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UBC Theses and Dissertations

Convention and the intensional concepts Hadley, Robert Francis 1973

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CONVENTION AND THE INTENSIONAL CONCEPTS by ROBERT FRANCIS HADLEY B.A. with High Honors, U n i v e r s i t y of V i r g i n i a , 1967 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Philosophy We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1973 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree th a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of Philosophy The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada i ABSTRACT The c e n t r a l theme of t h i s thesis i s that our use of language i s guided by l i n g u i s t i c conventions or l i n g u i s t i c r u l e s . S ubstantial arguments are produced to show that we must suppose language use to be guided by such conventions. Further arguments are produced to show that the theory that language use i s convention-guided can explain many facts which have not yet received s a t i s f a c t o r y explanations. Some of the main explanatory advantages of the convention-guidedness theory are: 1) i t explains the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n . 2) i t enables us to s t a t e , with f a i r p r e c i s i o n , exactly what a concept an a l y s i s i s , and how i t i s possible f o r people to use concepts without knowing the ana l y s i s of those concepts. 3) i t explains why people's i n t u i t i o n s about meaning and synonomy agree to such a large extent. 4) i t explains how l i n g u i s t i c d e s c r i p t i o n s of experience are j u s t i f i e d by experience. 5) i t explains why a l l the objects denoted by a given term often share some set of properties which can, f a i r l y e a s i l y , be described. One problem which has plagued e a r l i e r theories of l i n g u i s t i c con-vention has been the lack of any acceptable p r i n c i p l e of i n d i v i d u a t i o n f o r l i n g u i s t i c r u l e s . In t h i s thesis a s a t i s f a c t o r y p r i n c i p l e of i n d i v i d u a t i o n f o r l i n g u i s t i c rules i s developed. S i m i l i a r i t i e s are noted between the way computer behaviour i s guided by a program and human l i n g u i s t i c behaviour i s guided by l i n g u i s t i c r u l e s . It i s noted that very precise c r i t e r i a e x i s t f o r the i d e n t i t y of computer programs, and these c r i t e r i a suggest c r i t e r i a f o r the i d e n t i t y of l i n g u i s t i c r u l e s . i i Other questions investigated i n th i s thesis are: a) Whether Quine i s r i g h t i n thinking that absolutely any of our b e l i e f s might be abandoned i n the face of experiences which c o n f l i c t with an accepted theory. It i s concluded that t h i s doctrine of Quine's i s mistaken. b) Whether the notion of " l o g i c a l constant" can be elucidated with any p r e c i s i o n . This question i s answered negatively. It i s shown that we must take the general concepts of necessity and v a l i d i t y as fundamental b u i l d i n g blocks i n i n t e l l e c t u a l i n q u i r y . c) Whether a l l necessary truths are a n a l y t i c . I t i s shown that the answer to t h i s question i s to a large extent a r b i t r a r y . d) Whether necessary truths are the r e s u l t of l i n g u i s t i c convention. It i s shown that necessary truths are not, i n any i n t e r e s t i n g sense, the r e s u l t of convention. i i i CONTENTS Chapter 1 Introduction 1 Chapter 2 General Discussion . . . 7 Chapter 3 Conceptual Revision 36 Chapter 4 Concept Analysis and the Analytic-Synthetic Distinction 46 Chapter 5 Recalcitrant Experiences . 70 Chapter 6 Analytic Truth and Necessary Truth . . . 87 Chapter 7 Convention and Necessary Truth 103 Bibliography 133 Footnote Index 13 5 i v AC KNOWLED GEMENT I wish to thank my thesis supervisor, Mr. Jonathan Bennett, f o r his invaluable suggestions and c r i t i c i s m s i n the preparation of t h i s t h e s i s . Many of the ideas contained herein r e s u l t e d from our d i s c u s s i o n s . I would a l s o l i k e to thank Mr. Howard Jackson and Mr. John Stewart f o r t h e i r h e l p f u l suggestions i n the preparation of the f i n a l d r a f t . F i n a l l y , I would l i k e to thank the Canada Council and the U n i v e r s i t y of B r i t i s h Columbia f o r F i n a n c i a l Assistance during the l a s t four years. Introduction (a) "A rose by any other name would smell as sweet". In t h i s l i n e Shakespeare i s pointing to a c e r t a i n l i n g u i s t i c a r b i t r a r i n e s s about the words we use. He i s a l s o pointing to a c e r t a i n non-arbitrary e x t r a l i n g u i s -t i c f a c t , namely, how a rose smells. The t r u t h of the sentence "Roses smell sweet" depends upon both of these f a c t o r s . Quine makes a r e l a t e d point when he says, " I t i s obvious that t r u t h i n general depends on both language and e xtraUnguis t i c f a c t . The statement 'Brutus k i l l e d Ceasar' would be f a l s e i f the world had been d i f f e r e n t i n c e r t a i n ways, but i t would a l s o be f a l s e i f the word ' k i l l e d ' happened rather to have the sense of 'begat'. Thus one i s tempted to suppose i n general that the t r u t h of a statement i s somehow analyzable i n t o a l i n g u i s t i c component and a f a c t u a l component." 1 But Quine a l s o says, "My present suggestion i s that i t i s nonsense and the root of much nonsense, to speak of a l i n g u i s t i c component, and a o f a c t u a l component i n the truth of any i n d i v i d u a l statement." Quine thinks these two claims are consistent. However, on a c e r t a i n i n t e r p r e t a t i o n , his remarks are obviously i n c o n s i s t e n t . Quine himself provides us with a sentence whose truth value would be d i f f e r e n t i f e i t h e r (a) the world had been d i f f e r e n t or (b) the word ' k i l l e d ' happened to have the sense of 'begat It i s i n a r e a l sense a r b i t r a r y that the word ' k i l l e d ' does not have the sense of 'begat', and i t i s i n a r e a l sense not a r b i t r a r y that c e r t a i n thing happened i n the world. I t i s c l e a r that the t r u t h value of the sentence "Brutus k i l l e d Ceasar" depends upon an a r b i t r a r y element, i . e . , how we use b i t s of language 2 and a non-arbitrary element, i . e . , an e x t r a l i n g u i s t i c event. This c e r t a i n l y seems to refute Quine's claim that i t i s nonsense to speak of a l i n g u i s t i c component and a f a c t u a l component i n the t r u t h of any i n d i v i d u a l statement. Part of the motivation f o r Quine's claim i s that he thinks very l i t t l e can be said about the l i n g u i s t i c component, i . e . , the meaning, which a f f e c t s the t r u t h of a sentence. This i s c l e a r l y his p o s i t i o n i n "Two Dogmas of Empiricism". However, we have already said something about the l i n g u i s t i c component - that i t i s a r b i t r a r y i n a p a r t i c u l a r way. In the chapters which follow I s h a l l say a l o t more about t h i s l i n g u i s t i c component. I w i l l argue that the a r b i t r a r i n e s s we have noted i s a sure sign of l i n g u i s t i c convention. In part I s h a l l be leaning on an a n a l y s i s of convention given by David Lewis i n his book Convention. But I w i l l develop and apply the theory that our use of language i s convention-guided i n ways which Lewis does not consider, (b) In a d d i t i o n to the notion of l i n g u i s t i c convention, this thesis w i l l deal with a number of problems surrounding the s o - c a l l e d i n t e n s i o n a l concepts. Some of these concepts are expressed by ' a n a l y t i c 1 , 'synonomy1, 'necessity', ' p o s s i b i l i t y ' , 'meaning', 'concept', and perhaps ' b e l i e f and 'thought'. In "Two Dogmas of Empiricism" Quine discusses problems which pertain to the c l a r i f i c a t i o n of these concepts. I w i l l now b r i e f l y summarize some of his main points. Later when i t i s appropriate, I w i l l describe his arguments i n more d e t a i l . Quine focuses on the problem of c l a r i f y i n g our use of the terms 'a n a l y t i c ' and 'synthetic'. He notes that a n a l y t i c statements f a l l i n t o two c l a s s e s . The f i r s t c l a s s consists of formal l o g i c a l truths, e.g., "No unmarried man i s married". 3 Quine characterizes a l o g i c a l t r u t h as one "which remains true under a l l r e i n t e r p r e t a t i o n s of i t s components other than l o g i c a l p a r t i c l e s " where "a p r i o r inventory of l o g i c a l p a r t i c l e s , comprising 'no', 'un', 'not', ' i f , 'then', 'and', i s presupposed."^ The second class of a n a l y t i c truths i s t y p i f i e d by "(2) No bachelor i s married. The c h a r a c t e r i s t i c of such a statement i s that i t can be turned i n t o a l o g i c a l t r u t h by putting synonyms f o r synonyms; thus (2) can be turned i n t o (a formal l o g i c a l truth) by putting 'unmarried man' f o r i t s synonym 'bachelor'." The problem with t h i s c h a r a c t e r i z a t i o n of ' a n a l y t i c ' i s that i t appeals to the notion of "synonomy" which, Quine maintains, " i s no less i n need of c l a r i f i c a t i o n than a n a l y t i c i t y i t s e l f . Quine next investigates whether our notion of "synonomy" can be adequately c l a r i f i e d . He notes that we can s a f e l y i d e n t i f y synonomy with sameness of meaning, but he questions whether we can make sense of sameness of meaning. In Quine's view we cannot i d e n t i f y sameness of meaning with mere coextensiveness of terms (two terms are coextensive i f and only i f they apply to the same o b j e c t s ) . He says, "The general terms 'creature with a heart' and 'creature with a kidney 1 are perhaps a l i k e i n extension, but unlike i n meaning".^ Quine eventually concludes, a f t e r r e j e c t i n g various attempts at c l a r i f i c a t i o n , that our notion of sameness of meaning cannot be adequately c l a r i f i e d and i s u n i n t e l l i g i b l e . This i s a paradoxical r e s u l t , given that he c o r r e c t l y notes that sameness of meaning cannot be i d e n t i f i e d with co-extensiveness of terms. For on the one hand we f i n d Quine making a true a s s e r t i o n containing the expression 'unlike i n meaning', and on the other hand he concludes that the expression 'unlike i n meaning' does not have a 4 c l e a r use. This paradox i s the f o c a l point of an attack by Grice and Straw-son which I w i l l discuss i n the following chapter. One attempted c l a r i f i c a t i o n of "synonomy" which Quine discusses appeals to the notion of a d e f i n i t i o n . But th i s " c l a r i f i c a t i o n " i s rejected because i t places the cart before the horse. D e f i n i t i o n s merely report what we take to be e x i s t i n g synonomies. C e r t a i n l y we must already have the idea of synonomy before we can set about rep o r t i n g a synonomy. Consequently, the notion of a d e f i n i t i o n w i l l not help us to understand synonomy. Another attempted c l a r i f i c a t i o n of "synonomy" which Quine r e j e c t s i s the follo w i n g : "Two expressions are synonomous i f and only i f they may be interchanged i n a l l sentences i n which they occur without a f f e c t i n g the tru t h value of those sentences." The problem with this " c l a r i f i c a t i o n " , Quine thinks, i s that unless the language under consideration i s r i c h enough to contain modal adj e c t i v e s l i k e 'necessarily', i t i s j u s t f a l s e that i n t e r -changeability salva v e r i t a t e guarantees synonomy. Mere coextensiveness of terms w i l l guarantee i n t e r c h a n g e a b i l i t y i n an extensional language (one which contains no i n t e n s i o n a l terms), and we know that coextensive terms need not be synonomous. So unless the language under consideration contains intension-a l terms l i k e 'necessarily', the proposed c r i t e r i o n of synonomy i s j u s t f a l s e . However, i f we modify the proposed c r i t e r i o n i n such a way that i t requires i n t e r c h a n g e a b i l i t y i n necessity contexts as a condition of synonomy, then we appeal to the idea of necessity^which i s j u s t as problematical, Quine thinks, as the idea of synonomy and a n a l y t i c i t y . (Quine overlooks a synonomy c r i t e r i o n which Frege has proposed, namely, i n t e r c h a n g e a b i l i t y i n b e l i e f contexts. This i s a serious oversight, f o r the reason that this c r i t e r i o n has many advocates. I w i l l discuss this 5 c r i t e r i o n i n chapter 4.) By now a pattern may be seen i n Quine's i n v e s t i g a t i o n of a n a l y t i c -i t y and synonomy. His view i s that, with the exception of one clas s of a n a l y t i c sentences, i . e . , the formal l o g i c a l truths, our concept of an a n a l y t i c sentence can only be elucidated i n terms of other i n t e n s i o n a l concepts, which are ju s t as unclear and dubious as a n a l y t i c i t y i t s e l f . In a l a t e r chapter on Necessity I w i l l show that even the class of formal l o g i c a l truths, which Quine holds up as a paradigm of c l a r i t y , can only be i d e n t i f i e d i f we presuppose an understanding of e i t h e r informal v a l i d i t y or necessity (although Quine places both of these concepts i n a cla s s with the i n t e n s i o n a l concepts which he finds so unclear). (c) I have, so f a r , summarized only a small portion of Quine's a r t i c l e . However, this b r i e f summary s u f f i c e s to set the stage f o r a di s c u s s i o n of Grice and Strawson's paper, "In Defense of a Dogma", which i s an i n t e r e s t i n g reply to Quine's paper. I turn now to discuss Grice and Strawson's paper, and, i n so doing, to discuss f u r t h e r aspects of "Two Dogmas". 6 Chapter 1 1 w.V. Quine, From a L o g i c a l Point of View, Cambridge, 1953, p.36. 2 I b i d . , p. 42. 3 David Lewis, Convention, Cambridge, 1969. 4 Quine, Op. C i t . , pp. 22-3. 5 I b i d . , p. 23. 6 I b i d . , p. 23. 7 I b i d . , p. 21. Chapter 2 In this chapter I w i l l discuss aspects of a r t i c l e s written by Grice and Strawson, Jonathan Bennett, and H i l a r y Putnam on the Ana l y t i c - S y n t h e t i c d i s t i n c t i o n . I have chosen these a r t i c l e s f o r d i s c u s s i o n because they br i n g up many of the issues which I w i l l discuss i n l a t e r chapters. 8 I. Some Remarks on "In Defense of a Dogma" In this s e c t i o n I w i l l discuss some of the arguments which Grice and Strawson bring against Quine's "Two Dogmas of Empiricism". I t w i l l become apparent that although I l a r g e l y agree with Grice and Strawson, I think that t h e i r arguments are mainly suggestive and do not s u f f i c e to refute a s o p h i s t i c a t e d Quinean. In l a t e r chapters I attempt to follow up the suggestive arguments of Grice and Strawson with more powerful counter-Quinean arguments. But l e t us now consider some of Grice and Strawson's arguments. 1. Grice and Strawson take Quine to be denying the existence of the a n a l y t i c / s y n t h e t i c d i s t i n c t i o n altogether. This i s nat u r a l since Quine says, "That there i s such a d i s t i n c t i o n to be drawn at a l l , i s an unempirical dogma of e m p i r i c i s t s , a metaphysical a r t i c l e of faith."''- Grice and Strawson strongly object to t h i s view. They point out that there i s a community of philosophers who "apply the term ' a n a l y t i c ' to more or less the same cases, withold i t from more or less the same cases, and h e s i t a t e over more or less the same cases. This agreement extends not only to cases which they have been taught so to chara c t e r i z e , but to new cases. In short, 'analytic* and 'synthetic' have a more or less established p h i l o s o p h i c a l use; and this seems to suggest that i t i s absurd, even senseless, to say that there i s no such d i s t i n c t i o n . For, i n general, i f a p a i r of con t r a s t i n g expressions are h a b i t u a l l y and generally used i n a p p l i c a t i o n to the same cases, where these  cases do not form a closed l i s t , t h i s i s a s u f f i c i e n t c o n d i t i o n f o r saying that there are kinds of cases to which the expressions apply; and nothing more i s needed f o r them to mark a d i s t i n c t i o n . Now Quine admits i n "Two Dogmas" that the a n a l y t i c - s y n t h e t i c d i s -t i n c t i o n could be drawn i n terms of another d i s t i n c t i o n - that between expressions which mean the same and expressions which mean d i f f e r e n t things, 9 but he believes that this l a t t e r d i s t i n c t i o n i s a l s o suspect. In f a c t he doubts that we can attach any meaning to the claim that two expressions mean the same, apart from saying that the two expressions are coextensive. This p o s i t i o n of Quine's runs counter to the very ordinary b e l i e f that whereas 'oxygen' and 'a gas produced by plants during photosynthesis' may be coexten-s i v e , they c e r t a i n l y do not mean the same. Grice and Strawson point out that the ordinary language expression 'means the same as' has an established use, j u s t as the philosopher's tech-n i c a l term ' a n a l y t i c ' does. By and large people agree about which expressions mean the same, about which mean d i f f e r e n t things, and they hesitate over approximately the same group of expressions. This f a c t i s s u f f i c i e n t to e s t a b l i s h that there i s some d i s t i n c t i o n between expressions which are thought to mean the same and expressions which do not. Furthermore, i t c e r t a i n l y makes sense to say that term x has a meaning and that term y has a meaning. From t h i s i t i s quite p l a u s i b l e to i n f e r that i t makes sense to say that x and y have the same meaning. So i f Quine wishes to deny that there i s any d i s t i n c t i o n marked by the expressions 'means the same' and 'means something d i f f e r e n t ' , then he i s probably wrong. And by Quine's own admission, i f there i s a d i s t i n c t i o n between synonomous and non-synonomous expressions there i s a l s o a d i s t i n c t i o n between a n a l y t i c and synthetic sentences. In an a r t i c l e e n t i t l e d "Quine on Meaning and Existence" G i l b e r t Harman objects to the l i n e of argument I have been de s c r i b i n g . He argues as follows. The f a c t that many philosophers agree about what sentences are a n a l y t i c and synthetic (and about which expressions mean the same) does not 10 e n t i t l e us to i n f e r that some sentences a c t u a l l y are a n a l y t i c , any more than the f a c t that people once agreed i n t h e i r use of the terms 'witch' and 'non-witch' e n t i t l e s us to i n f e r that some things are witches. In Harman's view, to claim that a sentence i s a n a l y t i c i s to make an explanatory claim about how the sentence comes to be true. If no sentence f i t s this explanatory claim, then no sentences are a n a l y t i c . Harman does concede, however, that "There i s a d i s t i n c t i o n between truths that seem to be a n a l y t i c and truths that seem synthetic, and that d i s t i n c t i o n " u n d e r l i e s " general agreement on the use of ' a n a l y t i c ' and 'synthetic' with respect to an open c l a s s , " 3 Harman al s o concedes that there i s a d i s t i n c t i o n between people who seem to be witches and people who do not. Now given these concessions i t i s d i f f i c u l t to see that Harman has r a i s e d any serious problem f o r Grice and Strawson's l i n e of reasoning. For the i n t e r e s t i n g point which Grice and Strawson make s t i l l remains; namely, that there must be some d i s t i n c t i o n between those sentences which appear to be a n a l y t i c and those which appear to be s y n t h e t i c . Whether i t i s proper to describe this d i s t i n c t i o n as the A-S d i s t i n c t i o n i s a question worth invest-i g a t i n g . But regardless of how t h i s question i s answered there s t i l l remains the problem of explaining why c e r t a i n sentences appear, to large numbers of people, to be a n a l y t i c , while others do not so appear. Also, i f there i s to be any point to saying that some sentences appear to be a n a l y t i c , but no sentences r e a l l y are a n a l y t i c , then we must be able to say i n what way sentences which appear to be a n a l y t i c f a i l to be a n a l y t i c . And we should be able to say what i t i s about seemingly a n a l y t i c sentences which makes them appear to be a n a l y t i c . In order to be able to do both these things we would need to have a f a i r l y c l e a r account of what would count as an a n a l y t i c 11 sentence. (Just as we can give a f a i r l y c l e a r account of what would count as a witch.) I t i s al s o i n t e r e s t i n g to note that i f we were i n a p o s i t i o n to say i n what ways seemingly a n a l y t i c sentences resemble r e a l a n a l y t i c sentences, we would a l s o be able to say what dist i n g u i s h e s sentences which seem to be a n a l y t i c from those which seem to be syn t h e t i c . 2. It was mentioned i n the in t r o d u c t i o n that Quine has noticed that ' a n a l y t i c ' has usually been defined i n terms of a family of (allegedly) i n t e r d e f i n a b l e i n t e n s i o n a l terms, e.g., 'necessity', ' i m p o s s i b i l i t y ' , and 'synonomy'. Quine a l s o believes that the family of i n t e r d e f i n a b l e i n t e n s i o n a l terms i s closed i n s o f a r as no member of the family can be formally defined except i n terms of other members of the family. Consequently, i f one wishes to understand the i n t e n s i o n a l term, 'an a l y t i c ' , one can only turn toother i n t e n s i o n a l terms, which Quine claims, stand i n as much need of c l a r i f i c a t i o n as ' a n a l y t i c ' i t s e l f . In t h e i r defense of the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n Grice and Strawson are w i l l i n g to concede, f o r the sake of argument, that ' a n a l y t i c ' may belong to a closed c i r c l e of mutually i n t e r d e f i n a b l e i n t e n s i o n a l concepts, but they deny that t h i s f a c t c o n s t i t u t e s any reason f o r doubting the i n t e l l i g -i b i l i t y of ' a n a l y t i c ' . I t may be equally true of the term 'truth', that i t belongs to a closed c i r c l e of i n t e r d e f i n a b l e terms, e.g., ' f a l s e ' , 'statement 1, 'fact', 'denial', 'assertion', etc., but this does not lead us to doubt the i n t e l l i g i b i l i t y of the term 'truth' (a term which Quine contrasts favorably with ' a n a l y t i c ' ) . Grice and Strawson conclude that Quine must have some s p e c i a l reason f o r being suspicious of ' a n a l y t i c ' , apart from the f a c t that i t i s a l l e g e d l y definable only i n terms of i n t e n s i o n a l concepts. This con-12 elusion i s a safe one, given that Quine constantly remarks that ' a n a l y t i c ' can only be elucidated i n terms of notions which are j u s t as unclear as 'an a l y t i c ' i t s e l f . The question a r i s e s , why does Quine think that the family of i n t e n s i o n a l concepts i s unclear i n some way that extensional concepts l i k e 'truth' are not. Quine might say that he j u s t does not understand i n t e n s i o n a l terras l i k e , ' a n a l y t i c ' , 'synonymous'. This would be a paradoxical claim f o r Quine to make, given that he al s o claims that ' a n a l y t i c ' , 'synonymous', 'necessary', and 'inconsistent' are i n t e r d e f i n a b l e terms. For i n claiming that, e.g., 'necessity* and ' i m p o s s i b i l i t y ' are i n t e r d e f i n a b l e , he t a c i t l y admits that he understands the notion of synonomy and that philosophers do use these terms i n a f a i r l y c l e a r and systematic way. Perhaps Quine's d i f f i c u l t y with the c i r c l e of i n t e n s i o n a l terms i s expressed when he says, "I do not know whether the statement "Everything green i s extended" i s a n a l y t i c . Now does my i n d e c i s i o n over t h i s example r e a l l y betray an incomplete understanding, an incomplete grasp, of the mean-ings of "green" and "extended"? I think not. The trouble i s not with "green" or"extended" but with " a n a l y t i c " . " 4 But i f Quine's doubts about the i n t e n s i o n a l family of terms stem from his h e s i t a t i o n over whether to say "Everything green i s extended", and re l a t e d cases, are a n a l y t i c , then his doubts are i l l founded. Grice and Strawson point out that whatever h e s i t a t i o n e x i s t s about saying that "Every-thing green i s extended" i s a n a l y t i c a l s o e x i s t s when we replace ' a n a l y t i c ' with 'true'. But Quine would not conclude that our concept of tr u t h i s hopelessly vague j u s t because we cannot always say whether a sentence i s true. Grice and Strawson conclude that Quine does not produce convincing 13 reasons f o r doubting the i n t e l l i g i b i l i t y of the i n t e n s i o n a l concepts. I agree with Grice and Strawson, but I sympathize with Quine i n s o f a r as he seeks a t h e o r e t i c a l l y s a t i s f y i n g account of " a n a l y t i c " . 3. It was mentioned e a r l i e r that Grice and Strawson admit that i n t e n s i o n a l terms may be formally definable only i n terms of other intension-a l terms, but they maintain that i n t e n s i o n a l terms can a l s o be i n f o r m a l l y explained i n non-intensional terms. If they are r i g h t , then i t i s possible to break out of the c i r c l e of i n t e n s i o n a l terms, i n an informal way. Let us consider Grice and Strawson's example of such an informal explanation. They contrast two sentences: A. My three year old c h i l d understands Spinoza. B. My three year old c h i l d i s nine years o l d . They point out that i f anyone asserted A we would be very s k e p t i c a l , but would understand the a s s e r t i o n . However, i f someone asserted B we would be unable to make sense of that person's a s s e r t i o n , we would be bewildered. Statements which are bewildering i n the way that B i s bewildering are i n -consistent. Statements l i k e A are d i f f i c u l t to b e l i e v e , but they are con-s i s t e n t . Grice and Strawson conclude that "The d i s t i n c t i o n i n which we u l t i m a t e l y come to r e s t i s that between not b e l i e v i n g something and not understanding something; i t would be rash to maintain that t h i s d i s t i n c t i o n does not need c l a r i f i c a t i o n , but i t would be absurd to maintain that i t does not e x i s t . Now someone might object that Grice and Strawson have not r e a l l y broken out of the c i r c l e of i n t e n s i o n a l terms. One might claim that 'understand' i s an i n t e n s i o n a l term. But i t would be absurd f o r someone to 14 that they do not understand what i t i s to understand something, and as Grice and Strawson point out i t would be absurd to maintain that no d i s t i n c t i o n e x i s t s between not b e l i e v i n g something and not understanding what i t would be f o r a p a r t i c u l a r sentence to be true. So t h i s objection does not seem to have much f o r c e . Jonathan Bennett r a i s e s a d i f f e r e n t objection. In " A n a l y t i c -Synthetic" he points out that while i t i s true that a statement l i k e (C) " I t i s r a i n i n g and a l s o not r a i n i n g " i s bewildering, i t i s a l s o true that statements that are normally considered synthetic are bewildering when they are asserted i n c e r t a i n s i t u a t i o n s . For example, i f a f r i e n d i s s t a r i n g out the window at the sunshine and asserts (D) " I t i s r a i n i n g so hard that you shouldn't go out" h i s remark i s equally bewildering as (C). So i t appears that we cannot d i s t i n g u i s h i n c o n s i s t e n t sentences by t h e i r bewildering property. Grice has t r i e d to answer t h i s o bjection. He claims that we may d i s t i n g u i s h the former sentence from the l a t t e r by the f a c t that the former sentence i s prima-facie bewildering, whereas the l a t t e r i s bewildering only i n some circumstances. Bennett r e j e c t s t h i s answer on the grounds that the notion of "prima-facie bewilderment" can only be elucidated by some such notion as "a sentence's being bewildering to anyone who knows the meaning of i t s constituent terms even i f that i s a l l he knows",^ and t h i s r a i s e s a l l the problems about meaning which one wishes to avoid. I think i t can be shown that Bennett's objection does not have much force, however. For suppose we d i s t i n g u i s h the two cases of bewilder-ment as follows: "The only story we have to t e l l about C, f o r i t s a s s e r t i o n 15 to be bewildering, i s that the expressions i n C bear t h e i r usual meanings. The a s s e r t i o n of D, on the other hand, i s bewildering only i f the expressions i n D bear t h e i r usual meanings and we believe i t s a s s e r t e r believes i t to be f a l s e . What i s bewildering i n t h i s l a t t e r case i s that the a s s e r t e r seems to have contradictory b e l i e f s . It i s true that t h i s way of drawing the d i s t i n c t i o n appeals to the idea of a sentence bearing i t s usual meaning, but only i n a harmless way. Whenever a person advances a p h i l o s o p h i c a l theory there i s a background assumption that the sentences c o n s t i t u t i n g the theory bear t h e i r usual mean-ings. And whenever we judge the t r u t h of a sentence we assume that the sent-ence bears i t s usual meaning. It can hardly count against my way of c l a r i f y i n g the notion of prima-facie bewilderment that i t makes e x p l i c i t an assumption that i s always present i n any discourse. The f a c t that we must understand a sentence before we can t e l l whether i t i s bewildering does not count against the bewilderment/non-bewilderment d i s t i n c t i o n any more than i t counts against the t r u e / f a l s e d i s t i n c t i o n that we must understand a sentence before we can say that i t i s true. Perhaps t h i s answers Bennett's objection, but a f e e l i n g of d i s -s a t i s f a c t i o n may yet remain. One f e e l s r e l u c t a n t to say that our concept of inconsistency i s adequately c l a r i f i e d by the d i s t i n c t i o n between not b e l i e v i n g an a s s e r t i o n and not understanding an a s s e r t i o n (or being bewildered by an a s s e r t i o n ) , because t h i s d i s t i n c t i o n i s not t h e o r e t i c a l l y deep. Grice and Strawson concede t h i s when they say " i t would be rash to maintain that t h i s d i s t i n c t i o n does not need c l a r i f i c a t i o n . " I w i l l argue i n a l a t e r chapter that our concept of inconsistency (and i t s cousin, necessity) cannot be c l a r i f i e d i n a t h e o r e t i c a l l y deep way. Consequently our concept of formal 16 l o g i c a l truth cannot be c l a r i f i e d i n a t h e o r e t i c a l l y deep way, e i t h e r (or so I w i l l argue). But I al s o hope to show that the ana l y t i c - s y n t h e t i c d i s -t i n c t i o n can be c l a r i f i e d i n a t h e o r e t i c a l l y s a t i s f y i n g way, even though we must take the concept of l o g i c a l t r u t h as one of our b u i l d i n g blocks. In "Two Dogmas" Quine b r i e f l y discusses the kind of synonomy which r e s u l t s from s t i p u l a t i v e d e f i n i t i o n . Concerning i t he says, "Here the definiendum becomes synonymous with the definiens simply because i t has been created expressly f o r the purpose of being synonymous with the d e f i n i e n s . Here we have a r e a l l y transparent case of synonymy created by d e f i n i t i o n ; would that a l l species of synonymy were as i n t e l l i g i b l e . " ^ An example of the kind of s t i p u l a t i v e definition Quine i s r e f e r r i n g to i s the convention of w r i t i n g 'B.A.' f o r bachelor of a r t s . Quine finds this kind of synonymy acceptable and i n t e l l i g i b l e , but complains that he cannot make sense of other kinds of synonymy. Grice and Strawson point out that Quine's p o s i t i o n i s l i k e that of one who says " I can understand what i t means to say that one thing f i t s i n t o another, or that two things f i t together, i n the case where one was s p e c i a l l y made to f i t the other; but I cannot understand what i t means to say t h i s i n any other case."8 Grice and Strawson contend that Quine's view i s incoherent on t h i s point. We can only understand s t i p u l a t i v e d e f i n i t i o n because we know what i t i s to follow a l i n g u i s t i c p r a c t i c e over a period of time. And i f we know what i t i s to fo l l o w a l i n g u i s t i c p r a c t i c e over time, we should be able to understand that the same l i n g u i s t i c p r a c t i c e can govern the use of two d i f f e r e n t words. That, according to Grice and Strawson, amounts to under-standing synonymy. 