Measurement-Theoretic Observations on Field’s Instrumentalism and the Applicability of Mathematics

Abstracta 2 (2):148-171 (2006)
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Abstract

In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but also as conceptual schemata by means of which we can articulate our understanding of experience.

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Davide Rizza
University of East Anglia

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Science without Numbers.Michael D. Resnik - 1983 - Noûs 17 (3):514-519.
A set of independent axioms for extensive quantities.Patrick Suppes - 1951 - Portugaliae Mathematica 10 (4):163-172.

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