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

Authors
Øystein Linnebo
University of Oslo
Richard Pettigrew
Bristol University
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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkr024
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,437
Through your library

References found in this work BETA

Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
Structure in Mathematics and Logic: A Categorical Perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
Three Varieties of Mathematical Structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.

View all 10 references / Add more references

Citations of this work BETA

Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - 2016 - British Journal for the Philosophy of Science:axw006.
What We Talk About When We Talk About Numbers.Richard Pettigrew - 2018 - Annals of Pure and Applied Logic 169 (12):1437-1456.

View all 15 citations / Add more citations

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 2000:183-196.

Analytics

Added to PP index
2010-06-08

Total views
495 ( #15,470 of 2,449,149 )

Recent downloads (6 months)
5 ( #141,356 of 2,449,149 )

How can I increase my downloads?

Downloads

My notes