he nc e ,r e g a r dt h e“ t h a t ”a ss e ma n t ically superfluous, serving only to create an expression that can act as a grammatical object to the verb.6 It should be noted t h a twh i l ear e a l i s tma ya g r e et h a tt heme a n i ngo fas e nt e n c e“ x Vs that p”i sa f un c t i onpa r t l yf r o mt heme a ni ngo f“ p” ,h et a ke s this to be a consequence of the fact that the meaning of this sentence determines which proposition is r e f e r r e dt o by t h e“ t h a t ” -c l a u s e .Th ep r e s e n tc l a i m i st h a t“ t h a t ”i s s e ma n t i c a l l ys upe r f l uo us ,t h usc on t r a d i c t i ngt h er e a l i s t ‟ sa n a l y s i s . There seem to be special advantages to a view that combines the idea that ( 1)t h e“ t h a t ” -clause in a belief ascription is a singular term and the view that 6
Da v i ds o nha sa r gue d,s ur pr i s i n g l y ,t ha t“ wec a n n o tunderstand [sentences of the form “ t hepr o po s i t i o nt ha tp is true iff p” ]un l e s swec a ns e eh o wt oma k eu s eoft h es a me semantic features of the repeated sentence in both of its appearances– make use of them in gi v i ngt hes e ma nt i c so ft hes c he mai ns t a nc e s .Id on o ts e eh o wt h i sc a nb ed o n e . ”( 1 9 9 6 : 274, original emphasis). But, surely, we understand them! Furthermore, the fact that we cannot (now) give a compo s i t i o na ls e ma n t i ca c c o u n to f“ t h epr o po s i t i o nt h a tp”i ss u r e l y no reason to say that we do not understand it.
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(2) the meaning of the ascription is only a function from the subject, the verb and the sentence. To put the matter briefly, it seems that a theory which manages to combine (1) and (2) is more likely to be able to take the good and 7 e s c he wt h eba df r o m bo t hRus s e l l ‟ s“ mul t i pl er e l a t i o n sa n a l y s i s ” and the “ f a c e -v a l ue ” ,o r“ r e l a t i on a l ”a n a l y s i so fbe l i e fa s c r i pt i o n s(and other ascriptions of propositional attitudes). The latter is simply the view that belief is a r e l a t i o nbe t we e nabe l i e ve ra n dabe l i e ve dpr o po s i t i on ,wh e r e a so nRu s s e l l ‟ s account, belief is related to differing numbers of objects that are referred to by e x pr e s s i o n swi t h i nt he“ t h a t ” -c l a us e .Th u s ,Rus s e l ls a y s ,“ whe n Ot he l l o judges [e.g., believes] that Desdemona loves Cassio, Othello is the subject, whi l et heo b j e c t sa r eDe s de mon aa n dl o vi n ga ndCa s s i o ”( 1 9 1 2 :1 2 6 ) .Th i si s as yet only a very rough idea, of course, but it has attractive features.8 This is a l s ot hek i n do fa n a l y s i se nd o r s e dbypa r a ph r a s eno mi n a l i s t so fPr i o r ‟ sb r a n d . My idea, then, is that the various intuitions and arguments supporting these rivalling ideas could be better accommodated by a theory combining (1) and (2), than by either of the rivals. The present account does not agree with the r e l a t i o n a lt h e o r yt h a t“ be l i e ve s ”s ho ul dbee xpl a i ne da se x p r e s s i n gar e l a t i o n to propositions, of course. But this idea is only another realist intuition, which is to be accounted for by the nominalist semantics. The intuition is there taken t or e g i s t e rt het e r mho odof“ t h a t ” -clauses. The multiple relations analysis is also considered as right in a way, namely, insofar as it gives a semantic account which does not mentions propositions. More importantly, it is more c o ng e ni a lt ot h ei de at h a tt h eme a n i ngofas e n t e nc e“ x Vs that p”i saf un c t i on f r omt ho s eo f“ x” ,“ Vs ” ,a n d“ p” ,t a k i n g“ t h a t ”a sas y n t a c t i c a l l yr e q ui r e d ,b ut semantically redundant expression.9 Describing the meaning-functions for 7
Besides Russell (1910), (1912: XII) and (1918: IV), similar ideas have been vented by Prior (1971: 16ff.), Tye (1989), Matthews (1994), and Moltmann (2003), i.e., the very s a met ha ta c c e p tt hes y n t a c t i ca n a l y s i sof“ x Vs that p”i n t o“ x” , “ Vst h a t ”a n d“ p” . 8 Recently, the view has been promoted by Moltmann (2003) as avoiding various di f f i c ul t i e st ha ta f f l i c tt hev i e wt ha t“ t ha t ” -clauses refer to propositions. Note, then, that it i sno tt hec l a i mt h a t“ t h a t ” -clauses are singular terms that is unfavourably compared to the Russellian view, only the view that they refer. We will have reason to look closer at Mo l t ma nn‟ sa r gu me nt si nt h en e x ts e c t i o n. 9 Tos a yt ha tt heme a n i n gofas e n t e nc e“ x Vs that p”i saf u n c t i o np a r t l yf r o mt h a to f“ p” should not necessarily be taken to mean that sentences with the same semantic value can s ub s t i t ut eo n ea no t he ri nt h ema t r i x“ x Vst h a t . . . ”wi t h o u tc h a n g eo fs e ma ntic value. If semantic value is taken to be the proposition expressed, this could perhaps be said, but this is of course ruled out by (NC). An assertibility-conditional semantics could perhaps take the assertibility conditions o f“ p”t oc o nt r i bu t es y s t e ma t i c a l l yt ot h o s eo f“ x Vs that p” . Or ,
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various propositional attitude verbs is of course a major project, that cannot be as much as begin here (in 5.7, however, we will briefly discuss how (NC) relates to this task). The same, of course, goes for the project of seeing how the above account relates to the actual arguments that have emerged in the debate between Russellians and relational theorists. I hope, in any case, that this explains, if on a very general level, how the semantic contribution of a “ t h a t ” -clause is treated on this nominalist semantics, and how this enables a c o mpr o mi s ebe t we e nt woi mpo r t a n tr i v a la c c o un t sof“ t h a t ” -clauses. This, in turn, shows how the guiding idea behind paraphrase nominalism can be expressed without unnecessarily entering into discussion of syntax, deep structure, and the neural mechanisms underlying linguistic competence. In order to respect (NC), the nominalist semantics must also give some a l t e r n a t i vea c c o un to fwh a tl ook sl i keq ua n t i f i c a t i o n“ o v e rp r o po s i t i o n s ” ,i . e . , q ua n t i f i e ds e n t e nc e s wh o s ei n s t a nc e sh a ve “ t h a t ” -clauses as terms. An objectual account, of course, is both truth-theoretic and entails commitment to propositions. The obvious alternative for the nominalist is some kind of substitutional, or, in any case, intralinguistic, interpretation (cf. Schiffer (1987: 234ff.)). A substitutional interpretation of quantification is traditionally considered a part of the non-representational paradigm, and is also, as we shall see, more promising on this type of theory of meaning than on a truthconditional one, thus again supporting the claim that nominalists should not be truth-conditionalists. As a preparation for our intralinguistic account of the universal quantifier, let us neutrally call the semantic content of a term whatever should be taken to be relevant for the semantic value of sentences containing it. It may be a mere referent, descriptive contents, recognition-conditions, images before the mi n d ‟ se ye ,o rwh a t e ve rt her e a de r ‟ sl a t e s tbe tma yb e .Se c o ndly, I do not t h i n kun i ve r s a ls e n t e n c e sa r epr i ma r i l yo ft hef o r m“ Eve r y t h i n gi sF” ,b u t , r a t h e r ,“ Ev e r yF is G” ,t hef o r me rbe i n gas p e c i a lc a s eo ft h el a t t e r .No w,I propose:
the semantics may be yet more fine-grained, taking into account the semantic properties of the subsentential expressions in the sentence following the propositional attitude verb. These sentences of course pose major problems also for truth-theoretic semantics, and I will leave the issue here.
