Abstract

My thesis discusses the unique challenge that platonistic mathematics poses to philosophical naturalism. It has two main parts. ;The first part discusses the three most important approaches to my problem found in the literature: First, W. V. Quine's holistic empiricist defense of mathematical platonism; then, the nominalists' argument that mathematical platonism is naturalistically unacceptable; and finally, a radical form of naturalism, due to John Burgess and Penelope Maddy, which dismisses any philosophical criticism of a successful science such as mathematics. I find faults with all of these approaches. ;The second part attempts to do better. First, I develop an improved epistemological challenge to mathematical platonism. Roughly, this challenge asks for an account of what mathematicians' justification for believing in platonistic mathematics consists in. I argue this challenge is immune to the criticism I leveled against the traditional challenges. To show that it has bite, I apply this challenge to Quine's philosophy of mathematics. I argue this shows that Quine must invoke, in addition to his confirmational holism, a semantic indeterminacy thesis that is so radical as to be implausible. Finally, I attempt to develop a better response to the improved challenge. I defend an unorthodox view of the concept of an object and argue this makes room for a neo-Dedekindian view of mathematical objects which identifies mathematical existence with the logical coherence of the theory describing the structure in question. This view transforms metaphysical and epistemological questions about mathematical objects into corresponding, but more tractable questions about the logical notion of coherence