Parts of Structures

Article History & Philosophy Of Science

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

Hannes Leitgeb

Summary: This article defends non-eliminative structuralism about mathematics using a concrete case study of a theory of unlabeled graphs. It demonstrates how the theory avoids well-known problems concerning identity, objecthood, and reference, and discusses its relation to set theory and remaining tasks for non-eliminative structuralists.

PHILOSOPHIA MATHEMATICA (2021)

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Article Philosophy

Non-eliminative Structuralism, Fregean Abstraction, and Non-rigid Structures

John Wigglesworth

Summary: The paper presents a solution to the problem of non-rigid structures in non-eliminative mathematical structuralism by expanding the languages used to describe mathematical structures. The solution is deemed philosophically acceptable to those who endorse mathematical structuralism based on Fregean abstraction principles.

ERKENNTNIS (2021)

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Article History & Philosophy Of Science