law of double negation

noun

The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

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Meanings

noun
  1. human sciencesThe statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

    The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A#61;(0,1)#92;cup(1,2). Then #92;negA#61;(-#92;infty,0)#92;cup(2,#92;infty), #92;neg#92;negA#61;(0,2), #92;neg#92;negA#92;toA#61;(-#92;infty,1)#92;cup(1,#92;infty)#92;ne#92;mathbb#123;R#125;.

Cite this entry
APA

law of double negation. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/law%20of%20double%20negation

MLA

“law of double negation.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/law%20of%20double%20negation. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “law of double negation,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/law%20of%20double%20negation.

Source: law of double negation on Wiktionary, CC BY-SA 4.0.