Law of excluded middle

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In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. Symbolically expressed, the law is p ∨ ¬ p {\displaystyle p\lor \neg p} . The law of the excluded middle is also known as the law/principle of the excluded third, in Latin principium tertii exclusi. Another Latin designation for the law is tertium non datur or "no third [possibility] is given". In classical logic, the law of the excluded middle is taken as a tautology. Intuitionistic logic, by contrast, does not affirm the law. To prove p ∨ ¬ p {\displaystyle p\lor \neg p} in intuitionist logic, it is necessary to prove either p {\displaystyle p} or ¬ p {\displaystyle \neg p} .

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