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Difference between revisions of "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
 
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
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025910/c0259101.png" /></td> </tr></table>
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$$\neg(A\&\neg A)$$
  
 
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]]).

Revision as of 14:15, 17 March 2014

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

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

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
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article