Is There an Analytic a Priori

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Is There an Analytic a Priori? Bruce Aune The Journal of Philosophy, Vol. 60, No. 11. (May 23, 1963), pp. 281-291. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819630523%2960%3A11%3C281%3AITAAAP%3E2.0.CO%3B2-T The Journal of Philosophy is currently published by Journal of Philosophy, Inc..

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VOLUME LX, NO. 11

IS T H E R E AN ANALYTIC A PRIORI?

T

HE question whether there is a synthetic a priori, though debated for nearly two centuries, still occasionally provokes controversy. Yet a related question, which is apparently so simple that it generally gets an automatic "Yes," can be seen, on reflection, to be as complicated and as far from trivial as the first one. This is the question whether there is an analytic a priori. As I shall try to show in what follows, this question ought to be controversial today; for given a fair, non-question-begging definition of 'a priori', the very existence of a priori statements is implicitly denied by today's linguistic philosophers-and denied, evidently, for inconclusive reasons. I I n order to be clear about the question in point, one must find an adequate but fair definition of the term 'a priori'. This is plainly not given by the positivistic definition, according to which a n a priori truth is simply an analytic one. After all, the question whether there are synthetic a priori truths is presumably debatable, not something to be settled by mere definitional fiat.' Since 'necessary' is essentially a modal term, used primarily to rule out possibilities, a definition of 'a priori' as "absolutely necessary" seems I t may well be that all a priori truths are inaccurate as necessary and vice versa, but this is not to be defended by arbitrary stipulation. Indeed, the contrary contention, advanced occasionally by metaphysician^,^ is presumably to be ruled out by arguments to the effect that by examining the structure of this world one cannot This assumes that 'analytic' and 'synthetic' are mutually exclusive terms.

I think this is a fair assumption, for it does not imply that there are not hordes of borderline cases, which resist classification as either analytic or synthetic. 1 use the expression 'absolutely necessary' instead of the familiar 'logically necessary' because, again, the contention that there are necessary statements ( = statements holding in all possible worlds) that are not logical truths is a t least debatable, not to be dismissed by definitional fiat. Here I am thinking of metaphysical arguments which, beginning with such contingent facts as that there are beings which depend on other things for their existence, arrive a t such conclusions as "God exists necessarily" or "It is a necessary truth that God exists." @

Copyright 1963

by Journal of

Philosophy, Inc.

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legitimately expect to discover facts about all possible worlds, or that necessary truths cannot validly be defended by contingent premises. The best definition of 'a priori' appears to be a cousin of the traditional one: S is an a priori statement if and only if the truthvalue of S is properly decidable without essential reference to any premises that state contingent facts about sense experiences, observational data, the success of scientific theories, and the like. This definition is of course quite dumb about the precise means by which the decision is to be reached. But this is as it should be ; for whether the decision is to be reached by conceptual analysis or by some kind of intuition or intellectual illumination, it is in any case to be justified by argument, not by the loaded definitions that opposing factions are anxious to foist upon one another. Cartesians and others who maintain that basic a priori truths are self-evident, intuitively obvious, or innate furniture of the human mind, may be hopelessly befuddled or just plain wrong, but the fact of their error or befuddlement, if indeed it is a fact, is by no means an immediate consequence of the very definition of 'a priori'. Assuming, then, that we have a fair definition of 'a priori' in hand, what can be said about 'analytic'? Well, to call a statement analytic, unlike calling it 'a priori', is to say something about how its truth value is decided : it is to be decided by some kind of analysis, some kind of pulling apart and inspection. Since the term 'analytic' is used very broadly today and since the force of my argument will hinge more on the meaning of 'a priori' than on that of 'analytic', I shall simply accept the somewhat vague, rough and ready, but certainly not question-begging definition :

S is analytic if and only if the truth value of decidable by conceptual analysis; that is, if and if the truth or falsity of S is decidable from a ceptual unpacking of the force of S , with the perhaps, of basic logical principles.

