Criteria of Identity and Structuralist Ontology

Criteria of Identity and Structuralist Ontology

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate co...

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Veröffentlicht in:Philosophia mathematica 2008-10, Vol.16 (3), p.388-396
Hauptverfasser: Leitgeb, Hannes, Ladyman, James
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Mathematics
Ontology
Philosophy
Theory
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creator Leitgeb, Hannes
Ladyman, James
description In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view.
doi_str_mv 10.1093/philmat/nkm039
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subjects Mathematics
Ontology
Philosophy
Theory
title Criteria of Identity and Structuralist Ontology
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