Believing Necessary Propositions

Abstract

I wish to consider two claims discussed by Mr. Donald McQueen in his paper 'Evidence for Necessary Propositions',' (a) that 'a necessary truth has no truth-conditions, since it is unconditionally true' (p. 57), and (b), that no fact can be evidence for believing an a priori proposition. According to McQueen, although (a) is true, (b) is false. The view that (b) is false derives its appeal from the fact that it is proper language both to speak of believing a necessarily true proposition and to speak of having evidence which confirms it. The following description, for example, seems in no way to violate usage: 'Complete tables of primes of 12,000,000 and more have gradually been computed by refinements of [the method of Eratosthenes' sieve], and they provide us with a tremendous mass of empirical data concerning the distribution and properties of primes. On the basis of these tables we can make highly plausible conjectures (as though number theory were an experimental science) ..... '2 The question is whether the fact that there is no impropriety about such a description can be used to go on to the claim the necessary propositions, like empirical ones, are such that nothing in principle precludes their being believed or being rendered probable. Can the natural interpretation of statements of the form 'S believes that p' and 'It is probable that p' which disregards whether p is necessary or contingent avoid paradoxical consequences, and is there an interpretation which will escape paradox where 'p' expresses an a priori proposition? Any argument for the view that a fact, either contingent or noncontingent, can be evidence for a necessary proposition highlights similarities between a priori and empirical propositions. It is of the essence of empirical propositions that they can have a probability attached to them, that they can be confirmed by fact, and that they can be either believed or disbelieved.3 I shall try to bring out the paradox of characterizing in the same way propositions which are necessarily true or necessarily false, and go on to a reinterpretation of 'Evidence E makes p probable' and 'S believes p'. The main requirement the new interpretation must meet is that it be compatible with the fact that neither expression involves a misuse of language. As is well known, histories of mathematics report 'attempts' to trisect the angle with straight edge and compass, to duplicate the cube, to find a rational number which is the value of V;4 and everyone would agree in