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(2015) Axiomathes 25 (3).

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

Teresa Kouri

pp. 345-357

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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Kouri, T. (2015). A reply to Heathcote's On the exhaustion of mathematical entities by structures. Axiomathes 25 (3), pp. 345-357.

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