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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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The Case for Mathematical Realism

The Case for Mathematical Realism

Chapter:
(p.41) 3 The Case for Mathematical Realism
Source:
Mathematics as a Science of Patterns
Author(s):

Michael D. Resnik (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250142.003.0003

The application of mathematics to science and the enormous success that derives from it is, perhaps, the strongest evidence in favour of mathematical realism. Quine and Putnam have taken the indispensability of mathematics in doing science as the main premise in an argument for both the truth of mathematics and the existence of mathematical objects. This argument has been criticized, among other things, for presupposing a realist position with regard to science. In this chapter, I propose a new argument, the pragmatic indispensability argument that avoids the problem by failing to presuppose that our best scientific theories are true. I argue that the justification for doing science also justifies our accepting as true, the mathematics that science uses.

Keywords:   application of mathematics, indispensability, justification, mathematical realism, pragmatic, Putnam, Quine, success

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