On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A

Leitgeb, Hannes (2020): On Non-Eliminative Structuralism. Unlabeled Graphs as a Case Study, Part A. In: Philosophia Mathematica, Bd. 28, Nr. 3: S. 317-346

Abstract

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Philosophie, Wissenschaftstheorie und Religionswissenschaft
• Themengebiete: 100 Philosophie und Psychologie > 100 Philosophie
• ISSN: 0031-8019
• Sprache: Englisch