none that i can remember right now, i cannot think of a valid danish sentence in danish that contains a double negative (i'm sure there is)
What we are seeing here is not a double negative, but rather an answer to a statement "Det er umuligt (It is impossible)", where we first make a disagreement and then a statement of the opposite.
A quick distraction later i realize you might be referring to "ikke u[word]", not "Nej .. ikke" In that case it is (almost) always a positive. I'm saying almost because there are untold number of exceptions in danish, but i cannot remember anything for this.
Thank you for the reply. I think this isn't technically double negative but it's close so it gave the idea to ask about it. I meant the second interpretation "ikke u[word]". Here the meaning is apparent as you described it. But could I say something like "We can't not go" (and how would I say it)? Every English teacher said "no double negatives" but you can informally hear sentences like this and they are meant as the positive sentence (or at least I understand them this way) but add some doubt, hesitation or are trying to not say something potentially offensive. Is this mirrored in Danish?
We don't have a lot of negatives in danish, the only ones i can think of is ikke and u[word], so double negatives are only really present in cases as the one above.
your specific example can be translated to "vi kan ikke blive væk" but that is not a direct translation. Instead it means "we cannot stay away"
While i'm not quite familiar with english to know the concept you are describing in your second ("add some doubt, hesitation or are trying to not say something potentially offensive"), so i might misunderstand here, but the closest thing we have in danish is negating a word that have an opposite to imply that the opposite was expected: "Det er ikke helt dumt" (That is not totally stupid)", where it is implied that stupid is to be expected from that person. This is mostly used among friends as a jest, not formally.
So you just can't put two verbs negated by ikke in the same sentence. Even when you want to do this you can negate only one and use "opposite" verb for the other. The second one is exactly what I meant. I interpret the English translation of your example as either surprise (as you suggested) or hesitation to give credit (instead of saying "That's a good idea") or not the same level of the property as the positive sentence would convey (not a dumb idea, but still not quite smart). All in all it seems that the use is pretty similar to English and I don't have to flip a switch in my head :-). Thank you very much!
I thought the same thing when reading this sentence. It's not grammatically incorrect in English to say , "no, it is not impossible", although "no, it is possible" seems to sound better and would make our English teachers happier. Maybe Danish grammarians don't have the same hang-ups?