Contradiction, law of

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The logical law stating that no proposition can be true simultaneously with its negation. In the language of propositional calculus the law of contradiction is expressed by

$$\neg(A\mathbin\&\neg A)$$

This formula is derivable in classical as well as in intuitionistic constructive propositional calculus (cf. also Propositional calculus).

How to Cite This Entry:
Contradiction, law of. Encyclopedia of Mathematics. URL:,_law_of&oldid=43574
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article