Deeply Contingent A Priori Knowledge

The argument is not, however, problem-free. First: while the meaning of s might not guarantee a verifying state of affairs, mightn’t the fact of one’s believing that s is true guarantee a verifying state of affairs? And mightn’t this fact be exploited to secure knowledge of truths that are deeply contingent? Second: the argument seems to rely on the principle that if I can conceive that not P is actually the case, then I do not know that P. But it is generally agreed that a knowledge-conferring warrant for some P need not offer a watertight guarantee of P and thus need not render it inconceivable that the actual world falsifies P. Why then require such a guarantee when it comes to priori warrant? The first objection is that a guarantee of truth need not come from semantics. The second is that no such guarantee is required for a priori knowledge. I shall be exploring both of these ideas in what follows.