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εἴδεσιν -- εἴδη. On αὐτοῖς δἰ αὐτῶν see 510 B note εἴδεσιν may now be taken in its full force; for after the Idea of Good has been reached, the dialectician's conception of each εἶδος is accurate and complete: see last note. I formerly read αὐτοῖς δἰ αὑτῶν, rejecting εἰς αὐτά as superfluous on account of καὶ τελευτᾷ εἰς εἴδη. But αὑτῶν is certainly wrong (cf. 510 B), and εἰς αὐτά, which may well be taken loosely with καταβαίνῃ or a participle supplied from it, merely states that the conclusions of dialectic are likewise εἴδη: whereas καὶ τελευτᾷ εἰς εἴδη seems to lay emphasis on the fact that dialectic never descends below εἴδη to particulars (“und bei Begriffen endigt” Schneider). We may translate ‘and with Ideas end.’ Plato means to emphasize the fact that the Dialectician quâ Dialectician does not draw conclusions as to particulars: if he did, he could scarcely be said αἰσθητῷ παντάπασιν οὐδενὶ προσχρῆσθαι. See the Appendix to Book VII On Plato's Dialectic. ὅτι μέντοι κτλ. There is no anacoluthon as Engelhardt (Anac. Pl. Spec. III p. 9) supposes, but ὅτι depends on μανθάνω. With σαφέστερον cf. V 478 C and 509 D above. σαφής, originally ‘clear,’ often=‘true’ in Greek. Plato's comparison between Light and Truth in 507 C ff. gave a new and profound significance to the equation. The present passage should be compared with Phil. 57 B ff., where Dialectic is said to excel mathematical and all other sciences in respect of ‘the clearness’ (τὸ σαφὲς καὶ τἀκριβὲς καὶ τἀληθέστατον) of its object. In general, the higher a science is, the greater (according to Plato) is the amount of truth or knowability which its subjectmatter contains. Plato's theory on this subject is the source of Aristotle's doctrine of ἁπλῶς γνώριμα or γνωριμώτερα φύσει, for which see Stewart on Eth. Nic. I 4. 1095^{b} 2. τὸ -- καλουμένων . καλουμένων implies that τέχναι (‘Arts’) sometimes bore the specific meaning of ‘mathematical sciences’ as early as the time of Plato. This use of the word may have been introduced by some of the Sophists, perhaps Hippias: cf. Prot. 318 E, where Protagoras says οἱ μὲν γὰρ ἄλλοι λωβῶνται τοὺς νέους: τὰς γὰρ τέχνας αὐτοὺς πεφευγότας ἄκοντας πάλιν αὖ ἄγοντες ἐμβάλλουσιν εἰς τέχνας, λογισμούς τε καὶ ἀστρονομίαν καὶ γεωμετρίαν καὶ μουσικὴν (the medieval quadrivium) διδάσκοντες— καὶ ