Is the principle of contradiction a consequence of \(x^2=x\)?
type: Item
instance of: scholarly article
title: Is the principle of contradiction a consequence of \(x^2=x\)?
zbMATH Open document ID: 1408.03003
published in: Logica Universalis
publication date: 2018-08-06T00:00:00Z
review text: This paper examines Boole's three-step proof of the principle of non-contradiction (for Boole \(x(x-1)=0\)) from \(x^2=x\) in is original form, in first-order logic, in a Boolean algebra on \((0,1)\), in set theory, and on classical propositional logic. The discussion is punctuated by a variety of matters of dubious relevance. The Greek etymology of ``anecdote'' is described, but not its use as a pejorative for ``clinical observation'' in contrast to double blind large randomised sample field trials in medical research. The word ``class'' in early set theory (German \textit{Menge}) is conflated with ``class'' in Marxist political theory (German \textit{Klasse}) in a way reminiscent of \textit{A. Sokal}'s paper [``Transgressing the boundaries: toward a transformative hermeneutics of quantum gravity'', Social Text, Spring/Summer, 217--252 (1996)]. Observations such as that in equations letters used as variables are italicised, are described in great detail but no consequence is drawn from them. The paper is illustrated with photographs, including one of the mountain named after the uncle of Boole's wife.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 03B53
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03B05
Mathematics Subject Classification ID: 03B10
Mathematics Subject Classification ID: 03G05
zbMATH DE Number: 6913948
zbMATH Keywords: Boole
zbMATH Keywords: principle of contradiction
zbMATH Keywords: laws of thought
zbMATH Keywords: symbolic logic
zbMATH Keywords: subtraction
zbMATH Keywords: universal logic
zbMATH Keywords: Boolean algebra
zbMATH Keywords: square of opposition
author: Jean-Yves Béziau
reviewed by: Jim Mackenzie
MaRDI profile type: Publication
full work available at URL: s11787-018-0188-5
OpenAlex ID: W2515804137
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DOI: 10.1007/S11787-018-0188-5