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Indispensability argument and anti-realism in philosophy of mathematics

Indispensability argument and anti-realism in philosophy of mathematics The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Frontiers of Philosophy in China Brill

Indispensability argument and anti-realism in philosophy of mathematics

Frontiers of Philosophy in China , Volume 2 (4): 15 – Jan 1, 2007

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Publisher
Brill
Copyright
Copyright © Koninklijke Brill NV, Leiden, The Netherlands
ISSN
1673-3436
eISSN
1673-355X
DOI
10.1007/s11466-007-0040-0
Publisher site
See Article on Publisher Site

Abstract

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions.

Journal

Frontiers of Philosophy in ChinaBrill

Published: Jan 1, 2007

Keywords: philosophy of mathematics; indispensability argument; anti-realism; nominalism; realism; Quine

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