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ff. Plato's conception of Dialectic and dialectical science is fully discussed in App. III.

-- οἰκεῖα κτλ. Cf. [Epin.] 991 E ff. πᾶν διάγραμμα ἀριθμοῦ τε σύστημα καὶ ἁρμονίας σύστασιν ἅπασαν τῆς τε τῶν ἄστρων περιφορᾶς τὴν ὁμολογίαν οὖσαν μίαν ἁπάντων ἀναφανῆναι δεῖ τῷ κατὰ τρόπον μανθάνοντι, ἀναφανήσεται δὲ ἂνὀρθῶς τις εἰς ἒν βλέπων μανθάνῃ: δεσμὸς γὰρ πεφυκὼς πάντων τούτων εἷς ἀναφανήσεται διανοουμένοις: εἰ δ᾽ ἄλλως πως ταῦτα μεταχειριεῖταί τις, τύχην δεῖ καλεῖν. The apprehension of the ‘one in the many’ in these preliminary studies prepares us for the dialectical conception of the universe of Thought as an organic and correlated whole (VI 511 B—D notes); but the mere specialist in mathematics for example, or astronomy, can never become a dialectician. Cf. 537 C and Euthyd. 290 B ff.

νόμου: ‘song’ or ‘strain.’ There is no pun on νόμος ‘law,’ as Bosanquet supposes. Dialectic is not a ‘law’ in the Greek sense of the word.

οὐ γάρ που κτλ. Theodorus in the Theaetetus (146 B) is a good example, and everyone who knows men who are distinguished mathematicians and nothing more will heartily echo Glauco's emphatic οὐ μὰ τὸν Δία. Taught on the Platonic method, not as an end, but as a means, by teachers who have themselves penetrated into regions beyond and above the sphere of pure mathematics, and who are constantly on the alert to direct their pupils thither, the study of mathematics may prove one of the most valuable of all instruments of education. See App. II.

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