Something Funny about the Ayer

We discussed several problems with Ayer's verification principle at this week's meeting so I would like to elaborate a few of the more poignant issues.

1. Ayer attempts to describe mathematical and geometrical objects in terms of analyticity, but gives an insufficient account of this term. In several places he describes analyticity as being indicative of a proposition whose (a) truth depends on symbolic definitions, (b) whose denial is a contradiction, (c) is a tautology, or (d) something one can know independently of experience. Ayer wants to argue with Kant's description of mathematical expressions being synthetic by stating that Kant misapplies a psychological category to the determination of what is entailed by one side of a mathematical expression, like 2+2=4. Ayer then proceeds to say that the reason this is not synthetic, i.e. is analytic, is because of (b). Here is where things get interesting...

(2+2=4) is not logically contradicted by (2+2=5) for instance, because contradictions arise through conjunction. What would be a contradiction is if Ayer said [(2+2=4) AND not-(2+2=4)]. Unfortunately, this seems to require some form of mathematical description I doubt Kant would endorse...

2. Quine later raises an interesting argument against the Western tradition's use of the analytic/synthetic distinction in general. In Two Dogmas of Empiricism, Quine levels an attack against the tradition based on synonymy. For instance, while "All bachelors are unmarried," is often given as an example of something analytic, Quine argues that by traditional reasoning the proposition, "All creatures with a heart are creatures with kidneys," is synthetic because 'creatures with a heart,' is not synonymous with 'creatures with kidneys.' Quine thinks that there is an arbitrary privilege given to one meaning and that one cannot give a good non-circular account of analyticity.

This would seem to leave an enormous hole in Ayer's main thesis. Ayer argues that philosophy is concerned mainly with providing analytic truths while the scientific community develops empirical justifications for synthetic truths. If there is no distinction between the two then what exactly is philosophy supposed to do? Ayer, in response to Quine and this question some years later explained that he had no real answer, and would simply "point to my own work as an example."