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Optative in main clause with ἄν: modest opinion
εἴησαν δ’ ἄν οὗτοι Κρῆτες
‘Must have been Cretans.’ (Hdt. 1.2)
The optative with ἄν signals a modest opinion, i.e. that the speaker is certain of the reality of the action, but presents himself as uncertain. This type of optative may also be ironic.
In this usage the potential optative can often be translated 'can' or 'will' rather than 'could'.
This usage is not attested before the 5th century B.C.E.
οὐκ ἂν οὖν νήσων ἔξω τῶν περιοικίδων (αὗται δὲ οὐκ ἂν πολλαὶ εἶεν) ἠπειρώτης ὢν ἐκράτει, εἰ μή τι καὶ ναυτικὸν εἶχεν
So, as a continental [power], [Agamemnon] could not have ruled without the surrounding islands (and perhaps there were not many), unless he also had a navy. [provisional translation]
ἀρετὴ μὲν ἄρα, ὡς ἔοικεν, ὑγίειά τέ τις ἂν εἴη καὶ κάλλος καὶ εὐεξία ψυχῆς, κακία δὲ νόσος τε καὶ αἶσχος καὶ ἀσθένεια
Virtue, then, it seems, would be a kind of health, beauty and good spirits, and vice a disease, a disgrace and an unhealthy condition. [provisional translation]