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Mathematics as a Science of Patterns$
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Michael D. Resnik

Print publication date: 1999

Print ISBN-13: 9780198250142

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250142.001.0001

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Recent Attempts at Blunting the Indispensability Thesis

Recent Attempts at Blunting the Indispensability Thesis

Chapter:
(p.52) 4 Recent Attempts at Blunting the Indispensability Thesis
Source:
Mathematics as a Science of Patterns
Author(s):

Michael D. Resnik (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250142.003.0004

The indispensability thesis maintains both that using mathematical terms and assertions is an indispensable part of scientific practice and that this practice commits science to mathematical objects and truths. Anti‐realists have used several methods for attacking this thesis: Hartry Field has tried to show how science can do without mathematics by showing that it is possible to replace analytic mathematical scientific theories with synthetic versions that make no reference to mathematical objects. Phillip Kitcher and Charles Chichara have tried, instead, to maintain the mathematical formalism in science without being committed to mathematical realism, by giving a non‐realist account of mathematical objects. Finally, Geoffrey Hellman devised a modal structuralism that uses modal operators to translate standard mathematical language into a ‘structuralist’ language. In this chapter I discuss these positions and claim that, on the one hand, they have failed to show that science can do without mathematical objects, and on the other, that these approaches to mathematics do not represent an ontic and epistemic gain over standard realism.

Keywords:   Chichara, Field, Hellman, indispensability thesis, Kitcher, mathematical formalism, mathematical realism, mathematical structuralism, modal operators, structuralism

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