On the Exhaustion of Mathematical Entities by Structures
Axiomathes 24 (2):167-180 (2014)
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 pointDOI
10.1007/s10516-013-9223-6
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Citations of this work
A Reply to Heathcote’s: On the Exhaustion of Mathematical Entities by Structures.Teresa Kouri - 2015 - Axiomathes 25 (3):345-357.
Mohan Ganesalingam. The Language of Mathematics: A Linguistic and Philosophical Investigation. FoLLI Publications on Logic, Language and Information. [REVIEW]Andrew Aberdein - 2017 - Philosophia Mathematica 25 (1):143–147.
Identifying finite cardinal abstracts.Sean C. Ebels-Duggan - 2021 - Philosophical Studies 178 (5):1603-1630.
References found in this work
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931.Jean van Heijenoort (ed.) - 1967 - Cambridge: Harvard University Press.