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  1. Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
    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 (...)
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  • On the Exhaustion of Mathematical Entities by Structures.Adrian Heathcote - 2014 - Axiomathes 24 (2):167-180.
    There has been considerable discussion in the literature of one kind of identity problem that mathematical structuralism faces: the automorphism problem, in which the structure is unable to individuate the mathematical entities in its domain. Shapiro (Philos Math 16(3):285–309, 2008) has partly responded to these concerns. But I argue here that the theory faces an even more serious kind of identity problem, which the theory can’t overcome staying within its remit. I give two examples to make the point.
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  • Scientific Structuralism: On the Identity and Diversity of Objects in a Structure.James Ladyman - 2007 - Aristotelian Society Supplementary Volume 81 (1):23–43.
  • Mathematical Structuralism and the Identity of Indiscernibles.James Ladyman - 2005 - Analysis 65 (3):218–221.