Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 2742. When a verb of denying, refusing, hindering, forbidding, etc., is itself negatived, either directly or by appearing in a question expecting a negative answer, the infinitive has μὴ οὐ. Here both the introductory clause and the dependent clause have virtually an affirmative sense.

οὐδεὶς πώποτ᾽ ἀντεῖπεν μὴ οὐ καλῶς ἔχειν αὐτούς (τοὺς νόμους) no one ever denied that they (the laws) were excellent D. 24.24, τίνα οἴει ἀπαρνήσεσθαι μὴ οὐχὶ καὶ αὐτὸν ἐπίστασθαι τὰ δίκαια; who, think you, will deny that he too understands what is just? P. G. 461c ( = οὐδεὶς ἀπαρνήσεται). But μὴ οὐ is not used after οὔ φημι, οὐκ ἐῶ, οὐκ ἐθέλω (2692 a).

a. μὴ οὐ with the infinitive here, and elsewhere, is used only when the introductory word or words has an actual or a virtual negative. Since, in ἀρνοῦμαι μὴ ταῦτα δοᾶσαι I deny that I did this, μή confirms the negative idea in ἀρνοῦμαι, so in οὐκ ἀρνοῦμαι μὴ οὐ ταῦτα δρᾶσαι I do not deny that I did this, οὐ after the strengthening μή confirms the οὐ prefixed to the leading verb. Cp. “Je ne nie pas que je ne sois infiniment flatté” (Voltaire). In the first sentence μή repeats the ‘negative result’ of ἀρνοῦμαι (single sympathetic negative, untranslatable); in the second sentence οὐ is repeated with the infinitive to sum up the effect of οὐκ ἀρνοῦμαι (double sympathetic negative; both untranslatable). After verbs negative in meaning (deny, etc.) μή and μὴ οὐ cannot be translated in modern English (see 2739). After verbs not negative in character but preceded by a negative, and after virtually negative expressions, μή or μὴ οὐ has a negative force (2745, 2746).

b. μὴ οὐ with the infinitive regularly indicates a certain pressure of interest on the part of the person involved.