Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
DOUBLE NEGATIVE
Most kinds of double negative are inappropriate in spoken and written Standard English, except in jocular use: Dont never say that again. I cant do nothing about it. Eighteenth-century grammarians decided that since two negatives made a positive in mathematics and logic, they must do so in spoken and written English too. This was not always so, however, and the double negative remains one of the best illustrations of what was once a perfectly acceptable locution being driven by the decisions of grammarians, not out of the language, but out of Standard use. Chaucer used double and even triple negatives, and so did Shakespeare: these were simply powerful, heavily stressed, multiple negatives. And many speakers still use these constructions today, even though they are now shibboleths that mark speakers of Vulgar English.
Cant hardly is usually also classed as a double negative. You cant hardly expect her to be grateful, when analyzed, is doubly negative, in that You cant expect her to be grateful is renegated by the overlay of You can hardly expect her to be grateful. Other adverbs of a negative quality, such as scarcely, are also considered double negatives when used with a negative auxiliary such as cant or cannot.
Another kind of double negative occurs mostly in relatively Formal writing and at the higher levels of speech: Let me give you my address now, in the not unlikely event that the train is late. I was not uncomfortable on the terrace. The not un- construction can be the mark of the careful qualifier, the thoughtful speaker or writer trying to achieve an accuracy that may be, in fact, not inappropriate, but is, not improbably, hard to achieve; after all, if an act is described as not unwitting, it must be deliberate. Avoid pussyfooting unless you really must be that precise. Someone, somewhere, will dislike this sort of double negative because it is needlessly opaque and sounds stuffy. If it obtrudes, even when you think you are being amusing, it will not amuse. See LITOTES.