17 I think Grice and Strawson are on the r i g h t track here, but much more needs to be s a i d . For the sophisticated Quinean might object that we need to be able to d i s t i n g u i s h r e g u l a r i t i e s which are due to l i n g u i s t i c custom from r e g u l a r i t i e s which are due to n a t u r a l law. For example, why do we say that the coextensiveness of the expressions 'bachelor' and 'unmarried adult male' i s due to l i n g u i s t i c p r a c t i c e , but the coextensiveness of 'oxygen' with 'gas which plants release during photosynthesis' i s due to a n a t u r a l r e g u l a r i t y . I f we are not able to explain the d i s t i n c t i o n between coextensive-ness which i s due to convention and that which i s due to n a t u r a l law must we not conclude that there i s no such d i s t i n c t i o n ? I w i l l not t r y to answer t h i s question. Rather I w i l l attempt to show, i n a l a t e r chapter, how we can draw the required d i s t i n c t i o n . In so doing I w i l l say a l o t more about l i n g u i s t i c conventions and r u l e s , and attempt to give a much firmer foundation to the p o s i t i o n Grice and Strawson sketch. 4. Grice and Strawson challenge Quine's doctrine that absolutely any b e l i e f might be s a c r i f i c e d i n order to keep a theory consistent with experience. They contend that some sentences, i . e . , the a n a l y t i c ones, can only be rejected i f a change i n meaning occurs i n the sentence being r e j e c t e d . In t h i s way a n a l y t i c sentences d i f f e r from synthetic sentences. According to Grice and Strawson the r e j e c t i o n of a synthetic sentence may r e f l e c t "a change of opinion s o l e l y as to matters of f a c t . " But the r e j e c t i o n of an a n a l y t i c sentence always requires a meaning change. Once again, I agree with the p o s i t i o n Grice and Strawson sketch, but more needs to be s a i d . For the s o p h i s t i c a t e d Quinean may contend that 18 we cannot r e a l l y d i s t i n g u i s h the case where the r e j e c t i o n of a sentence r e f l e c t s only a change i n b e l i e f s from the case where the r e j e c t i o n a l s o r e f l e c t s a change i n meaning. He would probably i n s i s t that the idea of a meaning change i s what needs c l a r i f y i n g . In the following chapter I w i l l argue that we can d i s t i n g u i s h a meaning change from a change i n b e l i e f s . Also I w i l l attempt to elucidate the idea of a meaning change. The conclusion I w i l l reach e n t i r e l y supports Grice and Strawson when they say, "The point of substance that Quine i s making, by t h i s emphasis on r e v i s a b i l i t y , i s that there i s no absolute necessity about the adoption or use of any conceptual scheme whatever, or, more narrowly and i n terms that he would r e j e c t , that there i s no• a n a l y t i c p r o p o s i t i o n such that we must have l i n g u i s t i c forms bearing j u s t the sense required to express that p r o p o s i t i o n . But i t i s one thing to admit t h i s , and quite another thing to say that there are no n e c e s s i t i e s within any conceptual scheme we adopt or use, or, more narrowly again, that there are no l i n g u i s t i c forms which do express a n a l y t i c p r o p o s i t i o n s . " I I . Some Remarks on " A n a l y t i c - S y n t h e t i c " 1. R e c a l l the remarks of Grice and Strawson concerning the use of ' a n a l y t i c ' and 'synthetic'. They point out that most philosophers agree about which sentences to c a l l ' a n a l y t i c ' , which to c a l l ' s y n t h e t i c ' and most philosophers h e s i t a t e over roughly the same cases. This f a c t c o n s t i t u t e s very strong evidence f o r saying that these words do mark some d i s t i n c t i o n , though, i t i s quite possible that many philosophers hold mistaken b e l i e f s about the nature of this d i s t i n c t i o n . In " A n a l y t i c - S y n t h e t i c " (reprinted i n Necessary Truth, Summer 19 and Woods) Bennett describes a s o p h i s t i c a t e d Quinean. The s o p h i s t i c a t e d Quinean holds that ' a n a l y t i c 1 , 'synthetic' and other i n t e n s i o n a l terms mark genuine d i s t i n c t i o n s , but he desires a Quinean analysis of these d i s t i n c t i o n s . Bennett o f f e r s such an a n a l y s i s . In so doing he t r i e s to el u c i d a t e the Quinean theory that c e r t a i n b e l i e f s are deeply embedded i n our conceptual scheme, while others l i e near the periphery of our conceptual scheme, and s t i l l others l i e somewhere i n between. Bennett cashes the metaphors "deeply embedded" and "near the periphery" i n t o the more l i t e r a l notions of "highly i n d i s p e n s i b l e " and " r e l a t i v e l y d i s p e n s i b l e " . Roughly the p i c t u r e he describes i s as follows: "Accepted sentences of the form ( i ) 'The temperature of such-and-such a s t a r i s such-and-such' depend, f o r those who accept them, on sentences of the form ( i i ) 'Temperature c o r r e l a t e s with l i g h t emissions i n such-and-such ways', and these depend on sentences of the form ( i i i ) 'Temperature c o r r e l a t e s with mercury-column readings i n such-and-such ways', and these i n t h e i r turn depend on sentences along the l i n e s of (iv) 'Temperature has to do with the obtaining of such and such sensations.' Rejection of ( i i ) jeopardises ( i ) and a l l that depends on i t ; r e j e c t i o n of ( i i i ) jeopardises ( i ) and ( i i ) ; r e j e c t i o n of (iv) jeopardises a l l the other three."*° "When I wish to say that one sentence shares a general term with another and has more depending on i t than depends on the other, I s h a l l say that i t i s less dispensible than the other."H In order of d i s p e n s i b i l i t y ( i ) i s the most dispensible and (iv) the l e a s t d i s p e n s i b l e . A sentence i s less d i s p ensible than another i f and only i f the f i r s t forms part of the grounds f o r accepting the second, but not vi c e - v e r s a . According to Bennett, i f a l l the sentences sharing the same general term F are ranked according to d i s p e n s i b i l i t y , the least d i s p ensible sentence pro-vides the test f o r Fness which i s used i n e s t a b l i s h i n g the t r u t h of more dispensible sentences containing F, and these i n turn provide the test f o r Fness which i s used i n e s t a b l i s h i n g even more dispensible sentences containing 20 That f a i r l y accurately describes Bennett's picture of the d i s t i n c -t i o n between highly i n d i s p e n s i b l e and f a i r l y d ispensible sentences. It i s his view, i n " A n a l y t i c - S y n t h e t i c " that the a c t u a l d i s t i n c t i o n marked by 'a n a l y t i c ' and 'synthetic' i s t h i s d i s p e n s i b i l i t y d i s t i n c t i o n . It may be that most people who use these words would not recognize the d i s p e n s i b i l i t y d i s t i n c t i o n as the d i s t i n c t i o n they intend, but, according to Bennett, this would only show that most philosophers have been mistaken about the nature of t h i s d i s t i n c t i o n . If we look at the way people a c t u a l l y use ' a n a l y t i c ' and 'synthetic' we s h a l l f i n d that i t corresponds with Bennett's use of 'highly i n d i s p e n s i b l e 1 and ' r e l a t i v e l y d i s p e n s i b l e ' . According to Bennett t h i s reconstruction of the A-S d i s t i n c t i o n has the advantage that i t breaks out of the c i r c l e of i n t e n s i o n a l terms, and allows us to explain the d i s t i n c t i o n to someone who does not understand i n t e n s i o n a l terms. I am s k e p t i c a l whether t h i s i s true, since Bennett's theory appeals to the f a c t that one sentence can form part of the ground f o r the acceptance of another sentence, and t h i s involves the idea of l o g i -c a l consequence, which (I s h a l l argue i n a l a t e r chapter) involves the idea of necessity. I w i l l ignore this problem at present, however, f o r there i s a more straightforward problem to be d e a l t with. It i s t h i s : The s o p h i s t i -cated Quinean holds the view that absolutely any sentence (excluding perhaps a s p e c i a l class of observation sentences) may be s a c r i f i c e d i n the face of r e c a l c i t r a n t (with respect to our theories) experience, while any other sentence may be retained. This view e n t a i l s that under some circumstances we might be w i l l i n g to s a c r i f i c e the highly i n d i s p e n s i b l e sentence ( i v ) , and yet r e t a i n ( i ) , ( i i ) , and ( i i i ) . But i f t h i s i s so, then how can we say 21 that (iv) constitutes the grounds f o r the acceptance of ( i ) , ( i i ) , and ( i i i ) ? If (iv) i s more in d i s p e n s i b l e than the other three i n the sense that " r e j e c t i o n of (iv) jeopardises a l l the other three", then i t i s not possible to r e j e c t (iv) and yet r e t a i n a l l the other three. Furthermore, i f (iv) provides the test f o r temperature i n v i r t u e of which a l l the other three came to be established, i t i s d i f f i c u l t to see what one would be a s s e r t i n g when one asserted any of the other three a f t e r having rejected ( i v ) . The s o p h i s t i c a t e d Quinean, who wants to use Bennett's d i s p e n s i b i l -i t y ranking theory, might t r y to avoid the d i f f i c u l t y I describe by adopting the kind of p o s i t i o n Putnam describes i n "The A n a l y t i c and the Synthetic" when he discusses law-cluster concepts. According to Putnam many of our concepts are derived from c l u s t e r s of laws. For example, the word 'tempera-ture' does not derive i t s meaning from any s i n g l e law, but rather from a whole c l u s t e r of laws i n which i t appears. Consequently, there i s no s i n g l e law whose r e j e c t i o n would destroy our concept of temperature. We could r e j e c t any p a r t i c u l a r law containing 'temperature' and yet r e t a i n our other b e l i e f s about temperature, because our concept of temperature would remain nearly i n t a c t . It might s t i l l be true that some laws about temperature are more in d i s p e n s i b l e than others, because some laws might contribute more meaning to 'temperature' than others. It might a l s o be true that a s i n g l e c l u s t e r of laws about temperature i s more in d i s p e n s i b l e than a l l our other b e l i e f s about temperature, while no s i n g l e law i s absolutely i n d i s p e n s i b l e . Thus Putnam's view seems to be compatible with the kind of ranking of d i s p e n s i b i l i t y which Bennett describes. Unfortunately, f or the so p h i s t i c a t e d Quinean, t h i s m o d i f i c a t i o n w i l l not s u f f i c e . For while i t may, be true that the r e j e c t i o n of p a r t i c u l a r 22 laws about temperature does not s i g n i f i c a n t l y a l t e r our concept of tempera-ture, i t w i l l s t i l l be true (assuming a d i s p e n s i b i l i t y ranking)that the r e j e c t i o n of the whole c l u s t e r of high l e v e l laws about temperature jeopar-dises our low l e v e l b e l i e f s about temperature, and so i t w i l l s t i l l be true that we cannot simultaneously reject a l l our high l e v e l b e l i e f s about temperature and r e t a i n our low l e v e l b e l i e f s i n t a c t . There i s a basic i n c o m p a t i b i l i t y between holding that some b e l i e f s c o n s t i t u t e grounds f o r other b e l i e f s , and a l s o holding that any b e l i e f may be rejected while any other b e l i e f i s retained. An i n t e r e s t i n g point i s emerging here. Namely that anyone who holds that each of our b e l i e f s i s open to r e j e c t i o n while any other b e l i e f may be retained i s going to have an impossible time making sense of the idea that one b e l i e f c onstitutes the grounds f o r accepting another b e l i e f . I f any conclusion can always be rejected while any set of premises can be retained, then what sense can we make of l o g i c - not j u s t t r a d i t i o n a l l o g i c , but any lo g i c ? It w i l l not help to say that a premise p l o g i c a l l y e n t a i l s a conclusion q provided r e j e c t i o n of q and retention of p would e n t a i l an enormously complicated r e v i s i o n i n the remainder of our b e l i e f s , f o r i t i s the very concept of entailment which i s i n question. The upshot of a l l t h i s i s that i f the sop h i s t i c a t e d Quinean, or Bennett, wants to r e t a i n his d i s p e n s i b i l i t y ranking theory, he must r e j e c t the Quinean doctrine that any b e l i e f can be rejected while any other b e l i e f i s retained. This would eliminate one problem f o r the d i s p e n s i b i l i t y ranking theory, but other problems remain. For example, there i s s t i l l the problem that on th i s theory some b e l i e f s are l o g i c a l l y dependent upon others, and 23 th i s may well involve the i n t e n s i o n a l notion of n e c e s s i t y . Other problems a r i s e from Bennett's view that the least d i spensible sentence provides the test f o r Fness which i s used i n e s t a b l i s h i n g the tr u t h of more dispensible sentences containing F, and these i n turn provide the test f o r Fness which 12 i s used i n e s t a b l i s h i n g even more dispensible sentences containing F. There i s a problem about deciding which sentences provide the test f o r Fness. And to a Quinean the view that a d e f i n i t e class of sentences provides the test f o r Fness may appear j u s t as much a dogma as the view that the conventions guiding our use of 'F' are exact, or that 'F' can be p r e c i s e l y defined. In any case i t seems c l e a r that a l o t more needs to be said about what i t i s f o r a class of sentences to provide the test f o r Fness. I w i l l discuss t h i s issue at length ( i n a s l i g h t l y d i f f e r e n t form) when I discuss the question of how conventions guide the use of p a r t i c u l a r words, why there must be such conventions, and how we can d i s t i n g u i s h conventions from r e g u l a r i t i e s . But th i s d i s c u s s i o n , l i k e the di s c u s s i o n of n e c e s s i t y , must await a l a t e r chapter. 2. In "A n a l y t i c - S y n t h e t i c " Bennett argues f o r the view that "any a n a l y t i c sentence may become f a l s e through a meaning change which i s brought 1 o about by the occurrence of r e c a l c i t r a n t experiences." This accords with the p o s i t i o n Grice and Strawson adopt i n "Defense of a Dogma", but whereas Grice and Strawson st r e s s the f a c t that an a n a l y t i c sentence cannot become f a l s e unless a meaning change occurs, Bennett stresses the f a c t that an a n a l y t i c sentence can become f a l s e _ i f a meaning change occurs. Now Bennett's claim may not seem very c o n t r o v e r s i a l . Almost everyone concedes that the tr u t h value of a sentence i s p a r t l y a function 24 of the meaning of the sentence, and there i s nothing God-given about the meaning of a sentence; i t can change i f people's l i n g u i s t i c habits change. What i s c o n t r o v e r s i a l about Bennett's claim, however, i s the idea that a meaning change can be brought about by the occurrence of r e c a l c i t r a n t experiences. Bennett b r i e f l y describes how this might happen. He says, "Associated with any a n a l y t i c sentence there i s a range of syn-t h e t i c sentences s t a t i n g f a c t s about the world i n v i r t u e of which i t i s convenient that the words i n the a n a l y t i c sentence should have the meanings they do have; suppose a f a l s i f i c a t i o n of a j u d i c i o u s l y selected sub-set of these synthetic sentences, and you are w e l l on the way to describing a state of a f f a i r s which i n v i t e s the f a l s i f i c a t i o n of the a n a l y t i c sentence." 1^ Now there i s a c e r t a i n misleadingness when Bennett says "you are wel l on the way to de s c r i b i n g a state of a f f a i r s which i n v i t e s the f a l s i f i -c ation of the a n a l y t i c sentence." For this might e a s i l y lead us to believe that there i s some state of a f f a i r s which f a l s i f i e s the a n a l y t i c sentence, which, i n turn, would lead us to i n f e r that an a n a l y t i c sentence can assert something f a l s e . But this i s not i n f a c t Bennett's view. Rather Bennett i s claiming that a change i n our f a c t u a l b e l i e f s can make i t convenient to change the meaning of an a n a l y t i c sentence i n such a way that the sentence ceases to be a n a l y t i c , and ceases to be true. Of course, Bennett believes that at the time a sentence i s a n a l y t i c i t i s true. This, however, makes i t somewhat misleading f o r Bennett to claim that we may r e j e c t our b e l i e f i n any a n a l y t i c sentence. For i t i s strange to say, at T 2, that we have rejected our b e l i e f i n S, when we s t i l l believe that S was true at T^. We may have rejected some b e l i e f s concerning those " f a c t s about the world i n v i r t u e of which i t i s convenient that the words ( i n S) have the meaning they do have", but 25 those b e l i e f s are d i s t i n c t from the b e l i e f expressed by S at T^. In general, a sentence, S, does not make an a s s e r t i o n about the facts which make i t convenient f o r S to have the meaning i t has. Consequently, i f an a n a l y t i c sentence changes meaning because some of these meaning-related b e l i e f s have been f a l s i f i e d , that does not c o n s t i t u t e a reason f o r saying that the b e l i e f formerly associated with the a n a l y t i c sentence has been f a l s i f i e d . The reader may have noticed the use of i n t e n s i o n a l terminology i n the preceding"discussion. Bennett introduces this i n t e n s i o n a l language when he talks about circumstances which could lead us to change the meaning and t r u t h value of a n a l y t i c sentences. However, he o f f e r s a non-intensional a n a l y s i s of this i n t e n s i o n a l language when he says, "The proposition (mean-ing) expressed by S^ at t ^ i s d i f f e r e n t from the proposition (meaning) expressed by S\ at t 2 i f and only i f an appropriate set of sentences of the form "S^ i s true i f and only i f S n i s true" which are highly i n d i s p e n s i b l e at t\ are not highly i n d i s p e n s i b l e at t 2 . So that a h i t h e r t o a n a l y t i c sentence can be denied only i f i t comes to express a d i f f e r e n t proposition from the one i t formerly expressed."^ Now the success of this non-intensional analysis of meaning change depends upon the i n t e l l i g i b i l i t y of Bennett's " d i s p e n s i b i l i t y " ranking theory. But we have already seen that there are problems with t h i s theory, and a l o t more needs to be said about i t . Consequently, although I agree with Bennett that an a n a l y t i c sentence can only be rejected i f i t s meaning and truth value are changed, I do not think he has demonstrated t h i s t h e s i s , or c l e a r l y explained i t i n non-intensional language. 26 3. In the l a s t s ection of "A n a l y t i c - S y n t h e t i c " Bennett discusses possible c o n f l i c t s between Quine's b e l i e f s that (a) c e r t a i n experiences (the r e c a l c i t r a n t ones) can force us to make some r e v i s i o n i n our t o t a l network of b e l i e f s , and (b) that when we rev i s e our t o t a l set of b e l i e f s i n the face of a r e c a l c i t r a n t experience absolutely any b e l i e f i s a possible candidate f o r r e v i s i o n . I do not intend to discuss t h i s portion of Bennett's paper i n any d e t a i l , p a r t i a l l y because Bennett now re j e c t s the arguments contained therein. But I do wish to c a l l a t t e n t i o n to one of h i s arguments, because i t r e l a t e s to another argument which I w i l l examine i n a l a t e r chapter. Bennett shows that i f Quine i s to r e t a i n (b) then he must hold that our t o t a l set of b e l i e f s i s i n f i n i t e . He argues as follows: i f our set of b e l i e f s i s f i n i t e , and i f some experience occurs which i s r e c a l c i -trant with respect to those b e l i e f s , then we cannot simultaneously a f f i r m the existence of the r e c a l c i t r a n t experience and the conjunction of a l l the sentences we c a l l true, and so "there i s a sentence ( a l b e i t a long one) which i s , i n i s o l a t i o n , s trongly disconfirmed by experience." 1^ Bennett suggests that Quine might escape t h i s conclusion by supposing that our t o t a l set of b e l i e f s i s i n f i n i t e , and Bennett goes on to in v e s t i g a t e t h i s possible move on Quine 's part. Rather than discuss the complex arguments which Bennett considers, however, I suggest that the issue whether our theory consists of an i n f i n i t e or f i n i t e number of sentences i s i r r e l e v a n t . For whether our theory i s f i n i t e or i n f i n i t e i t i s cl e a r that we cannot simultaneously a f f i r m the existence of a r e c a l c i t r a n t experience and the tr u t h of our t o t a l theory. And th i s means that a c e r t a i n b e l i e f i s forced on us by experience, (namely the b e l i e f that 27 some r e v i s i o n i n our t o t a l set of b e l i e f s i s required) and i t s negation i s strongly disconfirmed by experience. (This argument i s but a sketch. It w i l l be considerably expanded i n my chapter on r e c a l c i t r a n t experience.) I I I . Some Remarks on Putnam's "The A n a l y t i c and the Synthetic" In t h i s s e c t i o n I w i l l discuss some aspects of Putnam's theory of the A-S d i s t i n c t i o n . Although I w i l l r e j e c t many of Putnam's doctrines, I think much of what he says i s very suggestive. In p a r t i c u l a r , his d e f i n i -t i o n of ' a n a l y t i c ' i s suggestive of a theory which I l a t e r develop. But l e t us now consider Putnam's theory. According to Putnam Quine i s wrong i n his l i t e r a l thesis that there i s no a n a l y t i c - s y n t h e t i c d i s t i n c t i o n at a l l . There are statements which i t would be unreasonable for anyone to hold to be f a l s e at any time and i n any circumstances. These are the statements which philosophers have c i t e d as paradigm cases of a n a l y t i c statements. There are a l s o statements which can be rejected on the basis of i s o l a t e d experiments. These are statements which philosophers have c i t e d as paradigm cases of synthetic or contingent statements. By and large people agree on what are the paradigms of a n a l y t i c and synthetic statements, and (as Grice and Strawson also point out) "Where there i s agreement on the use of the expressions involved with respect to an open c l a s s , there must n e c e s s a r i l y be some kind of d i s t i n c t i o n p r e s e n t . S o there i s an A-S d i s t i n c t i o n , but the importance of the d i s -t i n c t i o n has been immensely overestimated because people have f a i l e d to 28 r e a l i z e the f o l l o w i n g points: (a) The d i s t i n c t i o n i s not an exhaustive one. Many statements are neither a n a l y t i c nor synthetic, (b) Most philosophers have mistakenly taken some important and i n t e r e s t i n g statements to be a n a l y t i c . Among these are the statements of l o g i c and mathematics, and some statements of physics. Having mistakenly placed these statements i n a class with such u t t e r l y t r i v i a l statements as " A l l bachelors are unmarried", these philosophers have assumed that the i n t e r e s t i n g statements, l i k e the t r i v i a l statements, owe t h e i r t r u t h to l i n g u i s t i c convention. (c) Since a l l a n a l y t i c statements are obviously a n a l y t i c and u t t e r l y t r i v i a l one cannot hope to use the A-S d i s t i n c t i o n as a t o o l f o r discovering i n t e r e s t i n g t r u ths. Putnam puts the matter somewhat as follows: " 'Chair' may be synonymous with 'movable seat f o r one with a back' but that bakes no philosophic bread and washes no ph i l o -sophic windows. I t i s the b e l i e f that there are synonymies of a deeper nature -- synonymies and a n a l y t i c i t i e s that cannot be discovered by the lexicographer or the l i n g u i s t but only by the philosopher -- that i s i n c o r r e c t . Let us consider each of these three points i n turn. Concerning (a), we have already seen that the A-S d i s t i n c t i o n has some borderline cases. For example, the sentence "Everything green i s extended" i s not c l e a r l y a n a l y t i c or sy n t h e t i c , but i t i s not c l e a r l y true or f a l s e e i t h e r . The mere f a c t that the A-S d i s t i n c t i o n i s not exhaustive should not lead us to doubt the importance of this d i s t i n c t i o n , any more than i t should i n the case of the t r u e - f a l s e d i s t i n c t i o n . Concerning (b). Putnam holds that statements of mathematics and l o g i c belong i n a c l a s s with h i g h - l e v e l p h y s i c a l laws, that statements i n this c l a s s are n e i t h e r a n a l y t i c nor synthetic, and that any statement i n this indeterminate class can be rejected as f a l s e , without a l t e r i n g any of our concepts to a 29 s i g n i f i c a n t extent. Although Putnam never does prove that mathematical and l o g i c a l laws belong i n this class of statements, h i s reasons f o r holding this view are f a i r l y apparent. They stem from his theory about law-cluster concepts which I b r i e f l y described i n the s e c t i o n on Bennett. Remember that, according to Putnam, a l l mathematical, l o g i c a l , and s c i e n t i f i c terms derive t h e i r meaning from whole c l u s t e r s of laws i n which they occur, and none of these terms derive t h e i r meaning from s i n g l e laws. For t h i s reason he thinks that any s i n g l e mathematical, l o g i c a l , or p h y s i c a l law could be rejected, without destroying the concepts expressed by terms appearing i n the rejected law. For example, the word 'and' appears i n , and derives i t s meaning from countless l o g i c a l laws and theorems. Consequently, i t would be a r b i t r a r y to s i n g l e out any p a r t i c u l a r l o g i c a l law and claim that i t completely defines the meaning of 'and'. So i t would be a mistake, i n Putnam's opinion, to think that any l o g i c a l law i s "true by d e f i n i t i o n " , i n the sense that i t follows from the d e f i n i t i o n of 'and'. Putnam concludes that since l o g i c a l laws do not hold i n v i r t u e of any d e f i n i t i o n , or simple convention, they are not necessary truths, and are open to r e j e c t i o n . Perhaps this i s because he i d e n t i f i e s "necessary" with "true by d e f i n i t i o n or convention". In l a t e r chapters I t r y to show that this i d e n t i f i c a t i o n i s a mistaken one. I think there are some serious problems with Putnam's view (some of which have already been mentioned i n my disc u s s i o n of the so p h i s t i c a t e d Quinean). They are: (A) Putnam, who i s a so p h i s t i c a t e d Quinean, i s going to have an extremely d i f f i c u l t time making sense of the idea that a conclusion can l o g i c a l l y follow from c e r t a i n premises. For since he holds that any 30 l o g i c a l law (or ru l e of inference) could be rejected, he i s committed to holding that, i n p r i n c i p l e , any conclusion could be rejected while any set of premises i s retained. Of course, he w i l l want to claim that this i s possible only i f rev i s i o n s are made elsewhere i n our t o t a l system of b e l i e f s . That i s , he w i l l claim that the r e j e c t i o n of a l o g i c a l law or l o g i s t i c system l o g i c a l l y e n t a i l s a r e v i s i o n elsewhere i n our set of b e l i e f s . But the question a r i s e s , according to what l o g i c does the r e j e c t i o n of a l o g i c a l law e n t a i l some other r e v i s i o n ? Presumably i t i s not some second order l o g i c which i s not open to r e j e c t i o n . And not every l o g i c w i l l e n t a i l some other r e v i s i o n . So what happens i f the l o g i c being rejected i s the same as the l o g i c which i s supposed to e n t a i l some other r e v i s i o n ? For example, the l o g i c which now motivates us to make rev i s i o n s i n our theory i s a l o g i c i n which consistency i s a c e n t r a l requirement. Consequently, i f we r e j e c t t h i s l o g i c a l system, i n c l u d i n g the l o g i c a l requirement of consistency, we r e j e c t the motivation f o r some other r e v i s i o n . I think the reason Putnam, and Quine, have not faced up to th i s problem i s that they r e a l l y believe that we are, i n some absolute way, l o g i c a l l y committed to making some other r e v i s i o n when we r e j e c t a l o g i c a l p r i n c i p l e ; and th i s i s j u s t incompatible with t h e i r b e l i e f that any l o g i c a l p r i n c i p l e can be re j e c t e d . (B) Putnam denies ( i ) that there i s any set of l o g i c a l l y necessary and s u f f i c i e n t conditions which defines s c i e n t i f i c , mathematical, and l o g i c a l terms. He al s o holds ( i i ) that these terms derive t h e i r meaning from the c l u s t e r of laws i n which they occur. Now there i s a problem about