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Philosophia Mathematica Advance Access published online on June 29, 2009
Philosophia Mathematica, doi:10.1093/philmat/nkp010
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© The Author [2009]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Mathematical Nominalism and Measurement

Davide Rizza*

* Department of Philosophy, The University of Sheffield, Sheffield S10 2TN U.K. pip05dr{at}sheffield.ac.uk

In this paper I defend mathematical nominalism by arguing that any reasonable account of scientific theories and scientific practice must make explicit the empirical non-mathematical grounds on which the application of mathematics is based. Once this is done, references to mathematical entities may be eliminated or explained away in terms of underlying empirical conditions. I provide evidence for this conclusion by presenting a detailed study of the applicability of mathematics to measurement. This study shows that mathematical nominalism may be regarded as a methodological approach to applicability, illuminating the use of mathematics in science.


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