there is a song in russian to the tune of brother john:
i don’t know
i don’t know
nothing
nothing
nothing don’t know
nothing don’t know
good
good.
it does get laughs.
That’s cool - thanks for the info 
Exactly.
When Mick Jagger sings, “I can’t get no satisfaction,” does anybody truly believe that he can, actually, get satisfaction?
True 'nuff. But my question was in the context of formal grammar rules.
What do you mean by “formal grammar rules”? I mean, in the prescriptivist sense or the descriptivist sense?
In the prescriptivist sense, double negation (or negative concord, as it is sometimes called) fell out of favor for whatever reason – it had become associated with the lower class. In order to explain why double negation was “bad,” the whole mathematical logic reason (two negatives equals a positive) was invented and put into the grammar books we use in schools.
This, however, did not change the grammar people keep in their heads, and when someone hears someone using a double negative, we don’t get confused and think they mean it in the positive sense. Similarly, even those people who speak the most standard English can still, if they so chose, throw out a double negative and use it grammatically in the descriptive sense.
I’d be hesitant to call a construction a “double negative” unless it contains two things that would be grammatical single negatives. I don’t know Russian, but assuming that it’s the same as in French, the construction “ne <verb> pas” isn’t really a double negative, since even though “ne” and “pas” are both parts of the negative construction, neither one of them is grammatical by itself without the other. “ne <verb>” or “<verb> pas” isn’t a single negative, since neither is grammatical, so “ne <verb> pas” can’t be a double negative.
As for English multiple negatives, the most interesting construction I’ve seen was from the Family Ties theme song: “There ain’t no nothing we can’t love each other through”. There’s four negatives in that sentence, and they end up working out to a positive (“we can love each other through anything”), but it’s a combination of reinforced negatives and negated negatives: “Ain’t no nothing” all reinforce each other to form a strong negative of the sort that elementary-school grammar teachers try to discourage, but then the “can’t” flips that strong negative over into a positive.
There’s also what I would call an exclusionary positive that can really only be made from double negating. “You can not not do that.” It is functionally different from “you can do that” in that it completely excludes the negative case from the equation, and is even slightly different from adding the word “only” which could mean “if you are going to do something, that is the only thing you may do in this case, but may also choose to do nothing.”
You assume incorrectly - it’s not like in French, where ‘ne’ is not an independent negative. If you just want to have a negative sentence such as ‘I don’t know’, you would get’ - ‘Ya ne znayu’, ‘ne’ meaning not here. If the answer to some question would be ‘no one’, you would get ‘nikto’; but if you want to say ‘no one knows’, you need both ‘ne’ and ‘nikto’, resulting in ‘nikto ne znayet’.
I have no idea what that means. I can hear somebody sing, “I Ain’t Got Nobody” and of course I understand what they mean. I can also understand what somebody’s saying when they type, “LOL! RU TEH GHEY? NOOB! ROFLMAO!” But my ability to comprehend it doesn’t make it “correct” according to generally agreed-upon and formalized rules.
By “formal grammar rules” I simply mean opening up a typical English grammar textbook and finding it says, “don’t do that”. Specifically with regard to formal written or spoken communication, as opposed to the vernacular.
OK, but that still supports my main point. “Nikto ne znayet” still isn’t really a double negative, since “nikto znayet” isn’t a single negative. By contrast, in the English sentence “I didn’t do nothing”, you can reduce the sentence to either “I did nothing” or “I didn’t do anything”, removing a single one of the negatives, and be left with something that’s still grammatical.
I disagree. Nikto znayet is a single negative, it’s just not accepted, just like ‘I didn’t do nothing’ is considered to be wrong. But that doesn’t mean that it’s not a single negative, or that ‘nikto ne znayet’ is not a double negative. It is, in the very simple sense that it contains two negative elements, both of which can and do function independently.
That’s why you should have read the rest of her post.
In any case, it seems strange to only ask about formal speech, since the joke in question seems to imply that “2 negatives=positive” in English, which when you consider the language as a whole, is just not true. Even if you say that double negatives are not “correct,” it’s still not “because they equal a positive.” That is just silly. Language isn’t mathematics.
I did. The problem is that this is turning into an example of “can’t see the forest for the trees”. The question wasn’t about whether communication in English is still comprehensible when somebody uses a double-negative — actually, my OP wasn’t asking about English at all, I was asking about Russian. My primary reason for asking was this: I wasn’t sure if I was correctly remembering the non-English language mentioned in the joke. Since it is just a joke (or an adaptation of an actual quote, as ** ArmenE** pointed out) I think most English-speakers hearing the joke, assuming they took high school English classes, are going to remember being told that they shouldn’t use double-negatives. And that’s all that’s really necessary.
Because I assume the professor in the story/joke was speaking in the context of formalized grammar. Also, the odds are good that if you handed your English teacher an essay containing double-negatives, your English teacher is going to mark you down.
Well, it wouldn’t be correct in mathematics either. (-x) + (-y) = -z 
As in, it’s something that a native speaker might actually be expected to say? In that case, I concede the point.
A linguist would not be talking about the “formal” prescriptive grammar, just for the record.
Well, yes, but your thread had a false premise. And it’s also a partial answer to your question: English is an example of a language where a double negative can be used an an intensified negative.
Presumably this was a linguist (someone upthread posited J. L. Austen), and not a writing instructor, in which case they would probably not be talking about prescriptive grammar.
Unlike Russian, Esperanto is very clear about the double negative:
“When another negative word is used the word ne [“no,” “not”] is left out.”
In a book titled Dear Folks, a collection of letters from children, the text of one girl’s letter from camp is as follows:
“Hi Stinky Dear Daddy visiting day is in 2 weeks and dont not come.”
What do you suppose she meant by that?