Haecceities and Mathematical Structuralism

Philosophia Mathematica 26 (1):84-111 (2018)
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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 Bermúdez’s version of II but, rather, another easily falsified version. I close with some reflections on reference vis-à-vis structurally indiscernible objects.

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Christopher Menzel
Texas A&M University

References found in this work

Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
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Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.

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