Extending Hartry field's instrumental account of applied mathematics to statistical mechanics

Philosophia Mathematica 17 (3):273-312 (2008)
Abstract
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
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DOI 10.1093/philmat/nkn026
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The Explanatory Power of Phase Spaces.Aidan Lyon & Mark Colyvan - 2007 - Philosophia Mathematica 16 (2):227-243.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Conservativeness and Incompleteness.Stewart Shapiro - 1983 - Journal of Philosophy 80 (9):521-531.

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Quantitative Properties.Maya Eddon - 2013 - Philosophy Compass 8 (7):633-645.

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