Philosophical Studies

, Volume 173, Issue 10, pp 2591–2604 | Cite as

An anti-realist account of the application of mathematics

Article
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Abstract

Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of the application process. In this way, a better account of mathematical applications is, in principle, available.

Keywords

Application of mathematics Representation Inference, Realism Anti-realism Nominalism Platonism 
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Notes

Acknowledgments

My thanks go to Jody Azzouni, Newton da Costa, Steven French, Russell Marcus, and Ed Zalta for extremely helpful discussions.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MiamiCoral GablesUSA

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