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NEITHER CATEGORICAL NOR SET-THEORETIC FOUNDATIONS

Published online by Cambridge University Press:  26 April 2012

GEOFFREY HELLMAN
GEOFFREY HELLMAN*
Affiliation:
University of Minnesota
*
*UNIVERSITY OF MINNESOTA, 831 HELLER HALL, 271-19TH AVENUE SOUTH, MINNEAPOLIS, MN 55455 E-mail:hellm001@umn.edu
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Abstract

First we review highlights of the ongoing debate about foundations of category theory, beginning with Feferman’s important article of 1977, then moving to our own paper of 2003, contrasting replies by McLarty and Awodey, and our own rejoinders to them. Then we offer a modest proposal for reformulating a theory of category of categories that would actually meet the objections of Feferman and Hellman and provide a genuine alternative to set theory as a foundation for mathematics. This proposal is more modest than that of our (2003) in omitting modal logic and in permitting a more “top-down” approach, where particular categories and functors need not be explicitly defined. Possible reasons for resisting the proposal are offered and countered. The upshot is to sustain a pluralism of foundations along lines actually foreseen by Feferman (1977), something that should be welcomed as a way of resolving this long-standing debate.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 1 , March 2013 , pp. 16 - 23
Copyright
Copyright © Association for Symbolic Logic 2012

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References

BIBLIOGRAPHY

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