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τὰ πολλὰ διπλάσια are πρὸς μὲν τὸ διπλάσια, πρὸς δὲ τὸ ἡμίσεα, whereas the αὐτὸ διπλάσιον is always and in every relation διπλάσιον: see last note and VII 523 C ff., Phaed. 102 B, C. The examples of διπλάσια, μεγάλα, βαρέα are examples and nothing more; the others, καλά, δίκαια, ὅσια, are relevant in a wider sense, for the aim of the philosopherking is to frame his καλλίπολις on the model of the αὐτὸ ἀγαθόν. See on 476 A. ἀμφοτέρων ἕξεται: “utrisque adhaerescet” Stallbaum. τοῖς ἐν ταῖς κτλ. ἐπαμφοτερίζουσιν is certainly neuter, as Schneider shews, and not masculine: cf. ταῦτα ἐπαμφοτερίζει below. The word is very frequently used in agreement with neuter or inanimate subjects: see Stephanus Hase Thes. s.v. The ‘children's riddle’ is (according to one of the two versions given by the Scholiast) αἶνός τίς ἐστιν ὡς ἀνήρ τε κοὐκ ἀνὴρ | ὄρνιθα κοὐκ ὄρνιθ᾽ ἰδών τε κοὐκ ἰδών, | ἐπὶ ξύλου τε κοὐ ξύλου καθημένην | λίθῳ τε κοὐ λίθῳ βάλοι τε κοὐ βάλοι. Athenaeus (X 452 C) assigns it (on the authority of Clearchus) to Panarces. The interpretation is “a eunuch aimed at a bat which he saw imperfectly sitting upon a reed with a pumice-stone and missed him” (J. and C.). This riddle was used as an exercise in logic among the Stoics (Dümmler Antisth. p. 43), but that is not a sufficient reason for supposing (with Dümmler) that they took it from Antisthenes.
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