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Mathematics and Reality$
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Mary Leng

Print publication date: 2010

Print ISBN-13: 9780199280797

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199280797.001.0001

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Naturalism and Mathematical Practice

Naturalism and Mathematical Practice

(p.76) 4 Naturalism and Mathematical Practice
Mathematics and Reality

Mary Leng (Contributor Webpage)

Oxford University Press

‘Naturalism’, as we have used the term, is the commitment to look to science to discover what we ought to believe. If one reads ‘science’ broadly, to include pure mathematics, then this commitment might seem to lead directly to mathematical realism, since our pure mathematical theories prove the existence of many mathematical objects. But the indispensability argument focuses on the use of mathematics in our empirical theories, and holds that we have reason to believe in only those mathematical objects whose existence is confirmed by their indispensable presence as posits in our best empirical theories. This chapter argues that there is no tension between the naturalist's commitment to look to science, broadly construed, to discover what we ought to believe, and the indispensability argument's focus on the role of mathematics in empirical science, since pure mathematical theories need not be true to be good.

Keywords:   naturalism, science, pure mathematics, truth, confirmation, mathematical realism

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