Q: I recently heard someone on WNYC say “I know of no place that doesn’t have music.” Shouldn’t it be “I do not know of any place that does not have music”?
A: The statement “I know of no place that doesn’t have music” is perfectly correct English, though a bit convoluted. “I know of no place” is grammatically equivalent to “I don’t know of any place.” And by the way, the contractions “don’t” and “doesn’t” are respectable English.
So the longer statement simply means “I don’t know of any place that doesn’t have music.” Or (leaving the speaker out of it), “Every place has music.” Or, “No place lacks music.”
They’re all grammatically correct, and they’re all legitimate ways of expressing the same idea.
The statement as given has two negatives, a kind of construction that bothers some people. But “I know of no place that doesn’t have music” isn’t an example of the kind of “double negative” that’s grammatically incorrect (like “I didn’t do nothing”).