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ἐπὶ πᾶσι is doubted by Herwerden, who proposes ἐν πᾶσι or ἐν ἅπασι. ἐπί may however mean ‘with a view to,’ ‘for,’ as in 471 A. ἡ δ̓ οὔ . ἡ μέν is idiomatically omitted: see 451 D note ἄρα is better, I think, than ἆρα, though somewhat more difficult: the interrogative ἆρα is moreover generally elided before οὐ. The sentence (as J. and C. remark) is “an ironical negation with an interrogative tone.” The irony in this passage lies in ἄρα. As might be expected from the accumulation of negatives, late MSS shew a great variety of readings. Bekker follows q and reads καὶ γυμναστικὴ ἄρα καὶ πολεμική—an obvious but wholly superfluous attempt to simplify the authoritative text.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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