Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics

Synthese 190 (12):2141-2164 (2013)
  Copy   BIBTEX

Abstract

In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according to some speculative research programs

Author's Profile

Jean-Pierre Marquis
Université de Montréal

Analytics

Added to PP
2012-07-20

Downloads
399 (#47,403)

6 months
101 (#50,512)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?