What construction is used with φάθι εἶναι? (Plat. Rep. 6.508e)

Question

I think I have the gist of this short sentence, but I would like a little more clarity on one detail. What construction is governing the phrase φάθι εἶναι? I have parsed φάθι as the 2nd singular imperative of φημί ("to say") and εἶναι is clearly the infinitive of εἰμί ("to be").

I suppose it's possible that εἶναι is simply a complementary infinitive, complementing the imperative. Is that the case? Had Plato omitted the imperative, would εἶναι still be infinitive, or would it be conjugated instead?¹

τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν τὴν τοῦ ἀγαθοῦ ἰδέαν φάθι εἶναι:

This, then, which furnishes truth to the objects of knowledge and gives power to the knower, you must say is the idea of the good.

(Plat. Rep. 6.508e)

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¹ At first I suspected an ACI, but the imperative threw me off — I'm not accustomed to seeing this informal 2nd sg imperative in the middle of an ACI.

Answer 1

I think it's an ACI too, triggered by φημί.

But then the question is, can such a construction be used with an imperative? I couldn't find an answer to that in any of my grammar books.

So, then my question was, can we find other examples of this? Looking only for sentences with the imperative φάθι, I did indeed find examples. All of them were in Plato, except for one. Examples from Plato:

Τὴν αὐτὴν τοίνυν φάθι τριῶν οὐσῶν χαλεπὴν διαφερόντως γίγνεσθαι καὶ ῥᾴστην

Well then, you have to say that of the three forms, the same is both the hardest and the easiest

Plato, The Statesman, 302c

Τοῦτο τοίνυν, ἦν δ’ ἐγώ, φάθι με τότε βούλεσθαι λέγειν ...

“Then,” I said, “you must say that this is what I meant just now ..."

Plato, The Republic, 438e

Οὐδαμῶς. ἀλλὰ τρίτον φάθι με λέγειν ...

No, not at all. And as to the third class, you must agree that I mean ...

Plato, Philebus, 26d

And one example in Theocritus:

θάρσει· μήτ’ ἀδίκους μήτ’ ἐξ ἀδίκων φάθι λεύσσειν

Have no fear. You must understand that the men you are looking at are neither lawless nor sons of lawless parents.

Theocritus, Idylls, 22.56

I think these examples confirm that an accusative/infinitive construction is being used because of the simple fact that each example contains φημί + accusatives + infinitive. They also provide evidence that this construction could be used with the imperative φάθι.

I think they also show that the imperative of φημί could be used in an almost idiomatic way to provoke agreement and not just to command someone to say something. Perhaps it's a bit like when we say in English, "you must see that ..."