A reply to Heathcote's On the exhaustion of mathematical entities by structures

Teresa Kouri

pp. 345-357

in: Axiomathes 25 (3), 2015.

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.