how to i n t e r p r e t ( i i ) i n such a way that ( i i ) i s consistent with ( i ) . We might i n t e r p r e t ( i i ) as the claim that ( i i i ) the meaning of law-cluster terms i s 3 1 some complicated f u n c t i o n of the c l u s t e r of laws i n which they occur (or as the view that the use of law-cluster terms i s determined in some complicated way by the way we use the whole c l u s t e r of laws i n which they occur). But this i n t e r p r e t a t i o n of ( i i ) seems to be inco n s i s t e n t with ( i ) . For i f the meaning of some term, T, i s a function of some set of laws, L, then t h i s function must be describable. (I assume that whatever e x i s t s can be described, at l e a s t i n p r i n c i p l e ) . And i f the meaning function which r e l a t e s T to the set of laws L can be described, then we can construct a d e f i n i t i o n of T i n terms of the meaning function and L as follows: The meaning of T = f ( L ) There i s a mo d i f i c a t i o n of Putnam's view (or perhaps i t i s merely a generous i n t e r p r e t a t i o n ) which would avoid the d i f f i c u l t y j u s t described. It i s t h i s : suppose we admit that the meaning of s c i e n t i f i c terms i s a complicated function of some c l u s t e r of ph y s i c a l laws. We al s o admit that t h i s function i s describable, and that, i n p r i n c i p l e , s c i e n t i f i c terms are defin a b l e . From t h i s i t might follow that some general statements containing s c i e n t i f i c terms are "true by d e f i n i t i o n " or a n a l y t i c , but this i s c e r t a i n l y compatible with holding that the p a r t i c u l a r laws, which c o n s t i t u t e the de f i n i n g c l u s t e r of laws, are always open to r e j e c t i o n . For example, suppose that a s c i e n t i f i c term, T, can be defined i n the fol l o w i n g complicated way: We apply T to those cases where most of the following laws are s a t i s f i e d : L p l ^ .... L n . C l e a r l y the r e j e c t i o n of any one of the laws .... L>n would not bar us from applying T i n a p a r t i c u l a r case, (though r e j e c t i o n of very many of these laws would), On the other hand, not every statement i n which T occurs can 32 be rejected without destroying the concept expressed by T. Putnam might accept the mo d i f i c a t i o n j u s t suggested. If he does he should abandon h i s b e l i e f that there are no deep, or n o n - t r i v i a l synony-mies and a n a l y t i c i t i e s f o r philosophers to discover. For there i s no reason to believe that the meaning function which r e l a t e s a p a r t i c u l a r law-cluster term to a whole-cluster of laws w i l l usually be t r i v i a l or obvious. To say that a p a r t i c u l a r law-cluster term derives i t s meaning from some i d e n t i f i a b l e set of laws i s already to say something i n t e r e s t i n g about the meaning of the law-cluster term. But to describe i n any d e t a i l the meaning r e l a t i o n s h i p between a p a r t i c u l a r term and some c l u s t e r of laws should be a complex and i n t e r e s t i n g task. I t i s , of course, open to Putnam to deny that t h i s meaning r e l a t i o n s h i p , or meaning function, can be described i n any d e t a i l , but th i s would cast considerable doubt on the i n t e l l i g i b i l i t y of Putnam's claim that the law-cluster terms derive t h e i r meaning from a whole c l u s t e r of laws. Discussion of ( c ) . By now some reasons have been given f o r doubting (c ) , i . e . , the view that a l l a n a l y t i c sentences are u t t e r l y t r i v i a l and unint e r e s t i n g . I do not think Putnam has demonstrated that the truths of mathematics and l o g i c are non-analytic, and they are f a r from t r i v i a l . In what follows I w i l l argue that Putnam's view about the t r i v i a l i t y of a l l a n a l y t i c sentences i s not even consistent with his own formal d e f i n i t i o n of 'analytic sentences'. Here i s Putnam's d e f i n i t i o n : " ( 1 ) The statement has the form: "Something (Someone) i s an A i f and only i f i t (he, she) i s a B," where A i s a s i n g l e word. (2)The statement holds without exception,and provides us with a c r i t e r i o n f o r something's being the sort of thing to which term A a p p l i e s . " C r i t e r i o n i s defined as follows: "A state-ment of the form "Something i s an A i f and only i f i t i s a B" 33 provides a c r i t e r i o n f o r something's being a thing to which the term A applies i f people can and do determine whether or not something i s an A by f i r s t f i n d i n g out whether i t i s a B." Very l i t t l e r e f l e c t i o n w i l l show that a statement which i s a n a l y t i c according to Putnam's c r i t e r i a w i l l be obvious and t r i v i a l only i f the c r i t e r i o n i n question i s obvious and t r i v i a l . But there i s no reason, i n general, to think that the c r i t e r i o n , by which people determine whether some-thing i s an A, i s at a l l obvious or t r i v i a l . In the case of "Someone i s a bachelor i f and only i f he i s an unmarried adult male" i t may be obvious that we determine whether someone i s a bachelor by determining that he i s an unmarried adult male, but we apply many of our words without consciously knowing what considerations determine our a p p l i c a t i o n s of the words. Perhaps th i s i s because the procedure we f o l l o w when we apply many words i s very complicated, and we i n t e r n a l i z e the procedure at an e a r l y age. For example, people can and do determine whether sentences are grammatical. The f a c t that people agree to a great extent about which sentences are grammatical and which are not suggests that there may be some unconscious processing of auditory (or v i s u a l ) information which people f i r s t do before deciding whether a sentence i s grammatical. This unconscious processing of informa-t i o n might occur according to a complex d e c i s i o n procedure which i s conven-t i o n a l l y associated with the word 'grammatical'. Oddly enough Putnam argues f o r this view i n an a r t i c l e e n t i t l e d "Some Issues i n the Theory of Grammar". He says, "This act of c l a s s i f y i n g sentences as grammatical or ungrammatical seems to be one I can perform given no input except the sentences themselves. In short, i t seems that i n doing this job I am i m p l i c i t l y r e l y i n g on something l i k e an e f f e c t i v e 34 procedure." In Chapter 4 I w i l l expand this l i n e of thought and produce furt h e r arguments to show that although the procedures which guide our use of language are not obvious, and need to be discovered, this does not count against t h e i r existence. I w i l l argue that we must postulate such procedures (or conventions, at least) i f we are to explain why there i s widespread agree-ment on the use of a word with respect to an open c l a s s . But regardless of whether my l a t e r arguments are s u c c e s s f u l , I think i t i s c l e a r l y possible (at least) that the c r i t e r i o n ( i n Putnam's sense), which people use when they apply c e r t a i n words, i s not always obvious, or t r i v i a l , and may be complex and i n t e r e s t i n g . For this reason I think i t i s sheer dogma on Putnam's part to claim that there are no hidden synonymies to be discovered. C l e a r l y a l o t more would need to be said about c r i t e r i a to enable us to draw any f i r m conclusions on t h i s question. ( I t i s i n t e r e s t i n g to note the s i m i l i a r i t y between Putnam's use of ' c r i t e r i a ' and Bennett's claim that c e r t a i n h i g h l y i n d i s p e n s i b l e sentences provide the tes t f o r Fness i n v i r t u e of which other sentences about Fness come to be established. I think both of these notions are c l o s e l y r e l a t e d to the idea that there are conventions which guide our use of language. I t i s t h i s l a t t e r idea that I w i l l pursue i n the chapters which follow.) 35 Chapter 2 1 Quine, From a L o g i c a l Point of View, p. 37. Grice and Strawson, "In Defense of a Dogma", reprinted i n Necessity, ed. Sumner and Woods, New York, 1969, p. 143. Lbert Harman, "Quine on 1 v o l . XXI, 1967, p. 137. 3 G i l b e r t Harman, "Quine on Meaning and Existence", The Review of Metaphysics, 4 Quine, Op. C i t . , p. 32. Grice and Strawson, Op. C i t . , p. 152. Jonathan Bennett, "Analytic-Synthetic", reprinted i n Necessity, p. 175, ^ Quine, Op. C i t . , p. 26. 8 Grice and Strawson, Op. C i t . , p. 153. 9 I b i d - , P- 158. 1 0 Bennett, Op. C i t . , p. 164. 11 I b i d . , P. 165. 12 I b i d . , pp. . 165 13 I b i d . , P- 162. 14 I b i d . , P. 163. 15 I b i d . , P. 169. 16 I b i d . , P. 177 17 H i l a r y Putnam, Philosophy of Science, I I I , ed. by H. F e i g l e and G. Maxwell, Minneapolis, 1962, p. 360. 1 8 I b i d . , p. 362. 1 9 I b i d . , pp. 392-93. 20 Putnam, "Some Issues i n the Theory of Grammar", Proceedings of the Twelfth  Symposium i n Applied Mathematics, American Mathematical Society, Providence, 1961, p. 39. Chapter 3 Conceptual Revision 37 "Any statement can be held true come what may, i f we make d r a s t i c enough adjustments elsewhere i n the system. Even a statement very close to the periphery can be held true i n the face of r e c a l c i t r a n t experience by pleading h a l l u c i n a t i o n or by amending c e r t a i n statements of the kind c a l l e d l o g i c a l laws. Conversely, by the same token, no statement i s immune to r e v i s i o n . " ! In t h i s passage, and i n i t s adjacent paragraphs, Quine i s claiming that i n the face of an experience which c o n f l i c t s with an accepted theory absolutely any sentence might be given up as f a l s e , provided s u f f i c i e n t changes were made elsewhere i n our system of b e l i e f s . What I wish to show i n thi s chapter i s that some sentences, at l e a s t , cannot be rejected unless we e i t h e r make a mistake or change the meaning of the sentence, ( i . e . change the a s s e r t i o n made by the sentence). My proof i s as follows. 1. If a sentence S asserts the same thing, or can generally be used to express the same b e l i e f , at as at then i f S i s true at T^, then, a) S must be true at T 2 and b) the de n i a l of S must be f a l s e a t T 2 and c) whoever denies S at T 2 i s wrong. 2 . If the sentence P which presently asserts the law of Modus Ponens i s true, then whoever denies P, at any time, i s e i t h e r wrong or does not r e a l l y deny what the sentence P presently a s s e r t s . 3. The law of Modus Ponens i s true, and the sentence which presently asserts Modus Ponens i s true. 4. Whoever denies, at any future time, the sentence which we presently use to asse r t Modus Ponens i s e i t h e r wrong or he does not deny what we presently a s s e r t . 38 On a c e r t a i n usage of 'asserts the same thing', premise 1 admits of exceptions. For example, a t o k e n - r e f l e c t i v e statement such as "I am happy" may have d i f f e r e n t t r u t h values when asserted by d i f f e r e n t people, or when asserted by the same person at d i f f e r e n t times, even though, on a c e r t a i n understanding of 'assert the same thing', I assert the same thing when I ut t e r "I am happy" at d i f f e r e n t times. However, on my use of 'asserts the same thing' premise 1 does not admit of these exceptions. There i s a standard p h i l o s o p h i c a l usage (which I am here following) according to which i t i s correct to say that when I assert "I am happy" and you assert "I am happy" we are a s s e r t i n g d i f f e r e n t things. On t h i s usage a minimal condition f o r saying that two sentences make the same as s e r t i o n (or express the same b e l i e f ) i s that they have the same t r u t h value. Regarding premise 3, i f anyone chooses to deny premise 3 I do not wish to argue with that person, indeed I cannot argue with that person. The reader may wonder whether Quine's p o s i t i o n i s a f f e c t e d by the argument j u s t given, I think i t i s . For I have produced a case where i t i s c l e a r that we could not r e j e c t a p a r t i c u l a r sentence without e i t h e r making a mistake or changing i t s t r u t h value (and hence i t s meaning and a s s e r t i v e content). And i n the l a t t e r case, where we r e j e c t S by changing i t s truth value and i t s a s s e r t i v e content, i t i s c l e a r that we have not rejected the a s s e r t i o n made by S at T p since we s t i l l b e l i e v e S was true at T-^ . I t follows that we cannot r e j e c t the a s s e r t i o n made by some sentences, e.g., S, without making a mistake. But t h i s i s ju s t what Quine denies when he says, "No statement i s immune to r e v i s i o n . " Quine might t r y to counter t h i s argument by i n s i s t i n g that no r e a l 3 9 d i s t i n c t i o n e x i s t s between (a) cases where r e j e c t i o n occurs because a sentence which we formerly thought to be true i s discovered to have been f a l s e a l l along, and (b) cases where r e j e c t i o n occurs because the t r u t h value of a sentence i s being changed by changing the meaning of the sentence. But t h i s counter w i l l not work i n the present case because our evidence f o r saying that the meaning of S has changed would be that i t s t r u t h value had changed. One might claim that, i n general, no r e a l d i s t i n c t i o n e x i s t s between saying that our opinion about the t r u t h value of S has changed and saying that the t r u t h value of S has been changed. But t h i s would e n t a i l the absurd p o s i t i o n that no r e a l d i s t i n c t i o n e x i s t s between saying that a sentence S i s f a l s e at T-^  and T£, and saying that S i s true at and f a l s e at 1^. I t would a l s o e n t a i l the f a l s e p o s i t i o n that no r e a l d i s t i n c t i o n e x i s t s between what we believe to be the case and what i s the case. As I mentioned i n the l a s t chapter, Bennett has offered a Quinean account of how to d i s t i n g u i s h cases where we should say that S i s now f a l s e and has been f a l s e a l l along, though we once thought i t to be true. He claims that i f S was highly i n d i s p e n s i b l e i n our network of b e l i e f s ( i . e . a n a l y t i c on Bennett's theory), then we should say that S was true but now i s f a l s e . If S was not i n d i s p e n s i b l e i n our network of b e l i e f s ( i . e . not a n a l y t i c on Bennett's theory), then we should say that S was f a l s e a l l along though we once thought i t to be true. For reasons which were given i n the preceding chapter, I f i n d Bennett's account incomplete. Consequently, I would l i k e another account of the d i s t i n c t i o n between sentences which are "True then, f a l s e now" and sent-ences which are "False a l l along though we didn't know i t " . I think I can 40 provide a way of t e l l i n g , i n some cases at l e a s t , whether we should say that the possible future r e j e c t i o n of some sentence S, which we now b e l i e v e would prove us wrong, or whether we should say that future people assert something d i f f e r e n t than we do. (a) I f S i s now used to assert something which i s obviously true (e.g. there are people, people eat breakfast, 2+2=4, or -(p'-p) ), and future people regard S as obviously f a l s e , this would show that future people use S to assert something d i f f e r e n t from what we now a s s e r t , (b) If S i s not now used to assert something obviously true, then we may suppose we were mistaken i n our present b e l i e f i n S. Now someone might think that i n appealing to the notion of obvious tr u t h I am presupposing that some of our b e l i e f s are i n f a l l i b l e . But I am not. I t i s possible (perhaps) that we are mistaken i n thinking that any given sentence i s true. But t h i s should not prevent us from saying that the t r u t h value (and a s s e r t i v e content) of a sentence has changed, any more than i t should prevent us from saying that any object has changed. Any b e l i e f of the form "This object has changed f o r x to y" i s f a l l i b l e . Nevertheless, i t i s obvious that things do change. There i s j u s t as strong a case f o r saying that the t r u t h value of p a r t i c u l a r sentences change as there i s f o r saying that anything changes. The f a c t that i t i s possible that our most c e r t a i n b e l i e f s may be mistaken does not mean that these b e l i e f s cannot be used i n p h i l o s o p h i c a l argument. Any of Quine's premises could be f a l s e . That does not mean that they are not well enough known to be used as a premise i n an argument. The same holds true of premises l i k e the law of Modus Ponens and "There are people". These might turn out to be f a l s e , but i n f a c t they w i l l not. This 4 1 i s not dogmatism. It i s merely the recognition that i n p h i l o s o p h i c a l discus-sion we are e n t i t l e d to premises. And i f we are e n t i t l e d to any premises we are e n t i t l e d to these. It would be methodologically absurd to suspend judgement about these and to continue an i n t e l l e c t u a l i n q u i r y . This method-o l o g i c a l absurdity i s i l l u s t r a t e d by the oddness of saying " I t i s l o g i c a l l y possible (consistent with the laws of logic) that we are mistaken i n thinking the laws of l o g i c are true." In my argument at the beginning of t h i s chapter I say that whoever denies the sentence, S, which I now use to assert Modus Ponens i s e i t h e r wrong or does not deny what I have been a s s e r t i n g . A c t u a l l y we can decide between these a l t e r n a t i v e s . It would be much more reasonable to suppose that one who denied Modus Ponens was not denying what we asse r t than i t would be to suppose such a d e n i a l to be wrong. This i s because i t i s much more l i k e l y that people should change meanings than that they should be mistaken about something as obviously true as Modus Ponens. This conclusion i s very close to some of Quine's remarks where he says " P r e - l o g i c a l i t y i s a t r a i t i n j e c t e d by bad t r a n s l a t o r s . " Quine here implies that an assumption which should guide us i n the t r a n s l a t i o n of any h i t h e r t o unknown language i s the assumption that speakers of the language do not hold b e l i e f s i n v o l v i n g elementary l o g i c a l mistakes. This i s not because i t i s impossible that any beings might make elementary l o g i c a l or f a c u t a l mistakes, but rather that we always have better reason to suppose that our t r a n s l a t i o n i s wrong than that a l i n g u i s t i c community might make very elementary l o g i c a l mistakes. What I have said so f a r i s compatible with a kind of Quinean posi-t i o n which may come close to the theory which Quine sketches at the end of 42 "Two Dogmas of Empiricism" and which i s s t i l l acceptable to many t r a d i t i o n a l e m p i r i c i s t s . (This p o s i t i o n i s suggested by Grice and Strawson). The modified Quinean p o s i t i o n goes l i k e t h i s : "Our present set of concepts may not be t o t a l l y adequate to cope with d e s c r i b i n g r e a l i t y . Even our present l o g i c a l concepts might be improved on, and perhaps even our concept of truth may be too coarse f o r de s c r i b i n g r e a l i t y . Our t o t a l set of concepts might be likened to a g r i d of squares which we use to approximate a curve. An improved set of concepts would be more c l o s e l y grained; the g r i d of squares would be smaller and the curve more c l o s e l y approximated. (For example, a language which was not of subject-predicate form, and which d i d not involve subject-predicate concepts might be a better t o o l f o r understand-ing r e a l i t y than our present language.) I t i s hard to imagine a set of l o g i c a l concepts which could enable us to better deal with r e a l i t y than our present ones, but f o r a l l we know they could e x i s t . And these concepts might j u s t be l i n e a r descendents of our present concepts, and be expressed by the same words. Propositions might be expressed which are c l o s e l y r e l a t e d to the propositions we now express. These c l o s e l y r e l a t e d propositions might be expressed by the same sentences which now express t h e i r close r e l a t i v e s . For example, i n the future people might use the words ' i f p, then q 1 to express what we would express by ' i f p, then probably q 1 . And the other t r u t h f u n c t i o n a l connectives might undergo s i m i l a r changes. In this language of the future an inference of the form " I f p, then q. p, therefore q" would be i n v a l i d , since i t would not follow that q was true - only that q was probably true. I t might be that t h i s p r o b a b i l i s t i c concept of ' i f - t h e n ' and i t s r e l a t e d t r u t h - f u n c t i o n a l concepts would enable us to better cope with r e a l i t y 43 than our present concepts, and we might adopt these new concepts f o r this reason. We might r e j e c t our old concepts, and " r e j e c t " Modus Ponens i n the sense that we no longer used Modus Ponens. This would not show that Modus Ponens expressed an i n v a l i d inference i n our old language, or that people who once used Modus Ponens were making a mistake, but i t would mean that a more powerful or more e f f i c i e n t system of concepts and inferences had been developed which was re p l a c i n g our old system." In the above I t r i e d to sketch a way i n which one could be said to r e j e c t or abandon our present concepts. But there i s something p e c u l i a r about this sketch. This set of new, though r e l a t e d , concepts which are supposed to replace our present concepts can already be expressed i n our present language (and th i s must be true of any example we can describe) and can p e r f e c t l y happily coexist with our present set of concepts. Thus there seems to be no need f o r our present words to change meaning, even s l i g h t l y , i n order to express these new concepts. The question a r i s e s , therefore, how experience might influence us to change the meanings of our present words. Putnam, i n "The A n a l y t i c and the Synthetic" answers t h i s question with an example. His example i s roughly as follows: Suppose that the word 'bachelor' now means "a sane male adult who has never been married". And suppose a l s o that at some future time i t i s discovered that a l l bachelors have some neurosis, c a l l i t sexual f r u s t r a t i o n . (A very u n l i k e l y example - but that's another s t o r y ) . As f a r as anyone knows a l l and only bachelors s u f f e r from sexual f r u s t r a t i o n . And imagine that everyone acquires such a high degree of psychological i n s i g h t that they can t e l l w ithin a few minutes conversation with a person whether he i s sexually f r u s t r a t e d , and hence, whether he i s a 44 bachelor. Also suppose that a whole c l u s t e r of i n t e r e s t i n g psychological laws are discovered about sexually f r u s t r a t e d people. Now under these c i r -cumstances some f a c t u a l discovery might lead us to change the meaning of 'bachelor'. For example, i f i t were discovered that i n rare cases there are bachelors who are not sexually f r u s t r a t e d we should e i t h e r have to give up a whole c l u s t e r of completely general psychological laws about bachelors, or else change the extension (and meaning) of 'bachelor' s l i g h t l y so that 'bachelor' r e f e r r e d to a l l and only sexually f r u s t r a t e d people. Which of these a l t e r n a t i v e s we choose w i l l depend upon how int e r e s t e d we are i n the old concept of a bachelor, and how d i f f i c u l t i t would be to rephrase a whole c l u s t e r of psychological laws i n terms of some new word. If we lose i n t e r e s t i n the old concept of a bachelor (because marriage became an infrequent occurrence, f o r example) we might w e l l change the extension of the word 'bachelor' to allow " A l l bachelors are sexually f r u s t r a t e d " and a whole c l u s t e r of psychological laws to remain exceptionless. In that case the old law, " A l l bachelors are unmarried" would come to have exceptions. However, this would not mean that people were formerly mistaken when they asserted that a l l bachelors are unmarried. For since the extension of the word 'bachelor' would have changed there i s no reason f o r the old law to have the same tr u t h value as the new law. Some may question whether we should have good reason f o r saying that the extension of the word 'bachelor' had changed. My answer to this i s that we would have the best possible evidence f o r saying that the extension had changed, namely that " A l l bachelors are unmarried" had changed from a true law to a ge n e r a l i t y with exceptions. 45 Chapter 3 Quine, From a L o g i c a l Point of View, p. 43. Quine, The Ways of Paradox, New York, 1966, p. 102. Chapter 4 Concept Analysis and the A-S D i s t i n c t i o n 47 In this chapter I w i l l t r y to give a t h e o r e t i c a l basis to the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n . In order to do that I w i l l f i r s t describe what I think i s a very u s e f u l kind of concept a n a l y s i s , and then go on to define the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n i n terms of this s p e c i a l kind of concept a n a l y s i s . Before doing e i t h e r of these, however, I would l i k e to take a look at some f a m i l i a r notions of concept a n a l y s i s . I t i s often assumed by philosophers that there i s a large amount of agreement about what counts as a concept a n a l y s i s , and about what expressions are synonymous, but that we lack a t h e o r e t i c a l basis f o r making these d i s t i n c t i o n s . I think the problem i s more complicated than that. There i s i n f a c t a large amount of disagreement about s p e c i f i c cases, and that g r e a t l y complicates any attempt to give these d i s t i n c t i o n s a t h e o r e t i c a l b a s i s . Suppose we temporarily put aside Quine's doubts about synonomy, r necessity, and concept a n a l y s i s . And suppose we agree that "2" and "\3S" •St-are n e c e s s a r i l y coextensive concepts. Would we a l s o say that ""^32" i s an S. analysis of our concept of "2"? And would we say that '2' and '"S32* are synonymous expressions? Some philosophers would. Some philosophers are w i l l i n g to count any d e s c r i p t i o n which has structure of complexity as an analysis i f i t i s n e c e s s a r i l y coextensive with the concept to be analysed. I do not wish to argue with these philosophers. Perhaps there are a s u f f i c -i e n t number of philosophers to j u s t i f y that use of 'concept a n a l y s i s ' . I do think, however, that there are f i n e r and more us e f u l d i s t i n c t i o n s to be drawn than that between necessary and non-necessary truths. S. Some philosophers, on the other hand, r e j e c t the idea that ">|32' expresses an analysis of our concept of "2", or i s synonymous with '2', 48 because, they say, an expression cannot mean anything more than what people usually mean by i t . I t seems implausible to hold that when one says that there are two birds i n the tree, one means that there are the f i f t h root of 32 birds i n the tree . In general, i t i s claimed, one cannot mean that x when a s s e r t i n g y, unless one believes y only i f one believes x. On this account two expressions are synonymous only i f they are interchangeable with one another i n b e l i e f contexts, and the expression of the corre c t a n a l y s i s of a concept must be interchangeable with the expression of the concept to be analysed i n b e l i e f contexts. The view j u s t expressed comes close to a view discussed by Benson Mates i n h i s a r t i c l e "Synonymity".''' It would be convenient i f th i s view were true, because the c r i t e r i o n of synonymity expressed i s c l e a r and simple. Un-for t u n a t e l y , there i s no reason to beli e v e that the proposed c r i t e r i o n i s co r r e c t . This becomes apparent once we r e a l i z e that we r a r e l y know the ana l y s i s of concepts we normally use. (For example, most people could not produce an an a l y s i s of our concept of "grammatical" when asked, nor could they e a s i l y recognize i t s a n a l y s i s when presented with i t . In general, i t i s a d i f f i c u l t task to produce a corre c t concept a n a l y s i s , and i t often requires considerable r e f l e c t i o n to a s c e r t a i n whether one has a r r i v e d at the corre c t r e s u l t . ) Given t h i s f a c t , there i s no reason to think that the an a l y s i s of a concept w i l l be interchangeable with the expression of the analysed concept i n b e l i e f contexts. I t might be objected that i n some sense of 'know' we unconsciously know the an a l y s i s of a l l the concepts we use. But this sense of know, i f i t e x i s t s at a l l (which I doubt), i s not going to be h e l p f u l i n the present 49 case. For i n t h i s sense of 'know' i t i s possible to know that p and yet be unaware that p i s true. In t h i s sense of know someone could "know" that p and yet s i n c e r e l y assert "I do not believe that p." So the f a c t that someone "knows" the analysis of a concept does not give us any reason to think that the analysis w i l l be interchangeable with the analysandum i n b e l i e f contexts, unless we resort to t a l k i n g about what a person unconsciously b e l i e v e s . If we move i n t h i s d i r e c t i o n , however, the " s u b s t i t u t i v i t y i n b e l i e f contexts" c r i t e r i o n f o r synonomy becomes highly mysterious and problematical. I do not think the move from "synonomy" to "unconscious b e l i e f s " i s a move i n the d i r e c t i o n of c l a r i t y . Church has argued i n "Intensional Isomorphism and Identity of B e l i e f that i n f a c t the expression of a concept and i t s a n a l y s i s are always i n t e r -changeable i n b e l i e f contexts. His argument, b r i e f l y , i s t h i s : "There are many words i n , say, E n g l i s h which can only be translated i n t o another language say, German, by analysing the English concept i n t o i t s components, and then t r a n s l a t i n g the a n a l y s i s . For example, there i s no s i n g l e German word which means f o r t n i g h t . Consequently, one must t r a n s l a t e the word ' f o r t n i g h t ' i n t o the German expression f o r "two weeks", and the German t r a n s l a t i o n of "John believes a f o r t n i g h t has passed" (E) i s the same as the German t r a n s l a t i o n of "John believes two weeks have passed" ( E ' ) . C a l l the German t r a n s l a t i o n G. Church then claims that since any t r a n s l a t i o n has the same t r u t h value as the sentence being tr a n s l a t e d i t follows that G must have the same t r u t h value as both E and E'. Hence E and E' must have the same t r u t h value i n E n g l i s h . But E' i s j u s t the r e s u l t of r e p l a c i n g the expression of a concept i n E with i t s a n a l y s i s , and i n p r i n c i p l e " f o r t n i g h t " and "two weeks" could have been any 