Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 1824. Potential Optative.—The potential optative with ἄν states a future possibility, propriety, or likelihood, as an opinion of the speaker; and may be translated by may, might, can (especially with a negative), must, would, should (rarely will, shall). So in Latin velim, videas, cognoscas, credas.

““γνοίης δ᾽ ἂν ὅτι τοῦθ᾽ οὕτως ἔχει” you may see that this is so” X. C. 1.6.21, ““ἅπαντες ἂν ὁμολογήσειαν” all would agree” I. 11.5, ἡδέως ἂν ἐροίμην I (would gladly ask) should like to ask D. 18.64, ““οὐκ ἂν λάβοις” thou canst not take” S. Ph. 103, ““λέγοιμ᾽ ἂν τάδε” I will tell this” A. Supp. 928. The second person singular is often indefinite (one), as γνοίης ἄν (cognoscas) = γνοίη τις ἄν.

a. The potential optative ranges from possibility to fixed resolve. The aorist optative with ἄν and a negative is very common.

b. When stress is laid on the idea of possibility and power, necessity and obligation, Greek uses δύναμαι, δεῖ or χρή with the infinitive (statement of fact).

c. The potential optative with ἄν is also used in dependent sentences; in purpose clauses (2202 b), in object clauses after verbs of effort (2216) and verbs of fearing (2232), in causal clauses (2243), in result clauses (2278), in the apodosis of conditional (see 2356) and conditional relative sentences (2566). In indirect discourse the infinitive with ἄν or the participle with ἄν may represent the optative with ἄν (1845 ff.).