Difference between revisions of "Contradiction, law of"
From Encyclopedia of Mathematics
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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 | 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|constructive propositional calculus]] (cf. also [[Propositional calculus|Propositional calculus]]). | This formula is derivable in classical as well as in intuitionistic [[Constructive propositional calculus|constructive propositional calculus]] (cf. also [[Propositional calculus|Propositional calculus]]). | ||
Latest revision as of 13:51, 30 December 2018
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: http://encyclopediaofmath.org/index.php?title=Contradiction,_law_of&oldid=18707
Contradiction, law of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contradiction,_law_of&oldid=18707
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article