A Naturalistic Look into Maddy’s Naturalistic Philosophy of Mathematics

Abstract

This paper discusses Penelope Maddy’s (b. 1950) naturalistic philosophy of mathematics, which is one of the most influential forms of post-Quinean naturalism in the philosophy of mathematics. Two defining features of Maddy’s theory, namely the methodological autonomy of mathematics and the equivalence of Thin Realism and Arealism, are analyzed, and some criticisms of them are posed from within the naturalistic line of thought itself. In the course of this analysis and criticism, the paper will also consider Maddy’s objections to the Quinean Indispensability Argument, which are the starting point of her own version of naturalism.

Key words： philosophy of mathematics; naturalism; Penelope Maddy; indispensability; Thin Realism