Discernibility by symmetries

Rizza, Davide ORCID: https://orcid.org/0000-0002-1375-371X (2010) Discernibility by symmetries. Studia Logica, 96 (2). pp. 175-192.

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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.

Item Type:	Article
Uncontrolled Keywords:	ante rem structuralism,discernibility,homogeneity,symmetries
Faculty \ School:	Faculty of Arts and Humanities > School of Philosophy (former - to 2014)
UEA Research Groups:	Faculty of Arts and Humanities > Research Groups > Philosophy Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Philip Robinson
Date Deposited:	18 Mar 2011 14:17
Last Modified:	11 Nov 2024 09:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/26680
DOI:	10.1007/s11225-010-9287-x

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