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(UQ) As e n t e nc e“ Eve r yF is G”i sa s s e r t i b l ei f f ,f o ra n yt e r m t, it holds, irrespectively of t‟ ss e ma n t i cc o n t e n t ,t h a tg i ve nt h a t“ F(t) ”i s 10 a s s e r t i bl e ,s oi s“ G(t) ” . The idea here is that to assess the assertibility of a universal sentence, the only feature of the instantiating expressions that may be appealed to is that they are terms, i.e., their logico-syntactic identity, not what semantically distinguishes t h e mf r o mo t he rt e r ms .Se c ondl y ,t hea s s e r t i bi l i t yof“ F(t) ”mu s ts u f f i c e , irrespectively of t‟ ss e ma n t i cc o n t e n t ,f o rt h ea s s e r t i bi l i t yo f“ G(t) ” ,r e g a r d l e s s of wheth e r“ F(t) ”o r“ G(t) ”a r ei nf a c ta s s e r t i bl e .Th i r d l y ,( UQ)i st ohol da l s o when a universal sentence is assertible due to experience. This entails that assertibility is relative to time and speaker, but this I take to be in the concept in any case. One might say that a universal sentence is assertible only due to the contents of the predicates involved and (sometimes) experience. This means that if, for some term t,t hea s s e r t i bi l i t yo f“ F(t) ”i ss u f f i c i e n tf o rt h a to f “ G(t) ” ,i r r e s pe c t i veo ft hes e ma n t i cc ontent of t, then this holds for every term. No t ea l s ot h a tt hea d ve r b i a lph r a s e“ i r r e s pe c t i ve l yo ft h ec o n t e n to ft h et e r m” in the right-hand side of (UQ) has the whole conditional in its scope. Therefore, the right-h a n ds i dec a nbet r u ea l t h o u gh“ G(t) ”i s assertible partly due to the semantic content of t. Le tu snowt a k et hee x a mpl eof“ Eve r yo nei nt hi sr oo mi sbl o n d ” .Su p p o s e a and b a r et heon l ype r s on si n“ t her o om”a nda r ebo t hb l on d ,a n dt h a ta‟ s experience is indeed sufficient to make the universal sentence assertible. The i d e ai st h a t ,r e g a r d l e s so ft h es e ma n t i cc on t e n to f“ c” ,a‟ se xpe r i e n c ea n dt h e a s s e r t i bi l i t yo f“ c i si nt h er o o m”wi l lbee n o ught oma ke“ c i sbl o n d” a s s e r t i bl e ,i r r e s pe c t i ve o ft he s e ma n t i cc on t e n tof“ c” .( I twi l la l s o be suff i c i e n tt oma k e“ c is either a or b”a s s e r t i bl e ,b u tt h i si sn o tan e c e s s a r y i n t e r me d i a t es t e p. )Ot he r wi s eput ,gi ve nt hee xpe r i e n c ea n dg i v e nt h a t“ c is in t h er o o m”i sa s s e r t i bl e ,t h e r ei she r eno t hi nga b o u tt het e r m“ c”other than its being a term, due t owhi c h“ ci sb l on d ” .Weh a v ea nun pr o b lematic case when ne i t h e r“ c is a”o r“ c is b” ,no rt h e i rne g a t i on sa r ea s s e r t ible. This may be so whe n“ c”i s ,s a y ,“ t h epe r s o ni nt h er o omwh ob l i nk e de x a c t l yon ey e a ra g o ” . Trouble may seem to arise, however, whe nwec on s i de rt h ei n s t a n c e“ b is i nt her oo m” ,wh e r et het e r m“ b”r e f e r st ob and a knows it. In this case, both “ b i si nt h er o o m”a n d“ b i sbl o nd ”wi l lbea s s e r t i b l epa r t l yd uet ot he s e ma n t i cc on t e n to f“ b” .Ag a i n ,t hi si si nn oc o n t r a d i c t i onwi t ht heright-hand 10
Fo rs i mpl i c i t y , Ia mbe i ngs l o ppya bo utt hev a r i a b l e“ t”i nq u o t e -contexts.
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s i d eo f( UQ) ,s i n c et he“ i r r e s pe c t i ve l y”ph r a s et a k e st hewh o l ec o n d i t i o n a li n i t ss c o pe .Bu t ,on emi gh to b j e c t ,t heg r o und sf o rt hea s s e r t i bi l i t yo f“ b is in the r o om”a r en o ti nt he ms e l ve sg r o und sf o rt h ea s s e r t i bi l i t yo f“ bi sbl o nd ” .Bu t this only means that the contents of the predicates do not themselves suffice for the universal sentence to be assertible. That is, experience is needed to go f r om “ b i si nt her o om”t o“ b i sbl on d ”i ft h i si st obed o newi t ho u t assumptions of the content of “ b” .But ,t h eo b j e c t i o n mi g h tc on t i n ue , kn owl e dg et h a t“ b i si nt her oom”i sa s s e r t i b l ed oe sno ts uf f i c ef o rt h e a s s e r t i b i l i t yof“ bi sb l o nd ”i r r e s pe c t i v e l yo ft h ec on t e n to f“ b” ,s i n c ea needs t ok no ws o me t h i nga bo utt her e f e r e n to f“ b” .I nd e e d ,a needs certain perc e pt u a le x pe r i e nc e so fe v e r y onei nt her oom,i nc l udi ngt h er e f e r e n to f“ b” . But a n e e dno tk n ow wh a t“ b”r e f e r st o .The r ei sade re-de dicto ambiguity here. Speaker a must have certain experiences of the person who happens to be the referent o f“ b”( a ndo fo t he rpe r s o n si nt h er o o m) ,b u ti no r de rt o c o nc l udet h a t“ bi sb l on d”i sa s s e r t i bl ef r om t h ea s s u mp t i ont h a t“ b is in the r o om”i sa s s e r t i bl e( p l u st hee xpe r i e n t i a le v i d e n c e ) ,t hei n f o r ma t i o nt h a t“ b” refers to a certain individual is not necessary. It might also be thought that (UQ) will give the wrong result in a case wh e r eas p e a ke rh a so nl yt h et e r ms“ a”a n d“ b”i nh e rv o c a b ul a r ya n dt h e r ei s a third person in the room, d,wh oh a sd a r kh a i r .Bu tt h ea s s e r t i bi l i t yo f“ a is bl o n d”a nd“ b isbl on d ”wi l ln o ts uf f i c et oma k e“ Ev e r yo n ei nt h er o om i s bl o n d”a s s e r t i bl ei nt h i sc a s e ,f o rne i t he r“ ai sbl on d ”n o r“ bi sb l on d ”wi l lbe a s s e r t i b l ei r r e s p e c t i v eo ft h es e ma n t i cc o n t e n t so f“ a”a n d“ b” .I nt hi sa l l e g e d counter-e xa mpl e ,“ bi sb l on d”i sa ssertible partly due to the semantic associa t i onbe t we e n“ b”a n db ( o r ,i fy o uwi l l ,be t we e n“ b”a ndi t sr e c og n i t i o n conditions, etc.). It could not have been assertible irrespective of semantic content, since, in the case as imagined, the perception of d would bar one f r om go i ngf r om t h ea s s e r t i b i l i t yof“ bi si nt h er o om”t o“ bi sbl o nd ” ,i ft h i s s t e pi st obea s s e r t i bi l i t yp r e s e r vi ngi r r e s pe c t i veo ft h ec o n t e n to f“ b” . Th e r ema ya l s os e e mt obet r o ubl ewh e n“ c”i ss u c ht h a t“ c is not a”i s strongly assertible. For instance, what are we to say about the above case wh e n“ c”i s“ t hel a r g e s tg a l a xy ” ?I tma ys e e ma wkwa r dt od i s c u s swh a t f ol l o wsf r o mt h ea s s e r t i bi l i t yof“ t hel a r ge s tg a l a xyi sap e r s o ni nt h er o o m” , since this is so obviously non-assertible. But speakers are not supposed to make explicit assumptions in the way this objection assumes. The assertibility of universal sentences simply coincides with the conditions on the right-hand side of (UQ) –it in no way entails that speakers explicitly assume a given sentence. Principle (UQ) only states that the determination of the assertibility
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of a given universal sentence goes by taking experience and the contents of various expressions as input, and produces a universal sentence if no information about thec o n t e n t so ft e r msi sn e e d e dt og of r o m“ F(t) ”t o“ G(t) ” . We may metaphorically describe the process going on as one where a semantic homunculus a s s ume st hes e n t e n c e“ t h el a r g e s tg a l a xyi sap e r s o ni n t h er oom” ,ma ke sh i ms e l ff o r ge tt heme a ni ngo f“ t h el a r g e s tg a l a xy ” ,a n dt h e n c o n s ul t st hee xpe r i e n t i a le vi de nc et ode t e r mi n et hea s s e r t i bi l i t yo f“ t h el a r g e s t g a l a x yi sb l on d ” .Thef a c tt h a to nl yones uc hc a s ene e d st obed e t e r mi n e di n order to determine the assertibility of a universal sentence also adds some psychological plausibility to (UQ). In the above case, where we needed to di s t i n g ui s hbe t we e n ,ont heo neh a nd ,“ ai sbl o n d ”be i n ga s s e r t i b l ep a r t l yd ue t ot h es e ma n t i cc o n t e n to f“ a” ,a n d ,ont h eo t h e r ,i t sb e i n ga s s e r t i bl ed uet ot he assertibility of “ ai si nt h er o o m”i r r e s pe c t i v eo ft hes e ma n t i cc on t e n t ,s ho u l d not be taken as too subtle to be psychologically plausible. For this distinction is supposed to be made tacitly, or computationally, and so does not require that speakers actually manage to disregard the meaning of a term. Induction may be thought to present a problem for (UQ). An induction, it ma ybet h o ug h