Unity and identity of opposites in calculus and physics
type: Item
instance of: scholarly article
title: Unity and identity of opposites in calculus and physics
zbMATH Open document ID: 0858.18002
DOI: 10.1007/BF00122250
author: F. William Lawvere
published in: Applied Categorical Structures
publication date: 1997-03-25T00:00:00Z
review text: Unity and Identity (UI) in a category in the title of this paper means a map equipped with two sections, or equivalently, a common retraction for two subobjects whose underlying objects are identical. The particularly important case of UI is UIAO (unity and identity of adjointly opposites), known also as an ``essential localization''. The author argues that a significant fraction of notoriously disputable dialectical philosophy, developed by Hegel, Marx and others, can be grasped firmly with the above mathematical apparatus of UI and UIAO. The examples discussed in the paper include van der Waals' formula for the unity of the liquid and gaseous states, the foundations of differential calculus, and \textit{W. Noll}'s [Arch. Ration. Mech. Anal. 122, No. 3, 197-212 (1993; Zbl 0787.73006)] generalization of the usual concept of continuous body.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 18A05
zbMATH DE Number: 934053
zbMATH Keywords: unity and identity
zbMATH Keywords: essential localization
zbMATH Keywords: dialectical philosophy
zbMATH Keywords: van der Waals' formula
MaRDI profile type: Publication
cites work: Q3978982
cites work: Q4883222
cites work: Cohesive Toposes and Cantor's 'lauter Einsen'
cites work: The geometry of contact, separation, and reformation of continuous bodies
cites work: Homotopical algebra
description: scientific article; zbMATH DE number 934053