50 E n g l i s h expression and i t s concept a n a l y s i s . Therefore, i n p r i n c i p l e , the same argument could be given to show that the expression of any concept and i t s a n a l y s i s are interchangeable i n b e l i e f contexts salva v e r i t a t e . " Church's argument can quic k l y be shown to be inadequate. For Church gives no reason to think that the t r a n s l a t i o n of the E n g l i s h b e l i e f context, E, i n t o the German b e l i e f context, G, must have the same tr u t h value. Pre-sumably he would argue that E and G must have the same t r u t h value because they mean the same. But there i s no more reason f o r saying that E and G mean the same than there i s f o r saying that E and E 1 mean the same. Consequently, anyone who thinks that E and E' have d i f f e r e n t t r u t h values w i l l remain unmoved by Church's argument, since such a person would e i t h e r deny that E and E' mean exa c t l y the same, or would deny that b e l i e f contexts which mean the same must have the same t r u t h value. This would be more obvious i f E were "Mary be l i e v e s the theory i s true" and i f E' were "Mary believes the theory i s 0". (where '0' i s a d e s c r i p t i o n of the c o r r e c t a n a l y s i s of our concept of truth.) A c t u a l l y , Church's argument i s an unsuccessful attempt to solve the famous paradox of a n a l y s i s . The paradox i s u s u a l l y stated somewhat as fol l o w s : I t i s thought that any a n a l y s i s of a concept expresses the same concept as the concept being analysed. From t h i s i t follows (or i s u s u a l l y thought to follow) that any sentence, S, containing a p a r t i c u l a r expression, E, expresses the same p r o p o s i t i o n as the sentence which r e s u l t s from s u b s t i t u -t i n g f o r E i n S the concept a n a l y s i s of E. Thus, suppose that A i s an a n a l y s i s of the concept expressed by E. Then i t ought to be true that 'E = E' expresses the same pr o p o s i t i o n as 'E = A*. But that seems absurd, since 'E = A' expresses a concept a n a l y s i s whereas 'E = E' does not. 51 Furthermore, i t i s doubtful that whoever believes that E=E also believes that E=A. The problem, then, i s to re c o n c i l e these fa c t s with the claim that 'A' and 'E' express i d e n t i c a l concepts. I w i l l now try to describe a kind of concept analysis which (1) can explain the paradox of a n a l y s i s , (2) can explain why the term expressing a concept applies i n ju s t those cases i t does apply, and (3) can explain to some extent how we recognize that a term, and the concept i t expresses, apply i n a given s i t u a t i o n . The kind of concept analyses I w i l l describe constitutes a subclass of those statements which would be classed as concept analyses by the account given i n terms of the necessary coextensiveness of concepts, and w i l l contain as a subclass those statements classed as analyses by the in t e r c h a n g e a b i l i t y i n b e l i e f contexts c r i t e r i o n . This means that my account w i l l be more r e s t r i c t i v e than the "necessary coextensiveness" c r i t e r i o n , but not as r e s t r i c t i v e as the " i n t e r c h a n g a b i l i t y i n b e l i e f contexts" c r i t e r i o n . My account i s given i n terms of l i n g u i s t i c conventions or r u l e s . I w i l l argue that such conventions must e x i s t i f we are to explain why we apply language i n the s i t u a t i o n s we do apply i t , and i f we are to explain the r e g u l a r i t y that language e x h i b i t s . Of course, there i s a very obvious sense i n which the r e l a t i o n s h i p between a word and i t s denotation i s conventional. There i s nothing i n t r i n s i c about the word 'r a i n ' which makes us use i t as we do. We could j u s t as w e l l have interchanged the roles of the words 'r a i n ' and 'snow' i n our language. In what follows I w i l l t ry to connect t h i s element of conventionality with the notion of a l i n g u i s t i c rule and with concept a n a l y s i s . Now some philosophers have -suggested that concept analyses ought to state the rules which govern our use of words, and some philosophers (Kant, 52 Bennett) have said that concepts are r u l e s , or sets of r u l e s , f o r applying words or c l a s s i f y i n g objects, s i t u a t i o n s , e t c . In the case of terms applying to p h y s i c a l objects these rules or conventions may be vague or imprecise, or incomplete, but i n the case of l o g i c a l terms, numbers, and other abstract notions such as philosophers are prone to deal with, the rules may be very precise and exactly stateable. But some philosophers have r i d i c u l e d the idea that there unconscious rules governing our a p p l i c a t i o n of words to s i t u a t i o n s , or objects. Z i f f , f o r example, claims that behavioural r e g u l a r i t y i s rule-guided only i f the r e g u l a r i t y i s the r e s u l t of conscious i n t e n t i o n - only i f the r e g u l a r i t y i s planned. Z i f f scorns the idea that the r e g u l a r i t y which language e x h i b i t s i s rule-guided. At no time d i d people ever s i t down and draw up rules f o r language, and at no time did people ever plan to achieve a c e r t a i n end by inventing language. I want to grant Z i f f the point that l i n g u i s t i c r e g u l a r i t y i s not always, at l e a s t , the r e s u l t of planning or conscious i n t e n t i o n , but deny that t h i s f a c t counts against saying that l i n g u i s t i c r e g u l a r i t y i s rule-guided. I maintain that behaviour does not have to be the r e s u l t of conscious i n t e n t i o n i n order to be rule-guided. Perhaps rule-guided behaviour must be purposeful, but i t i s a mistake to think that a l l purposeful behaviour i s consciously intended. Now c e r t a i n l y l i n g u i s t i c r e g u l a r i t y e x i s t s f o r a purpose, namely, communication. Z i f f t r i e s to obscure t h i s point where he ways, "The import-ance of communication i s usually exaggerated", and he goes on to produce examples of l i n g u i s t i c utterances which he alledges are not intended to communi-cate anything. But Z i f f must admit, i f we are to take him s e r i o u s l y , that most assertions are made f o r the purpose of communicating something, at l e a s t . 53 I w i l l assume that most l i n g u i s t i c behaviour i s purposeful. Given this premise I think I can b u i l d a good case f o r saying that language i s rule-guided. I base this claim on the f a c t that language does s a t i s f y an a n a l y s i s of rule-guidedness which can e a s i l y be extrapolated from David Lewis' analysis of rules i n Convention,^ and I think Lewis' a n a l y s i s i s cor r e c t . Lewis' account of rule-guidedness i s roughly as follows: A behav-iour pattern i s rule-guided i f and only i f (a) P^ i s a voluntary system of r e g u l a r i t i e s which are performed by members of a group i n order to achieve some end (e.g. communication) which i s mutually desired by a l l members of that group, (b) that same end (e.g. communication) could be achieved i f members of the group had each chosen to act according to some d i f f e r e n t behaviour pattern, P2, and (c) i t matters l i t t l e to members of the group whether they act according to P^ or Pg, but i t matters to each member of the group that he/she s h a l l act according to whichever of the two patterns most other members adopt. Condition (c) insures the kind of a r b i t r a r i n e s s or conventionality required f o r rule-guidedness. The idea i s that members of the group are la r g e l y i n d i f f e r e n t to what behavioural pattern they f o l l o w as long as the desired r e s u l t occurs. I t matters l i t t l e to any of us, f o r example, whether we c a l l something 'red' or 'sned' as long as we succeed i n communication. Conditions a, b, and c are a l l met by human languages. Consequently, there i s no b a r r i e r to saying that our l i n g u i s t i c behaviour i s rule-guided (assum-ing Lewis' analysis i s r i g h t ) . We are now i n a p o s i t i o n to sketch what I think i s the i n t e r e s t i n g and perhaps most u s e f u l conception of a concept a n a l y s i s . A corre c t concept 54 analysis states a set of rules f o r applying words to objects or s i t u a t i o n s (or f o r d i s t i n g u i s h i n g objects and s i t u a t i o n s i n the n o n - l i n g u i s t i c case) (a) which w i l l s e l e c t a l l and only those objects or s i t u a t i o n s which s a t i s f y the concept being analysed, (b) on the basis of which we a c t u a l l y do apply the expressions which express the concept being analysed, i . e . , the rules a c t u a l l y do guide our use of these expressions i n something l i k e the way a computer's response to external s t i m u l i i s guided by i t s program. (In order to be as c l e a r as possib l e , I would l i k e to explain the analogy between rule-guided behaviour and computer-programmed behaviour. I t i s important that we have some explanation of how rules guide our l i n g u i s t i c behaviour, otherwise i t w i l l not explain much to say that our l i n g u i s t i c behaviour i s rule-guided. So here i s my explanation. On my theory, l i n g u i s -t i c rules constitute a p a r t i a l program of our bra i n s . This programming could occur i f each b r a i n were in n a t e l y programmed to program i t s e l f f u r t h e r , according to the p a r t i c u l a r l i n g u i s t i c environment which i t grows up i n . There i s nothing absurd i n this idea. A computer could be programmed to fur t h e r program i t s e l f according to the kind of environment i t was placed i n , and there i s no reason why humans could not do the same thing, at a neural l e v e l . It seems p l a u s i b l e that c h i l d r e n do something l i k e t h i s when they learn the grammar of the language they learn to speak. Ce r t a i n neural changes may occur when we learn to use a p a r t i c u l a r word, and these neural changes may cause us to use the word as i f we were consciously following a c e r t a i n r u l e . In such a case i t may be appropriate to say that the r u l e i s guiding our use of the word. For example, i f (a) a creature's neural structure changes as a r e s u l t of the creature's having 55 observed some l i n g u i s t i c r e g u l a r i t y which holds by convention ( i n Lewis' sense), and i f (b) the l i n g u i s t i c behaviour produced by that neural change i s such as would be produced by consciously following a p a r t i c u l a r r u l e , then we.may say that the l i n g u i s t i c behaviour i s guided by the l i n g u i s t i c r u l e . We may say th i s because (1) the relevant l i n g u i s t i c behaviour i s being guided by a neural change which occurred i n order to enable the creature to imitate a l i n g u i s t i c r e g u l a r i t y , and (2) the l i n g u i s t i c r e g u l a r i t y being imitated i s consequently determining the relevant l i n g u i s t i c behaviour, and (3) the l i n g u i s t i c r e g u l a r i t y being imitated i s a r e g u l a r i t y which e x i s t s by convention ( i n Lewis' sense). This, I suggest, i s the mechanism by which conventions guide l i n g u i s t i c behaviour.) More has to be sa i d about my sketch of concept analyses but f i r s t l e t us see how i t s a t i s f i e s the requirements I l a i d down. (1) The concept a n a l y s i s explains why the term expressing a concept applies i n j u s t those cases i t does apply, because the concept analysis states the rules f o r apply-ing the term and the rules l i n k the term to j u s t those cases to which the term can be c o r r e c t l y applied. (2) The concept analysis explains to some extent how we recognize that a term applies i n a given s i t u a t i o n , because the analysis states the rules which guide our l i n g u i s t i c response i n that s i t u a t i o n . We come to know whether the term applies to a given case because our response to the case i s guided by rules which we have learned i n language t r a i n i n g . (3) My account of a concept analysis explains the paradox of a n a l y s i s . To see this consider the following. On my account a concept a n a l y s i s describes the rules which guide the use of some word. The rules which guide our use of words need not be conscious 56 rules that we could formulate on demand; they need not be applied with our awareness. We can know how to use words without knowing what we are doing when we use them, ju s t as a musician may know how to play a piece without being able to describe the complex ways she i s moving her f i n g e r s . This explains how we can know how to use a concept without knowing the ana l y s i s of that concept. The rule-guidedness theory of l i n g u i s t i c behaviour can a l s o explain how a person can know the sentence "This sentence i s grammatical" to be true without knowing "This sentence i s XYZ" to be true (where 'XYZ' i s some complex d e s c r i p t i o n which i s n e c e s s a r i l y coextensive with the word 'grammatical'). The explanation i s t h i s : The denotation of the complex expression'XYZ1 i s a function of the rules guiding our use of'X*, our use of'Y', and our use of'z' (assuming *X*, V, and'Z* to be separate words or phrases). These rules are d i f f e r e n t from the r u l e guiding our use of 'grammatical', even though the combined e f f e c t of these rules l o g i c a l l y insures that the expression 'XYZ' applies to j u s t those sentences that 'grammatical' applies to. And the f a c t that the rules guiding 'XYZ' are d i f f e r e n t from the ru l e guiding 'grammatical' allows a person to c o r r e c t l y apply the sentence "This sentence i s grammatical" i n a given s i t u a t i o n without knowing whether the sentence "This sentence i s XYZ" would apply i n that s i t u a t i o n . In general the rules guiding the use of a simple expression are d i f f e r e n t from the rules guiding the use of a complex expression. That i s why the expression of a concept and the a n a l y s i s of that concept are not interchangeable i n b e l i e f contexts. Once we see the concept expressed by a word as a ru l e we are no longer tempted to think that the analysans and analysandum phrases express the same concept. 57 We can also see why i t i s misleading to say that simple sentences and complex sentences express the same thought or proposition. And i n s o f a r as i t makes sense to say that two words i n d i f f e r e n t languages express the same concept i t i s because i t makes sense to say that speakers of d i f f e r e n t languages are following p r a c t i c a l l y the same l i n g u i s t i c r u l e s . The words are d i f f e r e n t , but the rules are the same, i n the relevant way. I think I have now explained the paradox of a n a l y s i s . Much more could be sa i d about i t , but this i s not the place. (aside) It i s of i n t e r e s t to note that sometimes we can recognize a concept a n a l y s i s as c o r r e c t when i t i s presented to us. Something analogous happens with non-l i n g u i s t i c behaviour. It sometimes happens that we recognize that the reason we acted i n a p a r t i c u l a r way i s that we were following a c e r t a i n r u l e . For example, we might ask a tennis player whether the reason she acted i n a p a r t i c u l a r way i n a given s i t u a t i o n was that she had learned a ru l e to the e f f e c t that i n s i t u a t i o n s of such-and-such a kind i t i s best to act so-and-so. Our tennis player might c o r r e c t l y answer yes, even though she could not have produced the ru l e which would explain her action.. (end aside) I turn now to some problems with my sketch of a correct concept a n a l y s i s . An immediate problem a r i s e s when we t r y to decide which of the l o g i c a l l y equivalent a l t e r n a t i v e analyses a c t u a l l y states the true analysis of a concept. That i s , which of the a l t e r n a t i v e proposed analyses a c t u a l l y states the rules which guide our a p p l i c a t i o n of words to objects or s i t u a t i o n s ? If these rules are unconscious how are we to decide what rules guide our 58 l i n g u i s t i c behaviour? For example, our use of the expression 'grammatical i n E n g l i s h ' seems to be rule-guided. There i s widespread agreement about which sentences are grammatical and which are not. But i f we ask ourselves whether a p a r t i c u l a r transformational grammar i n f a c t states a l l the rules which govern our use of the word 'grammatical' we draw a blank. Parts of the grammar may be e a s i l y recognised as c o r r e c t , e.g., a rule which says that possessives such as 'the brother of John' may be converted i n t o 'John's brother', but t h i s i s not true of more complex rules p e r t a i n i n g to the deep structure of complex sentences. The question a r i s e s , how could we decide which ( i f any) of two complete transformational grammars states the rules which a c t u a l l y guide our judgements of grammaticality? Perhaps this question can be answered as follows. It seems i n p r i n c i p l e possible that we should at some future time be able to trace the c i r c u i t r y of the brain so completely that we could obtain a map or flow chart of the successive e l e c t r o n i c states of the brain when a person generates a given sentence, or when a person performs a given c a l c u l a -t i o n . And i t seems possible that there could be an isomophic mapping between the successive transformational stages which a grammar assigns to the generation of a p a r t i c u l a r sentence and the successive brain states which occur when that sentence i s generated. To see that this i s possible consider an analogous case with computers. It i s w e l l known that there i s an isomorphic mapping between statements i n the p r o p o s i t i o n a l calculus and c i r c u i t s i n computers. The formula 'p v q 1 , f o r example, corresponds to a c i r c u i t which has two branches, l i k e this — . If e i t h e r of the two branches has a current running through i t , i . e . , i s a closed c i r c u i t , then the major trunk has a current running through i t . Analogously, i f one of the p a i r p,q i s true, then the whole d i s j u n c t i o n i s 59 true. Truth i n a s e n t e n t i a l component of a formula corresponds to a closed c i r c u i t i n c i r c u i t r y , f a l s i t y corresponds to an open c i r c u i t , and d i s j u n c t i o n corresponds to a branched c i r c u i t . In general, given any formula i n the p r o p o s i t i o n a l calculus one can draw a c i r c u i t corresponding to i t , and v i c e -versa. Consequently, since d i f f e r e n t derivations of the same formula i n the s e n t e n t i a l calculus correspond to d i f f e r e n t conditionals having d i f f e r e n t antecedents and the same consequent, i t follows that d i f f e r e n t derivations of the same formula i n the p r o p o s i t i o n a l calculus correspond to d i f f e r e n t c i r c u i t s i n computers. Analogously, i f two computers were programmed to test sentences f o r grammaticality according to two non-isomorphic, but l o g i c a l l y equivalent, grammars, then the processes which take place i n each computer when the computers test a sentence would be d i f f e r e n t . And i f we knew what processes were taking place i n a computer when i t tests a sentence f o r grammaticality we could t e l l how the computer was programmed. Likewise, I think, i f we know what processes take place i n the human br a i n when a person judges a sentence f o r grammaticality, we should be able to reconstruct a program f o r the brain which i s isomorphic with the processes that take place i n the b r a i n . And i f we f i n d that a p a r t i c u l a r transformational grammar, G, i s isomorphic (at a c e r t a i n l e v e l of d e t a i l ) with the program we have reconstructed f o r the brain, and i f the i n d i v i d u a l sentences of the grammar G are isomorphic with the i n d i v i d u a l sentences of the reconstructed program with which they are paired, then we could conclude that G c o r r e c t l y represents the grammar which guides our judgements of the grammaticality of sentences. In this way we could decide which of two non-isomorphic, but l o g i c a l l y equivalent grammars, i f e i t h e r , expressed the rules which constitute our concept of grammaticality. 60 Whether i n fac t we w i l l ever be able to decide, i n j us t the way I have described, which of two non-isomorphic, but l o g i c a l l y equivalent grammars express our concept of grammaticality depends i n part upon whether the brain i s very much l i k e a computer. But even i f the brain i s not very much l i k e a computer, we might s t i l l decide this question i s some way which i s roughly analogous to the method I have described. ( I t might be h e l p f u l at th i s point to stress that the example j u s t produced appeals to the premise that we can i n f e r the program of a computer from a d e s c r i p t i o n of i t s structure and i t s i n t e r n a l processes. The converse of t h i s premise does not hold. From the f a c t that a computer i s programmed a c e r t a i n way we cannot i n f e r that the computer has a p a r t i c u l a r i n t e r n a l s t r u c t u r e . Two computers may follow the same program although they have d i f f e r i n g i n t e r n a l s t r u c t u r e s . By analogy, the f a c t that two people are foll o w i n g the same rule does not allow us to i n f e r that they have the same bra i n structure and brain processes. However, i f two people cio have the same brain structure and brain processes this constitutes evidence that they are following the same l i n g u i s t i c r u l e s . Also, i f two computers, which have i d e n t i c a l i n t e r n a l s tructures, go through d i f f e r e n t processes when s o l v i n g the same problem, we may i n f e r that they have been programmed d i f f e r e n t l y . Analogously, i f two people with i d e n t i c a l brain structures ( i n the relevant respects) need to go through d i f f e r e n t i n t e l l e c t u a l processes when judging, say, the grammaticality of a sentence, we may i n f e r that those two people are being guided by d i f f e r e n t rules.) A problem a r i s e s now, and that i s , i s n ' t i t implausible to suppose 61 that the corre c t a n a l y s i s of our concept "grammatical i n E n g l i s h " must await future psychological i n q u i r y , and i n general i s n ' t i t odd to suppose that concept a n a l y s i s i s an empirical enquiry which can y i e l d only p r o b a b l i s t i c results?. Perhaps so, but I think good reasons have been given to support this conclusion, and perhaps philosophers must, l i k e other thinkers, be prepared to accept some s u r p r i s i n g r e s u l t s . Arguments have been given to show that there have to be rules or conventions guiding our use of language, and i t j u s t i s an empirical question what these rules are. Arguments have al s o been given to show that i t explains a l o t to suppose that concept analyses state the rules which guide the use of words, (or guide us when we make d i s t i n c t i o n s i n the n o n - l i n g u i s t i c case). But I do not r e a l l y i n s i s t that we use the expression 'concept a n a l y s i s ' i n t h i s way. I do not care how we use the expression 'concept a n a l y s i s ' . My main concern has been to show that we can draw a d i s t i n c t i o n which i s f i n e r and more u s e f u l that the necessary/non-necessary d i s t i n c t i o n , and yet which i s not as r e s t r i c t i v e as the i n t e r c h a n g e a b i l i t y i n b e l i e f contexts c r i t e r i o n f o r synonomy. I think some d e f i n i t e epistemological advantages r e s u l t from focusing our a t t e n t i o n on the rules or conventions guiding the use of words. In a d d i t i o n to the merits already considered under points 1-3, there i s the following point. By focusing our a t t e n t i o n on rules governing the a p p l i c a t i o n of words, we can explain why a l l the objects or cases described by an expression have c e r t a i n properties i n common. We can explain why a l l the items i n class C have the property P, i f we can show that a rule f o r placing an item i n class C i s "the item must have property P". For example, i t genuinely explains why a l l the objects i n a c e r t a i n box have four sides i f we know that a rule f o r 62 p l a c i n g an object i n that box i s "the object must have four s i d e s " . Further explanation i s required to explain why a l l the objects i n the box have the cube root of 64 s i d e s . To explain t h i s l a t t e r f a c t we must t a l k about entailments between arithme-t i c a l p ropositions. So there i s an advantage to focusing our a t t e n t i o n on the rules governing the use of language that does not r e s u l t from merely focusing our a t t e n t i o n on the necessary coextension of concepts or the necessary entailments between propositions. To analyse a concept i n t o properties P, Q, and R does not explain why a l l the items s a t i s f y i n g the con-cept have properties P, Q, and R unless we point out that the concept i s a rule f o r s e l e c t i n g items according to whether they have the properties P, Q, and R. An objection to my l a s t s e r i e s of points may be made on the follow-ing grounds. What i s to prevent us from saying that a ru l e to the e f f e c t , say, that a word should be applied only to objects having four sides i s the same as a ru l e to the e f f e c t that the same word should be applied only to objects having the cube root of 64 number of sides? I f we can provide no reason f o r saying these are d i f f e r e n t r u l e s , must we not conclude that my account of concept a n a l y s i s has no advantages over the account i n terms of necessary coextensiveness? To reply to th i s objection: (1) No, even i f we can provide no reason f o r saying these are d i f f e r e n t r u l e s , i t i s s t i l l an advantage to see concepts as rules since i t s t i l l explains the f a c t that a l l the things classed under a s i n g l e term have the properties they share i n common. (2) I think we can provide a reason f o r saying these are d i f f e r e n t r u l e s , namely, one 63 would go through d i f f e r e n t processes i n following these two r u l e s . I submit the following as a general p r i n c i p l e f o r i n d i v i d u a t i n g r u l e s . " I f any person would need to go through d i f f e r e n t behavioural, or i n t e l l e c t u a l (thought) processes when consciously following r u l e x and ru l e y, then x and y are d i f f e r e n t r u l e s , " For example, most people would go through d i f f e r e n t i n t e l l e c t u a l processes when following the rules (a) "Put four-sided objects i n t h i s box" and (b) "Put objects i n the box having the cube root of 64 sides". When following r u l e (a) one might count the sides of objects or j u s t glance at objects to see whether they were four-sided. More than t h i s would be involved when an average person followed r u l e (b). The average person would have to c a l c u l a t e a couple of seconds when following r u l e (b) and then, a f t e r c a l c u l a t i n g , he or she would go through the same procedure one would go through i n following r u l e ( a). In t h i s example i t i s f a i r l y easy to say that d i f f e r e n t i n t e l l e c t -ual processes would occur when an average person followed rules (a) and (b). Not every case w i l l be so easy to decide. There may be some vagueness i n the notion of "same process". And f o r some purposes we may want to count s l i g h t l y d i f f e r e n t processes as the same process. But I think that the notion of "same process" i s s u f f i c i e n t l y c l e a r to enable us, i n many cases, to d i s t i n g u i s h l o g i c a l l y equivalent r u l e s . That i s s u f f i c i e n t f o r present purposes. I t i s al s o i n t e r e s t i n g to note that we do not always need to be i n a p o s i t i o n to say what rule a person i s following i n order to have strong reasons f o r saying that the person i s following some r u l e ( j u s t as we do not always need to be i n a p o s i t i o n to say what program a computer i s following i n order to know that i t i s fol l o w i n g some program). 64 I turn now to a question which may have occurred to the reader; i t i s t h i s : "How can we t e l l whether people who speak the same language are following the same l i n g u i s t i c r u l e s ? " Before attempting to answer t h i s question we should note that we o c c a s i o n a l l y have strong evidence that people are following d i f f e r e n t l i n g u i s t i c r u l e s . P r a c t i c a l l y everyone has had the experience of arguing with someone and discovering that the disagreement was r e a l l y a v e r b a l disagreement - that each party to the disagreement had a d i f f e r e n t use f o r some word. Often these verbal disagreements are uncovered by comparing m e t a l i n g u i s t i c remarks such as "Well, what would you count as a whale?" In examples such as these we can usually t e l l whether two people have extensionally d i f f e r e n t r u l e s . Sometimes, however, people make m e t a l i n g u i s t i c remarks about the meanings of words and about what sentences they take to be a n a l y t i c . The f a c t that these i n t e n s i o n a l remarks often agree i s e a s i l y explained by the hypo-thesis that many people follow the same l i n g u i s t i c r u l e s . But i t i s very d i f f i c u l t (at least) to explain t h i s f a c t by appeal to extensional considera-tions alone. The f a c t that the rule-guidedness hypothesis e a s i l y explains t h i s uniformity of i n t e n s i o n a l m e t a l i n g u i s t i c remarks, combined with the lack of competing explanations, gives us some reason to accept t h i s hypothesis. There are other reasons. People w i l l u s ually complete the number se r i e s "2,4,6,8..." i n the same way, even though there are i n f i n i t e l y many rules which could generate th i s sequence of numbers. This f a c t constitutes evidence that people's minds (or brains) often work i n a s i m i l i a r fashion. Also there are a small number of l o g i c a l systems which people f i n d easy and n a t u r a l to work with, although 65 there are i n f i n i t e l y many ways to construct, say, a system of the predicate c a l c u l u s . This fur t h e r supports the view that most people have s i m i l i a r i n t e l l e c t u a l equipment - that t h e i r "computers" are very s i m i l i a r . Further-more, what p h y s i o l o g i c a l evidence we presently have ind i c a t e s that people's brains and br a i n processes are s i m i l i a r . These facts suggest that people often are being guided by the same l i n g u i s t i c rules when t h e i r l i n g u i s t i c behaviour i s i d e n t i c a l i n the relevant respects. For i f people have stru c t u r -a l l y i d e n t i c a l i n t e l l e c t u a l equipment, and t h e i r behaviour i s i d e n t i c a l , then they are probably undergoing the same i n t e r n a l processes. In p r i n c i p l e , we could v e r i f y whether people do i n f a c t undergo s i m i l i a r b r a i n processes when they judge, say, the grammaticality of the same sentence. If we found the brain processes, brain s t r u c t u r e , and l i n g u i s t i c behaviour to be i d e n t i c a l i n the relevant respects we could say f o r sure whether people are being guided by the same r u l e s . We are nearly i n a p o s i t i o n to give a d e f i n i t i o n of the a n a l y t i c -synthetic d i s t i n c t i o n . But f i r s t I wish to introduce a t e c h n i c a l term, namely, 'the semantic transformation of a semantic r u l e ' , which may be understood somewhat as follo w s : In general the semantic rules which are described i n a concept analysis w i l l r e l a t e an expression, E, to a class of si t u a t i o n s or cases, C. The semantic transformations of a given r u l e i s the un i v e r s a l closure of a c o n d i t i o n a l , i n which the antecedent asserts that s i t u a t i o n C obtains, and the consequent expresses C i n terms of the expression 66 E, according to the semantical r u l e i n question. The following examples may be h e l p f u l : 1. Rule^, "You may apply ' s i s t e r 1 to any female s i b l i n g . " Semantic Transformation of Rule-^, "For any x, i f x i s a female s i b l i n g , then x i s a s i s t e r . " 2. Rule 2, "You may connect any p a i r of true sentences with the word 'and'." Semantic Transformation, "For a l l p and q, i f p i s true and q i s true, then rp and q* i s true." Although t h i s c h a r a c t e r i z a t i o n i s somewhat vague, i t should give the reader a general idea of how to form the semantic transformation (S-T) of a given r u l e . The motivation f o r introducing the idea of an S-T i s t h i s : by considering the l o g i c a l consequences of a given S-T we can uncover the purely l o g i c a l consequences of following a given l i n g u i s t i c r u l e . This brings us to my d e f i n i t i o n of an a n a l y t i c sentence, namely, "A sentence i s a n a l y t i c i f and only i f i t i s a l o g i c a l consequence of the semantic transfor-mation of the rules described i n some concept a n a l y s i s . " " I f a sentence i s not a n a l y t i c i s i t s y n t h e t i c " . I think that my d e f i n i t i o n of the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n nearly captures one standard conception of the d i s t i n c t i o n . I do not claim that i t accurately matches everyone's use of ' a n a l y t i c ' . In p a r t i c u l a r i t does not match that use of 'a n a l y t i c ' according to which ' a n a l y t i c ' i s t r i v -i a l l y interchangeable with 'necessary'. My d e f i n i t i o n of ' a n a l y t i c ' i s designed to caputre the idea that a n a l y t i c sentences r e l a t e to the ana l y s i s of a concept, or are i n some way the l o g i c a l consequence of the rules of language. The question whether, on my use of 'a n a l y t i c ' , a l l necessary truths are a n a l y t i c i s an i n t e r e s t i n g question which I w i l l consider i n a l a t e r 67 chapter. (In what follows I w i l l abbreviate my d e f i n i t i o n of ' a n a l y t i c ' by saying that a sentence i s a n a l y t i c i f f i t i s a l o g i c a l consequence of some concept a n a l y s i s ) . There i s another question which I would l i k e to consider at th i s stage, i . e . , Does my d e f i n i t i o n make the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n one of degree or of kind? Answer: In the sense that p r a c t i c a l l y every d i s t i n c -t i o n i s one of degree the a n a l y t i c - s y n t h e t i c d i s t i n c t i o n i s one of degree. But i n s o f a r as the question whether a sentence i s a n a l y t i c c l e a r l y depends on another question, e.g., what rules guide the use of t h i s expression?, the d i s t i n c t i o n i s a sharp one; i t i s one of kind. The questions of degree come i n when we t r y to decide what the p a r t i c u l a r rules guiding the use of an expression are. Sometimes the rule guiding the use of an expression i s vague,e.g., "Apply the term F to anything that has nearly a l l , of the properties P^ ....P ." This vagueness w i l l engender undecidable questions about whether something i s an F, but that should not lead us to suspect the concept of a r u l e , or any concepts i n v o l v i n g the concept of a r u l e . Again, sometimes the question whether something i s a ru l e guiding the use of a p a r t i c u l a r expression w i l l be very d i f f i c u l t to decide, but that should not lead us to r e j e c t my a n a l y s i s of a n a l y t i c i t y i n terms of r u l e s . Likewise, questions about the t r u t h of a sentence are sometimes undecidable, but that should not lead us to r e j e c t an an a l y s i s of knowledge i n terms of true b e l i e f . Questions about t r u t h are often unanswerable j u s t because the use of some term i s unclear, or because i t i s not c l e a r what rules do guide the use of a term. For th i s reason I think Quine i s wrong when he says that the concept of t r u t h i s respectable and t o l e r a b l y c l e a r , but that the concepts of meaning 68 and l i n g u i s t i c convention are neither respectable nor c l e a r . Questions about t r u t h can be s e t t l e d only i f there are d e f i n i t e conventions and rules guiding the use of terms. For i n s o f a r as the use of an expression i s indeter-minate, the use of any sentence containing that expression i s indeterminate, and so i s i t s t r u t h value. And i f there are d e f i n i t e conventions guiding the use of these terms, then questions about what these conventions are must be answerable i n p r i n c i p l e . I do not know of a d e c i s i o n procedure by which we can d i s t i n g u i s h l i n g u i s t i c conventions from non-conventions, but then I have never seen a d e c i s i o n procedure by which we can d i s t i n g u i s h true sentences from other sentences. I suggest, however, that we could never produce a d e c i s i o n procedure f o r t r u t h unless we could produce a d e c i s i o n procedure f o r l i n g u i s t i c conventions. 69 Chapter 4 Benson Mates, "Synonymity", U n i v e r s i t y of C a l i f o r n i a Publications i n  Philosophy, 1950. Alonzo Church, "Intensional Isomorphism and the Iden t i t y of B e l i e f " , P h i l o s o p h i c a l Studies, 1954. Z i f f , Semantic A n a l y s i s , I t h i c a , 1960, p. 36. Lewis, Convention. Chapter 5 R e c a l c i t r a n t Experience 71 In chapter 3 I considered and rejected Quine's claim that absolutely any b e l i e f might be rejected i n the face of an e x p e r i e n t i a l report which con-f l i c t e d with an accepted theory. In what immediately follows I hope to show that a counterexample to Quine's view i s provided by one of his other views about theories. In "Two Dogmas of Empiricism", and elsewhere, Quine expresses the b e l i e f that a l l theories must pass empirical t e s t s , or be answerable to experience. This b e l i e f e n t a i l s that there i s a c e r t a i n c l a s s of theories which adequately explains our experience, and another class which f a i l s to adequately explain our experience. Quine a l s o asserts that theories can and must be a l t e r e d i n the face of r e c a l c i t r a n t experience, and r i g h t l y so. For i f we do not hold that some theories, unmodified, must be abandoned i n the face of experience, then we can make no sense of the notion that theories must be answerable to experience, and so Quine's p o s i t i o n becomes u n i n t e l l i g -i b l e . But i f we admit that some theories, unless modified, must be abandoned i n the face of experience by any r a t i o n a l being, then we admit that a c e r t a i n b e l i e f i s forced upon us by experience. I t i s true, of course, that the sentence (S) "Some theories, unless modified, must be abandoned i n the face of experience by any r a t i o n a l being", might at some future time be regarded as f a l s e by most people, but th i s would not show that t h i s sentence i s not now true. And i t would be absurd f o r some-one to r e j e c t the b e l i e f now expressed by S i n order to save a theory. In much the same way i t would be absurd to r e j e c t the law of non-contradiction i n order to make one's theory consistent with experience. Now an argument could e a s i l y be constructed (exactly analogous to 72 to the argument given to defend Modus Ponens) which would show that whoever denies S i n the future i s e i t h e r wrong or does not deny the b e l i e f we now assert by S. We simply point out that assent to S i s a precondition of i n t e l l i g i b l e discourse at this time. This enables us to take S as a true premise i n any argument, and t h i s commits us to saying that anyone who denies S i n the future i s e i t h e r mistaken or else i s not r e a l l y denying what we now assert by S. The l a t t e r a l t e r n a t i v e might occur i f new experiences lead us to modify our present set of concepts i n some way, e.g., our concept of a theory, or our concept of experience, so that S comes to express something d i f f e r e n t from what S now expresses. What e n t i t l e s us to say with assurance that S would express something d i f f e r e n t from what S now expresses i s the f a c t that sameness of t r u t h value i s a precondition of sameness of b e l i e f or sameness of a s s e r t i o n . If S i s f a l s e at some future time and S i s true now, then S expresses something d i f f e r e n t i n the future from what S expresses now. So f a r we have shown that c e r t a i n theories must be excluded by experience. But the problem s t i l l remains, how does experience disconfirm a p a r t i c u l a r theory i n a p a r t i c u l a r formulation? What are r e c a l c i t r a n t exper-iences? K a r l Popper has discussed this problem i n Chapter V of The Logic of  S c i e n t i f i c Discovery.^ Popper introduces the problem by d i s c u s s i n g a trilemma which i s due to J.F. F r i e s . The trilemma i s t h i s . E i t h e r our b e l i e f s about experience are to be accepted dogmatically, with no j u s t i f i c a -t i o n , or they are to be j u s t i f i e d . I f we accept the p r i n c i p l e that any b e l i e f or statement can be j u s t i f i e d only by deducing i t from other b e l i e f s or statements, then we cannot j u s t i f y any statement without becoming involved i n an i n f i n i t e regress of j u s t i f i c a t i o n s . But i f we r e j e c t the p r i n c i p l e 73 that a l l b e l i e f s are to be j u s t i f i e d by deducing them from other b e l i e f s , then we must j u s t i f y our b e l i e f s some other way. Popper believes that the only other way b e l i e f s could be j u s t i f i e d i s by experience i t s e l f (as opposed to a l i n g u i s t i c d e s c r i p t i o n of experience). Popper c a l l s the doctrine that our b e l i e f s are j u s t i f i e d by experiences psychologism. Now although psychologism avoids the problems of both dogmatism and the i n f i n i t e regress, Popper r e j e c t s psychologism because he thinks that experiences could only cause b e l i e f s ; not j u s t i f y them. He believes that j u s t i f i c a t i o n i s a l o g i c a l r e l a t i o n which can hold only between sentences or b e l i e f s , and not between b e l i e f s and experiences. In Popper's view causal explanations are never l o g i c a l j u s t i f i c a t i o n s . Since Popper r e j e c t s psychologism he can only f a l l back e i t h e r on dogmatism or the i n f i n i t e regress. In f a c t he t r i e s to combine these two a l t e r n a t i v e s . B r i e f l y his theory of j u s t i f i c a t i o n i s as follows: In p r i n c i p l e statements can only be j u s t i f i e d i n terms of other statements, and the possible chain of j u s t i f i c a t i o n f o r a statement i s i n f i n i t e . But i n p r a c t i c e we must stop somewhere i n t h i s chain of j u s t i f i c a t i o n and j u s t decide to assume that p a r t i c u l a r statements are true. Statements of t h i s kind form the touchstone f o r science. They are the basic statements which describe i n t e r s u b j e c t i v e l y observable events, and they must have a l o g i c a l form such that t h e i r negations are in c o n s i s t e n t with general law-like statements. "Basic statements are therefore - i n the m a t e r i a l mode of speech - statements a s s e r t i n g that an 2 observable event i s occuring i n a c e r t a i n region of space and time." In p r a c t i c e , we decide whether to accept or r e j e c t a p a r t i c u l a r basic statement a f t e r performing a test or experiment. We do not j u s t i f y our d e c i s i o n to accept or r e j e c t a p a r t i c u l a r basic statement, however, since t h i s would 74 involve us i n an i n f i n i t e regress. Rather we just decide, f r e e l y ; though our d e c i s i o n i s rule-guided and not a r b i t r a r y . Also our d e c i s i o n i s not absolute. It can be changed i n the l i g h t of future experience i f we discover that some truth condition of a basic statement i s not f u l f i l l e d . But once we have decided to accept or r e j e c t a basic statement ( f o r the time being) we can use i t to t e s t our theories (for the time being). Thus our decisions to accept or r e j e c t basic statements j u s t i f y our other b e l i e f s , but these decisions and basic statements are not themselves j u s t i f i e d . That roughly i s Popper's p o s i t i o n . But Popper's view of basic statements i s open to a serious objection. Popper says, "Basic statements are accepted as the r e s u l t of a d e c i s i o n or agreement; and to that extent they are conventions. The decisions are reached i n accordance with a procedure governed by r u l e s . " (To that extent the decisions are not a r b i t r a r y con-ventions.) Now what i s Popper to say i f a group of s c i e n t i s t s decide to accept a basic statement not on the basis of an observation, but on the basis of s u p e r s t i t i o n , or r e l i g i o n , say? Popper w i l l t r y to exclude t h i s kind of case on the grounds that i t v i o l a t e s the rules f o r accepting basic statements. One of these r u l e s , presumably, w i l l say that basic statements must be accepted on the basis of observation. But can Popper exclude basic statements whose acceptance v i o l a t e s c e r t a i n r u l e s , and a l s o hold that our d e c i s i o n to accept basic statements need not be j u s t i f i e d i n any way? I think not. If a group of s c i e n t i s t s adopted c e r t a i n basic statements a r b i t r a r i l y we would not accept t h e i r d e c i s i o n to adopt those statements. We would claim they were being unreasonable, and I think Popper would make t h i s claim a l s o , or some equivalent claim. To say that a d e c i s i o n to adopt a c e r t a i n basic statement v i o l a t e d the 75 rules f o r adopting basic statements i s to say that the adoption of that basic statement was u n j u s t i f i e d . Popper's s o l u t i o n i s an attempt to deal with the problem of f a l l i b i l i t y and r e v i s a b i l i t y of a l l statements of objective f a c t . I think i t i s commonly recognised that a l l statements about the way things are (not the way things seem to be) are f a l l i b l e . Sense-datum t h e o r i s t s and others have attempted to provide an i n c o r r i g i b l e foundation for our knowledge of the external world. This foundation i s supposed to consist of reports of experiences or sense-data. (Even these kinds of reports are f a l l i b l e , however, since a l l reports about sensations involve comparison, and one can make a mistake i n comparing any two things, even sensations.) Now even i f one grants that sensation reports are i n f a l l i b l e we must allow (and the sense-datum the o r i s t s do) that when we move from sensation reports to objective claims about the external world we make assumptions, inductive and otherwise, and these assumptions may j u s t be f a l s e . I see no way to avoid admitting that b e l i e f s about the way things o b j e c t i v e l y are f a l l i b l e , but I do not see why t h i s i s e s p e c i a l l y a problem. Things do happen i n the world, and p a r t l y as a consequence of t h i s we adopt c e r t a i n b e l i e f s . These b e l i e f s are f a l l i b l e , of course, because sometimes b e l i e f s about events are caused i n us by things unconnected with the events we report. But we do have our b e l i e f s , neverthe-l e s s , and when we believe that c e r t a i n things have occurred which f a l s i f y some predictions of our theory, then we must modify our theory (provided we do not abandon our b e l i e f that the r e c a l c i t r a n t experiences occurred.) A l l that i s required to make sense of the idea of r e c a l c i t r a n t experience i s that we sometimes, c o l l e c t i v e l y , have more confidence that a c e r t a i n event E, or 76 class of events E, has occurred than we have that our theory i s c o r r e c t . Sometimes we are i n t h i s p o s i t i o n . The question a r i s e s , how do we get i n t h i s p o s i t i o n . The answer might be something l i k e the f o l l o w i n g : 1. Suppose 2 people report having had E - l i k e experiences (experiences such as they would have i f E occurred and they were si t u a t e d i n such a way as to be c a u s a l l y a f f e c t e d by E ) . 2. Assume that when a person s i n c e r e l y reports an E - l i k e experience i t i s probable that an event of type E has occurred, say the p r o b a b i l i t i e s are 10/1. 3. If 2 people report an E - l i k e experience the odds are 99/100 that an E-type event occurred. 4. If 100 people report an E - l i k e experience the odds approach c e r t a i n t y that E occurred. 5. Almost no theory has a p r o b a b i l i t y approaching c e r t a i n t y . 6. In the case described ( i n v o l v i n g 100 people) we would have greater con-findence that an E-type event occurred than that our theory i s r i g h t . The case j u s t described i s , of course, an o v e r s i m p l i f i c a t i o n . Yet, I think, something l i k e t h i s kind of reasoning goes on when we t e s t and r e j e c t theories i n the l i g h t of our b e l i e f s about experience. The procedure j u s t described assumes the t r u t h of c e r t a i n of our e x p e r i e n t i a l reports i n order to e s t a b l i s h the probable t r u t h of our e x p e r i e n t i a l reports. Does this r a i s e i n f i n i t e regress type problems? I think not. It would r a i s e i n f i n i t e regress problems i f we f i r s t had to e s t a b l i s h the t r u t h of c e r t a i n e x p e r i e n t i a l reports i n order to e s t a b l i s h the probable truth of other reports, but I do not think we must do that. Rather we assume the t r u t h of some of our e x p e r i e n t i a l 77 b e l i e f s on something l i k e Kantian grounds, that i s , on the grounds that i f our experience i s to be i n t e l l i g i b l e at a l l , then some of our e x p e r i e n t i a l b e l i e f s must be true. (For purposes of t h i s thesis I do not think i t i s necessary to defend the assumption that some of our e x p e r i e n t i a l b e l i e f s are true. But for c u r i o s i t y ' s sake I w i l l b r i e f l y o u t l i n e a Kantian defense of t h i s assump-t i o n . " I f we did not assume that some of our e x p e r i e n t i a l b e l i e f s are true then we should have no b e l i e f s about what constitutes experiences of an outer objective world, and no way of d i s t i n g u i s h i n g our own subjective states from states of the external world. Hence, we should have no way of d i s t i n g u i s h i n g ourselves from the outer objective world, and we would have no concept of our-se l v e s . But since we do d i s t i n g u i s h our inner states from an outer objective world, i t follows that we must assume the t r u t h of some e x p e r i e n t i a l b e l i e f s . Nothing d i c t a t e s which of our e x p e r i e n t i a l b e l i e f s we must assume to be true, but we n a t u r a l l y r e t a i n those b e l i e f s which enable us to form a coherent p i c -ture of the world.") It would, of course, be c i r c u l a r to assume the t r u t h of c e r t a i n e x p e r i e n t i a l b e l i e f s i n order to j u s t i f y a l l our b e l i e f s about experience, but I am not t r y i n g to do that. In f a c t I am denying that that can be done. The j u s t i f i c a t i o n of a l l of our b e l i e f s about experience i s not something we can give. That does not imply that the j u s t i f i c a t i o n of our b e l i e f s about exper-ience does not e x i s t . The j u s t i f i c a t i o n does e x i s t , but i t does not consist of a chain of reasons. In what follows I w i l l t r y to give a rough explanation of what j u s t i f i e s our b e l i e f s about the world. But t h i s explanation should not i t s e l f be construed as a j u s t i f i c a t i o n . In an e a r l i e r chapter I argued that there are rules guiding our use of language. These rules guide our use of p a r t i c u l a r words, phrases, 7 8 and sentences. There are grammatical rules as w e l l as semantical r u l e s , and we often use or follow these rules without knowing that we do so. Sometimes these rules are uncovered i n s t a t i n g concept analyses. There are a l s o rules t y i n g language to experiences which can only be known o s t e n s i v e l y . For example, there i s a rule which may be roughly stated as fo l l o w s : When you see something l i k e t h i s you may say "That i s red." (Wtiere the denotation of ' t h i s ' i s given o s t e n s i v e l y . ) The r u l e s which guide our use of language do not require us to respond to our experiences l i n g u i s t i c a l l y . Rather they allow us to respond to our experiences with a c e r t a i n range of d e s c r i p t i o n s . I f there i s no r u l e allowing a c e r t a i n l i n g u i s t i c response, then that response i s excluded by a closure r u l e which says that a response i s permitted only i f i t i s permitted by a r u l e . We are now i n a p o s i t i o n to ex p l a i n how l i n g u i s t i c d e s c r i p t i o n s of experience are j u s t i f i e d . What j u s t i f i e s us i n a s s e r t i n g a c e r t a i n d e s c r i p t i o n of our experience i s the f a c t (not the b e l i e f that i t i s a fact ) that our l i n g u i s t i c response was a response to an experience and was guided by the rules governing the use of language, i . e . , our response was l i n g u i s t i c a l l y acceptable. The f a c t that our l i n g u i s t i c responses are rule-guided does not imply that we make decisions or form b e l i e f s that we are f o l l o w i n g l i n g u i s t i c r u l e s c o r r e c t l y , and i t does not imply that we check to see that any conditions s p e c i f i e d by the ru l e s are s a t i s f i e d . To fo l l o w a l i n g u i s t i c r u l e c o r r e c t l y i t s u f f i c e s to react to an experience i n a c e r t a i n way. This r e a c t i n g to an experience may be a causal matter - the experience may be one causal c o n d i t i o n 79 among other conditions which j o i n t l y r e s u l t i n a l i n g u i s t i c response. Other conditions (not n e c e s s a r i l y causal) which must accompany an experience, E, i n order f o r a correct l i n g u i s t i c response to E to occur may include such factors as w i l l i n g n e s s to respond l i n g u i s t i c a l l y , and previous language t r a i n i n g , e t c . There might seem to be a problem i n saying that a l i n g u i s t i c response to an experience/can both be p a r t i a l l y caused ( i n the sense of 'provoked by'), and a l s o rule-guided. But I don't think the problem i s serious i n t h i s case. Suppose a computer i s programmed to respond to s t i m u l i according to c e r t a i n rules when c e r t a i n other causal f a c t o r s are present. The programming of the computer according to c e r t a i n rules then becomes one of the causal factors which j o i n t l y r e s u l t i n a p a r t i c u l a r l i n g u i s t i c response on the part of the computer. Thus the response of the computer i s both provoked by external s t i m u l i and guided by c e r t a i n r u l e s . Human beings, unlike computers, may not be programmed with a l l the rules they need to speak a language, but they learn these r u l e s , and can be c r i t i c i s e d i f they v i o l a t e these r u l e s , even though t h e i r response may be provoked. I think there i s no more problem i n supposing that human l i n g u i s t i c response may be both rule-guided and provoked by our experiences, than there i s i n supposing that the response of computers may both be programmed and provoked by external s t i m u l i . In f a c t the case i s easy to make f o r human beings, since a condition u s u a l l y necessary f o r human l i n g u i s t i c response i s w i l l i n g n e s s to respond l i n g u i s t i c a l l y . This means that l i n g u i s t i c response i s u s u a l l y voluntary. Thus, there can be no objection - to saying that l i n g u i s t i c responses are rule-guided - on the grounds that l i n g u i s t i c responses 80 are involuntary (though someone might object to c a l l i n g computer behaviour rule-guided). The remaining conditions f o r saying that our l i n g u i s t i c be-haviour i s rule-guided are al s o s a t i s f i e d (as I pointed out when I discussed David Lewis's account of rules i n an e a r l i e r chapter. I repeat them now to re f r e s h our memory. "A behaviour pattern, P^, i s rule-guided i f (a) P^ i s a voluntary system of r e g u l a r i t i e s which are performed by members of a group i n order to achieve some end (e.g. communication) which i s mutually desired by a l l members of that group, (b) that same end (communication)could be achieved i f members of the group had c o l l e c t i v e l y chosen to act according to some d i f f e r e n t behavioural pattern, and (c) i t matters l i t t l e to members of the group whether they act according to P^ or 1?^ , but i t matters to each member of the group that he/she s h a l l act according to whichever of the two patterns most other members adopt.) Now i t may sound strange to say that l i n g u i s t i c responses to experiences are both provoked and a l s o voluntary, and since rule-guided acts are voluntary one might think i t strange to say that l i n g u i s t i c responses are both provoked and rule-guided. But there i s no r e a l problem here. The strangeness of these claims a r i s e s , I think, from thinking that whatever we call'responses ' must be e n t i r e l y caused by external s t i m u l i , or must be co r r e l a t a b l e i n a 1-1 fashion with external s t i m u l i . But I do not intend to use 'response' i n such a narrow sense. When I say that some l i n g u i s t i c behaviour i s a response to an experience, or i s provoked by an experience, I only mean that the l i n g u i s t i c response w i l l occur whenever the experience occurs, provided c e r t a i n other conditions are s a t i s f i e d . These other conditions include things l i k e w i l l i n g n e s s to respond, having a reason to respond, having 81 language t r a i n i n g , etc. I do not claim that these other conditions are p a r t i a l causes of the l i n g u i s t i c response. That question i s l e f t open. Given t h i s account of the sense i n which l i n g u i s t i c responses are provoked by experience I see no i n c o m p a t i b i l i t y i n saying both that l i n g u i s t i c responses are provoked and voluntary. If the reader chooses he or she may suppose I am using the expression 'provoked' i n a te c h n i c a l sense. I neither intend to, nor am compelled to, take a stand on the question whether a l l human a c t i o n i s caused. (However, I am committed to saying that there i s some set of i n t e r n a l and external conditions which w i l l r e g u l a r l y be followed by a l i n g u i s -t i c response. This seems a f a i r l y safe claim once i t i s r e a l i z e d the i n t e r n a l conditions to which I r e f e r include things l i k e w i l l i n g n e s s to respond, having a reason to respond, etc.) So f a r I have t r i e d to explain the j u s t i f i c a t i o n of some l i n g u i s t i c responses to our experiences or sense impressions. The question a r i s e s whether t h i s kind of explanation can a l s o be given to explain the j u s t i f i c a t i o n of d e s c r i p t i o n s of objective states of a f f a i r s , e.g., "This i s water". For descriptions of objective states of a f f a i r s go beyond what i s j u s t i f i e d by some descriptions of experiences. We a l l know that we may have experiences which are l i k e those of water, without our experiences a c t u a l l y being of water. So what j u s t i f i e s our a s s e r t i o n "This i s water"? I think much the same kind of thing j u s t i f i e s d e s c r i p t i o n s of objective states as j u s t i f i e s d e scriptions of subjective s t a t e s . Our a s s e r t i o n that a p a r t i c u l a r objective state e x i s t s i s j u s t i f i e d by the f a c t (not the b e l i e f that i t i s a fact ) that our l i n g u i s t i c response was permitted by the rules governing the a p p l i c a t i o n of words. (Again, our reac t i n g to an 82 experience i n a rule-guided way need not involve any judgements on our part that the conditions f o r applying a rule are s a t i s f i e d . Rather our response to an experience may simply be provoked by the experience.) The rules which permit objective s t a t e - d e s c r i p t i o n s as responses to experiences are more complicated than those permitting subjective state-d e s c r i p t i o n s . Rules permitting objective s t a t e - d e s c r i p t i o n s w i l l l i n k l i n g u i s t i c responses to a whole network of experiences. For example, the l i n g u i s t i c response "This i s water" w i l l be permitted only when c e r t a i n , but f i n i t e l y many, background experiences e x i s t i n a d d i t i o n to water-type exper-iences. In general, background experiences w i l l be experiences of what philosophers often c a l l "standard conditions of observation". It should not be thought that because objective s t a t e - d e s c r i b i n g responses are allowed by l i n g u i s t i c rules these responses must be true. From the f a c t that objective s t a t e - d e s c r i p t i o n s are allowed by l i n g u i s t i c r u l e s , given c e r t a i n f a m i l i e s of experiences, i t only follows that the objective s t a t e - d e s c r i p t i o n s are j u s t i f i e d . I t i s possible f o r an a s s e r t i o n , A, to be j u s t i f i e d by c e r t a i n experiences and yet be f a l s e . This could happen i f c e r t a i n other experiences occurred which j u s t i f i e d some objective state-d e s c r i p t i o n incompatible with A. If the vast majority of our experiences j u s t i f y a d e s c r i p t i o n incompatible with A, then we conclude that A i s f a l s e , i n s p i t e of the f a c t that A was i n i t i a l l y j u s t i f i e d by c e r t a i n of our experiences. On the other hand, i f the vast majority of our experiences