Double negation
Propositional logic theorem / From Wikipedia, the free encyclopedia
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This article is about the logical concept. For the linguistic concept, see double negative.
In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true".[citation needed] This is expressed by saying that a proposition A is logically equivalent to not (not-A), or by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.[1]
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Type | Theorem |
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Statement | If a statement is true, then it is not the case that the statement is not true." |
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Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic,[2] but it is disallowed by intuitionistic logic.[3] The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:
- [4]
- "This is the principle of double negation, i.e. a proposition is equivalent of the falsehood of its negation."