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FOUNDATIONS AS TRUTHS WHICH ORGANIZE MATHEMATICS

Published online by Cambridge University Press:  09 May 2012

COLIN MCLARTY
COLIN MCLARTY*
Affiliation:
Departments of Philosophy and Mathematics, Case Western Reserve University
*
*DEPARTMENT OF PHILOSOPHY, CASE WESTERN RESERVE UNIVERSITY, CLEVELAND OH USA 44106 E-mail: [email protected]
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Abstract

The article looks briefly at Feferman’s most sweeping claims about categorical foundations, focuses on narrower points raised in Berkeley, and asks some questions about Feferman’s own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 1 , March 2013 , pp. 76 - 86
Copyright
Copyright © Association for Symbolic Logic 2012

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