Discernibility by Symmetries |
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Authors: | Davide Rizza |
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Institution: | 1.School of Philosophy,University of East Anglia,Norwich,UK |
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Abstract: | In this paper I introduce a novel strategy to deal with the indiscernibility problem for ante rem structuralism. The ante rem structuralist takes the ontology of mathematics to consist of abstract systems of pure relata. Many of such systems are totally symmetrical, in the sense that all of their elements are relationally indiscernible, so
the ante rem structuralist seems committed to positing indiscernible yet distinct relata. If she decides to identify them, she falls into mathematical inconsistency while, accepting their distinctness, she finds
herself unable to account for it. I show that the ante rem structuralist has in fact the resources to account for the distinctness of indiscernibles and that these resources come from
the very symmetry properties of the mathematical objects that seem to pose problems for her. |
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