Chapter

Nominalism

Charles Chihara

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print March 2005 | ISBN: 9780195148770
Published online July 2005 | e-ISBN: 9780199835560 | DOI: http://dx.doi.org/10.1093/0195148770.003.0015

Series: Oxford Handbooks in Philosophy

Nominalism

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Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.

Keywords: nominalism; abstract objects; mathematical objects; constructions; Rosen; Burgess; Quine; Putnam; indispensability argument

Chapter.  13456 words. 

Subjects: Philosophy of Mathematics and Logic

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