Philosophical Studies

, Volume 175, Issue 12, pp 3195–3215 | Cite as

The semantic plights of the ante-rem structuralist

  • Bahram AssadianEmail author


A version of the permutation argument in the philosophy of mathematics leads to the thesis that mathematical terms, contrary to appearances, are not genuine singular terms referring to individual objects; they are purely schematic or variables. By postulating ‘ante-rem structures’, the ante-rem structuralist aims to defuse the permutation argument and retain the referentiality of mathematical terms. This paper presents two semantic problems for the ante-rem view: (1) ante-rem structures are themselves subject to the permutation argument; (2) the ante-rem structuralist fails to explain reference in a way that makes her account different to, and privileged over, that of her eliminativist rivals. Both problems undercut the motivation behind ante-rem structuralism.


Permutation argument Mathematical structuralism Indeterminacy of reference Arbitrary reference Model-theoretic arguments 



This paper draws on Chapter 2 of my Ph.D. dissertation, Assadian (2016). For extremely helpful discussion and written comments, I am very grateful to Tim Button, Simon Hewitt, Keith Hossack, Daniel Isaacson, Jeff Ketland, Hannes Leitgeb, Øystein Linnebo, Jonathan Nassim, Richard Pettigrew, J. Robbie G. Williams, Jack Woods, Mohammad Saleh Zarepour, an anonymous referee of this journal, and the audiences at the universities of London, Manchester, and Munich.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of PhilosophyBirkbeck CollegeLondonUK

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