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Philosophia Mathematica Advance Access originally published online on October 1, 2008
Philosophia Mathematica 2009 17(3):273-312; doi:10.1093/philmat/nkn026
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Extending Hartry Field’s Instrumental Account of Applied Mathematics to Statistical Mechanics{dagger}

Glen Meyer*

* The Republic Group, 5525 LBJ Freeway, Dallas, Texas 75240-6241, U.S.A. meyersv1{at}yahoo.com

A serious flaw in Hartry Field’s instrumental account of applied mathematics, namely that Field must overestimate the extent to which many of the structures of our mathematical theories are reflected in the physical world, underlies much of the criticism of this account. After reviewing some of this criticism, I illustrate through an examination of the prospects for extending Field’s account to classical equilibrium statistical mechanics how this flaw will prevent any significant extension of this account beyond field theories. I note in the conclusion that this diagnosis of Field’s program also points the way to modifications that may work.

{dagger} Many thanks to those who helped me think through and express the ideas in this paper, especially my graduate advisor, Geoffrey Hellman. I also wish to thank David MacCallum, Hartry Field, James Hawthorne, and an anonymous referee for Philosophia Mathematica, among others.


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