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Axiomathes

, Volume 25, Issue 3, pp 345–357 | Cite as

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

  • Teresa KouriEmail author
Original Paper
  • 132 Downloads

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 

Notes

Acknowledgments

I am grateful to Stewart Shapiro for encouragement and valuable feedback on several earlier drafts, and to an anonymous reviewer for helpful comments throughout.

References

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  6. Shapiro S (2000) Philosophy of mathematics: structure and ontology. Oxford University Press, OxfordCrossRefGoogle Scholar
  7. Shapiro S (2008) Identity, indiscernibility, and ante rem structuralism: the tale of i and \(-\)i. Philos Math 16(3):285–309CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.The Ohio State UniversityColumbusUSA

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