Double negatives are grammatically correct English. Consider the sentence, "I do not think that course of action would be unwise."--that is a double negative, and I know of no one who thinks there's even a hint of problem with that sentence.

One facet of double negatives is that the English sense of negative + negative = positive isn't universal. In French, double negatives remain negative; consider "Je ne sais jamais rien." The literal translation is "I never know nothing," but the correct translation into English is "I never know anything."