law of double negation

law of double negation

  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} .

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.019
Offline English dictionary