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Davide Rizza, Mathematical Nominalism and Measurement, Philosophia Mathematica, Volume 18, Issue 1, February 2010, Pages 53–73, https://doi.org/10.1093/philmat/nkp010
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Abstract
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.