Law of excluded middle

Not to be confused with fallacy of the excluded middle.
This article uses forms of logical notation. For a concise description of the symbols used in this notation, see List of logic symbols.

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).

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.

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