Analyzing the A Priori

Abstract The traditional analysis of a priori warrant is negative: warrant for a belief is a priori just in case it does not depend on experience. To ward off obvious counterexamples, a standard exemption is made for learning experiences. In order to believe that the square root of two is irrational, I first needed to learn the relevant concepts, and this happened through experience. This standard exemption is not enough. I formed my warranted belief about the square root of two by reading the proof in Euclid’s Elements . This experience isn’t covered by the standard exemption, so the traditional analysis counts even basic mathematical beliefs as a posteriori . This is a disaster, but it can be fixed. The fix involves an ‘imagination test’ for determining which experiences are epistemically relevant and which are not. With the imagination test in hand, the negative approach may still provide the core of a satisfying analysis of the generative a priori , provided that various objections can be dealt with in a satisfying manner.