S is only conaid,

Thus, an analytically true statement is not decidable by some kind of intuition or intellectual illumination or by one's inability to "conceive" its f a l ~ i t y . ~ Now the question is: Are there analytic a priori statements? According to the definitions I have adopted, there might be many such statements. But according to the linguistic twist given to the notion of conceptual analysis by many philosophers today, for whom Cf. Father Copleston's examples of nonanalytic but still, he thinks, a priori truths, and his reasons for holding them, in his BBC debate with A. J. Ayer, reprinted in P. Edwards and A. Pap, A Modem Introduction to Philosophy (Glencoe, Ill., 1957), pp. 598 ff.

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analyzing a concept is nothing other than analyzing linguistic habits, there can be no a priori statements a t all! For if every argument demonstrating the analytic character of some truth must include premises stating contingent facts about linguistic habits, then, clearly, every analytically true (or false) statement must be a posteriori. Since synthetic statements are scarcely better candidates for the title of "a priori" than analytic ones, the conclusion is inescapable that, according to the assumptions of linguistic philosophy, no statements are strictly a priori a t all.

I t might be thought that I am simply trying to create fireworks with a child's cap pistol, that the import of what I have said is nothing but a trivial verbal matter. Actually, though, my intentions are not quite this modest. But even a verbal matter need not be insignificant; and in the present case it should be of some interest, for it emphasizes how fiercely nominalistic we are today, how far we have moved from the realism or conceptualism that lies a t the heart of our intellectual tradition. And that we should have reached a point where we are quite happy to say that there are no a priori statements, that all statements are a posteriori in the traditional sense, is by no means unexciting. But this, of course, is not all; for it is possible to cast some doubt on the credentials of our new outlook. I n fact I shall now argue that, given my definitions, the question whether there is an analytic a priori is really an open one, having no obvious answer. If I am right about this, if the contemporary view of the a priori really is a risky one, then my verbal point becomes an interesting challenge. But first a minor point. Since linguistic philosophers require contingent premises in support of even analytic statements, it is obvious that their general contention that analytically true statements are necessary is extremely dubious; it involves, that is to say, the questionable idea that necessary statements are properly established by inference from contingent premise^.^ Nevertheless, since my definition of 'analytic', vague as it is, does not commit me to this idea, I shall assume that the following is true:

(1)

If a statement S is analytically true, then S is a

necessary truth and it is absolutely impossible that

not-S.

Now, consider the statement made by the German sentence, 'Dreieckigheit ist eine Qualitat'. Assume, as is reasonable enough, 6 For a critique of this contention, see A. Pap, Semantics and Necessary Truth (New Haven, 1958), pp. 165-170.

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that this statement, call it "G," is necessary. As necessary, however, it cannot depend on the contingent truth that we might express with the English sentence, 'There is an English language'. But notice that G is just the statement t'hat we express in English by the sentence 'Triangularity is a quality'. Since, therefore, G does not depend for its truth on the contingent fact that there is an English language, it follows that the necessary truth of the statement we make by uttering the English words 'Triangularity is a qualityJ does not depend on the linguistic conventions of Englishmen.6 Of course, if there were no English language, we could not express this statement in English; but it does not follow from this that the truth of what is stated depends on the existence of the English language or, indeed, on the existence of any other language one would care to name. If we generalize the claim just made, it appears to be true that (11)

-

N (3L) (S) (S is necessary. >.S is expressible in L)

or as it might also be put: (111)

P(L) (38) (S is necessary and S is not expressible in L)'

where 'P' represents "possibility." Of course, it does not follow from this that (IV)

N (S) (3L) (S is necessary. >.S is expressible in L)

