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

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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.

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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
Subjects:	Specific Sciences > Mathematics
Date:	January 2010
URI:	https://philsci-archive.pitt.edu/id/eprint/5392

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