Maddy and Mathematics: Naturalism or Not

Penelope Maddy advances a purportedly naturalistic account ofmathematical methodology which might be taken to answer thequestion `What justifies axioms of set theory?' I argue thather account fails both to adequately answer this question andto be naturalistic. Further, the way in which it fails to answerthe question deprives it of an analog to one of the chief attractionsof naturalism. Naturalism is attractive to naturalists andnonnaturalists alike because it explains the reliability ofscientific practice. Maddy's account, on the other hand, appearsto be unable to similarly explain the reliability of mathematicalpractice without violating one of its central tenets.

1 Introduction

2 Mathematical Naturalism

3 Desiderata and the attractionof naturalism

4 Assessment: Naturalism and names

4.1 Taking‘naturalism’seriously

4.2 Second philosophy (orwhat's in a name)

5 A way out?

6 Or out of the way?

     

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