Category theory as an autonomous foundation

Philosophia Mathematica 19 (3):227-254 (2011)
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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DOI 10.1093/philmat/nkr024
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References found in this work BETA
Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2007 - Philosophia Mathematica 16 (3):388-396.
Three Varieties of Mathematical Structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
Exploring Categorical Structuralism.C. Mclarty - 2004 - Philosophia Mathematica 12 (1):37-53.

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Citations of this work BETA
Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - forthcoming - British Journal for the Philosophy of Science:axw006.
Category Theory is a Contentful Theory.Shay Logan - 2014 - Philosophia Mathematica 23 (1):110-115.

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