But it is difficult to see how (IV) is t o be ruled out. For consider the following. Because of (111) we can be confident that, no matter what L we take, there might be necessarily true SJs not expressible in it. Let us call such S's "possibly inexpressible." I t is thus possible that, for any L, there exist inexpressible 8's. Consider, then, all languages I . How can we rule out the possibility that there are a number of S's that are inexpressible with respect to all 6 This argument, which is a modification of the so-called "Church Translation Test" (after Alonzo Church), is due to Wilfrid Sellars; cf. his "Grammar and Existence: A Preface to Ontology," Mind, 69 (1960) : 499-533. I am aware that this assertion is "self-referential," in that it involves quantification over languages. But, as is well known, not all kinds of selfreference are pernicious, and it is generally difficult to distinguish pernicious from nonpernicious self-reference, especially when one is not proceeding in a formalized metalanguage. (Cf. R. M. Martin, Truth and Denotation [Chicago, 19581, p. 138 ff., and A. N. Prior, "On a Family of Paradoxes," Notre Dame Journal of Formal Logic, 2 [1961]: 16-32.) I am, accordingly, not sure whether the selfreference implicit in (11), (111), etc, is pernicious or not. If it is, my formulas can be taken as holding only for languages of a lower level, but then other formulas of higher levels, corresponding to those of the lower level, can be constructed, and so on. The same (intuitive) result will then be reached.

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languages whatever? I t appears that we cannot ; in fact, given the tenability of the so-called "NS-thesis," namely that if Np then NNp, (IV) is inescapable. For it is certainly not a necessary truth that languages, systems of communication, exist. But, for any S, if S is necessary, then it cannot be contingent. Thus, such S would be necessary even if, as is logically possible, no languages existed whatever. Since if no languages existed, necessary statements could plainly not be expressed, the very strong assertion (IV) seems every bit as unavoidable as (111). If so, we have no alternative but to admit that linguistic practices and conventions are not essential to the existence of necessary truths. Now, as against this argument it might be replied, "Just what is a necessary truth, anyway? Don't you have to identify such things very accurately if you expect us to take seriously your idea that there might be necessary truths not expressible in any existing language?" But the trouble with this reply is that it expects me to solve a problem that I am concerned only to raise. For when fully adequate definitions of all the key terms of the dispute are given, the way is cleared for sweeping away all the problems. Unfortunately, fully adequate, fair, and non-question-begging definitions are hard to come by; the concept of absolute necessity, for instance, is not an easy one to analyze, especially when it is a technical concept, involved in a bewildering variety of philosophical puzzles. Still, though the concept of absolute necessity is far from clear, certain facts about it, such as "Necessary statements hold in all possible worlds," seem to be generally accepted. In fact it appears that most linguistic philosophers would accept the following as true, which evidently tells us enough about necessity so that the question at issue in this paper can at least arise:

(v>

If S is necessary, then if S mere expressed in one's own language, one could come to recognize its necessity by a process of conceptual analysis.

I11 I have not been contending, so far, that a detailed analysis of linguistic behavior is never suficient to "certify" the necessity of certain statements. In fact I will agree that something which can be called "a process of certification" is often possible, though it is of such a kind that it does not support a linguistic theory of the a priori. To see that it does not support such a theory, consider the truth that we might express with the sentence, '11 fortnight is a period of two weeks1. Although our confidence that the truth expressed here is necessary is evidently based on the synonymy of 'fortnight' and 'period of two weeks', it is easy to see that a state-

THE JOURNAL OF PHILOBOPHY

ment of this synonymy is not by itself sufficient to permit us t o deduce : (VI)

I t is a necessary truth that a fortnight is a period of two weeks.

For all that we can deduce from the contingent statement that 'fortnight' and 'period of two weeks' are synonymous is the contingent statement that the words 'a fortnight is a period of two weeks' may be used to state an instance of the law of identity. In order t o infer (VI) we need the necessary premise that all instances of the law of identity are necessary truths, and this necessary premise is not a deductive consequence of contingent facts about verbal conventions. A similar result is attained if we approach the question with the notion of a synonymy rule. For a rule of this kind, or a substitution rule generally, is never sufficient to create necessity; it can only transmit necessity. Indeed, if we start from a false statement, a substitution rule will only permit the inference of another false statement; to obtain a necessary statement by the use of such a rule, we must begin with a statement that is itself necessary. Hence, unless we already have reason to think that certain statements are necessary, we could never obtain a necessary statement by an appeal to synonymy rules. I t is thus obvious that if one is to make even a prima facie case for the view that necessary statements are to be certified by linguistic rules, one must show that there is another kind of rule-different, that is, from a replacement rule-from which basic necessary truths may be inferred: such truths, namely, as the law of identity and the law of contradiction. But here again it is easy to see that the kind of rule generally advanced for this purpose is insufficient to establish the claims of any linguistic theory. For suppose one were to advance the rule :

(R-1)

All instances of 'A is A' (in the sense of 'A = A') are unconditionally assertable in English (or L).

