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.
Original Publication Citation
Kouri, T. (2015). A reply to Heathcote’s "On the exhaustion of mathematical entities by structures." Axiomathes, 25(3), 345-357. doi:10.1007/s10516-014-9241-z
0000-0001-6519-1723 (Kouri Kissel)
Kouri, Teresa, "A Reply to Heathcote's "On the Exhaustion of Mathematical Entities by Structures"" (2015). Philosophy Faculty Publications. 55.