Law of the excluded middle
From Encyclopedia of Mathematics
The law in classical logic stating that one of the two statements "A" or "not A" is true. The law of the excluded middle is expressed in mathematical logic by the formula 
, where 
denotes disjunction and 
denotes negation. From the intuitionistic (constructive) point of view, establishing the truth of a statement 
means establishing the truth of either 
or 
. Since there is no general method for establishing in a finite number of steps the truth of an arbitrary statement, or of that of its negation, the law of the excluded middle was subjected to criticism by representatives of the intuitionistic and constructive directions in the foundations of mathematics (cf. Intuitionism; Constructive mathematics).
Comments
References
| [a1] | D. van Dalen (ed.) , Brouwer's Cambridge lectures on intuitionism , Cambridge Univ. Press (1981) |
How to Cite This Entry:
Law of the excluded middle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Law_of_the_excluded_middle&oldid=31386
Law of the excluded middle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Law_of_the_excluded_middle&oldid=31386
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article