This kind of rule, which seems appropriate for certifying the "axioms" from which necessary truth may be transmitted by substitution, unfortunately loses its plausibility as soon as one focuses attention on the expression 'unconditionally assertable'. For, in order to perform the task a t hand, this expression must have the sense of "assertable in any conceptually possible circumstances" ; yet if one can understand this rule, one must know which circumstances are, and are not, conceptually possible-which means, since P p = N - p , that one must have a prior knowledge of necessary truths. In other words, in order to make sense of, and apply, the

-

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rules in question, one must already have the knowledge that these rules are supposed to certify. Without this knowledge, this grasp of necessary truths, one could make no sense of these rules a t all. It might be thought that this objection could be avoided by some other formulation of the appropriate rule, for instance :

(R-2)

'A

=

A' may be asserted come what may.

But this formulation is clearly inadequate for the reason just given, namely that the 'may' here must have the sense of "absolute possibility." For if we are confident, for instance, that (VII)

Pure water boils at 212OF at sea level.

expresses a law of nature, then this may be (truly) asserted in any physically possible conditions; that is, no matter what may (physically) come t o pass, it will always be safe to endorse (VII). There is, however, a fundamental reason why any rule will be insufficient to establish basic necessary truths. The reason for this is that any rule formulation will presuppose a conceptual scheme, the scheme, namely, in which the rules are formulated, and this scheme, like any other, will embody basic logical truths, which must be recognized by anyone who is to employ the scheme in a consistent, self-conscious manner. In view, actually, of the powerful arguments that have been advanced against the linguistic theory of necessary t r ~ t h it , ~is somewhat surprising that it is still so widely held. The reason for this, I suspect, is that philosophers still tend to confuse sentences with the statements, or propositions, that one expresses by using sentences. Because this confusion contributes to the so-called "paradox of analysis" and, in addition, prompts a rejection of the very plausible NN-thesis, an additional word on this topic should not be out of place here. IV Consider, first, such assertions as "A fortnight is a period of two weeks." If such assertions are t o be informative, then, presumably, they must convey purely linguistic information. But how can they convey this information if they are not about words? And that they are not about words seems easily established by a translation test, which would distinguish, for example, 'A fortnight is a period of two weeks' from 'The expressions "fortnight" and "period of two weeks" have the same conventional application'. But as against this argument it can be said that locutions of the form 'An A is a B' are often used to answer questions about meaning. That is, they q e e Pap, ch. 7, and W. Kneale, The Development of Logic (Oxford, 1962), pp. 628-651.

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are often used when someone does not know the meaning of 'A' or 'B', and wants this purely verbal information. True, such uses are puzzling t o the philosopher who maintains a meticulous distinction between use and mention; but they are not therefore illegitimate. Indeed, once one realizes that they have this verbal use, that the expressions 'A' and 'B' are functioning "autonomously" in the sentence as used, no puzzles about them ought to arise. Now, I think that this latter argument is entirely sound, that the use t o which sentences can be put is often surprising to a philosopher who characteristically restricts his attention to words as they occur in a sentence and neglects the contexts in which that sentence might naturally be used. But this fact unfortunately cannot aid the linguistic theorist; for to the extent that 'A fortnight is a period of two weeks' is used to talk about words, to that extent it is used to express a contingent, not a necessary, statement. I t is, after all, a purely contingent fact that the words 'fortnight' and 'period of two weeks' are applied to the same interval of time, and if the sentence is used to express this verbal fact, it obviously cannot be taken to express a necessary truth. These considerations have an obvious application to the so-called "paradox of analysis." Insofar as one is puzzled about how (1)

