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

Authors
Teresa Kouri Kissel
Old Dominion University
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
Keywords Identity  Complex numbers  Natural numbers  Mathematical structuralism  Mathematical objects
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DOI 10.1007/s10516-014-9241-z
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References found in this work BETA

Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2008 - Philosophia Mathematica 16 (3):388-396.
The Identity Problem for Realist Structuralism.J. Keranen - 2001 - Philosophia Mathematica 9 (3):308--330.
Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of Science Today. Clarendon Press.

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Citations of this work BETA

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