On the exhaustion of mathematical entities by structures
There has been considerable discussion in the literature of one kind of identity problem that mathematical structuralism faces: the automorphism problem, in which the structure is unable to individuate the mathematical entities in its domain. Shapiro (Philos Math 16(3):285–309, 2008) has partly responded to these concerns. But I argue here that the theory faces an even more serious kind of identity problem, which the theory can't overcome staying within its remit. I give two examples to make the point.
Heathcote, A. (2014). On the exhaustion of mathematical entities by structures. Axiomathes 24 (2), pp. 167-180.
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