Does The Necessity of Mathematical Truths Imply Their Apriority?



It is sometimes argued that mathematical knowledge must be a priori, since mathematical truths are necessary, and experience tells us only what is true, not what must be true. This argument can be undermined either by showing that experience can yield knowledge of the necessity of some truths, or by arguing that mathematical theorems are contingent. Recent work by Albert Casullo and Timothy Williamson argues (or can be used to argue) the first of these lines; W. V. Quine and Hartry Field take the latter line. I defend a version of the argument against these, and other objections.