On the other hand, double negatives formed with not followed by a word that begins with a negative prefix like un- or ir- are permissible in formal English.
This type of double negative is a stylistic device of understatement, a type of litotes: a figure of speech in which an affirmative is expressed by the negative of the contrary. Its use can convey a subtle difference in meaning that saying the same thing without not wouldn’t.
Some speakers who object to the “not un-” construction seem to believe that there’s a rule against it. This belief is bolstered by the often quoted example made up by George Orwell: “The not unblack dog chased the not unbrown cow across the not ungreen field.”
Orwell’s sentence is amusing, but simplistic. No English speaker is going to try to plant an un- on adjectives like black and green. Many English speakers, however, will use the “not un-” construction to achieve a nuanced meaning with adjectives like justifiable, intelligent, and convinced.
The following statements are not identical in meaning:
A note at the online Oxford Dictionaries site points out the difference: