Chapter

The Empirical Nature of Mathematical Knowledge

Mark Colyvan

in The Indispensability of Mathematics

Published in print April 2001 | ISBN: 9780195137545
Published online November 2003 | e-ISBN: 9780199833139 | DOI: http://dx.doi.org/10.1093/019513754X.003.0006
                   The Empirical Nature of Mathematical Knowledge

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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

Chapter.  10894 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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