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Definition 2024

law_of_double_negation

law of double negation

English

Noun

law of double negation ‎(uncountable)

(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 $\neg A=(-\infty ,0)\cup (2,\infty )$ , $\neg \neg A=(0,2)$ , $\neg \neg A\to A=(-\infty ,1)\cup (1,\infty )\neq \mathbb {R}$ .