Introduction

Part II was primarily concerned with the ontology of mathematics, although epistemological issues were never far off stage. However, in this final part of the book, we will be almost exclusively concerned with what are, broadly speaking, epistemological issues. We take up three interrelated topics: a priori truth, the normativity of mathematics, and the success of applied mathematics. All three of these topics have had a substantial presence in philosophy. For example, the success of applied mathematics played a significant role in motivating Kant 1965. Similarly, one or another notion of a priori truth has played a substantial role in the epistemology and metaphysics of many philosophers, even to this day. Finally, philosophers of mathematics have seen the normativity of mathematical law as a deep fact that rules out what might otherwise be appealing positions; for example, consider the use of it made by Frege and Husserl in their attacks on psychologism.

By contrast, I have fairly deflationary views on a priori truth, the normativity of mathematics, and the success of applied mathematics; in particular, I believe that not much of philosophical interest follows from a close examination of any of these.

Let us first consider a priori truth. Doctrines of a priori truth were motivated by the felt perception of a difference between the epistemic properties of mathematical truths and those of nonmathematical truths.