t ,i sas t e pf r om t hea s s e r t i bi l i t yo fi n s t a n c e s“ F(a) & G(a) ” , “ F(b) & G(b) ” ,. . . ,a n df u r t h e rc o n di t i o n sC (to be spelled out by the philos o phe ro fs c i e nc e ) ,t ot h ea s s e r t i bi l i t yo fau n i v e r s a ls e n t e n c e“ Ev e r yF is G” . But here, do not the particular instances matter for the assertibility of the universal sentence? If they do, then we can instead characterise induction as a step from the a s s e r t i bi l i t yo fi n s t a n c e s“ F(a) & G(a) ” ,“ F(b) & G(b) ” ,. . . ,a n d C,t ot hea s s e r t i b i l i t yo fa nys e n t e n c eo ft hef o r m“ G(t) ”g i ve nt h a to f“ F(t) ” , irrespective of the content of t. It need not even be thus sententially characterized at all, but can be taken to be a case where a certain type of series of e x pe r i e n c e sl i c e n s e son et oi n f e rf r om a nys e n t e n c e“ F(t) ”t oas e n t e n c e “ G(t) ” ,i r r e s pe c t i veo ft hec on t e n to ft ( t h a ti s ,g i ve no nl yt h ec on t e n t so f“ F” a n d“ G” ) .Onbo t ht h e s ec h a r a c t e r i z a t i on so fi nd uc tion, of course, (UQ) e n t a i l st h a t“ Ev e r yF is G”i sa s s e r t i b l ei nt h ec a s ed e s c r i b e d . Mark Lance (1996) gives a substitutional interpretation in much the same spirit, but he formulates the conditions in terms of the assertibility of sentences with arbitrary names. These are like the lower-c a s ei t a l i c“ a”i nt he assumption-s e n t e n c e“ Le ta bean a t ur a ln umbe r . . . ” .Th i si ss i mi l a rt o( UQ) , since arbitrary names precisely lack semantic content in our sense, and only has a grammatical identity. But it seems that we should try to avoid the consequence that any speaker who uses a universal quantifier must operate with arbitrary names. It seems quite contentious to say that earlier humans
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have used arbitrary names as long as they have used universal quantifiers. Even if this operation is taken to be tacit, (UQ) seems still less contentious since it only requires that the semantic content of universal sentences is sensitive to the semantic contents of its instances (namely, by disregarding that of the terms therein). Of course, (UQ) also has affinities with the introduction and elimination rules of the universal quantifier in natural deduction. It is difficult to see how this rule should be applied to cover cases where a universal sentence is assertible due to empir i c a le vi de n c e ,h owe v e r .Th i sr u l emi g h tbe“ s a f e r ”t o follow explicitly in practice, since it guarantees that we are not tacitly sneaking in assumptions depending on the content of the term used for deriving a universal sentence. But this seems to have little relevance for the semantics of quantifiers. There is another important advantage that (UQ) has over an account closer to the introduction rule of the universal quantifier in natural deduction. Take, for instance, a rule that allows one to infer a universal sentence if an instance is analytic and depends on no hypotheses containing t het e r m.Bu tf o ra n ya n a l y t i cs e n t e nc e“ p” ,t h ec o r r e s p on d i n g“ Th a tp i st r u e ” will likewise be analytic, by (D). But then, such an introduction rule would allow us to infer“ Eve r y t h i n gi st r u e ” .Wi t ht h ec o n s t r a i n to fc o n t e n t independence, however, this move is barred by the fact that this instance is a s s e r t i b l ebe c a us et hes e n t e n c e“ p”i sa n a l y t i c ,p a r to ft h ec on t e n to ft het e r m, i . e . ,t h e“ t h a t ” -clause. Here is now a further reason why nominalism, since it requires substitutional quantification, is not happily wedded to truth-conditional semantics: ( UQ)wo ul dn o tbei n t e l l i g i b l ei f“ a s s e r t i b l e ”we r er e pl a c e dwi t h“ t r u e ” ,f o ri t does not make sense to say that a sentence o ft h ef o r m“ F(t) ”i st r u e ,g i v e nt he truth of such and such a sentence (and excluding experience, of course), irrespective of the semantic content of t. A sentence simply cannot be true irrespective of the semantic content of its parts. A speaker may however be justified in holding a sentence true irrespective of this, and this is surely related to the corresponding fact about assertibility. It seems that the truthconditionalist needs to give truth-conditions of universal sentences by quantifying over every possible instance, including all non-actual instances. There is also a cogent argument by Tomberlin (1997) against the truthconditional substitutional interpretation of the universal quantifier. What, he asks, is to prevent us from inferring from t h ec l a i mt h a t“ Ev e r y t h i n gi sF”i s t r ue ,t h a t“ F(the unique non-F) ”i st r u e ?Het a ke st heo nl ypo s s i b l es o l ut i o nt o be to restrict the substituends to referring terms, which would conflict with
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the aims of the substitutional interpretation. A fortiori, this would not work for a nominalist, who must take all the relevant terms to be non-referring. For our purposes, the problem as formulated above does not arise. But something a n a l o go u smi g h t .Ta k e“ t h eun i q uenon -self-i d e n t i c a l ” .I ts e e mst h a tt he sentence “ Eve r y t h i ng i ss e l f -i de n t i c a l ”c a nn o tbea s s e r t i b l e ,s i n c ef o ra n i n s t a n c et oa s s e r t i b l e ,i tmus tbea s s ur e dt h a tt h et e r mi sn o tl i k e“ t h eun i q ue non-self-i d e n t i c a l ” ,s i n c en os e n t e n c ewi t hs uc hat e r mc a nbea s s e r t i b l e .Bu t this is to make an assumption a bo u tt h et e r m‟ sc o n t e n t .Is a i de a r l i e rt h a t s e n t e n c e so ft hef o r m“ Ev e r y t hi ngi sF”s h o ul db et r e a t e da ss p e c i a lc a s e sof s e n t e n c e so ft hef o r m“ Eve r yF is G” .Bu tt h e ya r es pe c i a lc a s e ss oc o mmon that the quantifier expression has merged in writing with t h en o u n“ t h i n g ” . For a sentence of this form to be assertible, on (UQ), it must be the case that gi ve nt h ea s s e r t i b i l i t yo f“ ti sat h i n g ” ,“ t is self-i d e n t i c a l ”mu s tbea s s e r t i b l e irrespective of the content of t.Bu tn ow wes e et h a t“ t h eun i q ueno n -selfi d e n t i c a l ”c r e a t e snopr o bl e ms i nc et hes e n t e nc e“ Th eu n i q uen o n -self-ident i c a li sat h i ng ”c a nn e v e rbea s s e r t i bl e .Tr u e ,i no t he rl a n g u a g e s ,t h e r ea r e un i ve r s a ls e n t e n c e st h a tt r a n s l a t e“ Eve r y t hi n gi ss e l f -i d e n t i c a l ”wi t h o u ta corresponding noun, e.g.,t heGe r ma n“ Al l e si s ts e l b s t i d e n t i s c h ” .Buts i n c e t h i si sn o to ft h es a mes yn t a c t i cf o r ma st heGe r ma ne q ui v a l e n to f“ Ev e r yma n i smo r t a l ” ,i tc a nn o tbeus e da sac o un t e r -example to (the German equivalent of) (UQ). It must be given a semantic analysis of its own, and therefore, it is not ad hoc t og i vei ta na c c o u n twhi c ha v o i d sp r o bl e mswi t h“ t h eun i q uen o n self-i de n t i c a l ” .Th a ta c c o un two ul ds i mpl ys a yt h a tas e n t e nc e“ Al l e si s tF”i s assertible iff for any term t, if (the German equiv a l e n to f )“ So me t h ing is t”i s assertible, then, irrespective of the content of t, “ t ist F”i sa s s e r t i b l e . J us ta st h ea b ovet r e a t me n tofs e n t e n c e so ft h ef o r m“ x Vs that p”p r o v i de s a mi d dl ewa y be t we e n Rus s e l l ‟ smul t i pl er e l a t i on st h e o r y( e n d o r s e db y paraphrase nominalists) and the relational analysis (endorsed by realists), the present account of the universal quantifier, enables a middle way between the syntactic analysis of Prior (in terms of propositional quantification) and an objectual interpretation (endorsed by realists). It agrees with the former that a q ua n t i f i e ds e n t e n c el i k e“ Hes a y se ve r y t h i n gIbe l i e ve ”d o e sl i t t l emo r e , s e ma n t i c a l l y ,t h a n“ p(If I believe that p, then he says that p) ” ,n a me l yt o l i c e n s ei n f e r e n c e st oa ndf r om t hei n s t a n c e so f“ I fIbe l i e v et hat p, then he says that p” .Ye ti ta g r e e swi t ht h er e a l i s t ‟ sa c c o u n tt ha tt h es e n t e nc ei sb o t h syntactically and semantically cotypical with other universally quantified sentences.