continue to j u s t i f y the a s s e r t i o n that A, then we conclude that A i s true. Perhaps an example would be us e f u l here. A rule which would permit the objective state d e s c r i p t i o n "This i s water" might be something l i k e the 83 the following: We may say "This i s water" i f most of the fol l o w i n g sets of experiences occur: E-jTi^. . .E n. Thus i f a person has most of the experiences E^...E n, that person w i l l be j u s t i f i e d i n claiming "This i s water." Now i t may be that each member of the set E^...E n i s r e g u l a r l y c o r r e l a t e d with other experiences, e.g., E^ may be co r r e l a t e d with F^,F2, and E 2 may be corr e l a t e d with G^ ,G2, and so on. And i t may be that t h i s t o t a l set of c o r r e l a t e d experiences, Fj_,F2,G^,G2. • .M^ ,M2 i s considered relevant to the question whether something i s water. So the t r u t h of the statement "This i s water" may depend i n a given case, upon whether t h i s f u r t h e r set of c o r r e l a t e d experiences can be made to occur. I f t h i s f u r t h e r set of correlated experiences never occurs i t may be appropriate to override the i n i t i a l judgement "This i s water", and to su b s t i t u t e the judgement "This i s s u l f u r i c a c i d " . This would not mean, however, that the i n i t i a l judgement "This i s water" was u n j u s t i f i e d . (The example j u s t given i s merely speculation on my part. I do not want to commit myself to the p a r t i c u l a r structure of this example. I merely wish to suggest a possible way i n which a j u s t i f i e d , rule-guided response to a set of experiences may be overridden by other experiences.) In the example j u s t described I say "The tr u t h of the statement "This i s water" may depend, i n a given case, upon whether t h i s f u r t h e r set of cor r e l a t e d experiences can be made to occur." There i s , i n f a c t , a d i f f i c u l t and i n t e r e s t i n g problem about what makes a statement true, as opposed to merely j u s t i f i e d . Some claim that to say a p a r t i c u l a r objective state-d e s c r i p t i o n i s true means that the vast majority of our experiences j u s t i f y , and w i l l continue to j u s t i f y that s t a t e - d e s c r i p t i o n , and not i t s d e n i a l . This view i s a t t r a c t i v e because i t supports the view that we i n some way construct 84 our world from our experiences, and there can be no meaningful questions about the objective state of the world which cannot be reduced to questions about possible experiences. On the other hand, i t does not seem to do j u s t i c e to our concept of other people to say that they are constructions of our exper-iences. I do not wish to take a stand on th i s controversy here. I bring up the issue to point out that my account of j u s t i f i c a t i o n can stand whether (a) we think the claim - that assertions which the vast majority of our experiences j u s t i f y are true - expresses an analysis of our concept of t r u t h , or (b) whether we think t h i s claim expresses some transcendent or metaphysical t r u t h . Someone might object that my explanation of how some of our e x p e r i e n t i a l b e l i e f s are j u s t i f i e d presupposes the existence of an objective world which causes, i n part, c e r t a i n b e l i e f s i n us. For example, I claim that we w i l l strongly favor a d e s c r i p t i o n which the vast majority of our experiences j u s t i f y . This seems to imply that usually the vast majority of our experiences w i l l support a p a r t i c u l a r b e l i e f , and that the s i t u a t i o n w i l l not often a r i s e where our experiences do not strongly support e i t h e r a p a r t i c u l a r a s s e r t i o n or i t s d e n i a l . The question a r i s e s whether we are e n t i t l e d to make t h i s assumption. To answer t h i s objection: F i r s t , I do not think I need to j u s t i f y assumptions which I make i n my explanation of how e x p e r i e n t i a l b e l i e f s are j u s t i f i e d . I am o f f e r i n g a theory, and the theory i s confirmed to the extent to which i t explains what i t i s intended to explain. Second, within the context of the present d i s c u s s i o n i t seems odd to c a l l i n t o question the assumption that there i s an objective world, and that the vast majority of our experiences w i l l support c e r t a i n b e l i e f s and not other b e l i e f s . In fac t i t 85 seems odd i n any t h e o r e t i c a l d i s c u s s i o n to question the existence of an objective r e a l i t y . If we do not assume the existence of an objective r e a l i t y , then what are we t h e o r i z i n g about? Chapter 5 K a r l Popper, The Logic of S c i e n t i f i c Discovery, London, 1968. I b i d . , p. 103. I b i d . , p. 106. Chapter 6 A n a l y t i c Truth and Necessary Truth 88 This chapter w i l l deal with the question whether a l l necessary truths are a n a l y t i c . One way of attacking t h i s question would be to examine some d e f i n i t i o n of a n a l y t i c t r u t h , f o r example, my own d e f i n i t i o n , and see whether anything about the d e f i n i t i o n of a n a l y t i c t r u t h would enable us to decide the question whether a l l necessary truths are a n a l y t i c . I w i l l follow t h i s procedure here. R e c a l l my d e f i n i t i o n of a n a l y t i c t r u t h . According to that d e f i n i -t i o n a sentence i s a n a l y t i c i f and only i f i t i s a l o g i c a l consequence of a corre c t concept a n a l y s i s . Now, depending on how we construe the expression ' l o g i c a l consequence of a correct concept a n a l y s i s ' we may or may not have a ready answer to the question whether a l l necessary truths are a n a l y t i c . Most people construe ' l o g i c a l consequence' i n such a way that any conclusion which n e c e s s a r i l y follows from c e r t a i n premises i s a l o g i c a l consequence of those premises. Many l o g i c i a n s a l s o hold that every necessary t r u t h follows from any premises whatsoever, since, i f the conclusion of an argument i s necessar-i l y true, then i t i s impossible that the premises should be true and the con-c l u s i o n f a l s e . Given the t r u t h of my claim that ' a n a l y t i c ' a p p l i e s to any l o g i c a l consequence of a corr e c t concept a n a l y s i s , i t i s l i k e l y that these l o g i c i a n s would want to claim that every necessary t r u t h i s a n a l y t i c , since they hold that every necessary t r u t h i s a l o g i c a l consequence of any concept a n a l y s i s . Some l o g i c i a n s , however, construe ' l o g i c a l consequence' more narrow-l y . And i f we do construe ' l o g i c a l consequence' i n a more narrow way the question whether a l l necessary truths are a n a l y t i c may be much more d i f f i c u l t to answer. But, i n a way, the disagreement over how we should construe the 89 expression ' l o g i c a l consequence' may seem i d l e . A f t e r a l l , what does i t matter how we construe t h i s expression as long as we see the consequences of construing the expression each way? The answer to t h i s question i s t h i s : I think i t i s i n t e r e s t i n g to consider whether there i s a more i n t e r e s t i n g connection between concept analyses and the set of a l l necessary truths than the mere f a c t that necessary truths cannot be f a l s e at the same time that a concept analysis i s true. I t would be i n t e r e s t i n g to see whether we can f i n d a sense f o r ' l o g i c a l consequence' i n which i t would be true to say that a given necessary t r u t h i s a l o g i c a l consequence of one concept a n a l y s i s , but not another. So l e t us consider whether we can f i n d such a sense f o r ' l o g i c a l consequence'. Most l o g i c i a n s claim that we can d i s t i n g u i s h informal v a l i d con-sequences from formal v a l i d consequences (a formally v a l i d consequence being one which follows from the premises of a given argument purely i n v i r t u e of the form of the argument). These l o g i c i a n s would regard "x i s a t r i a n g l e ; therefore, x has three s i d e s " as an informal inference, on the grounds that although t h i s inference i s v a l i d i t i s not v a l i d i n v i r t u e of i t s l o g i c a l form. There i s a problem, however, about how to d i s t i n g u i s h those arguments which are formally v a l i d from other arguments. Usually people t r y to make th i s d i s t i n c t i o n by making another d i s t i n c t i o n , that between l o g i c a l and n o n - l o g i c a l constants. Formally v a l i d inferences are then defined as those i n which only l o g i c a l constants occur e s s e n t i a l l y . (A term T i s s a i d to occur e s s e n t i a l l y i n a v a l i d argument i f and only i f there i s a possible replacement of T by a d i f f e r e n t term which renders the argument i n v a l i d . ) Likewise formal l o g i c a l truths are sometimes defined as true sentences i n which only l o g i c a l constants 90 occur e s s e n t i a l l y . ( I t i s commonly recognized that formally v a l i d arguments and formal l o g i c a l implications are r e l a t e d i n the fo l l o w i n g way: If a co n d i t i o n a l i s formed which has as i t s antecedent the conjunction of the premises of a formally v a l i d argument, and as i t s consequent the conclusion of that argument, then that c o n d i t i o n a l i s a formal l o g i c a l t r u t h . Such a co n d i t i o n a l i s c a l l e d the corresponding c o n d i t i o n a l of the argument. In general i f an argument i s v a l i d then i t s corresponding c o n d i t i o n a l i s neces-s a r i l y true. In what follows I s h a l l sometimes be di s c u s s i n g the v a l i d i t y of an argument and sometimes the necessity of a corresponding c o n d i t i o n a l . I t should be understood that u s u a l l y when I discuss v a l i d i t y i n th i s chapter analogous remarks could be made about necessity, and vice-versa.) Now i f we had an adequate d e f i n i t i o n of ' l o g i c a l constant' we could make use of the definitions of 'formally v a l i d ' and 'formally true' and then we could r e s t r i c t the class of a n a l y t i c truths to those which are formally v a l i d consequences of concept analyses. But do we have an adequate d e f i n i t i o n of ' l o g i c a l constant 1? There i s an ex c e l l e n t d i s c u s s i o n of th i s question by Arthur Pap i n Ch. 6 of Semantics and Necessary Truth.* Pap concludes that there i s no important d i s t i n c t i o n between inferences which are formally v a l i d and those which are inf o r m a l l y v a l i d . I w i l l b r i e f l y e x p lain how Pap reaches th i s conclusion. Pap f i r s t r e j e c t s attempts to define ' l o g i c a l constant' by complete enumeration of instances. I t i s of no t h e o r e t i c a l i n t e r e s t to be given a l i s t of l o g i c a l constants which includes s e n t e n t i a l connectives, the e x i s t e n t i a l and u n i v e r s a l q u a n t i f i e r s , the i d e n t i t y s i g n , set membership sign, but which excludes things l i k e ' i s larger than', ' i s the father o f , 'is round', etc., without being t o l d why members of the f i r s t l i s t are l o g i c a l constants while members of the second l i s t are not. I t i s even l i k e l y that people would 9 1 disagree about whether c e r t a i n terms, e.g., the set membership sign, belong i n a complete enumeration of l o g i c a l constants. Next Pap considers some proposed d e f i n i t i o n s of ' l o g i c a l constant' and finds these inadequate. I w i l l discuss only the most p l a u s i b l e d e f i n i t i o n s . 1. One proposed d e f i n i t i o n i s the fo l l o w i n g : "A term i s a l o g i c a l constant i f and only i f i t occurs e s s e n t i a l l y i n some necessary i m p l i c a t i o n . " Pap e a s i l y produces a counter-example to this pro-posal, namely: The word ' t r i a n g l e ' occurs e s s e n t i a l l y i n the inference schema "x i s a t r i a n g l e ; therefore, x has three s i d e s " , although almost no one wants to say that ' t r i a n g l e ' i s a l o g i c a l constant. 2. A m o d i f i c a t i o n of the above proposal i s a l s o considered by Pap. It i s t h i s : "A term i s a l o g i c a l constant i f and only i f i t occurs e s s e n t i a l l y i n every necessary i m p l i c a t i o n i n which i t occurs".^ pap a t t r i b u t e s t h i s d e f i n i t i o n to Reichenbach. He re j e c t s i t f o r the following reason. In the necessary i m p l i c a t i o n ((p*q) V (q*r)) D ((q'r) V (p*q)) the occurrence of the conjunctive sign i s i n e s s e n t i a l (the necessity of the i m p l i c a t i o n requires only the commutability of d i s j u n c t i o n ) . But almost everyone, i n c l u d i n g Reichenbach, admits that the conjunctive sign i s a l o g i c a l constant. So Reichenbach's c r i t e r i o n i s too narrow; i t excludes something which i s a l o g i c a l constant. Pap's counter-example to Reichenbach's d e f i n i t i o n makes use of the f a c t that the occurrence of any s e n t e n t i a l component i n a tautology i s i n e s s e n t i a l . Consequently, i f a l o g i c a l constant i s a part of such a senten-t i a l component i t s occurrence i s i n e s s e n t i a l . I suggest that we avoid Pap's counter-example by modifying Reichenbach's proposal as follows: R' "L i s a l o g i c a l constant i f and only i f L occurs e s s e n t i a l l y i n every v a l i d argument 92 i n which i t occurs, excluding those arguments where L occurs i n a sentence whose occurrence i n the v a l i d argument i s a l s o i n e s s e n t i a l . " This m o d i f i c a t i o n avoids Pap's,counter-example. In Pap's counter-example the conjunctive sign '•' occurred i n a v a l i d inference, but i t a l s o occurred i n a sentence whose occurrence i n that inference was i n e s s e n t i a l . Also, i t seems c l e a r that the modified c r i t e r i o n , R', would exclude something l i k e ' t r i a n g l e ' from the cla s s of l o g i c a l constants. For i n the following argument the word ' t r i a n g l e ' occurs i n e s s e n t i a l l y w i t h i n a sentence whose occurrence i n the argument i s e s s e n t i a l : A t r i a n g l e e x i s t s . Therefore, something e x i s t s . This m o d i f i c a t i o n , R', looks promising at f i r s t , but there are d i f f i c u l t i e s with i t . For example, consider the following inference; Some doors are not rot t e n . Therefore, something i s a door. In t h i s v a l i d inference the occurrence of 'not' i s i n e s s e n t i a l . And prima  f a c i e the occurrence of 'not' i s within a sentence whose occurrence w i t h i n the argument i s e s s e n t i a l . So i t seems that according to the modified proposal 'not' would not be a l o g i c a l constant. Someone might t r y to meet th i s d i f f i c u l t y by suggesting that we concern ourselves only with formal representations of v a l i d arguments. For i f we symbolize the argument j u s t considered we get: (3x)(Dx» -Rx) Therefore ( 3x)(Dx). In t h i s f o r m a l i z a t i o n the occurrence of '-Rx', which we may read as "x i s not rotte n 1 1 i s i n e s s e n t i a l . And so, the occurrence of '-' (the negation sign) w i t h i n t h i s formalized argument i s wit h i n a s e n t e n t i a l component whose occurrence within the v a l i d argument i s i n e s s e n t i a l . Con-sequently, i f we concern ourselves only with formalizations of ordinary language arguments then the argument I have produced would not create a 93 problem f o r the modified c r i t e r i o n of l o g i c a l constants. However, there i s something odd about the suggestion j u s t considered, i t i s t h i s . We are attempting to f i n d a c r i t e r i o n f o r saying whether something i s a l o g i c a l constant. Given t h i s goal i t i s odd to include i n the statement of our c r i t e r i o n the requirement that we consider only formalized arguments. For the question a r i s e s , what for m a l i z a t i o n s of ordinary language arguments are we to count as acceptable? Not every formal language i s a system of v a l i d inferences, and not every t r a n s l a t i o n of a v a l i d ordinary language argu-ment i n t o a formal language preserves v a l i d i t y . For example, we could t r a n s l a t e the inference, "Some doors are not r o t t e n . Therefore, something i s a door." i n t o some s e n t e n t i a l c a l c u l u s i n the f o l l o w i n g way: "p, therefore q" (where 'p' and 'q' are s e n t e n t i a l constants). C l e a r l y t h i s f o r m a l i z a t i o n i s unacceptable f o r purposes of 'applying the c r i t e r i o n under co n s i d e r a t i o n . We might avoid t h i s problem by r e s t r i c t i n g the c r i t e r i o n i n question to formalizations which preserve the v a l i d i t y of . ordinary language arguments, but t h i s r e s t r i c t i o n r a i s e s two serious problems. They are: (a) a l l e x i s t i n g f o r malizations of acceptable l o g i c a l systems pre-suppose a p r i o r inventory of l o g i c a l constants. I t would hardly make sense to advance a c r i t e r i o n f o r l o g i c a l constants which presupposes a p r i o r inven-tory of l o g i c a l constants. (b) I f we count "T i s a t r i a n g l e , therefore, T has three s i d e s " as a v a l i d argument i n ordinary language, then i t i s j u s t f a l s e that any e x i s t i n g formalized system preserves the v a l i d i t y of a l l ordinary language arguments. At best, a l o g i s t i c system such as the predicate calculus preserves the v a l i d i t y of those ordinary language arguments which are, i n some sense, v a l i d i n v i r t u e of form. Now we might construe the expression 94 'ordinary language argument which i s v a l i d i n v i r t u e of form' as r e f e r r i n g to those arguments which can s u c c e s s f u l l y be translated i n t o a formal l o g i s t i c system, but t h i s r a i s e s the problem c i t e d i n (a). On the other hand we might t r y to c l a r i f y the notion of an "ordinary language argument which i s v a l i d i n v i r t u e of form" by compiling a l i s t of ordinary language l o g i c a l constants. But t h i s a l t e r n a t i v e i s f r u i t l e s s because i t again raises the question "What i s a l o g i c a l constant?" In view of the problems j u s t c i t e d , I doubt that there i s any hope of salvaging the c r i t e r i o n f o r l o g i c a l constants which appeals to any p r e c i s e l y defined notion of a formalized v a l i d argument. Following the next three paragraphs I w i l l o f f e r a vague account of l o g i c a l constants and formal systems which bypasses these problems. But my vague account of formally v a l i d arguments does not meet the standards of c l a r i f i c a t i o n which Reichenbach and Pap have been applying. Pap discusses another way i n which Reichenbach t r i e s to d i s t i n g u i s h between l o g i c a l and n o n - l o g i c a l terms, and that i s as follows: n o n - l o g i c a l terms are denotative terms - terms which denote objects, properties, etc,, whereas l o g i c a l terms do not denote anything and cannot be reduced or defined i n terms of denotative terms. Pap e a s i l y produces a counter-example to t h i s d e f i n i t i o n by pointing out that we could construe the l o g i c a l constant 'or' as denoting a two-place r e l a t i o n a l property. And i n general we could construe a l l the s e n t e n t i a l connectives as denoting t r u t h - f u n c t i o n a l r e l a t i o n a l p r o p e r t i e s . Thus, the expression 'p or q' could be construed as saying that the propositions "p" and "q" s a t i s f y a p a r t i c u l a r t r u t h - f u n c t i o n a l r e l a t i o n s h i p , i . e . , the one denoted by 'or'. If i t i s objected that we could not construe e x i s t i n g truth-95 f u n c t i o n a l connectives as denoting r e l a t i o n a l properties, because they do not have the appropriate meaning, then we could reply that i t would be easy to construct a p r o p o s i t i o n a l calculus C, isomorphic to some e x i s t i n g p r o p o s i t i o n a l calculus D, such that terms i n C which denote r e l a t i o n a l properties correspond to terms i n D which are t r u t h - f u n c t i o n a l connectives. That would show that we could construct a l o g i s t i c system i n which the l o g i c a l constants denoted t r u t h - f u n c t i o n a l r e l a t i o n s h i p s . Such l o g i c a l constants would be denotative terms, and, i n f a c t , i f we count the set membership sign as a l o g i c a l constant, then some l o g i c a l constants now denote r e l a t i o n s h i p s . For the set membership sign denotes the r e l a t i o n a l property of set membership. Perhaps even the qu a n t i f i e d ' ( x ) 1 denotes a r e l a t i o n which holds between a formula and a l l objects i n the universe of discourse, namely, the r e l a t i o n s h i p " s a t i s f i a b l e by". It i s c e r t a i n l y arguable, at l e a s t , that 1 ( x ) ' does denote t h i s r e l a t i o n - at le a s t as arguable as that words l i k e 'even' and 'as' denote (I assume Reichenbach would want to say that 'even' and 'as' are not l o g i c a l terms, i . e . , they do denote.) Looking back, we see that a l l the proposed d e f i n i t i o n s of ' l o g i c a l constants' we have considered have serious problems, even when modified to meet i n i t i a l o bjections. I think i t u n l i k e l y that any c l e a r d i s t i n c t i o n between l o g i c a l and n o n - l o g i c a l constants can be drawn. Perhaps the best we can do i s give a vague account of the d i f f e r e n c e between l o g i c a l and non-l o g i c a l constants. We might say that l o g i c a l constants are terms which most frequently have e s s e n t i a l occurrences i n v a l i d inferences. Or perhaps the following suggestion i s be t t e r . Those expressions are l o g i c a l constants which may s u c c e s s f u l l y be taken as constants i n a very general theory of v a l i d 96 inference. I f by t r e a t i n g a given set of terms as constants we can construct a formal system of inferences, i n a f a i r l y economical way, then we may consider that set of terms l o g i c a l constants. Formally v a l i d inferences may then be defined as those i n which only l o g i c a l constants occur e s s e n t i a l l y . Or, more d i r e c t l y , we might bypass l o g i c a l constants and define formally v a l i d inferences as those inferences which could occur i n a very general and f a i r l y economical system of v a l i d inference. I f we accept t h i s account of formal inferences, we should note two things, (a) the d i s t i n c t i o n between formally v a l i d and other inferences i s l e f t vague. I t i s l e f t unclear, f o r example, whether the inference "A i s lar g e r than B. Therefore, B i s not larger than A" i s formally v a l i d or not, (b) We have defined formally v a l i d inferences as a subset of v a l i d inferences, and we have not attempted to define ' v a l i d i t y ' (except i n terms of n e c e s s i t y ) . This i s important, because i f there i s no s a t i s f a c t o r y account of formal v a l i d i t y and formal deduction which does not presuppose the concepts of v a l i d -i t y and necessity, then my account of a n a l y t i c i t y can c e r t a i n l y not be taken as an explanation of the concepts of necessity and v a l i d i t y , since my account of a n a l y t i c i t y i s given p a r t l y i n terms of l o g i c a l consequences, which can only be explained i n terms of v a l i d i t y and necessity i n general. Now some philosophers, e.g., Quine, would r e j e c t the conclusion that our notions of l o g i c a l consequence, l o g i c a l truth, and formal v a l i d i t y can only be explained i n terms of v a l i d i t y and necessity i n general. In h i s a r t i c l e "Mr. Strawson on L o g i c a l Theory" Quine c a u s t i c a l l y attacks Strawson f o r having founded a l o g i c a l theory on "too s o f t and f r i a b l e a keystone" ( a n a l y t i c i t y and entailment). Quine would object with equal strength i f 9 7 Strawson had founded his system upon the concepts of necessity and v a l i d i t y . (In f a c t Strawson was not d i s t i n g u i s h i n g between necessity and a n a l y t i c i t y i n his book on l o g i c a l theory). Quine believes that we only understand v a l i d i t y and necessity i n s o f a r as we understand formal v a l i d i t y and l o g i c a l t ruth. 'Formal v a l i d i t y ' and ' l o g i c a l t r u t h ' should be defined, according to Quine, i n terms of "statement forms which are l o g i c a l , i n the sense of containing no constants beyond l o g i c a l vocabulary, and (extensionally) v a l i d , i n the sense that a l l statements exemplifying the form i n question are true."-^ Quine admits that " l o g i c a l vocabulary i s s p e c i f i e d . . .only by enumeration'.', and admits f u r t h e r that t h i s enumeration i s apparently a r b i t r a r y . ^ So Quine does not r e a l l y come to terms with the problem of d e f i n i n g ' l o g i c a l constant'. Perhaps Quine thinks i t unnecessary to define ' l o g i c a l constant', or perhaps he thinks a s u f f i c i e n t reason f o r taking c e r t a i n terms as l o g i c a l constants i s that they have always been recognized as such by l o g i c i a n s . In any case, Quine has no answer to the conclusion I have so f a r derived, namely, that ' l o g i c a l constant' can only be defined i n terms of the general concepts of v a l i d i t y or nec e s s i t y . But l e t us temporarily suppose, f o r the sake of argument, that there could be a corre c t account of l o g i c a l constants which d i d not pre-suppose an understanding of v a l i d i t y or necessity. Then i t would be possible to define l o g i c a l truths i n the way Quine wants to do, namely, as those truths which remain true under a l l r e i n t e r p r e t a t i o n s of no n - l o g i c a l constants. What I wish to point out, i s that any a p p l i c a t i o n of this d e f i n i t i o n of l o g i c a l t r u t h presupposes p r i o r i n t u i t i o n s about what inferences are v a l i d and what truths are necessary. For the question a r i s e s , how could we ever decide, f o r 98 example, that a l l r e i n t e r p r e t a t i o n s of n o n - l o g i c a l constants i n the law of non-contradiction, -(P'-p), leave the truth of the law unaffected? Since the number of r e i n t e r p r e t a t i o n s of 'p' are i n f i n i t e , we could not t e s t the law under every possible r e i n t e r p r e t a t i o n . Furthermore, we could not prove that a l l r e i n t e r p r e t a t i o n s of the law do not a f f e c t the truth value of the law without presupposing the v a l i d i t y of some other law of l o g i c . We cannot get away from the f a c t that we cannot e s t a b l i s h formal truth of formal v a l i d -i t y without presupposing that we know, a p r i o r i , that c e r t a i n truths are necessary and that c e r t a i n inferences are v a l i d . And i t i s s i l l y to pretend that we i n any way prove the law of non-contradiction i s l o g i c a l l y true. The way we know that a l l occurrences of n o n - l o g i c a l constants i n the law of non-c o n t r a d i c t i o n are i n e s s e n t i a l i s that we can see that the law could not be f a l s e , that i s , the law i s n e c e s s a r i l y true. Because of t h i s I think that Quine i s wrong when he claims that the concept of l o g i c a l truth i s on a much firmer f o o t i n g than the concepts of v a l i d i t y and necessity. We can say nothing about what truths are formally true and what inferences are formally v a l i d without appealing i n a general way to i n t u i t i o n s of necessity and v a l i d i t y . I have been arguing that the concepts of v a l i d i t y and necessity are more fundamental than the concepts of formal v a l i d i t y and l o g i c a l t r u t h . Both Pap and I have serious doubts whether we can even d i s t i n g u i s h formal reasoning and formal t r u t h from other kinds of necessary t r u t h (unless my suggestion that we draw the d i s t i n c t i o n i n terms of those inferences which can be systematized i s c o r r e c t ) . Given this p o s i t i o n someone might ask, "What i s your account of v a l i d i t y and necessity? It would be p o i n t l e s s to define 99 necessary truths as the c l a s s of a l l a n a l y t i c truths since your d e f i n i t i o n of 'analytic t r u t h ' involves the concept of l o g i c a l consequence, which involves an understanding of v a l i d i t y and necessity. So how do you define v a l i d i t y and n e c e s s i t y ?" Answer, I don't. I think v a l i d i t y and necessity are concepts we learn o s t e n s i v e l y . Someone says, " I f i t rains, then the spinach w i l l grow. It r a i n s , so i t n e c e s s a r i l y follows that the spinach w i l l grow." We get the idea of necessity and v a l i d i t y from this and s i m i l i a r cases. We can get the idea of necessity from playing games with r u l e s . "You can't do that, i t breaks the r u l e s . I f you abide by the rules you can only make c e r t a i n moves." We use the modals 'can' and 'can't' a l l the time, often to denote absolute p o s s i b i l i t y and i m p o s s i b i l i t y . Perhaps we are now i n a p o s i t i o n to examine the question whether a l l necessary truths are a n a l y t i c . I have defined a n a l y t i c truths as those truths which are l o g i c a l consequences of a c o r r e c t concept a n a l y s i s . We have reason to b e l i e v e that i t i s to a large extent a r b i t r a r y whether we c a l l a v a l i d inference a formally v a l i d inference. Consequently, there may be no point i n d i s t i n g u i s h i n g between formally v a l i d consequences of concept analyses and any other v a l i d consequences of concept analyses, at l e a s t f o r present purposes. When we say that a n a l y t i c truths are any l o g i c a l consequences of concept analyses we could mean that a n a l y t i c truths are any v a l i d consequences of concept analyses. This has the r e s u l t of making absolutely every necessary tr u t h a n a l y t i c , provided we accept the p r i n c i p l e that an argument i s v a l i d i f and only i f i t i s impossible that the premises are true while the conclusion i s f a l s e . Unfortunately f o r our i n t u i t i o n s , this has the r e s u l t that the necessary truth which i s Goedel's incompleteness theorem i s a l o g i c a l con-1 0 0 sequence of the concept a n a l y s i s of "brother". We might t r y to avoid t h i s paradoxical r e s u l t by r e s t r i c t i n g l o g i c a l consequences to those consequences of v a l i d inferences which inferences can be r e a d i l y systematized or included i n a general theory of inference. This would r u l e out rules of inference l i k e , "From any premise you may i n f e r Goedel's theorem". But\Jiat about the ru l e of inference which says that we may i n f e r any necessary t r u t h from any premise whatsoever? That i s a v a l i d rule of inference which i s of general form and which i s included i n some systems of modal l o g i c . I f we accept that r u l e of inference, then we are once again stuck with paradoxical r e s u l t s . (For example, within a p a r t i c u l a r formal system which included t h i s r u l e of inference we might derive the r e s u l t that Goedel's theorem i s a necessary t r u t h . Then by applying t h i s r u l e we derive the r e s u l t that Goedel's theorem i s a l o g i c a l consequence of "2+2=4".) However, I can think of no reason, other than ad hoc reasons, f o r excluding t h i s as a r u l e of inference f o r our purposes. So why not accept the para-d o x i c a l r e s u l t that every necessary t r u t h i s a l o g i c a l consequence of any concept a n a l y s i s , and accept the c o r o l l a r y that every necessary t r u t h i s a n a l y t i c ? I f the reader finds t h i s r e s u l t too c o u n t e r i n t u i t i v e to accept, he or she i s welcome to construe ' l o g i c a l consequence' as narrowly as seems appropriate. We could construe ' l o g i c a l consequence' to mean l o g i c a l consequence i n the predicate c a l c u l u s , f o r example. This might have the e f f e c t of making many necessary truths, e.g., truths of arithmetic, non-a n a l y t i c (since set theory may al s o be required to derive the truths of arithmetic from a set of d e f i n i t i o n s ) . I t does not much matter which conven-t i o n we adopt as long as we r e a l i z e that we are adopting conventions. If we 101 construe ' l o g i c a l consequence' very broadly we w i l l have the L e i b n i z i a n r e s u l t that a l l necessary truths are a n a l y t i c and vic e - v e r s a . If we construe ' l o g i c a l consequence' very narrowly we w i l l have the Kantian r e s u l t that not a l l necessary truths are a n a l y t i c . (I do not mean to imply that e i t h e r Leibniz or Kant a r r i v e d at these r e s u l t s by the kind of reasoning I have been presenting.) 