Difference between revisions of "Law of the excluded middle"
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| − | 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 | + | {{TEX|done}} |
| + | 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 $A\lor\neg A$, where $\lor$ denotes [[Disjunction|disjunction]] and $\neg$ denotes [[Negation|negation]]. From the intuitionistic (constructive) point of view, establishing the truth of a statement $A\lor\neg A$ means establishing the truth of either $A$ or $\neg A$. 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|Intuitionism]]; [[Constructive mathematics|Constructive mathematics]]). | ||
Latest revision as of 12:49, 17 March 2014
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 $A\lor\neg A$, where $\lor$ denotes disjunction and $\neg$ denotes negation. From the intuitionistic (constructive) point of view, establishing the truth of a statement $A\lor\neg A$ means establishing the truth of either $A$ or $\neg A$. 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) |
Law of the excluded middle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Law_of_the_excluded_middle&oldid=17830