David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 18 (1):53-73 (2010)
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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References found in this work BETA
Mark Balaguer (1996). Towards a Nominalization of Quantum Mechanics. Mind 105 (418):209-226.
Reinhard Niederée (1992). What Do Numbers Measure? A New Approach to Fundamental Measurement. Mathematical Social Sciences 24:237-276.
Michael D. Resnik (1985). How Nominalist is Hartry Field's Nominalism? Philosophical Studies 47 (2):163 - 181.
Stewart Shapiro (1983). Conservativeness and Incompleteness. Journal of Philosophy 80 (9):521-531.
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