Linnebo, Øystein and Pettigrew, Richard
(2010)
Only up to isomorphism? Category Theory and the Foundations of Mathematics.
[Preprint]
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 categorytheoretical approach will be highly appropriate. But if sets have a richer 'nature' than is preserved under isomorphism, then such an approach will be inadequate.
Item Type: 
Preprint

Creators: 
Creators  Email  ORCID 

Linnebo, Øystein    Pettigrew, Richard   

Keywords: 
Category theory; Foundations of Mathematics; Structuralism; Set theory; Categorical Set Theory 
Subjects: 
Specific Sciences > Mathematics 
Depositing User: 
Richard Pettigrew

Date Deposited: 
09 Jun 2010 
Last Modified: 
07 Oct 2010 15:19 
Item ID: 
5392 
URI: 
http://philsciarchive.pitt.edu/id/eprint/5392 
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