On the Exhaustion of Mathematical Entities by Structures

Axiomathes 24 (2):167-180 (2014)
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Abstract

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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Citations of this work

Identifying finite cardinal abstracts.Sean C. Ebels-Duggan - 2020 - Philosophical Studies 178 (5):1603-1630.
Multiplicity and indiscernibility.Adrian Heathcote - 2020 - Synthese 198 (9):8779-8808.
Five Indistinguishable Spheres.Adrian Heathcote - 2022 - Axiomathes 32 (2):367-383.
Countability and self-identity.Adrian Heathcote - 2021 - European Journal for Philosophy of Science 11 (4):1-23.

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References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.

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