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Discussing English grammar, the term "double negative" is often, [9] though not universally, [10] [11] applied to the non-standard use of a second negative as an intensifier to a negation. Double negatives are usually associated with regional and ethnical dialects such as Southern American English , African American Vernacular English , and ...
Double negative elimination is a theorem of classical logic, but not of weaker logics such as intuitionistic logic and minimal logic. Double negation introduction is a theorem of both intuitionistic logic and minimal logic, as is ¬ ¬ ¬ A ⊢ ¬ A {\displaystyle \neg \neg \neg A\vdash \neg A} .
Double negatives as negative concord – e.g., "We don't need no education" [15] Certain double modals – e.g., "You might could do it" – not considered standard, but used for example in Southern American English [16] Double copula [17] – e.g., "What has to happen is, is that the money has to come from somewhere" [18] Preposition stranding ...
But the term "double negative" can sometimes refer to the standard English constructions called litotes or nested negatives, e.g., using "He is not unhealthy" to mean "He is healthy". In some cases, nested negation is used to convey nuance, uncertainty, or the possibility of a third option other than a statement or its negation.
Much of the criticism comes from the double negative pairing of the prefix (ir-) and suffix (-less), which stands in contrast to the negative polarity exhibited by most standard varieties of English. Critics also use the argument that irregardless is not – or should not be – a word at all, because it lacks the antecedents of a "bona fide ...
Within a system of classical logic, double negation, that is, the negation of the negation of a proposition , is logically equivalent to . Expressed in symbolic terms, . In intuitionistic logic, a proposition implies its double negation, but not conversely. This marks one important difference between classical and intuitionistic negation.
Because standard English does not have negative concord, that is, double negatives are not used to intensify each other, the language makes frequent use of certain NPIs that correspond in meaning to negative items, and can be used in the environment of another negative.
In rhetoric, litotes (/ l aɪ ˈ t oʊ t iː z, ˈ l aɪ t ə t iː z /, US: / ˈ l ɪ t ə t iː z /), [1] also known classically as antenantiosis or moderatour, is a figure of speech and form of irony in which understatement is used to emphasize a point by stating a negative to further affirm a positive, often incorporating double negatives for effect.