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The semantic plights of the ante-rem structuralist Assadian, Bahram 2018 Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition , Vol. 175 , Issue 12 , S. 3195 ff. ( Zeitschrift ) Englisch 0031-8116 | 1573-0883 Abstract
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.
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