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Leitgeb, Hannes (2020): On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A. In: Philosophia Mathematica, Vol. 28, No. 3: pp. 317-346
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This is Part A of an article that defends non-eliminative structuralism about mathematics by means of a concrete case study: a theory of unlabeled graphs. Part A summarizes the general attractions of non-eliminative structuralism. Afterwards, it motivates an understanding of unlabeled graphs as structures sui generis and develops a corresponding axiomatic theory of unlabeled graphs. As the theory demonstrates, graph theory can be developed consistently without eliminating unlabeled graphs in favour of sets;and the usual structuralist criterion of identity can be applied successfully in graph-theoretic proofs. Part B will turn to the philosophical interpretation and assessment of the theory.