A fortnight is a period of two weeks.

can be necessary, yet informative in a way in which (2)

A fortnight is a fortnight.

is not informative, one is simply confused. For to the extent that (1) is informative, to that extent it is verbal and contingent; and to the extent that it is necessary (i.e., used to make a necessary statement), to that extent it is trivial. Similarly with (2). The only reason that (2) strikes us as trivial is that we think of it as having only one interpretation, one use, namely that of stating an instance of the law of identity. But it could have other uses, too: it could, given a suitable, though perhaps far-fetched, context, have the sense of the false verbal statement:

(3)

A fortnight is a night spent in a fort.

The point is, it is partly because there are two quite distinct uses of (I), an important as well as a trifling use, that we are prone to get befuddled about it and take seriously the idea that necessary propositions must be nothing other than perfectly respectable verbal truths. The application of these remarks to the NN-thesis is quite natural. The plausibility of this thesis arises from the fact that

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necessary propositions, if they are not basic necessities, incapable of proof, are properly established as necessary only if they are deducible from other necessary propositions. Since the procedure here is purely a priori, it appears that what is established is a necessary result; hence, if 'Np' is such a result, then it too is necessary, which is to say that 'NNp' follow^.^ Now the arguments against this, which generally spring from an anxious wish to defend a form of the linguistic theory, seem also to involve a confusion of sentences with statements (or propositions). For what could the force of 'It is a contingent fact that it is necessary that a fortnight is a period of two weeks' possibly be, anyway? The only sense I can attribute to it is the idea that it is a contingent fact that (A fortnight is a period of two weeks' may be used to express a necessary statement. But while this is quite obviously true, it in no way conflicts with the tenability of the NN-thesis. The latter thesis is concerned, after all, with the necessity of statements or propositions, not with the necessity of what sentences may be used to assert; and it states that if a proposition is necessary, then it is a necessary, a priori fact about it that it is necessary. T o deny this thesis, without confusing it with a thesis about what certain sentences may be used to assert, is tantamount to affirming that the validity of an argument-something expressed by a sequence of sentences-is merely a contingent matter; for corresponding to every valid argument is a necessary conditional, and it is a contingent fact that this conditional is necessary if and only if it is a contingent fact that the argument is valid. Since it is generally acknowledged that the validity of an argument is an a priori, necessary matter, it is hard to see how it could be a contingent fact that a certain statement, or proposition, is necessary. Indeed, when we are careful to maintain a distinction between sentences and statements (propositions), the tenability of the NN-thesis seems inescapable.1° Once we have the NN-thesis in hand, however, it seems clear that necessary statements cannot depend on linguistic conventions. That is, it cannot be a logically necessary condition of a statement's necessity that there be a language in which it may be expressed. This is an immediate consequence of the fact that any conditional statement whose consequent is contingent but whose antecedent is See again Pap, loc. cit., and Kneale, pp. 548 ff. I realize that many philosophers are anxious to reject this distinction. But unless one is prepared to defend a Quinean theory of linguistic regimentation, the distinction is indispensable. For a recent, thoroughgoing, and rigorous examination of the sentence-statement distinction, and for a proof that statements cannot be identified, e.g., with uses of sentences, see R. Cartwright, "Propositions," in R. J. Butler, ed., Analytical Philosophy (Oxford, 1963). lo

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necessary is itself contingent, not necessary. Hence, if we accept the NN-thesis and go along with the distinction between sentences and statements, we must evidently accept:

(IV)

-- N (8) (3 L) ( 8 is necessary. >.S is expressible in 1,)."

