Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 2725. μή is often used with verbs and other expressions of asseveration and belief, after which we might expect οὐ with the infinitive in indirect discourse. Such verbs are those signifying to hope, expect, promise, put trust in, be persuaded, agree, testify, swear, etc. The use of μή indicates strong assurance, confidence, and resolve; and generally in regard to the future. Cp. 2723.

ἐλπὶς ὑ_μᾶς μὴ ὀφθῆναι there is hope that you will not be seen X. C. 2.4.23, ““ὑπι_σχνοῦντο μηδὲν χαλεπὸν αὐτοὺς πείσεσθαι” they promised that they should suffer no harm” X. H. 4.4.5, ““πιστεύω . . . μὴ ψεύσειν με ταύτα_ς τὰ_ς ἀγαθὰ_ς ἐλπίδας” I trust that these good hopes will not deceive me” X. C. 1.5.13, ““θαυμάζω ὅπως ἐπείσθησαν Ἀθηναῖοι Σωκράτην περὶ θεοὺς μὴ σωφρονεῖν” I wonder how the Athenians were persuaded that Socrates did not hold temperate opinions regarding the gods” X. M. 1.1.20, ““ὁμολογεῖ μὴ μετεῖναί οἱ μακρολογία_ς” he acknowledges that he cannot make a long speech” P. Pr. 336b, ““αὐτὸς ἑαυτοῦ καταμαρτυρεῖ μὴ ἐξ ἐκείνου γεγενῆσθαι” he proves by his own testimony that he is not his son” D. 40.47, ““ὤμοσεν ἦ μὴν μὴ εἶναί οἱ υἱὸν ἄλλον μηδὲ γενέσθαι πώποτε” he swore that he had no other son and that none other had ever been born to him” And. 1.126, ““ὤμνυε . . . μηδὲν εἰρηκέναι” he swore that he had said nothing” D. 21.119, ““ὀμοῦμαι μήποτ᾽ . . . ἀλεξήσειν κακὸν ἦμαρ” I will swear that I will never ward off the evil day” Φ 373. Cp. Ar. Vesp. 1047, 1281, And. 1.90, Lyc. 76. With ὄμνυ_μι the infinitive may refer to the present, past, or future.