, 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


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.


Identity Complex numbers Natural numbers Mathematical structuralism Mathematical objects 



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


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.The Ohio State UniversityColumbusUSA

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