law of double negation

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English[edit]

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Noun[edit]

law of double negation (uncountable)

  1. (logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically:  \neg \neg A \to A .
    • The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let  A = (0,1) \cup (1,2) . Then  \neg A = (-\infty,0) \cup (2,\infty) ,  \neg \neg A = (0,2) ,   \neg \neg A \to A = (-\infty,1) \cup (1,\infty) \ne \mathbb{R} .