Category theory as an autonomous foundation

Philosophia Mathematica 19 (3):227-254 (2011)
  Copy   BIBTEX

Abstract

Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other branches of contemporary mathematics. If such a specification suffices, then a category-theoretical approach will be highly appropriate. But if sets have a richer `nature' than is preserved under isomorphism, then such an approach will be inadequate.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 89,446

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

(Math, science, ?).M. Kary - 2009 - Axiomathes 19 (3):61-86.
Sets, classes, and categories.F. A. Muller - 2001 - British Journal for the Philosophy of Science 52 (3):539-573.
Category theory: The language of mathematics.Elaine Landry - 1999 - Philosophy of Science 66 (3):27.
Set-Theoretic Foundations.Stewart Shapiro - 2000 - The Proceedings of the Twentieth World Congress of Philosophy 6:183-196.

Analytics

Added to PP
2010-06-08

Downloads
582 (#26,123)

6 months
42 (#82,657)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Øystein Linnebo
University of Oslo
Richard Pettigrew
University of Bristol