TITLE

Category Theory as an Autonomous Foundation†

AUTHOR(S)
Linnebo, Øystein; Pettigrew, Richard
PUB. DATE
October 2011
SOURCE
Philosophia Mathematica;Oct2011, Vol. 19 Issue 3, p227
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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. We argue that, while a strong case can be made for its logical and conceptual autonomy, its justificatory autonomy turns on whether or not mathematical theories can be justified by appeal to mathematical practice. If they can, a category-theoretical approach will be fully autonomous; if not, the most natural route to justificatory autonomy is blocked.
ACCESSION #
66731537

 

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