What we talk about when we talk about numbers |
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Affiliation: | Department of Philosophy, University of Bristol, Cotham House, Cotham Hill, Bristol, BS6 6JL, United Kingdom |
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Abstract: | In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki, and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism. |
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Keywords: | Mathematical structuralism Foundations of mathematics Philosophy of mathematics Nominalism Set-theoretic foundations |
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