This, however, not only spells doom to the linguistic theory of necessity, but raises the possibility that necessary truth is prior to all conventions-in the sense that we might attain a grasp of such truths even if we lacked the verbal ability to communicate our knowledge to others.

v

To modern ears, all of this may sound hopelessly old-fashioned and metaphysical. Perhaps it is. But the translation argument in its favor, given above, is unfortunately quite difficult to refute. Besides, other, less rarefied considerations are easily advanced here. For one thing, it appears to be logically possible for a person to lack a language and yet exhibit such complicated behavior-in fighting, hunting, tool-making, say-that we can attribute it only to his ability to think, to be aware of certain truths, both necessary and empirical. For another, since even highly sophisticated men can engage in very abstruse thought without the aid of mental imagery, verbal or otherwise, it does not appear to be a logical truth that all thinking, even highly abstract thinking, involves the exercise of those verbal skills which are necessary for communication with others. Thus, though it might in fact be true that only men with highly developed verbal skills can engage in such sophisticated conceptual activities, it is evidently not logically necessary that they have these skills, and the contention that one may indeed engage in abstract thought without the aid of language or linguistic conventions does not, therefore, appear to be absurd in principle. Now, if complicated thinking could proceed without the existence of language, of contingent verbal conventions, it appears that it is not just necessary truths that are language-independent. And indeed, though the translation argument, in the form that I have given jt, seems to hold only for necessary truths, it can actually be seen to work for concepts generally; that is, with just a little tinkering it can serve to show that the existence of concepts is just as

"

Note that even if we reject the NN-thesis we can still, on the assumption that the existence of languages is a contingent matter and that there is at least one necessary statement, derive the assertion, '-N (8) (3L) (S is true.3.S is expressible in L)'. This may seem obvious, on the ground that there are, no doubt, truths about hitherto undiscovered "scientific" entities not yet expressible in the language of any existing theory. But, if one can accept the possibility of presently inexpressible truths, the possibility of (presently) inexpressible necessary truths should not, then, be excessively frightening.

COMlMENTS A N D CRITICISikl

29 1

language-independent as that of necessary truths. In fact, an analogue of (IV), holding for concepts, is easily constructed, and it is just as difficult to rule out as (IV) is. If, however, it cannot be ruled out by a decisive argument, then the possibility arises, in uninhibited traditional colors, that there are countless true statements, capable of being known to be true by the analysis of concepts, which need not, perhaps cannot, be expressed in any existing language and which are, therefore, analytically a priori in the traditional sense. I am not, however, concerned to argue that there surely are analytically true a priori statements in the sense described. In fact I am strongly inclined to think that reasoning of any kind is intrinsically linguistic in character and that the very idea of analyzing concepts nonverbally expressed represents some kind of confusion. But I am not prepared to locate this confusion on the present occasion; indeed, it might not, in the end, be confusion at all. My purpose in the present essay is not to solve a problem but to raise one: Are there, then, analytic a priori statements? BRUCEAUNE UNIVERSITY O F PITTSBURGH

COMMENTS AND CRITICISM ON T H E METALINGUISTIC I N T E R P R E T A T I O S O F

COUXTERFACTUALS "

is generally accepted that subjunctive conditionals cannot adeITquately be interpreted as material implications. Thus, Ernest Nagel, in The Structure of Science, asserts that "a counterfactual cannot be translated in a straightforward way into a conjunction of statements in the indicative mood using only the standard nonnlodal connectives of formal logic" (71). This does not mean, however, that a Humean analysis of causality is unworkable, for "the content of counterfactuals can nevertheless be plausibly explicated without recourse to any unanalyzable modal notions" (71). A third alternative is possible, and Nagel proposes that

. . . a counterfactual can be interpreted as an implicit metalinguistic statement (i.e., a statement about other statements, and in particular about the logical relations of these other statements) asserting that the indicative form of its consequent clause follows logically from the indicative form of its antecedent clause, when the latter is conjoined with some law and the requisite initial conditions for the law (73). * I would like to express my gratitude to Mr. Herbert Heidelberger for a discussion which led to this paper and to Professor Carl Hempel for his critical comments which enabled me to eliminate several mistakes.

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[Footnotes] 6

Grammar and Existence: A Preface to Ontology Wilfrid Sellars Mind, New Series, Vol. 69, No. 276. (Oct., 1960), pp. 499-533. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28196010%292%3A69%3A276%3C499%3AGAEAPT%3E2.0.CO%3B2-G

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