On p. 151, Mastronarde says, ‘Formal English does not tolerate double negatives, but in Greek idiom a simple negative can be followed by additional negative forms in the same clause with reinforcing emphasis. (The English translation has to convert the additional negatives to positive equivalents.)’
The example sentence he gives is:
οὐκ ἐπαινέσομαι οὔτε τοὺς Ἀθηναίους οὔτε τοὺς βαρβάρους.
I shall not praise either the Athenians or the Persians.
I am a bit bothered by that “can” of Mastronarde’s. I am at home with negative polarity in Russian, where it not only can but must be “I never told nobody nothing.” If this is a stylistic choice in Greek, I can imagine things could get confusing.
No man will not get punishment for being unjust.(=‘Everyone who is unjust will be punished.’; the second negative is simple and both negatives belong to the same predicate, so they cancel each other.)
56.4 If the second negative is a compound, it intensifies the first (only one should be translated as negative):
It was not because they did not throw (lit. ‘not because of the not-throwing’) that they did not hit him. The first οὐ modifies the prepositional phrase διὰ …ἀκοντίζειν, μὴ modifies ἀκοντίζειν, the second οὐκ modifies ἔβαλον: the suggestion is ‘It was not for a lack of trying that they missed him’.