Ontological Regress of Maddy’s Mathematical Naturalism

Abstract

This chapter is an attempt to probe the question as to why Maddy gave up mathematical realism and moved to her own version of mathematical naturalism. According to one widespread hypothesis, Maddy’s change of mind was brought up by her criticism of Quine-Putnam indispensability argument. Though quite convincing, it is not good enough to explain why one has to give up mathematical realism. The analogy of science and mathematics will instead be shown to be the better perspective to fathom Maddy’s changing beliefs. For this purpose, we have to understand to what extent Maddy’s thought in her realist years, which was strongly influenced by Quine and Godel, was governed by the analogy between science and mathematics. Also, we have to understand why Maddy gave up the analogy, and thereby gave up mathematical realism. Finally, some criticisms against Maddy’s abandonment of the analogy will be examined so as to hint at the reasons why I believe Maddy’s intellectual journey in mathematical ontology is rather regress than progress.