A.J. Ayer, answered from the texts and cited to the page.
Analytic propositions (the truths of logic and mathematics) are necessarily true but factually empty: they are tautologies that tell us nothing about the world, true in virtue of the meanings of the terms they contain.1 Synthetic propositions (the truths of natural science and ordinary empirical knowledge) are contingent and empirical: they make claims about the world that observation can confirm or disconfirm.
The distinction is exhaustive: there is no third category of synthetic a priori truth. Kant's claim that the propositions of mathematics, the categorical imperative, and various metaphysical principles are synthetic and known a priori rests on confusions the verificationist analysis dissolves: the mathematical truths are analytic; the moral pronouncements are pseudo-propositions; the metaphysical principles are meaningless.23
Quine's 'Two Dogmas of Empiricism' (1951) attacked the analytic/synthetic distinction by arguing that no principled criterion of analyticity can be given without circularity, and that empirical confirmation is holistic (statements face the tribunal of experience as a body, not individually).4 The attack identifies real difficulties at the margins but does not establish that the distinction cannot be drawn or that the empiricist framework requires it to be sharp; the considered position preserves the distinction while acknowledging the holistic character of theory-confirmation Quine identified.5
They will form a special class of analytic propositions, containing special terms, but they will be none the less analytic for that. For the criterion of an analytic proposition is that its validity should follow simply from the definition of the terms contained in it, and this condition is fulfilled by the propositions of pure mathematics.Language, Truth and Logic, pp. 81–82
I think that we can preserve the logical import of Kant's distinction between analytic and synthetic propositions, while avoiding the confusions which mar his actual account of it, if we say that a proposition is analytic when its validity depends solely on the definitions of the symbols it contains, and synthetic when its validity is determined by the facts of experience.Language, Truth and Logic, p. 78
Thus, the true propositions of mathematics are necessarily true, in Kant's system, because they flesh out the a priori intuitions that process the material to which our understanding applies its categories. But then, if one dismisses those ---------------------------------------- REPLY TO F. MIRO QUESADA 479 ---------------------------------------- REPLY TO F.Intellectual Autobiography and Replies
The two dogmas, both of which Quine rejects, are first that there is a fundamental distinction between analytic and synthetic propositions and secondly the dogma of reductionism, 'the belief,' as he puts it, 'that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience'.4 An analytic proposition, as we have seen, is one that is supposed to be true solely in…Philosophy in the Twentieth Century, pp. 258–259
It is a general feature of our use of predicates that they are sorted into categories in such a way that if something is characterized at any given time by one member of a category it is not characterized by another. Thus, being red is incompatible with being blue in the same way as being round is incompatible with being square, or being just 2 inches long is incompatible with being 3 inches long.The Central Questions of Philosophy, p. 201
The empiricist account of meaning in LTL is one of the central twentieth-century positions in philosophy of language. Quine's 'Two Dogmas of Empiricism' (1951) is the central post-war attack; the Quine-Carnap debate runs through the 1950s and shapes the post-positivist tradition. Grice and Strawson 'In Defense of a Dogma' (1956) defended the distinction against Quine. Kripke's Naming and Necessity (1972/1980) introduced the necessary-a-posteriori category that the LTL framework had excluded; Putnam's natural-kind argument develops the same challenge. The empiricist account remains contested but is preserved in modified form by neo-Carnapians (Stalnaker, Chalmers) and by Ayer's late writings.