Grammar Puss - S Pinker
At this point, defenders of the standard are likely to pull out the notorious double negative, as in [I can't get no satisfaction.] Logically speaking, the two negatives cancel each other out, they teach; Mr. Jagger is actually saying that he is satisfied. The song should be entitled "I Can't Get [Any] Satisfaction."
But this reasoning is not satisfactory. Hundreds of languages require their speakers to use a negative element in the context of a negated verb. The so-called "double negative," far from being a corruption, was the norm in Chaucer's Middle English, and negation in standard French, as in [Je ne sais pas] where [ne] and [pas] are both negative, is a familiar contemporary example.
Come to think of it, standard English is really no different. What do [any], [even], and [at all] mean in the following sentences?
I didn't buy any lottery tickets.
I didn't eat even a single french fry.
I didn't eat fried food at all today.
Clearly, not much: you can't use them alone, as the following strange sentences show:
I bought any lottery tickets.
I ate even a single french fry.
I ate fried food at all today.
What these words are doing is exactly what [no] is doing in nonstandard American English, such as in the equivalent [I didn't buy no lottery tickets] -- agreeing with the negated verb. The slim difference is that nonstandard English co-opted the word [no] as the agreement element, whereas Standard English co-opted the word [any].