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Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
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What is Realistic Mathematics?
I may be wrong, missing the point and in way over my head, but given that category theory is useful in physics (is it?) and that category theory deals with classes, then I don't think that set theorie …