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εἰ with optative: possible condition

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οὐδ᾽ ἂν βοῦς ἀπόλοιτ᾽, εἰ μὴ γείτων κακὸς εἴη.

‘If the neighbour was not bad, not so much as a cow would be lost.’ (Hes. WD 348)

A subordinate clause in the optative, introduced by εἰ, signals a possible condition as a satellite. The main clause usually contains an optative with ἄν.

Translation tips

English does not always make the distinction between a possible and a counterfactual condition. The choice between a conditional form (with the auxiliary 'would' or 'should') and a past tense is determined mainly by stylistic considerations.
If one wishes to express possibility in a more explicit way, the adverb 'ever' or the auxiliary 'should' can be added. Compare 'if I were rich...' to 'if I were ever to be rich...' or 'should I ever be rich...'

Syntactic usage

In epic texts the particle ἄν in the main clause may be omitted.

Historical background

Homer sometimes uses εἴ κε in the conditional clause, with the same meaning as εἰ.

Varia

Note that it is possible for the speaker to present a condition as possible, but at the same time not believe that it can ever be fulfilled.
In traditional grammars the possible condition is called potentialis.

Example Sentences: 

ἐθέλοιτ᾽ ἂν οὖν, εἰ μηχανὴν εὕροιμ᾽ ἐγώ,

μετ᾽ ἐμοῦ καταλῦσαι τὸν πόλεμον;

If I should find a strategy, would you want to end the war with me? ֍

μάθοιμ’ ἄν, εἰ λέγοι τις ἐμφανῆ λόγον

I might understand it if someone were to tell the story clearly. ֍

γνοίητε δ’ ἄν, εἰ σκέψαισθ’ ἐκείνως

You might understand it if you look at it this way. ֍

οἷον καὶ Ἡσίοδος περὶ ἁμάξης λέγει τὸ “ἑκατὸν δέ τε δούραθ’ ἁμάξης.” ἃ ἐγὼ μὲν οὐκ ἂν δυναίμην εἰπεῖν, οἶμαι δὲ οὐδὲ σύ· ἀλλ’ ἀγαπῷμεν ἂν ἐρωτηθέντες ὅτι ἐστὶν ἅμαξα, εἰ ἔχοιμεν εἰπεῖν τροχοί, ἄξων, ὑπερτερία, ἄντυγες, ζυγόν

For instance, Hesiod says of a cart: one hundred pieces of wood in a cart. I would not be able to list those pieces, and neither, I think, would you. But if we are asked what a cart is, we would be satisfied if we could say: wheels, axles, frame, knob for the reins, yoke.