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

作者：H. Leitgeb · 发表于：Philosophia Mathematica · 年份：2020 · DOI：10.1093/philmat/nkaa009 · 被引用次数：10

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.