A Reply to Heathcote’s: On the Exhaustion of Mathematical Entities by Structures

Axiomathes 25 (3):345-357 (2015)
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Abstract

In this article I respond to Heathcote’s “On the Exhaustion of Mathematical Entities by Structures”. I show that his ontic exhaustion issue is not a problem for ante rem structuralists. First, I show that it is unlikely that mathematical objects can occur across structures. Second, I show that the properties that Heathcote suggests are underdetermined by structuralism are not so underdetermined. Finally, I suggest that even if Heathcote’s ontic exhaustion issue if thought of as a problem of reference, the structuralist has a readily available solution

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Teresa Kouri Kissel
Old Dominion University

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Identifying finite cardinal abstracts.Sean C. Ebels-Duggan - 2020 - Philosophical Studies 178 (5):1603-1630.

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References found in this work

Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of science today. New York: Oxford University Press.
Criteria of identity and structuralist ontology.Hannes Leitgib & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.

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