Studia Logica 96 (2):175 - 192 (2010)

Davide Rizza
University of East Anglia
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
Keywords Ante Rem Structuralism  Discernibility  Symmetries  Homogeneity
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DOI 10.1007/s11225-010-9287-x
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References found in this work BETA

Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.

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