102 Chapter 6 1 A. Pap, Semantics and Necessary Truth, New Haven, 1958. 2 Ibid., p. 136. 3 Quine, The Ways of Paradox, pp. 138-9. 4 Ibid., p. 139. Chapter 7 Convention and Necessary Truth 1 0 4 In the preceding chapter I examined the question whether a l l necessary truths are a n a l y t i c . The conclusion reached was that a l l necessary truths are a n a l y t i c , provided we construe the concept of l o g i c a l consequence very broadly. I f , on the other hand, we construe the concept of l o g i c a l consequence i n a more narrow, and admittedly a r b i t r a r y way, then not a l l necessary truths are a n a l y t i c . In t h i s chapter I w i l l consider the question whether a l l necessary truths are the r e s u l t of l i n g u i s t i c convention. Some philosophers have i d e n t i f i e d the thesis that a l l necessary truths are. a n a l y t i c with the conventionalist thesis that a l l necessary truths are the r e s u l t of convention. In what follows I hope to show that these two issues are d i s t i n c t , and that necessary truths are not the r e s u l t of convention - i n any i n t e r e s t i n g sense. Of course, i t i s always open to someone to s t i p u l a t e a use of 'res u l t of convention' which i s i d e n t i c a l with my use of ' a n a l y t i c ' . In that case my answer to the question whether a l l necessary truths are the r e s u l t of convention would be the same as my answer to the question whether a l l necessary truths are a n a l y t i c . But, as I w i l l now argue, i t would be very misleading to e s t a b l i s h such a use f o r 'res u l t of convention'. (a) Suppose someone claims that a necessary t r u t h (or v a l i d inference) r e s u l t s from our l i n g u i s t i c conventions i f and only i f that necessary t r u t h (or the corresponding c o n d i t i o n a l of that v a l i d inference) i s a v a l i d consequence of a d e s c r i p t i o n of the l i n g u i s t i c rules guiding the use of some word or words i n our language. (Wherever possible i n the following d i s c u s s i o n I w i l l r e f e r to only one of the p a i r , v a l i d inference/necessary c o n d i t i o n a l , i t being understood that analogous remarks could be made about the remaining member of t h i s pair.) It would be n a t u r a l to construe t h i s claim as implying that necessity i s i n some way 105 created by l i n g u i s t i c convention (otherwise, why say that necessary truths r e s u l t from l i n g u i s t i c convention?). Now suppose that we could deduce some necessary i m p l i c a t i o n from a d e s c r i p t i o n of the r u l e guiding the use of the E n g l i s h word ' o r 1 . For example, from the rule "the word 'or' may be inserted between any two sentences p and q, provided one of the pair i s true" we may r *i v a l i d l y derive i f p, then p or q , which i s the corresponding c o n d i t i o n a l of p, therefore, p or q . But from the f a c t that we could perform this deduction we cannot i n f e r that our l i n g u i s t i c rules create l o g i c a l necessity or l o g i c a l v a l i d i t y . For, assuming i t makes sense to t a l k of " c r e a t i n g necessity", i t i s not the l i n g u i s t i c rules alone that create l o g i c a l necessity (or v a l i d i t y ) . Rather our l i n g u i s t i c rules together with c e r t a i n v a l i d rules of inference create l o g i c a l necessity ( v a l i d i t y ) . But i t i s absurd to suppose that l o g i c a l n e c essity i s created i n part by l o g i c a l v a l i d i t y , since a v a l i d inference i s j u s t one where the conclusion n e c e s s a r i l y follows from the premises. The point can be more c l e a r l y and less metaphorically put as follows: l o g i c a l truths and l o g i c a l l y v a l i d rules of inference are not i d e n t i c a l with our l i n g u i s t i c r u l e s . We may s t i p u l a t e what our l i n g u i s t i c rules are, but we may not s t i p u l a t e what the consequences of our l i n g u i s t i c rules are. The consequences of c o r r e c t l y following a given set of rules are l i m i t e d by the rules themselves. In a c e r t a i n sense i t i s true that we can s t i p u l a t e what rule-guided e f f e c t s w i l l occur by deciding what rules to follow, but once we have decided to follow a given set of rules we can no longer s t i p u l a t e the consequences of following those r u l e s . In t h i s sense we may not s t i p u l a t e l o g i c a l t r u t h or v a l i d i t y , and i n t h i s sense i t i s mis-leading to say that l o g i c a l necessity r e s u l t s from l i n g u i s t i c convention. 106 Michael Dutnmett makes th i s argument i n a s l i g h t l y d i f f e r e n t (and less d e tailed) form when he discusses what he c a l l s modified conventionalism. Modified conventionalism i s the view that although some necessary truths are d i r e c t r e g i s t e r s of convention, others are "more or less remote consequences of conventions".^ Dummett's c r i t i c i s m of t h i s view i s , " I t appears that i f we adopt the conventions registered by the axioms, together with those re g i s t e r e d by the p r i n c i p l e s of inference, then we must adhere to the way of t a l k i n g embodied i n the theorem, and t h i s necessity must be one imposed upon us, one that we meet with. It cannot i t s e l f express the adoption of a convention." 2 Against Dummett's argument and my argument one might object as follows: It may be true that c e r t a i n necessary truths are merely l o g i c a l consequences of conventions, and not themselves conventions, but these truths can s t i l l be explained i n terms of conventions. For to explain x i n terms of y i t surely s u f f i c e s to show that x can l o g i c a l l y be deduced from y. When we say that a necessary t r u t h i s the r e s u l t of convention we mean only that the necessary t r u t h i s a l o g i c a l r e s u l t of convention, or that i t can be l o g i c a l l y explained i n terms of convention. Consider another example, suppose the r u l e guiding our use of ' s i s t e r ' i s that we may apply t h i s word to a l l and only female s i b l i n g s . Surely, the c i t i n g of t h i s r u l e would explain why everthing which can c o r r e c t l y be c a l l e d ' s i s t e r ' i s female, and that explains the t r u t h of " A l l s i s t e r s are female". To be sure t h i s explanation involves the use of l o g i c -any explanation does. So f a r so good. But what s h a l l we say when we apply these considera-tions to a l l l o g i c a l l y necessary t r u t h s . I f every explanation presupposes the use of l o g i c , or the making of v a l i d inferences, then i n a sense we can 107 explain v a l i d i t y and necessity i n terms of convention, but i f we say t h i s we should also note the oddity of saying that convention i s the source of v a l i d -i t y and necessity. If there were no v a l i d i t y and necessity there would be no l o g i c a l r e s u l t s and no explanation. The problem i s whether we can explain the existence of something which i s a precondition of a l l explanation. I think we cannot. (Jonathan Bennett discusses t h i s problem b r i e f l y i n "On 3 Being Forced to A Conclusion". He concludes that e i t h e r conventions explain the existence of l o g i c , or else the existence of l o g i c cannot be explained at a l l . I choose the l a t t e r a l t e r n a t i v e . ) (b) I turn now to consider another version of conventionalism -one which Quine discusses i n "Truth by Convention". 4 In that a r t i c l e (which contains much that Quine l a t e r r e j e c t s i n "Two Dogmas of Empiricism") Quine gives an argument s i m i l a r to the one I presented i n ( a ) . He points out that the l o g i c a l consequences of s t i p u l a t i v e d e f i n i t i o n s w i l l be true by convention only i f a l l of l o g i c i s true by convention. He then attempts to show how we might construe a l l of l o g i c as true by convention. The method he describes i s commonly known as i m p l i c i t d e f i n i t i o n . B r i e f l y , the method i s t h i s : "We take one of the many formalizations of the predicate c a l c u l u s ; one i n which the l o g i c a l vocabulary i s reduced to a few p r i m i t i v e s and i n which the basic axioms and rules of inference have been kept to a minimum. We then treat the formal system as an uninterpreted calculus (completely devoid of meaning). Next we s t i p u l a t e that the basic axioms and rules of inference of the system are to be taken as true. We do not thereby predicate t r u t h of the axioms, that would presuppose that the axioms had meaning. Rather we e s t a b l i s h a use f o r the axioms (and i m p l i c i t l y f o r t h e i r parts) by d e s c r i b i n g the circumstances 1 0 8 i n which they may be counted as true. We count l o g i c a l axioms as true i n any circumstances whatsoever. (More accurately, our formal system contains axiom schemas and inference schemas, and we s t i p u l a t e that a l l s u b s t i t u t i o n instances of these schemas are to be counted as true and v a l i d , r e s p e c t i v e l y ) . This appears to solve the problem of how l o g i c a l necessity and v a l i d i t y r e s u l t from convention d i r e c t l y . L o g i c a l axioms and inferences are true and v a l i d because we use them as i f they were true and v a l i d , and i t i s the use of an expression which determines i t s meaning. Our l i n g u i s t i c behaviour i s such that we l e t the l o g i c a l p a r t i c l e s have any meaning which preserves the v a l i d i t y of our inferences. When we are dealing with a formal system, the s t i p u l a t i o n s as to which axioms are true and which inferences are v a l i d are made e x p l i c i t and are v e r b a l i z e d . In ordinary language, however, these s t i p u l a t i o n s are not made e x p l i c i t . What j u s t i f i e s us i n taking the formal system as a model f o r what happens i n ordinary language i s the f a c t that there i s a correspondence between sentences and inferences which are accepted within the formal system and sentences and inferences which we regard as true and v a l i d i n ordinary language." There are numerous problems with the " i m p l i c i t d e f i n i t i o n " account of the o r i g i n of l o g i c a l necessity j u s t described. Here are some of them (those due to Quine are so i n d i c a t e d ) . 1. (Quine) Absolutely any body of doctrine can be rendered true by d e f i n i t i o n i f we follow the method we have considered. For example, we could s t i p u l a t e that the axioms of physics are true by l e t t i n g the p r i m i t i v e terms occurring i n those axioms take on the required sense. As i n the case of l o g i c , the r e s u l t of for m a l i z i n g the axioms of physics and s t i p u l a t i n g t h e i r truth would 1 0 9 preserve our ordinary b e l i e f s about which sentences of physics are true, and which are f a l s e . Unfortunately, such a procedure would not preserve our or-dinary b e l i e f s about what sentences are necessary and what sentences are contingent. Therefore, those who hold that the.necessity of l o g i c and math-ematics derives from i m p l i c i t d e f i n i t i o n must explain why we conventionally treat the axioms of mathematics and l o g i c as true, but do not so trea t the axioms of physics and every other empirical science. Quine suggests an explanation, namely, that we trea t the axioms of l o g i c and mathematics as true by convention, i n contrast with p h y s i c a l theories, because of t h e i r a p r i o r i nature or because they are very deep i n our conceptual scheme. Quine's explanation i s un s a t i s f a c t o r y , however. The a p r i o r i nature of l o g i c and mathematics i n ordinary language may explain why we trea t c e r t a i n formulations of these d i s c i p l i n e s as conventionally true, but i t cannot explain why we treat these d i s c i p l i n e s as conventionally true when they are expressed i n unformalized ordinary language. We could only claim that the ordinary language expressions of l o g i c and mathematics were a p r i o r i i f they had some meaning. But on the account we are considering our de c i s i o n to t r e a t l o g i c and mathematics as true by convention i s what endows these d i s c i p l i n e s with meaning. Since meaningless theories are not i n any conceptual scheme, we can hardly decide to t r e a t a meaningless theory as conventionally true on the grounds that the meaningless theory i s a p r i o r i . 2. (Quine) When we s t i p u l a t e that a l l s u b s t i t u t i o n instances of the basic axiom schema and inference schema of some l o g i c a l theory are to be counted as true we do so i n order to render a l l l o g i c true by convention. But from the f a c t that a l l s u b s t i t u t i o n instances of the basic axiom schema are true 110 we can derive the r e s u l t that a p a r t i c u l a r s u b s t i t u t i o n instance i s true only by inference. This inference i s not i t s e l f an inference made wi t h i n the system under consideration, since the system under consideration contains only axiom and inference schema - not p a r t i c u l a r inferences. Hence any p a r t i c u l a r s u b s t i t u t i o n instance we can name w i l l not be true purely by convention. It w i l l be the j o i n t r e s u l t of convention and inference. We might t r y to avoid t h i s consequence by s t i p u l a t i n g that each and every sub-s t i t u t i o n instance of a p a r t i c u l a r schema i s true. But then we are faced with an i n f i n i t e task. 3. At t h i s point we could repeat Dummett's objection to modified convention-alism, since that i s the kind of conventionalism Quine describes. Dummett's objection, remember, i s that even granting that a l l the axioms and rules of inference of a system r e g i s t e r conventions to t a l k a c e r t a i n way, we s t i l l cannot explain why we must accept a c e r t a i n theorem given the axioms and rules of inference, unless we presuppose the v a l i d i t y of c e r t a i n l o g i c a l inferences. Conventions, by themselves, cannot explain t h e i r own consequences. We can see that Dummett's objection i s re l a t e d to Quine's objection at (2), i n s o f a r as both objections point out that convention, by i t s e l f , does not s u f f i c e to get us moving, l o g i c a l l y speaking. Logic i s al s o required. 4. Quine a l s o makes the point that even the verbal formulation of our adoption of the axioms and rules of inference as conventions presupposes the use of l o g i c a l vocabulary, i . e . , the very idioms which we are purporting to convention-a l l y define. It seems, therefore, that a l l l o g i c cannot be true by convention i f we require l o g i c a l vocabulary,and consequently l o g i c , to even formulate conventions. I l l Quine suggests a way of avoiding t h i s o bjection. He points out that i n ordinary language the convention to adopt c e r t a i n ways of speaking need never be v e r b a l i z e d . Indeed, i f a l l l i n g u i s t i c conventions had to be introduced by e x p l i c i t v erbal agreement, language could never get o f f the ground, since we would need a language to s t a r t a language. Consequently, there i s no need to suppose that the conventions to adopt c e r t a i n axioms and rules of inference i n ordinary language ever were, or ever need be ver b a l i z e d Thus the problem i s avoided. That our l i n g u i s t i c behaviour i s guided by convention, someone could maintain, i s shown by the r e g u l a r i t y our l i n g u i s t i c behaviour e x h i b i t s , quite apart from e x p l i c i t v erbal conventions. Quine does not r e j e c t t h i s s o l u t i o n (not i n "Truth by Convention" at l e a s t ) . He does point out, however, that the idea that there might be unverbalized, u n e x p l i c i t conventions which are manifested by behavioural r e g u l a r i t y i s i n need of c l a r i f i c a t i o n . I have argued ( i n an e a r l i e r chapter that such a c l a r i f i c a t i o n has been given by David Lewis, I am r e f e r r i n g to the c r i t e r i a f o r rule-guidedness which I described i n chapter 4. (c) The next ve r s i o n of conventionalism I wish to consider i s as follows. " L o g i c a l necessity and v a l i d i t y r e s u l t from l i n g u i s t i c conventions i n the sense that i f any person denies a necessary t r u t h , S, we are j u s t i f i e d i n concluding that the person does not know the meaning of some word or words i n S, i . e . , does not know a l l the l i n g u i s t i c conventions guiding the use of a l l or part of S." For example, i f someone asserts that "Grass i s green and the sky i s blue" i s true, but denies that "Grass i s green" i s true, we would have to conclude that the person does not know how to use the word 'and', i. e the person's use of 'and' i s not guided by the proper r u l e s . If the person 112 did not be l i e v e that "Grass i s green" i s true, then he or she i s not per-mitted by the rules guiding the use of 'and' to conjoin "Grass i s green" with any other sentence. Roughly, the r u l e guiding our use of 'and' i s that we may i n s e r t 'and' only between sentences that we be l i e v e are true. Although the example we have just considered i s a convincing one, a l o t more i s required to demonstrate that whenever a person denies a neces-sary t r u t h or v a l i d inference that person displays a misunderstanding of some piece of language. For the example we have j u s t considered i s much too s p e c i a l a case. There seems to be no room f o r mistake, other than a l i n g u i s t i c one, when, f o r some p and q , one asserts r p and q* and denies p. In t h i s sense we can explain the v a l i d i t y of the inference from rp and q"1 to p by d e s c r i b i n g the rules guiding our use of the word 'and 1. But other v a l i d inferences are more complex and cannot be so c l o s e l y linked with l i n g u i s t i c rules governing the use of l o g i c a l p a r t i c l e s . Because one can know a l l the l i n g u i s t i c rules guiding our use of l o g i c a l vocabulary without seeing a l l the consequences of these r u l e s , one can f a i l to see that v a l i d i t y of a complex inference without thereby d i s p l a y i n g a misunderstanding of any l o g i c a l vocabulary. Likewise, one can know a l l the rules of chess without seeing a l l the consequences of these rules i n a p a r t i c u l a r chess board s i t u a t i o n . This i s not a new observation, or a very c o n t r o v e r s i a l observation, but I think i t would be i n t e r e s t i n g to see why it i s true. To t h i s end I w i l l t r y to explain i n more d e t a i l how, f o r example, i t i s possible f o r someone to deny even so simple a necessary t r u t h as that 7+5=12 without thereby d i s p l a y i n g a misunderstanding of any a r i t h m e t i c a l symbol or ignorance of any l i n g u i s t i c conventions. My explanation i s as follows; Suppose we take Frege's account of 113 numbers to be c o r r e c t . On th i s supposition numbers are sets. The number zero, f o r example, can be defined as the set of a l l objects which are not s e l f - i d e n t i c a l . The number one can be defined as the set whose only member i s the number zero. The number two can be defined as the set whose only members are the numbers one and zero. And so on. Each number a f t e r zero can be construed as the set S whose only members consist of a l l the numbers which occur e a r l i e r i n the s e r i e s of sets than S. On th i s account, and indeed on every other theory of numbers which i s adequate, the integers c o n s t i t u t e an ordered, l i n e a r s e r i e s of objects. This means that we can s a f e l y view the whole numbers as a s e r i e s of points on a l i n e , some numbers appearing l a t e r i n the s e r i e s than others. Now i t i s a convention that we use '12' to denote a number which occurs l a t e r i n the number s e r i e s than the number we denote by '5'. But the f a c t that the number so denoted occurs l a t e r i n the s e r i e s i s no convention; i t i s something given to us. Thus even the simple arithmetic t r u t h that 12 i s greater than 5 i s neit h e r a convention, nor purely the r e s u l t of convention. Rather i t i s the j o i n t r e s u l t of convention and f a c t . Con-sequently, the t r u t h that 12=5+c, where 'c' denotes some p o s i t i v e number, i s not purely the r e s u l t of convention. We a l l know that c turns out to be the number 7, but that c=7 once had to be discovered; i t i s not a convention. One way to discover that c=7 i s to count the integers i n the closed i n t e r v a l from 6 to 12. Now i t i s possible to make a mistake i n counting without thereby demonstrating that one misunderstands any numerals or how to count. As a consequence i t i s possible to think that 7+5=13, and to deny that 7+5=12,with-out thereby d i s p l a y i n g that i n general one does not know how to use numerals or to count. 114 I have portrayed our discovery that 7+5=12 as a discovery of f a c t . The question a r i s e s , how do I rec o n c i l e this view with the common b e l i e f that "7+5=12" i s an a p r i o r i necessary truth? I w i l l t r y to answer t h i s question. We can formulate a general r u l e f o r adding numbers. To add a number x to a number y s t a r t with the immediate successor to x i n the number ser i e s and count, i n order, the integers following x u n t i l you a r r i v e at the yth such integer. The yth integer w i l l be the sum of x and y. Now, i n a sense, when we sum two numbers according to the ru l e j u s t given we make an empirical discovery; we are counting some objects. But the objects we are concerned with, i . e . , the integers, can be generated according to an exact r u l e (e.g., construct each number by adding one to i t s antecedent. The f i r s t number i s zero.) Integers are also named according to an exact r u l e , and the summation procedure i s purely a rule-guided process. So, i n a sense, the r e s u l t of a p a r t i c u l a r summation i s determined by the r u l e f o r generating integers, the naming r u l e , and by the ru l e guiding the process of summation. Of course, i n a p a r t i c u l a r case i t i s always possible to miscount by accident-a l l y o m i t t i n g an integer or by counting twice. In that sense the r e s u l t of an i n d i v i d u a l count i s contingent. But, provided we follow the counting rules c o r r e c t l y , the r e s u l t of an i n d i v i d u a l count of the integers between 5 and 12 i s not contingent. Analogous remarks can be made concerning l o g i c a l proofs. Suppose we b l i n d l y apply some rules of inference to a set of premises and generate an unexpected conclusion. Each step i n our proof i s the r e s u l t of applying a rule (which may i m p l i c i t l y embody a convention) but the conclusion we generate 115 comes as a s u r p r i s e to us. And when we discover that our conclusion can be deduced from our o r i g i n a l set of premises we discover a f a c t , pure and simple. It i s , of course, contingent that we generated the conclusion we d i d , but i t i s not contingent whether the conclusion can be generated by correct a p p l i c a -t i o n of the rules of inference. When we discover, i n a given proof, that a c e r t a i n conclusion follows l o g i c a l l y from p a r t i c u l a r premises we discover a f a c t , namely,that the parts of the conclusion-sentence stand i n a p a r t i c u l a r geometrical r e l a t i o n R to the parts of the premise-sentences. But i t i s not a contingent question, given the v a l i d r u l e s of inference, whether objects which stand i n the r e l a t i o n R are r e l a t e d as l o g i c a l consequence to premise. There i s more to be s a i d . We see that the f a c t that summation and proof are rule-guided processes does not s u f f i c e to explain the source of necessary t r u t h , though i t might explain why the r e s u l t s of a p a r t i c u l a r i n v e s t i g a t i o n are determined, given that the i n v e s t i g a t i o n i s c a r r i e d out c o r r e c t l y , and given the f a c t s being i n v e s t i g a t e d . For example, we can explain why someone who counts the integers i n the closed i n t e r v a l from 6 to 12 w i l l always count 7 integers, provided the count i s c o r r e c t l y made, and given that there are 7 integers i n that i n t e r v a l . But how do we explain the f a c t that there are, and must be, seven integers i n that i n t e r v a l ? Well, we could point out that unless there were 7 integers i n that i n t e r v a l we could not be t a l k i n g about that i n t e r v a l . Since numbers do not change through time the r e l a t i o n s between numbers do not change through time. Consequently, there w i l l always be 7 integers i n that i n t e r v a l . Also the c r i t e r i a f o r i d e n t i t y of numbers i s exact. I think t h i s r e s u l t s from the f a c t that the rules governing our use of numerals are p e r f e c t l y exact. 116 This exactness i s possible because numbers do not change through time, and because (as we have noted) the r e l a t i o n s between numbers do not change through time. I think the case i s s i m i l i a r f o r l o g i c a l terms. The rules guiding t h e i r use are very exact, because two sentences e i t h e r stand i n a p a r t i c u l a r t r u t h - f u n c t i o n a l r e l a t i o n or they do not. Consequently, the c r i t e r i a f o r i d e n t i t y of l o g i c a l truths i s very exact. Perhaps a l l necessary truths involve t h i s kind of exactness. This i s not very c l e a r , but I think i t i s suggestive. (d) I turn now to discuss Dummett's view of Wittgenstein's brand of conventionalism. According to Dummett, Wittgenstein once believed that any t r u t h which we accept as necessary expresses a convention to t a l k a c e r t a i n way. For example, the mathematical t r u t h that 7+5=12 i s not a consequence of convention, but i s i t s e l f a convention. 