Geoffrey Hellman
Philosophy Department
University of Minnesota

"Structuralism and the Open-Endedness of Mathematics""

ABSTRACT: Structuralism in mathematics comes in four main varieties, set-theoretic, sui-generis, modal, and category-theoretic. None is problem-free, but the first two are plagued by problems arising from platonistic commitments to a fixed, all-embracing universe for mathematics, in tension with indefinite extensibility of key mathematical concepts and with the creative side of mathematical thought. Modal-structuralism explicitly avoids these problems, and, we will suggest, category-theoretic structuralism should and can as well.

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