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Wec a nnow a l s os how t h a tt hepr o bl e m Gupt af o undwi t hHo r wi c h ‟ s theory (cf. 1.5 and 2.12) can be solved in a simple way. The problem was that of explaining universal facts such as the fact that everything known is true. As de t a i l e di n3 . 4,t hi si st a k e no nt hel i ng ui s t i ca c c o un to f“ t r u e ”t obeama t t e r of explaining the (uncond i t i on a l )a s s e r t i b i l i t y ,o ra n a l y t i c i t y ,o f“ Ev e r y t h i n g kn owni st r u e ” .Te r ms ,l i k e“ Eng l a nd ” ,t h a tf o r ms e ma n t i c a l l ya n o ma l o u s instances fall out as irrelevant since such instances can never be assertible. We suppose, therefore, that an arbitrary sentenceo ft hef o r m“ Th a tp is kn own ”i sa s s e r t i bl e .Th e n ,t h a nk st ot hef a c t i v i t yo f“ k n o w” ,wes e et h a ti f t h i ss e n t e n c ei sa s s e r t i bl e ,t h e ns oi s“ p” ,i r r e s pe c t i veo ft h ec o n t e n to ft he “ t h a t ” -c l a us e .Th i si sj u s ta ni n s t a n c eo ft hei n f e r e n c ef r o m“ x knows that p” t ot h ec o r r e s po ndi n g“ p” ,whi c hi sp a r to f ,o rac o n s e qu e nc eo f ,t hes e ma n t i c s o f“ kn ow” .Th i sr u l e ,f ur t h e r ,doe sno tne e dt obef o r mu l a t e di nt e r mso f “ t r u e ”a ndc a nbef o l l o we dbyas pe a ke rwh o s el a n gua g ed o e sn o tc o n t a i n “ t r u e ”o ra n ys yn o nym.Now,g i ve n( D) ,t h ec o r r e s p o n di ng“ Th a tp i st r u e ” mus tun c o n di t i on a l l ybea s s e r t i bl e ,t oo .Th i si si n de p e n d e n to ft h e“ t h a t ” c l a us eweu s e ,s i n c e( D)do e sn o tc on c e r na n y“ t h a t ” -clause in particular. In t h i sc a s e ,t he n ,t hes e n t e n c e“ Th a tp i st r ue ”i sa s s e rtible due to no other fact a b o utt he“ t h a t ” -c l a us et h a nt h a t“ Th a tp i sk n o wn ”i sa s s e r t i bl e .Asn o t e d above, if for one term t,t h ea s s e r t i bi l i t yo f“ ti sk n o wn ”s u f f i c e sf o rt h a to f“ t i st r ue ”i r r e s pe c t i veoft h ec o n t e n to ft, then this holds for any term. By (UQ), t he n ,“ Ev e r y t h i ngk nowni st r ue ”i s( un c on d i t i on a l l y)a s s e r t i b l e . A corresponding proof is not available for Horwich, since he would need to appeal to a specific fact about a specific proposition, one of the propositions in the Minimal Theory, whence the derivation would not be independent of the specific proposition chosen. His own proposal (cf. 2.12) may be considered less obvious, in that the rule requires that the person inferring must know infinitely many propositions, and also have second-order knowledge about this knowledge. What is worse, it seems that Horwich cannot explain the above fact without assuming that the theory of knowledge is infinite in the way (MT) is. For the explanation of the fact that everything known is true may not go by assuming that the theory of knowledge contains the claim that everything known is true. This is because he has promised to be able to explain every fact about truth with only (MT) and facts that do not pertain to truth. The fact that everything known is true is of course a fact “ p e r t a i n i n gt ot r ut h ” ,i nt her e l e v a n ts e n s e .How,t h e n,c a nHo r wi c he x pl a i n this fact without assuming that the theory of knowledge contains (inter alia) e v e r ypr o po s i t i ono ft hef o r m“ I fonek nowst h a tp, then p” ?On ei d e awould
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be to let the theory of knowledge contain the propositionally quantified claim that (p)(If someone knows that p, then p). But given the possible ways of elucidating this claim, as detailed in 3.3, this seems merely to disguise the problem. It may not be explained in terms of truth, and it seems odd to take it to be inferentially explained, since one could then equally say that the theory o fkno wl e d gec on t a i n sar u l el i c e n s i ngi n f e r e n c e sf r om “ x knows that p”t o “ p” .Th e r ei snog o odwa yo fe x pr e s s i ngthis in ordinary English, and the infinitistic interpretation is of course what is to be avoided. In any case, if this claim can be in the theory of knowledge, it should also be possible to use a propositional quantifier in the theory of truth. The upshot is that the infinity of (MT) will contaminate other theories, since they may not be formulated in terms of truth. On the present proposal, by contrast, we can give the finite c l a i mt h a tt hei n f e r e n c ef r om “ x knows that p”t o“ p”c h a r a c t e r i z e s“ kn o w” , which is clearly a claim independent from (D). Ho r wi c h‟ st he o r ya l s of a c e sac e r t a i nd i l e mmawh i c hwec a na v o i d :i n order for his theory to be general and not only concern propositions we can a c t u a l l ye xp r e s s ,hemu s te i t he rpo s i tas t r uc t u r e( o r“ f o r m” )o fp r opositions or speak of possible, non-actual sentences. In (D), by contrast, we need not quantify over non-actual sentences. Principle (D) can of course remain true of Eng l i s ho ro fag i v e ns pe a k e r ‟ si d i ol e c tn oma t t e rwhi c hn e we x p r e s s i o n sa r e introduced. If new expressions are introduced in the language, the new sentences formed with them will be subject to (D) just as the old ones. So, (D) is in force in a language (or idiolect) at t if it applies to every sentence that can be formed at t. When a speaker l e a r n s“ t r u e ” ,s h ebe g i n st os pe a ki n a c c o r d a n c ewi t h( D) ,a n dt h i swi l la l l owhe rt oa pp l y“ t r u e ”t oa n yn e w“ t h a t ” clause she may be able to formulate. That is, once in force, (D) will continue to be in force provided nothing special happens (like a reinterpretation of “ t r ue ” ,a mne s i a ,e t c . ) .Le t t i ng( D)q ua n t i f yo ve rp o s s i b l es e n t e n c e swo ul d only have the superfluous intent of allowing speakers to apply it to non-actual s e n t e n c e s .Ho r wi c h ‟ sp r o bl e mi st h a thene e dst os pe a ko fe v e r yp r o po s i t i o n , whether expressible or not. We only speak of a form of linguistic expression, “ t h a t ” -clauses.
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5.6 THE PHILOSOPHICAL NOTION OF “ PROPOSITION ” I ti sn o wt i met ol oo kc l o s e ra tt her e l a t i o nbe t we e n“ t h a t ” -clauses and the wo r d“ pr o p o s i t i o n ” .Wh e r e a si nn a t ur a lEn g l i s h ,the latter usually means s ome t hi n gl i ke“ pr o p o s a l ” ,Ih a vebe e nus i n gt h el a t t e ri nt h emo r ee n c o mpassing, philosophical way. The reason the more general sortal term does not exist in natural languages seems to be that no restriction on the quantifier in, e . g . ,“ Ev e r y t h i ngh ebe l i e v e si st r ue ”i sn e e de d .Si nc et e r mso t h e rt h a n“ t h a t ” c l a us e sa n da ppr o p r i a t ed e s c r i pt i on s( “ wh a th ebe l i e ve s ” )c r e a t es e ma n t i c a l l y a n oma l o usi n s t a n c e s( l i k e“ Hebe l i e v e st h eEi f f e lTo we r ” ) ,i two ul d be superfluous to have a rest r i c t i onont h eq ua n t i f i e r ,a si n“ Ev e r yproposition he be l i e v e s. . . ” . Ho ws h o ul dt he ph i l o s o phi c a lus eo f“ pr o po s i t i on ” be c h a r a c t e r i z e d consistently with our nominalism? Note that this is not an empirical matter of ho wt oe x pl a i ns pe a ke r s ‟us eo ft hee xpression, but a stipulative one. I would l i ket os ugg e s tt h a twei n t r od uc et hee xp r e s s i o n“ p r o p os i t i o n ”byd e c l a r i n gt h e instances of the schema (P)
That p is a proposition
t obea n a l y t i c .“ Pr o po s i t i o n”i st h usde f i ne da shy pe r nymo u st o“ t h a t ” -clauses, j us ta s“ n umbe r ”i sh y pe r nymoust on ume r a l s .I th a sb e e na l l e g e dt h a t a p pl y i n g“ pr o p o s i t i on ”t h usge ne r a l l yc r e a t e sv a r i o uss e ma n t i ca n ds y n t a c t i c a n oma l i e s .Fo ri n s t a n c e ,t h o ugh“ xf e a r sap r o p o s i t i o n”i si n t e l ligible (if odd), it should not, as (P) entai l s ,b eac o n s e q ue nc eo f“ xf e a r st h a ti twi l lr a i n ” . Fur t h e r mo r e ,t h es e n t e nc e“ x s a y sa p r o po s i t i o n” j u s ts e e msa wk wa r d . St r a n ge l y ,h o we v e r ,t h e s ep r o bl e msdono ts e e mt oa r i s ei f“ k n o ws ”r e pl a c e s 11 “ f e a r s ”a n d“ s a y s ” . I have already contended that my use o f“ p r o p o s i t i o n ”i s technical and need not, therefore, do justice to intuitions the way analyses of ordinary expressions must. However, this does not seem to be an ordinary kind of stipulation, since stipulations normally do not provoke objections from awkwardness in this way. I would like to suggest something of a trivialization of this problem. Mo l t ma n nn o t e st h a ts p e a k e r s ‟i n t ui t i o n sdi f f e rr a t he rwi d e l ya st ot h e 11
These issues have been discussed by cf. Prior (1971: Ch. 2), Asher (1987), Bach (1997), King (2002), Moltmann (2003) and Schiffer (forthcoming).
