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International Studies in Phenomenology and Philosophy

Journal | Volume | Article

168408

On the exhaustion of mathematical entities by structures

Adrian Heathcote

pp. 167-180

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.

Publication details

Published in:

(2014) Axiomathes 24 (2).

Pages: 167-180

Full citation:

Heathcote Adrian (2014) „On the exhaustion of mathematical entities by structures“. Axiomathes 24 (2), 167–180.