ABSTRACT

It is likely that intuitions have something important to do with mathematical knowledge. And it is quite common for contemporary naturalists to be skeptical of the ability of intuitions to generate substantial amounts of knowledge. This chapter departs from this trend. It offers a naturalistic theory of intuitions and then uses this theory to generate an answer to Benacerraf’s epistemological problem in the philosophy of math. The upshot of the argument is that naturalists can explain the connection between intuition and mathematical knowledge; a corollary of this argument, though, is that mathematical knowledge consists, at least in some part, of a set of approximate truths.