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meaning and intelligibility (and even the grammaticality) of various relevant sentences wi t h“ p r o po s i t i o n ” ,a nds o me t i me sd i f f e rd e pe n di ngo nt he i rd e g r e e o fph i l o s o ph i c a lt r a i n i n g( 2 003:90f . ) .So mee ve nr e f u s et ot a k e“ x knows a pr o po s i t i o n ”t obeac on s e q ue nc eof“ x knows that p” ,t a k i n gi tt obei n t e l l i gi bl eo n l yo nt her e a d i ng ,“ x is acqua i n t e dwi t hap r o p o s i t i o n ” .Ibe l i e vet he trivial reason most philosophers accept this inference, but not the ones with “ f e a r s ” ,“ s a y s ” ,e t c . ,i st h a tt h e ya r efamiliar with it. We do naturally speak of “ t h i ng son ema ykn ow” ,a nd ,e pi s t e mol ogybe i ngs u c ha common topic, the br o a d e n e du s eo f“ p r o po s i t i on ”h a sg r a d ua l l yg r ownup o nu s .Ha df e a rb e e n as commonly discussed as knowledge, the same would have been the case with this word. Those philosophers who know some French (but do not philosophize in it the la n g u a g et ooo f t e n )wi l lno t et h a t“ J es a i su n ep r o po s i t i on ”s o u nd smo r eod dt h a n“ Iknow ap r o po s i t i on ” .Th er e a s o ns o me pr o po s i t i o n a la t t i t ud eve r b ss e e me s pe c i a l l yr e c a l c i t r a n tt o( P) ,l i k e“ s a y ” ,i s pr o ba bl ybe c a u s et h e yd i f f e rf r om “ k now” ,“ f e a r ” ,e t c ., in not allowing terms in general as grammatical objects. One can know or fear anything, in the sense of being afraid of or acquainted with, but one cannot say the Eiffel Tower, Winston Churchill, and so on. With a little open-mindedness, however, I thin ka ny onec a n“ f e e l ”t h es e n s eo f“ x f e a r sap r o p o s i t i o n ”a sa n e n t a i l me n to f“ xf e a r st h a ti twi l lr a i n” .Af t e ra l l ,wec a ns a yt h a twh e no n e fears or says, that p, that q, etc., it follows that there are things one fears and says, namely, that p, that q. But then, there should be no additional problem wi t hc a l l i n gt he s et hi n g s“ p r o po s i t i on s ” .Th e r e f o r e ,i ns umma r y ,It h i n kwe s ho u l d us e( P)a sa d e f i ni t i on o fo urt e c h n i c a luso f“ p r o p o s i t i o n ”i n philosophy and, simply, get used to it! There remain certain special problematic cases, however, that we will discuss before closing this investigation. The following inference is apparentl yl e g i t i mi z e dby( P) :f r o m“ Hewa sh a pp yt h a tp”t o* “ Hewa sh a pp ya pr o po s i t i o n ”( c f .As h e r( 1 987) ) .Th i si sa no b j e c t i onf r om grammaticality. Ho r wi c h ,c on c e r n i n gt h emo r ede ba t e di s s uewh e t he r“ t h a tp”i sa l wa y si n t e r s ub s t i t u t a bl ewi t h“ t hepr o po s i t i ont h a tp”wi t h o u tl o s so fg r a mma t i c a l i t y ,h a s noted that there are uncontroversial cases of co-referring terms where substitution, however, yields ungrammatical sentences. For instance, if we subs t i t ut e“ Pa v a r o t t i ”f o r“ Th eg r e a t e s tt e no r ”i n“ Th eI t a l i a ns i n g e rPa v a r o t t i ne ve rs i ng sWa g ne r ” ,weg e t* “ TheI t a l i a ns i n ge rt heg r e a t e s tt e n o rn e v e r s i ng sWa gn e r ”( s e eSc hi f f e r( f o r t h c oming)). Likewise, one cannot straightforwardly apply an existential generalisation to this sentence, since this would yi e l d* “ TheI t a l i a ns i n ge rs ome onene ve rs i ng sWa gn e r ” .So ,( P) ,wh i c h
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seems to legitimize such inferences may be saved by appeal to independent grammatical facts. I ts e e mson ec o ul df o r mul a t es ome t hi n ga n a l ogo u st oQui n e ‟ sTh e s i st o shed further light on these cases. The thesis I have in mind is that one can i n f e ras e n t e n c e“ F( apr o po s i t i o n) ”f r o m“ F(that p) ”on l yi ft h ee x p r e s s i o n “ Th e thing such that F( i t ) ”i swe l l -f o r me d .Cl e a r l y ,on ec a ni n f e r“ Hebe lieves ap r o po s i t i on ”f r o m“ Hebe l i e ve st h a ts n o wi swh i t e ” ,a n d ,i n d e e d ,t he e xp r e s s i on“ Th et h i ngs uc ht h a thebe l i e v e si t ”i swe l l -formed. However, c o nc e r ni ng“ Hewa sh a p pyt h a tp” , t h ec o r r e s p o n di n gd e s c r i p t i o n ,* “ Th et hi n g s uc ht h a th ewa sh a p pyi t ”i sno twe l l -formed. These facts seem related, and indicate that there is something special about those expressions that yield s e n t e n c e swi t h“ t h a t ” -clauses, but which are recalcitrant to (P). One can of c o u r s et a ket h i st os h ows i mpl yt h a t“ t h a t ” -clauses are not singular terms, but the obvious term-like behaviour in other cases, in particular, the obvious predicate-l i kebe h a vi o uro fe x p r e s s i o n st h a tc on ne c twi t h“ t h a t ” -clauses to form sent e n c e s ,l i k e“ i st r ue ” ,“ Hebe l i e v e s ” ,s e e mst omet os h o wt h a ta n alternative solution would accommodate the data best. In fact, the very charge we have been discussing can easily be turned against those who deny that “ t h a t ” -clauses are singular terms. The charge will then be that if expressions l i ke“ Hewa sh a ppy ”a r eno tt obec o n s i d e r e da ss yn t a c t i ce xceptions, why is it that it cannot, as opposed to other expressions which yield sentences with “ t h a t ” -c l a us e s ,b ef o r me di n t oad e s c r i p t i on* “ Thet hi n gsuch that he was h a ppy i t ” ?Ibe l i e v et he s ec a s e smi g h tr e q ui r epr a g ma t i ct r e a t ment. For i n s t a n c e ,as e n t e nc e“ Hewa sh a ppy( s ur pr i s e d / up s e t / . . . )t h a tp”mi g h tbe e l l i p t i cf o r“ Hewa sh a pp y( e t c . )to find out that p” ,o rs omes uc h .Ont h i s view, the expressions which do not satisfy the condition of well-formedness, as stated in the thesis, are indeed not predicates, but they are ellipses of pr e d i c a t e s .Th i s ma k e st he c l a i mt h a t“ t h a t ” -clauses are singular terms c o n s i s t e n twi t ht h ede ni a lt h a t“ Hewa sh a p py ”i sap r e di c a t e ,wh i c h ,i nt u r n , accounts for the apparent counter-examples to (P). Fi n a l l y ,t he r ei st hei n f e r e n c ef r om “ Hes a i ds ome t hi n gn i c e ,n a me l y ,t h a t p”t o“ I ti sn i c et h a tp”( Mol t ma n n( 20 0 3:8 9 ) ) .Th el a t t e rs ho ul dbeun de r stood as a grammatica lv a r i a n to f“ Th a tp i sn i c e ” ,a si n4 . 3.Ont h emo s t natural interpretations of these sentences, however, they seem logically inde pe n de n t .I nt h ef i r s ts e n t e n c e ,“ i sni c e ”do e sn o ts e e mt obep r e d i c a t e do f the proposition. If it were, the inference should be unproblematic. It seems rather predicated of the act of saying. The sentence might, then, be equivalent t o“ Hes a i ds ome t h i n ga ndhi sa c to fs a y i n gi twa sni c e ” .Abe t t e ra n a l y s i s ,i t
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s e e mst ome ,ma k e si te q ui v a l e n tt o“ Hes a i ds ome t hi n gwh i c hi ti snice to s a y ”( i . e . ,“ Hes a i ds ome t h i ngs uc ht h a tt os a yit i sni c e ” ) .Th u s ,t h ep r o pe r o bj e c to f“ i sni c e ”h e r ei s“ t os a yx” ,wh e r e a si nt h el a t t e rs e n t e n c e ,i t so bj e c t i sa“ t h a t ” -c l a us e .I ti st h usa ne q ui vo c a t i ono f“ n i c e ” .Wen e e dn o two r r yh e r e abouth o wt oc a t e go r i z ee xp r e s s i on so ft hef o r m“ t o” .Pe r h a p st h e yr e f e rt o action-types. What is important is that we have, again, an ellipsis which seems to explain why the apparently invalid inference is indeed invalid.
5.7 ON ASSERTIBILITY Much of what has been said in this book presupposes the correctness and feasibility of a non-traditional semantics, that is, a semantics where truth does not play any role. I will therefore give a few, admittedly speculative and freewheeling, comments on this aspect of t h ede f l a t i on i s t ‟ sd i a l e c t i cs i t u a t i on . Logical space of course offers an unsurveyable amount of candidates for nona l e t h i cs e ma n t i c s ,b uton en o r ma l l yt hi nk so ft he a l t e r n a t i v e sa s“ u s e t h e o r e t i c ”a c c o un t s ,i . e . ,r o ughl ys pe a k i ng ,s e ma n t i ct h e o r i e st a k i n g as central concepts defined in terms of linguistic behaviour. It is natural to think of inferentialism as an exception here, but in my opinion, a correct inference is just one which preserves the central semantic property. Those expressions whose meaning is given an inferentialist treatment are simply those that are treated intralinguistically, but this leaves it open what relation between expressions or s e n t e n c e st h a ta r er e l e v a n ti na c c o un t i ngf o rt hee x pr e s s i on ‟ sme a n i n g . That deflationism has seemed to require such an alternative semantics has probably been the major reason for not endorsing it. On the other hand, though much technical work has been done within the Tarski-Davidson paradigm, much with the appearance of empirically well-evidenced, applied semantics, the debates about the very idea of thus explaining or illuminating meaning are inconclusive at best.12 It simply remains unclear just what Tarskian truth-definitions have to do with meaning. One thing that remains fairly safe to say, however, is that truth-definitions for a set of sentences of a certain language needs to be coupled with much further theory in order that pe o pl e ‟ sl i n g ui s t i cbe h a v i o uri st o uc he dup on .Us e -theories make this con-
12
See Soames (2003: 309ff.) on another discrepancy between philosophical discussions about Davidsonian semantics and its applications.
