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BENACERRAF’S DILEMMA AND INFORMAL MATHEMATICS

Published online by Cambridge University Press:  01 December 2009

GREGORY LAVERS
GREGORY LAVERS*
Affiliation:
Department of Philosophy, Concordia University
*
*DEPARTMENT OF PHILOSOPHY, CONCORDIA UNIVERSITY, 1455 DEMAISONNEUVE BOULEVARD, MONTREAL, QUEBEC, CANADA H3G 1M8 E-mail:[email protected]
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Abstract

This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerraf’s dilemma. The account builds upon Georg Kreisel’s work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a Fregean account of the objectivity and our knowledge of abstract objects. It is then argued that the resulting view faces no insurmountable metaphysical or epistemic obstacles.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 4 , December 2009 , pp. 769 - 785
Copyright
Copyright © Association for Symbolic Logic 2009

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