Thought: A Journal of Philosophy 4 (4):237-242 (2015)

Marcoen J. T. F. Cabbolet
Vrije Universiteit Brussel
Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory
Keywords foundations of mathematics  Russel paradox  logical inconsistency  naive category theory  definition of category
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DOI 10.1002/tht3.183
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References found in this work BETA

General Theory of Natural Equivalences.Saunders MacLane & Samuel Eilenberg - 1945 - Transactions of the American Mathematical Society:231-294.
What is Required of a Foundation for Mathematics?John Mayberry - 1994 - Philosophia Mathematica 2 (1):16-35.

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