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A double negative is a construction occurring when two forms of grammatical negation are used in the same sentence. This is typically used to convey a different shade of meaning from a strictly positive sentence ("You're not unattractive" vs "You're attractive").
a. I have gone (affirmative) b. I have not gone (negative; have is the auxiliary) (9) a. He goes (affirmative) b. #He goes not (negative) but that wording is considered archaic and is rarely used. It is much more common to use the dummy auxiliary to render He does not go (since there is no auxiliary in the original sentence)
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.
In a three-form system, the affirmative response to a positively phrased question is the unmarked affirmative, the affirmative response to a negatively phrased question is the marked affirmative, and the negative response to both forms of question is the (single) negative. For example, in Norwegian the affirmative answer to "Snakker du norsk?"
The actual set of contexts that license particular polarity items is not as easily defined as a simple distinction between affirmative and negative sentences. Baker [ 2 ] noted that double negation may provide an acceptable context for positive polarity items:
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.
Although it semantically speaking comes natural that positive is the opposite of negative, and therefore should be completely synonymous with affirmative, grammatically speaking, once again they tend to be separate entities; depending on specificity.
Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises. For example: No fish are dogs, and no dogs can fly, therefore all fish can fly.