# Category Theory and Philosophy

## Abstract

This paper considers the role that category theory can play in philosophy. Category theory is a source of problems, methods and inspiration when it comes to considering both some new and some longstanding philosophical issues. Among the former, the paper draws attention to the ontological interaction between categories and sets, as well as the quantificational criterion of being—to mention just two. Among the latter, it highlights the problem of cognitive access to mathematical objects, and that of the way in which such objects exist. In the context of the development and the ontology of mathematics, I argue in favour of the thesis that category theory is the most “platonic” theory in mathematics. I also point out that category theory impacts significantly upon many standard philosophical positions, providing many counter-examples to popular, often repeated, yet unjustified philosophical claims. The influence of category theory on the foundations and ontology of mathematics is also briefly explored here.

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