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Introduction

Philosophical Quarterly 54 (214):1-15 (2004)

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  1. I—James Ladyman: On the Identity and Diversity of Objects in a Structure.James Ladyman - 2007 - Aristotelian Society Supplementary Volume 81 (1):23-43.
    The identity and diversity of individual objects may be grounded or ungrounded, and intrinsic or contextual. Intrinsic individuation can be grounded in haecceities, or absolute discernibility. Contextual individuation can be grounded in relations, but this is compatible with absolute, relative or weak discernibility. Contextual individuation is compatible with the denial of haecceitism, and this is more harmonious with science. Structuralism implies contextual individuation. In mathematics contextual individuation is in general primitive. In physics contextual individuation may be grounded in relations via (...)
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  • Criteria of identity and structuralist ontology.Hannes Leitgib & 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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  • Scientific structuralism: On the identity and diversity of objects in a structure.James Ladyman - 2007 - Aristotelian Society Supplementary Volume 81 (1):23–43.
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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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  • Dummett on abstract objects.George Duke - 2012 - New York: Palgrave-Macmillan.
    This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.
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  • S cientific S tructuralism: O n the I dentity and D iversity of O bjects in a S tructure.James Ladyman - 2007 - Aristotelian Society Supplementary Volume 81 (1):23-43.
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  • Mathematical structuralism and the Identity of Indiscernibles.Jac Ladyman - 2005 - Analysis 65 (3):218-221.
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