Annals of Pure and Applied Logic 169 (12):1437-1456 (2018)

Authors
Richard Pettigrew
Bristol University
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.
Keywords mathematical structuralism  instrumental nominalism  foundations of mathematics  ontology of mathematics  philosophy of mathematics  ante rem structuralism  eliminative structuralism  set theory
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Reprint years 2018
DOI 10.1016/j.apal.2018.08.009
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References found in this work BETA

Philosophical Explanations.Robert Nozick - 1981 - Harvard University Press.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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Why Can’T There Be Numbers?David Builes - forthcoming - The Philosophical Quarterly.

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