Axiomatizing mathematical conceptualism in third order arithmetic

Weaver, Nik

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Axiomatizing mathematical conceptualism in third order arithmetic

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Author(s): Nik Weaver

Publication date: 2009-05-11

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Abstract

We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the basic principles of conceptualism in a formal system CM set in the language of third order arithmetic.