Article

Nominalism Reconsidered

Gideon Rosen and John P. Burgess

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print June 2007 | ISBN: 9780195325928
Published online September 2009 | | DOI: http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0016

Series: Oxford Handbooks

Nominalism Reconsidered

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Nominalism is usually formulated as the thesis that only concrete entities exist or that no abstract entities exist. But where, as here, the interest is primarily in philosophy of mathematics, one can bypass the tangled question of how, exactly, the general abstract/concrete distinction is to be understood by taking nominalism simply as the thesis that there are no distinctively mathematical objects: no numbers, sets, functions, groups, and so on. As to the nature of such objects (if there are any), it can be said that it has come to be fairly widely agreed, under the influence of Frege and others, that they are very different both from paradigmatically physical objects (bricks, stones) and from paradigmatically mental ones (minds, ideas). Modern nominalism emerged in the 1930s as a response to the view of Frege and others that numbers, sets, functions, groups, and so on belong to a “third realm.”

Keywords: nominalism; philosophy of mathematics; mathematical objects; Frege; sets; functions

Article.  9344 words. 

Subjects: Philosophy ; Philosophy of Mathematics and Logic ; Metaphysics

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