Fallible Intuitions: The Apriori in Your Mathematics

Abstract

In his: The Nature of Mathematical Knowledge,! Philip Kitcher argues that we do not have apriori knowledge of mathematical truths. While arguing that nothing warrants holding a mathematical claim with the certainty required for knowledge of it to be apriori, he reminds so-called apriorists that some mathematical lrnowledge is based on long and complex proofs. Kitcher has his apriorists suggest that we need not be certain of all our apriori knowledge. At this suggestion Kitcher warns: