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Philosophia Mathematica Advance Access published online on September 30, 2009
Philosophia Mathematica, doi:10.1093/philmat/nkp014
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© The Author [2009]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

The Applicability of Mathematics as a Scientific and a Logical Problem{dagger}

Feng Ye*

* Department of Philosophy, Peking University, Beijing 100871, China. fengye63{at}gmail.com

This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce a plan for resolving the logical puzzles of applicability.

{dagger} This research is supported by Chinese National Social Science Foundation (grant number 05BZX049). I am deeply indebted to my PhD advisors John P. Burgess and Paul Benacerraf for all my research in philosophy of mathematics. I am also greatly indebted to two anonymous referees of this paper. Without their patient comments and kind help, this paper would have been impossible.


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