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The Indispensability of Mathematics$
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Mark Colyvan

Print publication date: 2001

Print ISBN-13: 9780195137545

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/019513754X.001.0001

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The Empirical Nature of Mathematical Knowledge

The Empirical Nature of Mathematical Knowledge

Chapter:
(p.115) 6 The Empirical Nature of Mathematical Knowledge
Source:
The Indispensability of Mathematics
Author(s):

Mark Colyvan

Publisher:
Oxford University Press
DOI:10.1093/019513754X.003.0006

Any version of mathematical realism motivated by Quinean indispensability arguments must yield a mathematics that is a posteriori and fallible. Such a consequence is considered unacceptable by many – mathematical realists and antirealists alike. For example, Musgrave and Sober find that such a conclusion sits rather uneasily with scientific practice, while Hale and Wright take issue with any account of mathematics that yields the contingent existence of mathematical objects. In this chapter, these and other related objections are addressed.

Keywords:   a posteriori, contingent existence, Hale, Musgrave, scientific practice, Sober, Wright

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