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Originally posted by Meerkat:
just as double negative is correct in French (I believe that this particular grammar came from Haiti, if I remember my linguistics classes right).
Perhaps some native French speakers can contribute, but as I remember my French and my linguistics course (singular), the negations in French are not so much "double negative" as the negative moneme taking the form of two words. Combining several of them, such as "Personne n'a rien fait a aucun d'eux," isn't a double-negative because there's only one "ne" no matter how many other negative words are used.

Of course, since in spoken French the "ne" is less and less often enunciated clearly....

French makes the original question a little more straightforward, with "Oui - Yes" "Non - No" and "Si - Your negative statement is incorrect; the truth is positive."

"Je ne peux rien faire?"
"Mais si!"

If nothing could be done, I would expect a "Non," though.