Phrase guide

law of double negation

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: human-sciences, logic, mathematics, philosophy, sciences

Examples

  • 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;.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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