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nection immediately. Here, then, is a sweeping and tentative (and biased) comparison between truth-theoretic and use-theoretic semantics: the former is simple and clean, and often gets things right (whether explanatory or not), while various use-theorists are lucky if they manage to say something that is both clear enough to judge and is not immediately subject to clear counterexamples. However, this disadvantage of use-theories is compensated by the relatively higher gains of success: namely an account which connects more with actual speakers and their linguistic behaviour, which ought to be a main explanandum. The factual adequacy and simplicity of truth-theoretic descriptions are not ne c e s s a r i l yt r a i t st h a ts up p o r tt he m,f ur t h e r .A d e f l a t i o n i s t ‟ sv i e wo ft h i s endeavour should be that it is a gathering of disguisedly folk-semantic descriptions and connections between them, which in the end do nothing by way of explanation. For instance, the truth-functional account of sentential connectives has been proved by Field (1994a: 256ff.) to be derivable from a simple disquotational truth-theory (another example of this type of trivialisation was given in 2.4). Truth-theoretic semantics, from this perspective, is merely a matter of applying those concepts (and various complex derivative concepts) that a more thoroughgoing theory should take as its data. The more complex the truth-theoretic accounts, the more difficult it is for the deflationist to prove that this is the case, of course. But this is no reason to doubt that they can eventually be thus trivialised. In fact, no arguments that this should be impossible have, to my knowledge, been presented. Of course, ma nyi n s i gh t so f ,s h a l lwes a y ,a“ s t r uc t u r a l ”k i n d ,ma yh a v ebe e ng a i n e dby truth-theoretic semantics along the way, and should be kept. But the basic substantial question of what central semantic concept to employ seems, on balance, quite open. Let me in these closing pages express my own sympathies and interests pertaining to this basic question. The notion of assertibility is usually thought of as epistemological. However, this seems to make it conceptually dependent on propositional and intentional notions, to wit, on the notion of belief in a proposition. Besides ruled out by (NC), assertibility thus understood will be unfit for playing a role in semantics for the same reason that propositional truth is: it presupposes that one know what it is for a sentence to express a proposition, but this is too close to that which the semantics should explain (cf. the argument in 4.4). To explain the meaning of an expression or sentence by recourse to the assertibility (conditions) of sentences thus requires that assertibility is primarily a property of sentences, not of propositions.
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Accordingly, I believe semantics should be entirely naturalistic in the sense that intentional terms are ruled out from the meta-language. But note that this naturalism will not be of the demanding kind required by a truththeoretic semantics. For giving naturalistic truth-conditions of sentences with intentional vocabulary requires naturalistic reduction, this being the nature of truth-conditions. A use-theoretic naturalist semantics, by contrast, need only avail itself of defeasible assertibility conditions of sentences with intentional terms, plausibly taking such conditions to c o n c e r np e o pl e ‟ so b s e r v a b l ebe h a vi o u ra n de nv i r on me n t .Thi si sat y peo f“ i n t e r p r e t i v i s t ”s e ma n t i c s ,b u tn o t one which states equivalences between belief-sentences, etc. and sentences de s c r i bi ngbe h a vi o u r( o r ,e ve nwo r s e ,o bs e r ve r s ‟a t t r i bu t i o n so fbe l i e f s, etc.). This, I think, is more in line with the intuitive idea that one can always be wrong about what people believe, even if one is right about how they behave, and use this knowledge appropriately for deriving belief-attributions. If a correct statement of such defeasible assertibility conditions can also be coupled with an explanation of the function of expressions governed by such assertibility conditions, then it can also be argued that one has given an explanation of the cognitive state itself, though, of course, in the same type of indirect way that (D) is taken as an explanation of truth itself. We have not yet said what assertibility is, only that (NC) rules out any definition in intentional terms. Possible candidates, then, include that of an utterance simply being assented to in certain circumstances. More sophisticated are the notions of correctness and incorrectness relative to a community, explained in terms of positive and negative reinforcements, which can themselves be naturalistically exp l a i n e d .Th u s ,o nBr a n d o m‟ sd e ve l opment of Ha u ge l a n d ‟ s( 19 82 )a c c o u n to fno r ms ,“ [ p] o s i t i v e l yr e i n f o r c i n gad i s po s i t i on to produce a performance of a certain kind as a response to a stimulus of a certain kind is responding to the response in such a way as to make it more likely in the future that a response of that kind will be elicited by a stimulus of t h ec o r r e s po nd i ng ki n d ”( 1994:35) .Ne g a t i v er e i nf o r c e me n ti ss i mi l a r l y de f i ne da sar e s p on s ema k i ngi tl e s sl i ke l yt h a tt hes u bj e c t ‟ sb e haviour will be repeated in the given kind of circumstance. A sentence can then be said to have C as its necessary and sufficient assertibility conditions iff utterances of the sentence tend to be positively reinforced by the community members when C obtain and negatively reinforced when C do not obtain. Being subject to positive reinforcement may look as an intuitive account of some notion of “ c o r r e c t ” ,whi c hi ss t i l le n t i r e l yn a t ur a l istic. (On the other hand, one may discuss whether the semantic concept is more reasonably taken to be the final
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state of competent speakers, i.e., their speech dispositions, rather than what looks more like the causal route to this state, i.e., the reinforcements.) A different use-theory takes into account not only the conditions under which sentences are (correctly) uttered, but also the consequences of uttering t he m,t h usgi v i n gmo r eofa“ c a us a lr o l es e ma n t i c s ” .Su c ha ni d e ama ybe motivated by the heuristic principle that we should look at simpler examples of the phenomenon to be explained (language), and then extend the theory for these to the more complex phenomenon. To account for the signals of simpler animals, it seems sufficient to describe precisely the causal role of productions of signal-types. A typical cause could be, e.g., the presence of a predator, and the typical effect a fugitive behaviour of conspecifics. Why could not human languages be simply immensely more complex systems of sounds with associated causal roles? Thanks to superior intelligence and memory, the causes and effects of utterances can be much more distant and indirect than those of the signals of simpler animals. Further, human languages are compositional, so subsentential expressions will contribute systematically to the causal roles of sentences where they occur. On this type of theory, then, the central semantic property of a primitive expression is its causal role, which, in turn, is identical to the contribution it makes to the causal roles of sentences containing it. Expressions that intuitively lack empirical content will be treated intralinguistically, and will serve the purpose of partaking in sentences that function as bridges between sentences which do have empirical content. Insofar as a sentence has assertibility conditions that eventually depend, if only via other sentences, on environmental features, they have a causal role of practical relevance. Of course, on all these theories, there will be non-semantic inhibiting factors complicating the story. One does not, for instance, normally make irrelevant utterances, even when their assertibility conditions obtain. Otherwise, we would constantly utter analytic sentences, since their assertibility conditions always obtain. But as long as the inhibiting factors can be isolated fairly well, the semantic properties of expressions can be isolated as well. For any linguistic piece of behaviour, there is intuitively a semantic part of the explanation to the behaviour, and all kinds of non-semantic ones. There are cognitive factors (different speakers will assent to different sentences because they have undergone different perceptual stimulations, etc.), social (speakers may differ in humour), and so on and so forth. Irrelevance, by the way, seems to be a notion particularly suitable for a causal explanation (cf. Sperber and Wilson (1986: Ch. 3)).
