The Synthetic a Priori
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A.J. Ayer and conventionalism - his reply to Kant
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Empiricism asserts that all our knowledge must derive from experience. Since conceptual ideas are a form of knowledge, concepts, or meanings, must also derive from experience. That is, if we have any knowledge of concepts, meanings or what words signify, this knowledge must be derived from experience of sense-data. For Ayer the basic unit of meaning is a simple sentence. This is an example of a molecular theory of meaning. An atomic theory would define meaning in terms of the understanding of the parts of the sentence – subject and predicate – from which the sentence is constructed, just as a molecule is a construction of atoms. However, Ayer takes the sentence (the molecule) as the primary unit of meaning, and ignores how meaning might be generated from its individual parts. In reply to Kant, Ayer adopts conventionalism. For Ayer there are just two kinds of simple sentence: (a) a synthetic and factual sentence, and (b) an analytic sentence, which is a statement about the meaning of words, or derived from the meanings of words. A factual simple sentence is something like "Lucy weights 75 kilos". A simple sentence always makes an assertion – that is, it states something that can be either true or false. The truth of a factual sentence can only be established by experience, that is, by direct acquaintance with sense-data. An analytic sentence is something like, for example, "A goulash is a kind of beef stew using onions and paprika". An analytic sentence is true by definition. A sentence is analytic if its validity depends on the definitions of the terms involved in it. An analytic sentence is also called by Ayer a tautology. He writes, "In saying that the certainty of a priori propositions depends upon the fact that they are tautologies, I use the word 'tautology' in such a way that a proposition can be said to be a tautology if it is analytic; and I hold that a proposition is analytic if it is true solely in virtue of the meaning of its constituent symbols, and cannot therefore be either confirmed or refuted by any fact of experience. Ayer maintains that Kant's explanation of the distinction between analytic and synthetic sentences in terms of the subject/predicate distinction is only a matter of psychology. Just because we do not in fact think of a predicate when we think of a given subject does not make a sentence logically synthetic. A logically analytic sentence depends only on Kant's other criterion, which involves the law of non-contradiction. There is nothing psychological about logic. He maintains that the laws of logic are not laws of thought. The laws of geometry are not laws about space. Thus, for Ayer, an analytic sentence, or tautology, is one that to deny the truth of which would involve denying the law of non-contradiction. It is because analytic sentences involve denying the law of non-contradiction that they are called tautologies. He accuses Kant of confusing logic with psychology, and confusing certain limitations in human thinking with limitations in logic. Here is what he writes, "Kant does not give one straightforward criterion for distinguishing between analytic and synthetic propositions; he gives two distinct criteria, which are by no means equivalent. Thus his ground for holding that the proposition '7 + 5 = 12' is synthetic is, as we have seen, that the subjective intension of '7 + 5' does not comprise the subjective intension of '12'; whereas his ground for holding that 'all bodies are extended' is an analytic proposition is that it rests on the principle of contradiction alone. That is, he employs a psychological criterion in the first of these examples, and a logical criterion in the second, and takes their equivalence for granted. But, in fact, a proposition which is synthetic according to the former criterion may very well be analytic according to the latter. For, as we have already pointed out, it is possible for symbols to be synonymous without having the same intensional meaning for anyone: and accordingly from the fact that one can think of the sum of seven and five without necessarily thinking of twelve, it by no means follows that the proposition '7 + 5 = 12' can be denied without self-contradiction. From the rest of his argument, it is clear that it is this logical proposition, and not any psychological proposition, that Kant is really anxious to establish. His use of the psychological criterion leads him to think that he has established it, when he has not." Kant would turn in his grave if he could read this! We will do our best to explain how Kant would reply, if he were alive to do so. Firstly, the argument as to whether '7 + 5 = 12' could be derived from the principle of non-contradiction would require a good deal of very sophisticated mathematics – in fact, set theory. Even if there were space to present that argument here, it would only force the problem of the justification of mathematics back onto the problem of the justification of set theory. Something needs to be justified – it is either mathematics, or logic or set theory. It is probably best to keep it simple, and ask, what makes mathematics true and useful? It is the second of these questions, what makes mathematics useful? that A. J. Ayer and conventionalists generally seem to miss. We only deal here with the simplest statements of arithmetic such as '7 + 5 = 12'. If this were true by definition, then it would be possible to offer alternative definitions. We could say, '7 + 5 = 1' for instance. But it is a truth about our world that '7 + 5' does not equal '1'. If I take seven sheep and add them to a pen containing five sheep I cannot end up with just one sheep. It is this application of mathematics that makes 7 + 5 = 12' synthetic. If it were analytic then the meaning of '12' would be contained in the meaning of '7 + 5', but the only application of '7 + 5 = 12' would be to fix the meaning of '12' as being identical to '7 + 5'. The next question is how do we know that '7 + 5 = 12'? It is here that Kant's second argument is introduced, which Ayer accepts. Namely, that '7 + 5 = 12' has a greater degree of certainty than any empirical generalisation ever could have, so it is not a posteriori knowledge. Kant would reply that Ayer confuses the necessity that '7 + 5' is equal to '12' with the claim that '7 + 5' means '12'. The necessity that '7 + 5 = 12' does not derive from definitions, but from some other source that lies outside those definitions, nor yet is sense-experience either. Hence the problem of empiricism. In conclusion, Kant's argument regarding the existence of the synthetic a priori remains the deepest thorn in empiricism's side. A. J. Ayer's attempt to refute it is not compelling. However, other approaches by W.V.O. Quine or Wittgenstein may be more convincing.
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Contents of
The Synthetic a Priori
1 Empiricism, Platonism, Innate Ideas and the A Priori
2 Analytic a priori
3 Kant and the synthetic a priori
4 Compound (molecular) and atomic sentences
5 Logically atomic sentences and the philosophy of logical atomism
6 Complex sentences and attitudes
7 Subject and predicate, individual and property
8 Synthetic and analytic, definitions offered by Kant
9 A priori and a posteriori
10 The synthetic a priori in Kant - the Critique of Pure Reason
11 Kant, The Critique of Pure Reason, the self and transcendental apperception
12 Empiricist philosophies of mathematics - conventionalism (formalism)
13 Empiricist philosophies of mathematics - the empiricism of J.S. Mill
14 Hybrid empiricist philosophies of mathematics
15 Empiricist philosophies of mathematics - Wittgenstein and non-cognitivism
16 A.J. Ayer and conventionalism - his reply to Kant
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