7+5=12 because our c r i t e r i o n f o r saying that someone has added 7 and 5 c o r r e c t l y i s that the r e s u l t be 12. At f i r s t glance t h i s kind of conventionalism seems very implausible. One i s tempted to say that i t i s not open to us to s t i p u l a t e the t r u t h of 7+5=12, because the t r u t h or f a l s i t y of that statement i s already determined by the conventions we have l a i d down governing a d d i t i o n i n general. For example, we might construe the convention governing a d d i t i o n as follows: to obtain the sum a+b simply count b d i g i t s past the number a. The bth d i g i t past the number a i s the sura of a and b. Thus, to add 7 to 5 we simply count 7 d i g i t s past the number 5. The 7th d i g i t we count w i l l be the sum. Now i t c e r t a i n l y seems that the sum of 7+5 i s determined by t h i s counting procedure, and any convention we lay down d i c t a t i n g what t h i s sum should be runs the 117 r i s k of c o n f l i c t i n g with the conventions we have already l a i d down. We could not, f o r example, s t i p u l a t e that the sum of 7+5 i s 13, because this would c o n f l i c t with other conventions. Wittgenstein might reply as follows: In what sense i s the sum of 7+5 determined by e x i s t i n g conventions of counting rules? The sum i s not determined i n the sense that whoever counts 7+5 objects must a r r i v e at the number 12, f o r i t i s always possible to miscount. Likewise, the sum i s not determined by any proof, since i t i s always possible that any proof we con-s t r u c t contains some mistake. Both the counting method and other methods of proof are f a l l i b l e . Consequently, neither method forces any conclusion on us. Since both methods are f a l l i b l e processes we need some c r i t e r i o n f o r deciding whether we have counted c o r r e c t l y or c a r r i e d out the proof c o r r e c t l y . And since, most people do a r r i v e at a count of 12 when counting a c o l l e c t i o n of 7 objects and 5 objects i t i s convenient to make the sum, 12, the c r i t e r i o n f o r a correct summation of 7 and 5. But t h i s i s purely a p r a c t i c a l matter. So far we have stated an objection to Wittgenstein's theory and suggested a possible answer on Wittgenstein's behalf. But t h i s answer i s inadequate. This i s apparent once we consider that we do not need to take the a r r i v a l at an orthodox r e s u l t as the c r i t e r i o n f o r saying whether the r e s u l t was c o r r e c t l y deduced. We have independent ways of checking, f o r example, whether a count was c o r r e c t l y made, or whether a theorem was c o r r e c t l y derived. We merely check to see whether each move was made according to the r u l e s . We can check someone's counting of a set of objects by having the person number the objects as he counts. We then check to make sure that each object was numbered by a d i f f e r e n t number and i n the correct sequence. Of course i t i s 118 possible that we a l l make the same mistake i n our checking, but the chances that we would a l l a r r i v e at the same r e s u l t by accident are very small. Consequently, i f a large number of people check a person's count (proof) and a r r i v e at the same r e s u l t , we have very good evidence that the count (proof) i s c o r r e c t or i n c o r r e c t , as the case may be. This, then, constitutes one important objection to the proposed answer. There are other problems as w e l l . For example, Wittgenstein has no way of explaining why, when most people count 7+5 and a r r i v e at 12, we can fi n d no mistake i n t h e i r counting, i . e . , no place at which they v i o l a t e d a counting r u l e . And he cannot explain why we can always discover a mistake when a person counts 7+5 and does not get 12. On my account i t i s easy to explain these matters. Miscounting consists i n v i o l a t i n g a counting r u l e ; not i n a r r i v i n g at a c e r t a i n wrong number. The reason people u s u a l l y get 12 when they count 7 objects and 5 objects i s that they u s u a l l y follow the counting rules c o r r e c t l y (usually we can discover no mistake), and i t i s an absolute necessity that i f one counts 7 objects and 5 objects c o r r e c t l y , then one w i l l have counted 12 things. This necessity cannot i t s e l f be explained i n terms of other conventions, however, since i t w i l l always be true of any conventions we c i t e that when they are followed c e r t a i n r e s u l t s must occur. Wittgenstein would be r i g h t to point out that i t i s always possible to miscount. And there i s no v e r i f i c a t i o n of the f a c t that 7+5=12 which does not re s t upon some f a l l i b l e procedure such as counting or proof. In order to r e c o n c i l e this f a c t with the f a c t that we a l l regard 7+5=12 as an unassailable t r u t h , Wittgenstein might suppose that we i n f a c t t r e a t 7+5=12 as a convention, that i s , we w i l l not allow 7+5=12 to be f a l s i f i e d . I think 119 Wittgenstein's reasoning may take the following form. "The conclusion of any proof i s f a l l i b l e , since any proof may contain a mistake. "7+5=12" i s an a p r i o r i necessary t r u t h . Conventions are not f a l l i b l e . Therefore, "7+5=12" expresses a convention." The f a l l a c y i n this reasoning, I suggest, l i e s i n equating a p r i o r i necessary truths with i n f a l l i b l e t r u t h s. But, as I have argued i n an e a r l i e r chapter, there i s no absolute i n f a l l i b i l i t y . Any judgement can be mistaken - in c l u d i n g the judgement that we are adopting a convention. Wittgenstein would be r i g h t to note that i f the v e r i f i c a t i o n of "7+5=12" i s made to r e s t upon counting, or upon proof of any kind, then that v e r i f i c a t i o n i s f a l l i b l e , and the r e s u l t of that v e r i f i c a t i o n comes as a discovery. But I have been arguing that the f a c t that "7+5=12" must be d i s -covered i s compatible with that truth's being a p r i o r i , necessary, and non-e m p i r i c a l . What ensures the non-empirical character of t h i s a r i t h m e t i c a l p r o p o s i t i o n i s that, although i t s proof must be discovered or invented by us, that proof must be generated according to r u l e s , i f i t i s to be co r r e c t . And i f a proof i s generated according to the proper r u l e s , then the conclusion w i l l be n e c e s s a r i l y true, provided the premises are n e c e s s a r i l y true. In the preceding s e c t i o n I have t r i e d to dispose of one possible argument Wittgenstein might use to support h i s brand of conventionalism. There i s , however, another l i n e of argument which i s discussed by Jonathan Bennett i n "On Being Forced to a Conclusion"^. I t r e l a t e s to the argument j u s t con-sidered i n that i t a l s o focusses on a problem about proof. What follows i s a s i m p l i f i e d account of Bennett's reconstruction of Wittgenstein's argument. As Bennett sees i t Wittgenstein was led to r e j e c t modified conventionalism i n favor of a bolder form of conventionalism, because 120 Wittgenstein believed that his behavioural theory of meaning (to be explained i n a minute) i s incompatible with the t r a d i t i o n a l picture of l o g i c a l committal and because modified conventionalism requires the tr u t h of the t r a d i t i o n a l p i c t ure of l o g i c a l committal. Bennett describes the t r a d i t i o n a l p i c t u r e of l o g i c a l committal as that according to which we are absolutely committed to c e r t a i n conclusions by the adoption of c e r t a i n premises. (There i s no room for choice on the t r a d i t i o n a l p i c t u r e of l o g i c a l committal.) Now i t i s c l e a r that modified conventionalism does indeed require the t r u t h of the t r a d i t i o n a l theory of l o g i c a l committal, since according to modified conventionalism we are absolutely committed to the tr u t h of c e r t a i n sentences by the conventions of language we adopt. So i f there r e a l l y i s an i n c o m p a t i b i l i t y between Wittgen-s t e i n ' s behavioural theory of meaning and the t r a d i t i o n a l theory of l o g i c a l committal, Wittgenstein was r i g h t to r e j e c t modified conventionalism. Let us consider whether such an i n c o m p a t i b i l i t y does e x i s t . Bennett describes the behavioural theory of meaning as the view that the only evidence f o r what a piece of language means i s how we use i t . Further-more, "to mean such and such by a noise is j u s t to be disposed to use i t i n c e r t a i n ways." Our use of language i s not guided by meanings or r u l e s , as i f meanings and rules were over and above behaviour. Rather, our l i n g u i s t i c behaviour defines the meanings of words and determines l i n g u i s t i c r u l e s . L i n g u i s t i c rules do not prescribe l i n g u i s t i c behaviour, rather they describe i t . Now the prima f a c i e i n c o m p a t i b i l i t y between the behavioural theory of meaning and the t r a d i t i o n a l p i c t ure of l o g i c a l committal i s t h i s . The u t t e r i n g of c e r t a i n sounds or the w r i t i n g of c e r t a i n signs at one time cannot commit one to u t t e r i n g or w r i t i n g any s p e c i f i c thing at another time. There can be 1 2 1 nothing i n c o r r e c t about a community's using words according to one pattern before time T and according to a d i f f e r e n t pattern a f t e r T. For the two patterns taken together create a pattern which give t h e i r words a unitary meaning. Thus there seems to be nothing to prevent a community of people from assenting to a c e r t a i n set of wr i t t e n premises and denying a conclusion we normally think of as being e n t a i l e d by those premises. Such l i n g u i s t i c be-haviour may be deviant with respect to our l i n g u i s t i c behaviour, but we cannot say the behaviour i s wrong. We can conclude that such a dev i a t i n g community must mean something d i f f e r e n t by the premises and conclusion than we do, but on the behavioural theory of meaning t h i s i s j u s t another way of saying that the d e v i a t o r s ' l i n g u i s t i c behaviour i s d i f f e r e n t from ours. We cannot say to people i n the d e v i a t i n g community "You are committed to accepting a c e r t a i n conclusion by the meaning you attach to these premises," because what meaning they attach to the premises i s determined, i n part, by what conclusion they are w i l l i n g to draw. We can form inductive hypotheses about other people's future l i n g u i s t i c behaviour, and hence about what they mean by c e r t a i n words, but there i s no necessity about what people's future l i n g u i s t i c behaviour w i l l be l i k e . The p o s s i b i l i t y that some sub-community of our l i n g u i s t i c community w i l l deviate l i n g u i s t i c a l l y from our community cannot be ruled out a p r i o r i . This i s the source of the problem about saying that other people are l o g i c a l l y committed to c e r t a i n conclusions. Whether the problem can be solved we s h a l l now consider. In his a r t i c l e "On Being Forced to a Conclusion" Bennett r e c o n c i l e s the behavioural theory of meaning with the t r a d i t i o n a l p i c t ure of l o g i c a l committal i n much the same way that many philosophers of science r e c o n c i l e 122 everyday s c i e n t i f i c p r a c t i c e with the problem of induction. S c i e n t i s t s do not make room within s c i e n t i f i c reasoning f o r the p o s s i b i l i t y that nature should cease to be lawlike - p r i m a r i l y because science would not be possible i n that case. Likewise we do not make room within l o g i c i t s e l f f o r the p o s s i b i l i t y that some l i n g u i s t i c sub-community w i l l deviate from us s i g n i f i c a n t l y i n t h e i r l i n g u i s t i c behaviour, f o r i f that p o s s i b i l i t y should be r e a l i z e d i n a general-ized way communication would breakdown, at le a s t i n a lim i t e d area. Bennett put the matter thus: "We make no room within the communication-game f o r the p o s s i b i l i t y that the game w i l l become unplayable, j u s t as we make no room with-i n science f o r the p o s s i b i l i t y that science w i l l cease to be a possible kind of a c t i v i t y . The question a r i s e s , what do we mean by saying "we make no room within l o g i c f o r the p o s s i b i l i t y of l i n g u i s t i c deviation"? I take t h i s expression to mean that a l l proof takes place r e l a t i v e to the assumption that we are not dealing with l i n g u i s t i c deviators. On the behavioural theory of meaning t h i s assumption i s equivalent to the assumption that we are dealing with people who mean by words approximately what we mean by them. This agrees with what most philosophers, i n c l u d i n g those who p o s i t the existence of propositions, have t r a d i t i o n a l l y s a i d . Most philosophers would say that assenting to c e r t a i n sentences commits one to c e r t a i n conclusions only on the assumption that one means by the premise-sentences c e r t a i n things and not other things. The behavioural theory of meaning supports t h i s t r a d i t i o n a l view, but unlike t r a d i t i o n a l theories of meaning the behavioural theory of meaning does not i n any way explain why people usually draw the same conclusion from the same premises. On the behavioural theory nothing i s explained by 123 saying that people who mean the same things by premises P w i l l u s u a l l y draw the same conclusion, and nothing i s explained by saying that one can avoid being committed to c e r t a i n conclusions by assigning a d i f f e r e n t meaning to the premises. This i s because, on the behavioural theory, what one means by premises P i s determined, i n part, by what conclusions one i s w i l l i n g to draw, not v i c e versa. So f a r I have described, i n a s i m p l i f i e d way, how Bennett reconciles the behavioural theory of meaning with the t r a d i t i o n a l p i c t ure of l o g i c a l proof. As f a r as the r e c o n c i l i a t i o n goes, I think i t i s the best r e c o n c i l i a -t i o n that could be given, but I am doubtful whether i t i s e n t i r e l y s u c c e s s f u l . My reasons are as f o l l o w s . Bennett's theory does not explain how i n d i v i d u a l s can know about themselves that they are committed to a c e r t a i n conclusion. For example, i f I accept both " I t i s r a i n i n g " (P) and " I f i t i s r a i n i n g , then the p o l l u t i o n w i l l c l e a r " (Q), I can see that I am committed to the conclusion "The p o l l u t i o n w i l l c l e a r " (R). And, i n general, I often know what conclusions I am committed to, and I f e e l that I must accept these conclusions. Now the behavioural theory of meaning does not explain why we often f e e l that we must accept a c e r t a i n conclusion i f we are to be f u l l y r a t i o n a l , though i t might explain how we could know that we are going to accept a given conclusion. On Bennett's theory we could c o r r e c t l y say that someone must accept conclusion R i f he or she accepts premises P and Q and i f that person i s not a l i n g u i s t i c d e v i a t o r . But t h i s i s not relevant to our present case, since, when a person sees that he or she i s committed to R on a c e r t a i n understanding of P and Q, i t i s i r r e l e v a n t to that person whether he or she i s a l i n g u i s t i c deviator. 1 2 4 Even l i n g u i s t i c deviators can be committed to c e r t a i n conclusions on t h e i r understanding of the premises. A person can f e e l and be committed to a con-c l u s i o n without even knowing whether he or she i s a l i n g u i s t i c deviator, or i s disposed to be a l i n g u i s t i c deviator. I think we must conclude that i t i s one's understanding of the premises which determines whether one i s committed to a c e r t a i n conclusion - not one's d i s p o s i t i o n s to deviate l i n g u i s t i c a l l y . (Of course, someone holding the behavioural theory of meaning may claim that to understand a set of premises i n a c e r t a i n way i s j u s t to have c e r t a i n l i n g u i s t i c and other d i s p o s i t i o n s . But we could hardly explain the f a c t that we f e e l compelled to accept c e r t a i n premises by appealing to our present l i n g u i s t i c d i s p o s i t i o n s , f o r a large part of the evidence that we have c e r t a i n l i n g u i s t i c d i s p o s i t i o n s i s that we f e e l compelled to accept c e r t a i n conclusions.) Now t h i s d i f f i c u l t y could be avoided by a p a r t i c u l a r m o d i f i c a t i o n of Bennett's p o s i t i o n . The m o d i f i c a t i o n i s t h i s . Instead of t r y i n g to explain the o r i g i n of the f e e l i n g of l o g i c a l committal by t a l k i n g about l i n g u i s t i c d e v i a t o r s , we recognize that l i n g u i s t i c d e v i a t i o n i s i r r e l e v a n t to whether an i n d i v i d u a l JJJ or f e e l s committed to a c e r t a i n conclusion. What .is relevant, however, i s one's own i n t e r n a l neural s t a t e . Presumably, when one learns to speak a language some change occurs i n one's b r a i n . (Such a neural change, or something l i k e i t , must e x i s t i f we are ever to e x p l a i n , p h y s i o l o g i c a l l y , how someone passes from a p r e - l i n g u i s t i c state to a state of l i n g u i s t i c competence.) Also, we may assume, people who speak the same language have c e r t a i n neural or brain structures i n common. Now, given that an E n g l i s h speaker, say, has c e r t a i n brain features unique to E n g l i s h speakers, these b r a i n featrues may o c c a s i o n a l l y cause an E n g l i s h speaker to accept a c e r t a i n 125 conclusion once he or she has accepted c e r t a i n premises. This could account f o r those cases where people f e e l they must accept a p a r t i c u l a r conclusion. People f e e l they must accept the conclusion because they are p h y s i o l o g i c a l l y compelled by t h e i r neural structure to accept i t . This m o d i f i c a t i o n of Bennett's p o s i t i o n does explain why people often f e e l they must accept a c e r t a i n conclusion. It a l s o can be used to explain a r e l a t e d problem, namely, why people who accept the same premises generally can be made to accept the same conclusion. But this m o d i f i c a t i o n does not adequately explain a l l aspects of the t r a d i t i o n a l p i c t ure of l o g i c a l committal. For example, suppose a group of En g l i s h speakers a l l accepted a set of premises, and suppose a l s o that one day the old laws of brain/neural physiology ceased to hold. I t might then be true that the En g l i s h speakers would no longer f e e l committed to accept any conclusions, since they would no longer by p h y s i o l o g i c a l l y compelled to accept any conclusion. But according to the t r a d i t i o n a l p i c t u r e of l o g i c a l committal the group would s t i l l be committed to c e r t a i n conclusions. According to the t r a d i t i o n a l p i c t u r e people are committed to conclusions whether or not anyone f e e l s committed. I t i s d i f f i c u l t to see, therefore, how Bennett could explain the existence of l o g i c a l committal i n such a circumstance (given the m o d i f i c a t i o n we are considering). He might deny i t s existence, but then he would have f a i l e d to re c o n c i l e the behavioural theory of meaning with the t r a d i t i o n a l picture of l o g i c a l committal. This completes my l i s t of doubts about the success of Bentmett's r e c o n c i l i a t i o n of the behavioural theory of meaning with the t r a d i t i o n a l view of l o g i c a l committal. I do not claim that the problems I have uncovered d i s -126 prove Bennett's view, but they are problems which can be avoided altogether i f one r e j e c t s the behavioural theory of meaning. Very l i t t l e r e f l e c t i o n w i l l show that I have, so f a r i n t h i s t h e s i s , adopted a p o s i t i o n inconsistent with the behavioural theory of meaning. For i t has been part of my thesis that the r e g u l a r i t y which language e x h i b i t s i s explained by the f a c t that our use of language i s rule-guided - rule-guided i n the sense that there are rules which underlie our use of language. In my sense of rule-guided, to say that language i s rule-guided i s not j u s t to say that language use f a l l s i n t o regular patterns. I be l i e v e that the rules which guide our use of language are i n f e r r e d e n t i t i e s which explain the r e g u l a r i t y of language i n something l i k e the way i n which a computer program explains the behaviour of a computer. Thus I r e j e c t the behavioural theory of meaning i n favor of the theory which says that language use i s rule-guided. In "On Being Forced to a Conclusion" Bennett says that "The st r e s s of r u l e s , which i s legitimate i n i t s e l f , could mislead us i n t o denying that l o g i c a l committal i s reducible to r e l a t i o n s amongst complex sets of noises. Wittgenstein saw t h i s danger, and i n s i s t e d at length that problems about meanings cannot be s e t t l e d j u s t by an appeal to r u l e s , because there w i l l always remain the problem of the meanings of the r u l e s . " In adopting the theory of rules I have adopted I have i m p l i c i t l y rejected the simple-minded theory of rules which Wittgenstein appears to have i n mind. People do not learn the rules of language by being to l d what the rules are, rather they learn the rules by observing people's behaviour. And the evidence f o r what l i n g u i s t i c rules a person i s following i s the person's l i n g u i s t i c behaviour -not what the person says about r u l e s . Consequently, i f a l i n g u i s t i c sub-127 community of our l i n g u i s t i c community s t a r t s d e v i a t i n g l i n g u i s t i c a l l y with respect to what proofs they accept as l o g i c a l l y v a l i d , and i f i t s members cannot be made to admit a mistake, then we have extremely good evidence f o r saying that t h e i r use of some portion of our language i s guided by d i f f e r e n t rules than our use. This remains true regardless of what rules they say they are fol l o w i n g , since, although they may say they are following the same verbal r u l e as we are, they may understand that v e r b a l r u l e d i f f e r e n t l y from us. (This view seems a n a t u r a l one - Bennett even seems to adopt t h i s view i n his a r t i c l e when he says, "We could show him (a l i n g u i s t i c deviator) that his use of the word required the learning of rules f o r our use of i t , plus, as a sheer Q a d d i t i o n , the lear n i n g of rules f o r h i s use of i t . " 7 The idea that the use of language requires the learning of rules i s c l o s e l y connected with the view that language use i s guided and explained by r u l e s , and does not s i t happily with the behavioural theory of meaning which Bennett endorses elsewhere i n his a r t i c l e . It has always been a part of the t r a d i t i o n a l p i c t u r e of l o g i c a l committal that premises commit one to a c e r t a i n conclusion only on a c e r t a i n i n t e r p r e t a t i o n of those premises. On my theory, to i n t e r p r e t premises i n a p a r t i c u l a r way i s to allow one's use of those premises to be guided by c e r t a i n l i n g u i s t i c r u l e s . Also, on my theory, i t i s c l e a r that we have very good evidence f o r saying that l i n g u i s t i c deviators are fo l l o w i n g d i f f e r e n t l i n g u i s -t i c rules from our l i n g u i s t i c group. Consequently, i f one adopts the theory of rules I have been defending, i t i s easy to explain why l i n g u i s t i c deviators do not present a problem f o r the t r a d i t i o n a l p i c t u r e of proof. L i n g u i s t i c deviators who r e j e c t t r a d i t i o n a l proofs are following deviant l i n g u i s t i c r u l e s , and thus are not committed to conclusions we standardly accept (given 12 8 standard l i n g u i s t i c r u l e s ) . This i s one explanatory power of the r u l e -guidedness theory. There are others. For example, on this theory, the reason why people often f e e l that they must accept a c e r t a i n conclusion, i s that t h e i r l i n g u i s t i c behaviour i s guided by c e r t a i n r u l e s . If they were to deny the conclusion which they f e e l they must accept, then they would, at some point, be v i o l a t i n g a l i n g u i s t i c r u l e they have learned (without knowing i t ) . This point connects with a problem mentioned e a r l i e r , namely, why most members of a l i n g u i s t i c community who accept the same premises can be made to accept the same conclusion. The s o l u t i o n to t h i s problem, I think, i s that those people are guided by the same l i n g u i s t i c rules ( i n the relevant areas). Con-sequently, those people can be presented with an argument whose i n d i v i d u a l steps are small enough to enable those people to f e e l that they must accept the conclusion of each step. And i f we can get a person to accept the immediate conclusion of each step of an argument we can get that person to accept the conclusion of the l a s t step of the argument, that i s , the conclusion of the e n t i r e proof. A question which may now occur to the reader i s , "In what way do rules guide our l i n g u i s t i c behaviour?" or "By what mechanism do rules guide our l i n g u i s t i c behaviour?" This question was answered when I f i r s t introduced the rule-guidedness theory, but because the question i s important and relevant to the present d i s c u s s i o n I repeat my answer here. I said e a r l i e r that l i n g u i s t i c rules guide our l i n g u i s t i c behaviour i n something l i k e the way i n which a computer program guides a computer. In f a c t I think l i n g u i s t i c rules c o n s t i t u t e a p a r t i a l program of our brains. This programming could occur i f each b r a i n were innately programmed to program 12 9 i t s e l f f u r t h e r , according to the p a r t i c u l a r l i n g u i s t i c environment i t was placed i n , and there i s no reason why humans could not do the same thing, at a neural l e v e l . It seems p l a u s i b l e that c h i l d r e n do something l i k e t h i s when they learn the generative grammar of the language they learn to speak. Ce r t a i n neural changes may cause us to use the word as i f we were consciously f o l l o w i n g a c e r t a i n r u l e . In such a case i t may be appropriate to say that the r u l e i s guiding our use of the word. For example, i f (a) a creature's neural structure changes as a r e s u l t of the creature's having observed some l i n g u i s t i c r e g u l a r i t y which holds by convention ( i n Lewis's sense), and i f (b) the l i n g u i s t i c behaviour produced by that neural change i s such as would be produced by consciously following a p a r t i c u l a r r u l e , then we may say that the l i n g u i s t i c behaviour i s guided by the l i n g u i s t i c r u l e . We may say t h i s because (1) the relevant l i n g u i s t i c behaviour i s being guided by a neural change which occurred i n order to enable the creature to imitate a l i n g u i s t i c r e g u l a r i t y , and (2) the l i n g u i s t i c r e g u l a r i t y being imitated i s consequently determining the relevant l i n g u i s t i c behaviour, and (3) the l i n g u i s -t i c r e g u l a r i t y being imitated i s a r e g u l a r i t y which e x i s t s by convention ( i n Lewis's sense). This, I suggest, i s the mechanism by which conventions guide l i n g u i s t i c behaviour. Now the question a r i s e s , what i s the advantage to saying that people's l i n g u i s t i c behaviour i s guided by rules rather than by neural impulses of a c e r t a i n kind. The advantages are s e v e r a l . For one thing, (as was pointed out i n an e a r l i e r chapter) i f we suppose l i n g u i s t i c behaviour i s rule-guided we can explain why i t i s appropriate to c r i t i c i z e deviant l i n g u i s t i c behaviour as i n c o r r e c t . For another thing, we can explain the obvious element of convention involved i n using the word ' r a i n ' to denote r a i n , rather than the word 'snain'. 130 A t h i r d advantage i s that we can explain (where Bennett's theory f a i l e d to explain) why people would s t i l l be committed to a c e r t a i n conclusion by the adoption of c e r t a i n premises even i f the laws of physiology should cease to hold. To see th i s consider the following. According to my theory, i f the laws of physiology should break down, then our l i n g u i s t i c programming would f a i l to be c a r r i e d out, but i t would s t i l l be true that we were program-med to follow c e r t a i n r u l e s . Likewise, i f a computer breaks down i t s program may f a i l to be c a r r i e d out, but i t w i l l remain true that the computer was programmed. Now given the l i n g u i s t i c rules that program our l i n g u i s t i c behaviour, and given that we are programmed to follow these rules (by our l i n g u i s t i c t r a i n i n g ) , and given that we assent to c e r t a i n sentences, we are committed to c e r t a i n conclusions, even i f the laws of physiology cease to hold. This i s because, what conclusions we are committed to are determined by what l i n g u i s t i c rules we have been programmed to follow. The program need not a c t u a l l y be c a r r i e d out f o r t h i s committment to e x i s t , because we are committed to those conclusions which we would accept i f we did follow the l i n g u i s t i c rules of our mental program. This ends my di s c u s s i o n of how Bennett attempts to render the behavioural theory of meaning compatible with the t r a d i t i o n a l p i c t ure of l o g i c a l committment. I conclude that the two theories cannot be made com-p a t i b l e and that Wittgenstein was r i g h t to r e j e c t the t r a d i t i o n a l p i c t ure of l o g i c a l committment given h i s acceptance of the behavioural theory of meaning. However, I think I have given good reasons f o r r e j e c t i n g the behavioural theory of meaning i n favor of the rule-guidedness theory of 13 1 meaning. So I think Wittgenstein was wrong to hold the behavioural theory of meaning, and consequently h i s reasons f o r r e j e c t i n g modified convention-ali s m were a l s o wrong (Assuming Bennett i s correct i n thinking that Wittgenstein's behavioural theory of meaning led to h i s r e j e c t i o n of modified conventionalism.) 132 Chapter 7 ^ Michael Dummett, "Wittgenstein's Philosophy of Mathematics", reprinted i n Wittgenstein, ed. by Pitche r , Garden C i t y , N.Y., 1969, p. 424. 2 I b i d . , p. 425. 3 Bennett, "On Being Forced to a Conclusion", Proceedings of the A r i s t o t e l i a n  Society, Supplementary Vol. 35, 1961. 4 Quine, The Ways of Paradox. 5 Bennett, Op. C i t . ^ I b i d . , p. 16. 7 I b i d . , p. 32. 8 I b i d . , p. 17. 9 I b i d . , p. 32. 133 SELECTED BIBLIOGRAPHY Aune, B., "Is There an A n a l y t i c A P r i o r i ? " , Journal of Philosophy, Volume 60, 1963. Ayer, A.J., Language, Truth and Logic, London, 1946. Bennett, J.F., (1) "An a l y t i c - S y n t h e t i c " , reprinted i n Necessity, ed. by Sumner and Woods, New York, 1969. (2) "A Myth About L o g i c a l Necessity", A n a l y s i s , Volume 22, 1961. (3) "On Being Forced to a Conclusion", Proceedings of the A r i s t o t e l i a n Society, Supplementary Volume 35, 1961. Bradley, R.D., "Geometry and Necessary Truth", P h i l o s o p h i c a l Review, Volume 73, 1964. Carnap, R., "Meaning and Synonomy i n Natural Languages", P h i l o s o p h i c a l Studies, Volume 6, 1955. Casteneda, H-N., " '7+5=12' as a Synthetic Proposition", Philosophy and  Phenomenological Research, Volume 21, 1960-61. Church, A., "Intensional Isomorphism and Iden t i t y of B e l i e f " , P h i l o s o p h i c a l  Studies, Volume 5, 1954. Dummett, M., "Wittgenstein's Philosophy of Mathematics", reprinted i n Wittgenstein, ed. by Pitc h e r , Garden C i t y , New York, 1966. Gasking, D.A.T., "Mathematics and the World", reprinted i n Logic and Language, Second Ser i e s , ed. by A. Flew, New York, 1965. Grice, H.P., and Strawson, P.F., "In Defense of a Dogma", reprinted i n Necessity, ed. by Sumner and Woods, New York, 1969. Harman, G., "Quine on Meaning and Existence", Review of Metaphysics, Volume XXI, 1967. Hintikka, J . , "Are L o g i c a l Truths A n a l y t i c ? " , reprinted i n Necessity, Op. C i t . Kant, I., C r i t i q u e of Pure Reason, translated by N.K. Smith, London, 1933. Katz, J . J . , (1) " A n a l y t i c i t y and Contradiction i n Natural Language", The Structure of Language, ed. by Fodor and Katz, Englewood C l i f f s , N.J., 1964. (2) "Some Remarks on Quine on A n a l y t i c i t y " , reprinted i n Necessity, Op. C i t . 134 Kneale, W.C., and Kneale, M. , The Development of Logic, Oxford, 1962. Lewis, D., Convention, Cambridge, 1969. Mates, B., "Synonymity", U n i v e r s i t y of C a l i f o r n i a Publications i n Philosophy, Volume 25, 1950. Pap, A., Semantics and Necessary Truth, New Haven, 1958. Popper, K.R., The Logic of S c i e n t i f i c Discovery, London, 1968. Putnam, H., (1) "The A n a l y t i c and the Synthetic", Minnesota Studies i n the Philosophy of Science, I I I , ed. by H. F e i g l and G. Maxwell, Minneapolis, 1962. (2) "Some Issues i n the Theory of Grammar", Proceedings of the Twelfth Symposium i n Applied Mathematics, American Mathema-t i c a l Society, Providence, 1961. Quine, W.V., (1) "Truth by Convention", The Ways of Paradox, New York, 1966. (2) "Mr. Strawson on L o g i c a l Theory", Ibi d . (3) "Carnap and L o g i c a l Truth", I b i d . (4) "Two Dogmas of Empiricism", From a L o g i c a l Point of View, Cambridge, 1953. (5) "The Problem of Meaning i n L i n g u i s t i c s " , I b i d . (6) "On a Suggestion of Katz", reprinted i n Necessity, Op. C i t. Sommers, F., "Meaning Relations and the A n a l y t i c " , Journal of Philosophy, Volume 60, 1963. Z i f f , P., Semantic A n a l y s i s , I t h i c a , 1960. FOOTNOTE INDEX Footnotes f o r each Chapter appear on the following pages Chapter 1 6 Chapter 2 35 Chapter 3 45 Chapter 4 69 Chapter 5 86 Chapter 6 102 Chapter 7 132 

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