William Watson Goodwin, Syntax of the Moods and Tenses of the Greek Verb

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[*] 13. This is seen especially in independent sentences, where the optative either expresses a wish or exhortation, or is used (regularly with ἄν or κέ) in a potential sense.

Thus ἴοιμεν, may we go, corresponds as a weaker form to ἴωμεν, let us go. Corresponding to ἐξελθών τις ἰδέτω, let some one go out and see, we have “ἐξελθών τις ἴδοι,” “may some one go out and see,” Od. xxiv. 491 . Ἕλοιτο ἄν, he would take or he might take, corresponds to the Homeric ἕληται or ἕληταί κε, he will take or he may take (201, 1).

We find in Homer a few optatives expressing concession or permission, which have a neutral sense and can hardly be classed as either potential or wishing. See Il. iv. 17, “εἰ δ᾽ αὖ πως τόδε πᾶσι φίλον καὶ ἡδὺ πέλοιτο, ἦ τοι μὲν οἰκέοιτο πόλις Πριάμοιο ἄνακτος, αὖτις δ᾽ Ἀργείην Ἑλένην Μενέλαος ἄγοιτο” , where we may translate the apodosis either let the city still be a habitation and let M. carry away Helen, or the city may still be a habitation and M. may carry away Helen. In iii. 72 we have γυναῖκά τε οἴκαδ᾽ ἀγέσθω, and in iii. 255 τῷ δέ κε νικήσαντι γυνὴ καὶ κτήμαθ᾽ ἕποιτο, where ἀγέσθω and ἕποιτό κε refer to essentially the same thing with ἄγοιτο in iv. 19. Following Il. iii. 255(above) we have οἱ δ᾽ ἄλλοι ναίοιμεν Τροίην, τοὶ δὲ νέονται, i. e. the rest of us may remain dwellers in Troy, while they will return to Greece. From such neutral future expressions were probably developed the two distinct uses of the optative. In its hortatory sense as a form of wishing, the optative was distinguished by the use of μή as a negative; while in its potential sense it had οὐ as its negative (as in οὐ μὴν γάρ τι κακώτερον ἄλλο πάθοιμι, for really I can suffer nothing worse, Il. xix. 321), and it was soon further marked by the addition of κέ or ἄν. (See Appendix I.)