Is the principle of contradiction a consequence of \(x^2=x\)?
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.
scientific article; zbMATH DE number 6913948
scientific article