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I would also like to note that there is an important sense in which we may still appeal to the truth-conditions of certain sentences when accounting for their meaning. We may do so in the special sense that we may take the assertibility-conditions of those sentences to be those in which, as we casually have it, they are true. For instance, we are free to say, e.g., that the semantic me a n i ngof“ I ti sr a i n i n g ”c on s i s t si nt hef a c tt h a ts pe a ke r sa r ec o n d i t i o n e dt o utter it when and only when it is raining (at the place of utterance). Here, we have not used “ t r u e ” ,bu to n l yg i ve nac ond i t i onf o ra s s e r t i bi l i t y( no td e f i n e d in terms of truth), which happens to be the condition under which, casually speaking, it says something true. Of course, attitude-ascribing sentences will no tbee xp l a i n e dont h i smo de l .St a t i n gt h a t“ Ab e l i e ve st h a tp”i sa s s e r t i bl e when and only when A believes so and so (roughly speaking) will of course violate (NC). There is good reason to take simple empirical sentences to have precisely such assertibility conditions. Consider the predator-indicating signal of a simple animal. It may first be thought that the typical cause of this signal should be taken to be a certain kind of perception, perhaps referred to as a certain series of stimulations on the retina. But it may happen that the predator always makes a certain noise, which the signalling animal comes to associate with the visual stimuli in such a way that it will emit the signal upon hearing the noise, even absent the visual stimuli. We should not say then that the signal has changed in meaning. It was always a sound indicating the presence of a predator, independently of what causal chains between the predator and the signal. Therefore, although the signalling animal will emit the signal more often in conditions individuated in terms of stimuli than in conditions in which there is a nearby predator, the latter makes more sense to take as semantically relevant. Plausibly, the causal roles of a type of sound-pattern should be such that the cause is what motivates the effect. The fugitive behaviour should not ultimately be explained by reference to the perceptual stimulation of the conspecific, but to what tends to cause those stimulations, namely, the presence of a predator, since the latter is what makes the effect of the signal beneficial. Language, on this model, is at base an extension of the senses. Instead of having to be there to see or hear what is happening, one takes the requisite me a s ur e st h a nk st oo t h e ri n d i vi d ua l s ‟s e e i ngo rhe a r i n gi t .Wi t h greater intelligence, the language can develop so as to enable sound-patterns with more intricate connections to observation-related sound-patterns, thus
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creating sentential connectives, quantifiers, non-referring singular terms that can instantiate quantifications, etc. A word, of course, has an infinite amount of causal roles of various kinds. The task of the semanticist is to capture that role which is semantically relevant. Intuitively, the meaning of an unambiguous word is a single thing that partakes in the semantic part of the explanation of any piece of linguistic behaviour involving the word, and does so uniformly. On this account, this “ t h i ng ”wi l lbeage ne r a lpa t t e r n ,n a me l y ,age ne r al contribution to the causal roles of sentences. These roles will mesh in complicated ways with nonsemantic factors, such as perceptions and inferences. Sometimes, people end up s a y i n gt hewr o n gt hi ng ,l i ke“ Th eEa r t hi sf l a t ” .Th i sma ybo t h be universally assented to and even positively reinforced. 13 This does not contradict the idea of a dispositionalist or assertibility-conditional semantics. For each word in this sentence has a general effect on sentences, and the most basic sentences containing these words will always and only be assented to in the right circumstances. These are sentences such that the things and properties figuring essentially in the specification of the causal roles of their words are readily perceptually accessible. It is plausibly by exposure to such basic sentences that the words are learnt. The semantically relevant causal roles of words (i.e., their contribution to the roles of any sentence containing them) should be sought by looking at their roles in these basic sentences. The r e a s on“ Th eEa r t hi sf l a t ”i sut t e r e dh a sa si t ss e ma n t i ce x p l a n a t i o nt h e relevant causal roles of the words therein, and, as its non-semantic explanation, the fact that certain perceptions and non-demonstrative inferences have been made. The semantic content of the whole sentence is just given by giving the general causal roles of its parts and its mode of composition. Taking this as input, together with (very many) non-semantic facts, including assumptions about cognitive normal functioning, a speakers‟b e h a v i o u rwi l l f ol l o wa so ut pu t .I nt hep r e s e n tc a s e ,t h i swi l lbet heu t t e r a n c eo f“ Th eEa r t hi s f l a t ” .Th es a mec a us a lr o l e swi l lde t e r mi net h ee f f e c tt h a ta nu t t e r a n c eh a so n other speakers, given their general cognitive state. 13
Though this is not the main response to the alleged problem, I believe that the possible po s i t i v er e i nf o r c e me nto fut t e r a nc e sof“ TheEa r t hi sf l a t ”wi l lb eq u a l i t a t i v e l yd i f f e r e n t from those that institute semantic competence. When teaching a child how to speak, different sanctions are applied than when teaching social codes or extralinguistic kno wl e dge .Me r ei mi t a t i o na nds e ns i t i v i t yt o“ n o tbe i n gu n d e r s t o o d ” ,i . e . ,no tp r o mp t i n g appropriate conversational reactions may be powerful cues in acquiring semantic competence.
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An explanation in the same spirit should be given for cases in which we fail to assent to an analytic sentence, perhaps because it is very complex. Now, how can one say that the assertibility conditions for a sentence are unconditionally fulfilled although perhaps all speakers fail to assent to it? Obviously, the assertibility conditions of a sentence will not be such that always, when an utterance is made in that condition, there will be assent and a positive reinforcement. A plausible assignment of an assertibility condition C for a sentence s is had by balancing the actual reinforcement conditions with simplicity. Thus, a good assignment should be both such that utterances of the sentence are normally positively sanctioned in those conditions and negatively sanctioned outside, and such that learners of the language can readily internalise the condition. So, even if there were conditions one could formulate for the assertibility of conditionals which would include those cases where speakers fallaciously assent to conditionals, we ought to formulate them in a simpler way and accept the slack between the formulation and s pe a ke r s ‟s a n c t i on s .Wewi l lt he n ge tg e ne r a l ,n on -universal assertibility conditions of sentences as their central semantic content, statements of the f o r m“ I nge neral, s is assertible iff p” .An dn ow,wec a ns i mpl ys a yt h a t analytic sentences are those whose general assertibility conditions are trivially fulfilled. Suppose we take the central semantic character of conditionals to be the fact that, in general, a conditional is assertible iff the consequent is assertible if the antecedent is. And suppose we take the semantic character of disjunctions to be that, in general, a disjunction is assertible iff either disjunct is assertible if the negation of the other is assertible. Now, we can see that the ge ne r a la s s e r t i b i l i t yc o nd i t i on so ft hes e n t e n c e“ I fi ti sr a i n i n go ri ti ss n o wing, t h e ni fi ti sno ts n owi ng ,i ti sr a i ni ng”a r et r i v i a l l yf u l f i l l e d .I fs pe a k e r sd on o t always assent to this, this just shows that various cognitive factors prevent their semantic competence from being properly executed. Something along these lines could perhaps even be used to argue for the analyticity of mathematics. Finally, we may address the question what motivates the claim that the above proposals are candidates for semantic theories, i.e., that they could somehow explain meaning, given that this notion is ruled out from the language of the theory? Since we do not reduce this term naturalistically, there must be some other connection between it and the claims of the semantics. But note that the semantic theory, if complete, will also describe t h es e ma n t i cc h a r a c t e ro ft hewo r d s“ me a n ”a n d“ me a n i n g ” ,i nas y s t e ma t i c way. The defence of the claim that the theory is worthy of the label“ s e m-
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a n t i c ”mu s te ve n t u a l l yc o n n e c ts ome h ow wi t ht h i sa c c o u n t .Wh a tmu s tbe shown is that the naturalistic properties of sentences that the theory takes as essentially semantic are also those that are tracked wh e nweu s e“ me a n ”a n d “ me a n i ng ”( o r ,b e t t e r ,“ l i t e r a lme a n i ng ” ) .Wh a tt h i st r a c ki ngc ome st oe xa c t l y may be a matter of discussion. But since the assertibility conditions of sentences containing intentional vocabulary will be ones concerning speake r s ‟ behavioural dispositions in relation to events in the environment, and since it is such facts that are taken as essentially semantic by the semantic theory, it might seem that there is some hope of explaining what the tracking comes in s uc hawa yt h a tl a be l l i n gt het he o r ya s“ s e ma n t i c ”i sj us t i f i e d . These were some very programmatic and preliminary ideas about how to replace a Platonist, representational outlook with a non-reductive naturalistic one. Despite being at such an embryonic stage, it should be clear how direct the motivational connection with the preceding claims. Deflationism and nominalism separately rule out the use of truth in the metalanguage, and propositional attitudes are ruled out from the metalanguage because of their association with propositions. These notions are to be treated linguistically by the naturalistic, non-representational semantics, but, hopefully, still in such a way as to justify the claim that they have been exhaustively explained.
194
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203
INDEX ambiguity, 14f., 35ff., 39, 55, 87f., 90ff., 145f., 151, 175 analysis, 13ff., 18ff., 25f., 46f., 48ff., 102, 111ff., 113ff., 131, 153, 164 analytic, 29f., 93, 115ff., 152, 154, 160ff., 177f., 180f., 187, 189f. Aristotle, 43 Asher, N., 181n, 182 assertibility, 24, 35, 65f., 82, 102, 108, 115, 117ff., 154, 159ff., 162ff., 172n, 173ff., 5.7 Austin, J. L., 21, 77, 100, 142 axiom, 15, 28, 40ff., 86, 94, 98, 103, 157 Ayer, A. J., 23n, 78, 95n Baker, G. P., 81 Baldwin, T., 25n, 50n, 98n, 108, 111n Bar-On, D., 119 Bealer, G., 168n Beebe, J. R., 76n Belnap, N., 62, 2.5 Black, M., 56, 56n, 142 Blackburn, S., 19, 46n, 97n blind truth-ascriptions, 29f., 48ff., 95f., 4.3 Boghossian, P., 28, 75ff. Brandom, R., 62, 67, 2.6-7, 186 Brentano, F. C., 62 Buchanan, R., 93 Burgess, J. P., 126n Camp, J., 62, 2.5 Carnap, R., 24n, 121n, 150, 151
Carroll, L., 103 causal role semantics, 186ff. Chihara, C., 126n Chisholm, R., 97n Cohen, J., 78 coherence theory, 12f. compositionality, 127f., 186f. correspondence theory, 12ff., 1.3, 26, 45ff., 51, 54, 57, 59ff., 62, 74f., 83f., 88f., 93, 123 Cozzo, C., 45 David, M., 19n, 25n, 27, 50n, 91f., 98n, 111n Davidson, D., Davidsonian, 22n, 38, 59ff., 171n, 184f., 184n, Devitt, M., 26, 59 Dewey, J., 13 disquotationalism, 23ff., 70, 2.1011, 126, 133, 142ff., 146f., 184 Dodd, J., 19n Dummett, M., 14ff., 25, 40, 46, 48, 83, 110, 118f., 144f., 173, 173n ellipsis, 95, 100, 142f., 4.4, 186f. empirical content, 31, 163, 177ff., 190f. entailment, 10, 30, 120, see also “ i n f e r e n c e ” epistemic truth-theories, 1.2, 55, 57, 62 Etchemendy, J., 146n existence, 16, 19n, 20f., 27, 116f., 131f., 156f., 164ff.
