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Leitgeb, Hannes (2021): On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part B. In: Philosophia Mathematica, Vol. 29, No. 1: pp. 64-87

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This is Part B of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A motivated an understanding of unlabeled graphs as structures sui generis and developed a corresponding axiomatic theory of unlabeled graphs. Part B turns to the philosophical interpretation and assessment of the theory: it points out how the theory avoids well-known problems concerning identity, objecthood, and reference that have been attributed to non-eliminative structuralism. The part concludes by explaining how the theory relates to set theory, and what remains to be accomplished for non-eliminative structuralists.

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