PhilSci Archive

Only up to isomorphism? Category Theory and the Foundations of Mathematics

Linnebo, Øystein and Pettigrew, Richard (2010) Only up to isomorphism? Category Theory and the Foundations of Mathematics. [Preprint]


Download (352kB)


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.

Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
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

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item