what is the meaning of κατά in εἴπερ ἕν γέ τι ζητεῖς κατὰ πάντων. Steadman says over, but it can also mean under. κατὰ πάντων may also mean ‘in general’.
In this context, κατά means ‘concerning’, “with respect to”.
εἴπερ ἕν γέ τι ζητεῖς κατὰ πάντων
“if, indeed, you are seeking some one thing with respect to all(ie, the cases already mentioned)”.
Socrates is here in pursuit of a general definition of virtue, one that will apply to all of the examples given earlier(that of a child, of an elderly person, of a man, of a woman), and any new ones that might come up. Almost immediately, however, under his continued questioning, the definition offered by Meno/Gorgias(“to be able to rule men”) begins to fall apart.
LSJ does have
- [select] in respect of, concerning, “μὴ κατ᾽ ἀνθρώπων σκόπει μόνον τοῦτο” Pl. Phd.70d; “κ. τῶν ἄλλων τεχνῶν τοιαῦτα εὑρήσομεν” Id.Sph.253b; οἱ κ. Δημοσθένους ἔπαινοι praises bestowed on D., Aeschin.3.50; ἐρεῖν or λέγειν κατά τινος to say of one, Pl.Ap.37b, Prt.323b, etc.; “εἰ κ. θηλείας φαίης” A.D.Synt.198.10; “εἴπερ ἕν γέ τι ζητεῖς κ. πάντων” Pl.Men. 73d, cf. 74b; “ὅπερ εἴρηται καθόλου κ. πασῶν τῶν πολιτειῶν” Arist.Pol. 1307b2; freq. in the Logic of Arist., κατά τινος λέγεσθαι or κατηγορεῖσθαι to be predicated of . . , Int.16b10, Cat.1b10, etc.; καταφῆσαί (or ἀποφῆσαί） τι κατά τινος to affirm (or deny) of . . , Metaph.1007b21; so “κ. τινὸς ὑπάρχειν” Int.16b13: and in Adv. καθόλου (q.v.).
But Sedley and Long have" Assuming, that is, 73d that you’re seeking one thing covering all cases." The Loeb has “…if you want some single description to cover all cases.”
So I can understand why Steadman glosses as “over” as in “over all cases”. “In respect of” is hardly idiomatic English even if it reflects the grammatical structure.
Although “in respect of” is somewhat more formal English, I find it perfectly idiomatic(in my translation, I actually used “with respect to”, which I slightly prefer). On the other hand, I think “over all cases” is both less idiomatic and ambiguous(see the original post, where ‘over’ is viewed as in opposition to ‘under’).
In any case, there are a number of perfectly acceptable alternatives to “in respect to” which convey a similar meaning: ‘concerning’, ‘regarding’, “covering (all cases)”, “applying to” (this last is Sharples suggestion).
If we’re trying to understand the Greek, the thing to notice here is that it’s not accusative. The “over all cases” would make me expect (perhaps naively) κατα + accusative in Greek, and it would probably be good for us to understand why he chose genitive instead.