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The British Journal for the Philosophy of Science Advance Access published online on June 7, 2007
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axm016
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Copyright © The Author 2007. Published by Oxford University Press on behalf of British Society for the Philosophy of Science.

Maddy and Mathematics: Naturalism or Not

Jeffrey W. Roland

Louisiana State University, Department of Philosophy, Baton Rouge LA 70803-3901, USA

jroland{at}lsu.edu


  Abstract

Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question `What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets.

1 Introduction
2 Mathematical Naturalism
3 Desiderata and the attraction of naturalism
4 Assessment: Naturalism and names
4.1 Taking ‘naturalism’ seriously
4.2 Second philosophy (or what's in a name)

5 A way out?
6 Or out of the way?


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