204
Index
existential quantification, 27, 116f., 156f., 159f., 164ff. expressive strength, 9f., 22, 28, 29-32, 38, 49f., 51f., 63, 74, 85f., 91f., 3.5, 140, 168 facts, 10, 1.3, 26f., 32, 33ff., 40ff., 55, 76, 84, 96, 97, 119ff., 152f., 155, 157, 165, 182ff. falsity, 106, 142f., 156 fictionalism, 161-3 Field, H., 8, 28, 59f., 71, 2.10-11, 100n, 111, 131, 4.4, 161, 188 Forbes, G., 31n, 100n, 112f. Freddoso, A. J., 160 Frege, G., 44, 49f., 49n, 98, 126, 133, 158, 173, 173n García-Carpintero, M., 146n Geach, P., 65, 79, 173n generality, 9f., 22, 29ff., 40ff., 51f., 68, 70, 85f., 91f., 117f., 129, 177ff. glossogeny, 174 grammar, 24n, 31, 49n, 50ff., 62, 64ff., 70, 72ff., 74n, 85, 93, 98, 113, 130ff., 138f., 139n, 159ff., 168ff., 174f., 177, 181 Grice, P., 94, 133, 142 Grover, D., 31n, 2.5, 69, 71 Gupta, A., 41, 42n, 97, 123, 151, 182 Haack, S., 100n Hacker, P. M. S., 81 Halbach, V., 93n, 146n Hale, B., 173n Haugeland, J., 190 Heck, R., 173n Hempel, C., 23n Hill, C., 100n, 113n
Horisk, C., 2.5 Horwich, P., 7, 20f., 21n, 28, 31n, 32, 33f., 35, 41f., 42n, 44, 79, 83, 2.12, 99f., 100n, 103ff., 110f., 118n, 125, 126n, 139, 140, 151, 182ff., 186 induction, 179f. inference, 34f., 77, 79, 83, 86, 89, 89n, 92, 103ff., 108, 110f., 114, 119ff., 122f., 128f., 134, 136, 139f., 140f., 163ff., 171ff., 180, 183, 184ff., 190f. infinity, 10, 22, 30, 41ff., 48, 96, 97, 99f., 102, 107, 111f., 115, 125, 162, 182ff., 192 interpretivism, 189 James, W., 13 Johnson, W. E., 49n Kalderon, M. E., 100n, 113n Katz, J., 162 King, J., 185n Kirkham, R., 13, 26, 51, 52, 59, 74n, 80, 81, 100n, 136 Kovach, A., 100n, 106n Kripke, S., 110 Lance, M., 63, 76f., 180 Leeds, S., 29n Lewis, D., 59f., 77 Lewy, C., 59, 92n logical form, 52, 74n, 159ff. Lycan, W., 119 Mackie, J. L., 100n Martin-Löf, P., 8, 14 mathematics, 14, 41, 161ff., 194 Matthews, F., 160n, 175n McGee, V., 59, 100n, 113n McGinn, C., 26 McGrath, M., 100n, 106n, 139n
205
Index
minimalism, 10, 41f., 2.12, 182ff. modality, 88, 93, 93n, 125, 138, 146f., 148 Moltmann, F., 160, 185, 185n Mönnich, U., 171n multiple relations theory, 175f., 182 Næss, A., 36f. natural deduction, 180 naturalism, 35, 189ff. Neurath, O., 23n Nietzsche, F., 131 nominalism, 129f., 132, Ch. 5 Ockham, W., 94, 160 ordinary language, 14, 35ff., 86, 87, 91, 92ff., 121, 129, 4.3, 156, 184 Pagin, P., 7, 30n, 36n, 47n, 59n, 142, 170n Pap, A., 100n paradoxes, 129n paraphrase, 2.3, 63f., 67, 72ff., 97f., 112f., 114, 135, 156, 160f., 163, 175f., 182 Parsons, T., 171n Peirce, C. S., 13 Plato, Platonism, 126, 158, 173, 194 Platts, M., 100n pragmatics, 32, 2.8, 132ff., 135, 138, 142f., 4.4, 186f., 191 pragmatism, 13f. Prawitz, D., 8, 14 Price, H., 81n primary truth-bearers, 19n, 25, 51, 57, 60, 84, 90, 92ff., 95, 99, 129, 132, 138, 143, 144ff., 150, 151, 152f., 154, 158, 167, 189
Prior, A. N., 31, 100n, 113, 160f., 160n, 171, 175, 175n, 182, 185n proof, 13, 14ff., 182 properties, property of truth, 10, 28f., 32, 45f., 46f., 52, 60f., 63, 2.7, 96, 123, 125f., 145, 156 proposition, nature of, 15, 132, 150, 158ff., 173, 5.6 propositional attitudes, 24n, 93, 132ff., 138, 142, 151, 153, 159, 163, 175f., 176n, 185, 189, 194 propositional quantification, 10, 26n, 27n, 31, 51, 52, 56, 62f., 91f., 97f., 99, 100f., 3.3, 160, 182, 183 Prosententialism, 31, 2.4-2.7, 136, 141 Putnam, H., 13f. quantification, 26n, 52, 57, 69, 72ff., 74n, 80, 99, 100f., 105f., 3.3, 135, 139f., 151, 152ff., 160, 161, 174, 176ff., 184, 192 Quine, W. V., 18, 25, 29n, 2.102.11, 119, 123f., 124n, 130, 153, 186 quotation, 24n, 25, 49n, 54, 69, 74n, 84, 89, 92, 93, 130f., 132, 136, 177n Raatikainen, P., 97 Ramsey, F., 18, 24n, 2.3, 63f., 72f., 74n realism, 12, 17, 116, 158, 163ff., 173 Redundancy theory, 10, 2.3, 63f., 74
206
Index
reference, 16, 18, 27, 46f., 67n, 71, 77f., 90, 126f., 140f., 148, 152f., 161, 172f., 174, 181, 192 Resnik, M. D., 85, 100n, 162 Russell, B., 21, 50, 147n, 175f., 175n, 182 satisfaction, 16, 53, 55, 56-63, 67n, 90, 109, 114 scepticism, 26, 86f., 88, 118, 156 schema, 15, 21, 21n, 22, 24n, 25, 28, 29f., 33, 41, 53f., 58f, 72, 81ff., 84, 96, 99-100, 101, 102f., 103ff., 107, 108n, 118, 120, 184 Schiffer, S., 171n, 176, 185n, 186 Schlick, M., 23 Schuurman, H., 160 Shapiro, S., 28f. singular term, 66f., 77, 89, 135, 139, 151, 158-161, 164, 165f., 5.4, 175, 175n, 177ff., 186 Smith, P., 137 Soames, S., 29n, 31, 45, 48, 57, 61, 62, 78ff., 97, 98, 100n, 144f., 188n Sosa, E., 100n, 106n Sperber, D., 133, 191 Srzednicki, J., 36 stipulation, 21, 24, 35ff., 57, 59f., 86, 90, 91ff., 104, 112, 115, 123ff., 164, 184f. Strawson, P. F., 18, 2.8, 141, 145 substitutional quantification, 65, 89n, 91f., 110-111, 176ff. s yn t a x, s e e“ g r a mma r ” Tarski, A., 38, 40, 2.4, 92n, 100n, 115, 145, 188
“ t h a t ” -clause, 25, 61n, 73f., 117, 131, 135, 138f., 139n, 143, 150, 152ff., 158ff., 164, 167f., 169ff., 174ff., 182, 184ff. Tomberlin, J. E., 181 translation, 71f., 88ff., 93, 141, 181 truth-conditions, truth-conditional semantics, 13f., 33, 53ff., 57, 60ff., 61n, 76, 78, 88f., 90, 94, 96, 108f., 108n, 110, 121f., 142, 144f., 145ff., 158ff., 161, 163, 164, 176, 180f., 188f., 191f. Tye, M., 160n, 175n universal quantification, 29ff., 34f., 49ff., 64ff., 72ff., 80, 85f., 97f., 101, 105, 117, 153f., 160, 176ff. use-theory, 83, 119, 128f., 129n, 157f., 163f., 5.7 van Inwagen, 26n, 51n, 100n, 113n variable, 24n, 53, 56f., 61ff., 64, 73f., 81f., 89n, 92, 101, 107115, 177n Vision, G., 93 Warnock, G. J., 79 Williams, C. J. F., 2.3, 63f., 74 Williams, M., 23n, 33n Wilson, D., 133, 191 Wittgenstein, L., 21, 58, 2.9 Wright, C., 17, 19, 28, 46, 172f., 173n Yngve, V. H., 139n
207
