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AbstractionismEssays in Philosophy of Mathematics$
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Philip A Ebert and Marcus Rossberg

Print publication date: 2016

Print ISBN-13: 9780199645268

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780199645268.001.0001

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The Existence (and Non-existence) of Abstract Objects

The Existence (and Non-existence) of Abstract Objects

Chapter:
3 (p.50) The Existence (and Non-existence) of Abstract Objects
Source:
Abstractionism
Author(s):

Richard G. Heck

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199645268.003.0003

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon the ‘proliferation problem’: Hale and Wright’s account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation is as good as any other. The paper then develops a response to this objection, and offers an account of what it is for abstracta to exist that is Fregean in spirit but more robust than familiar views.

Keywords:   abstract objects, nominalism, platonism, existence

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