On the Exhaustion of Mathematical Entities by Structures |
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Authors: | Adrian Heathcote |
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Affiliation: | 1. Department of Philosophy, The University of Sydney, Sydney, Australia
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Abstract: | 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. |
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