id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
en-wikipedia-org-7278		Contradiction - Wikipedia			.html	text/html	2970	354	59	;[2] a proposition is a contradiction if false can be derived from it, using the rules of the logic. The notion of contradiction in an axiomatic system and a proof of its consistency[edit] When Emil Post, in his 1921 "Introduction to a General Theory of Elementary Propositions", extended his proof of the consistency of the propositional calculus (i.e. the logic) beyond that of Principia Mathematica (PM), he observed that with respect to a generalized set of postulates (i.e. axioms), he would no longer be able to automatically invoke the notion of "contradiction"—such a notion might not be contained in the postulates: Since the ordinary notion of consistency involves that of contradiction, which again involves negation, and since this function does not appear in general as a primitive in [the generalized set of postulates] a new definition must be given.[9] "Contradiction (logic)".	./cache/en-wikipedia-org-7278.html	./txt/en-wikipedia-org-7278.txt