Haecceities and Mathematical Structuralism

Philosophia Mathematica:84-111 (2018)

Authors
Christopher Menzel
Texas A&M University
Abstract
Recent work in the philosophy of mathematics has suggested that mathematical structuralism is not committed to a strong form of the Identity of Indiscernibles (II). José Bermúdez demurs, and argues that a strong form of II can be warranted on structuralist grounds by countenancing identity properties, or haecceities, as legitimately structural. Typically, structuralists dismiss such properties as obviously non-structural. I will argue to the contrary that haecceities can be viewed as structural but that this concession does not warrant Bermdez’s version of II but, rather, another easily falsified version. I close with some reflections on reference vis-à-vis structurally indiscernible objects.
Keywords mathematical structuralism  haecceities
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DOI 10.1093/philmat/nkw030
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References found in this work BETA

Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
Identity and Indiscernibility.K. Hawley - 2009 - Mind 118 (469):101-119.

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