Foundations of Mathematical Structuralism

Georg Schiemer (Editor), John Wigglesworth (Editor)

Publications: BookSpecial IssuePeer Reviewed

Abstract

Structuralism, the view that mathematics is the science of structures, can be characterized as a philosophical response to a general structural turn in modern mathematics. Structuralists aim to understand the ontological, epistemological, and semantical implications of this structural approach in mathematics. Theories of structuralism began to develop following the publication of Paul Benacerraf’s paper ‘What numbers could not be’ in 1965. These theories include non-eliminative approaches, formulated in a background ontology of sui generis structures, such as Stewart Shapiro’s ante rem structuralism and Michael Resnik’s pattern structuralism. In contrast, there are also eliminativist accounts of structuralism, such as Geoffrey Hellman’s modal structuralism, which avoids sui generis structures.
Original languageGerman
Place of PublicationOxford
PublisherOxford Academic
Number of pages157
Publication statusPublished - 31 Aug 2020

Publication series

SeriesPhilosophia Mathematica: philosophy of mathematics, its learning, and its application
Number3
Volume28
ISSN0031-8019

Austrian Fields of Science 2012

  • 603109 Logic

Cite this