Duality as a category-theoretic concept

Corfield, David (2015) Duality as a category-theoretic concept. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, . ISSN 1355-2198. (doi:https://doi.org/10.1016/j.shpsb.2015.07.004) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.shpsb.2015.07.004

Abstract

In a paper published in 1939, Ernest Nagel described the role that projective duality had played in the reformulation of mathematical understanding through the turn of the nineteenth century, claiming that the discovery of the principle of duality had freed mathematicians from the belief that their task was to describe intuitive elements. While instances of duality in mathematics have increased enormously through the twentieth century, philosophers since Nagel have paid little attention to the phenomenon. In this paper I will argue that a reassessment is overdue. Something beyond doubt is that category theory has an enormous amount to say on the subject, for example, in terms of arrow reversal, dualising objects and adjunctions. These developments have coincided with changes in our understanding of identity and structure within mathematics. While it transpires that physicists have employed the term ‘duality’ in ways which do not always coincide with those of mathematicians, analysis of the latter should still prove very useful to philosophers of physics. Consequently, category theory presents itself as an extremely important language for the philosophy of physics.

Item Type: Article
Uncontrolled keywords: Duality; Mathematics; Category theory
Subjects: B Philosophy. Psychology. Religion
B Philosophy. Psychology. Religion > B Philosophy (General)
Divisions: Faculties > Humanities > School of European Culture and Languages
Faculties > Humanities > School of European Culture and Languages > Philosophy
Depositing User: Jacqui Martlew
Date Deposited: 15 Feb 2017 12:16 UTC
Last Modified: 17 Feb 2017 09:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60387 (The current URI for this page, for reference purposes)
Corfield, David: https://orcid.org/0000-0003-0432-3221
  • Depositors only (login required):