Theorems in propositional logic | Rules of inference | Classical logic

Double negation

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." 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. Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic, but it is disallowed by intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: "This is the principle of double negation, i.e. a proposition is equivalent of the falsehood of its negation." (Wikipedia).

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Related pages

Converse (logic) | Negation | Theorem | Hypothetical syllogism | Tautology (logic) | Propositional calculus | Hilbert system | Metalogic | Well-formed formula | Minimal logic | Sequent | Symbol (formal) | Inference | Law of thought | Involution (mathematics) | Formal proof | Validity (logic) | Equivalence relation | Principia Mathematica | Intuitionistic logic | Logical equivalence | Bertrand Russell | Double-negation translation | Alfred North Whitehead | Classical logic | List of Hilbert systems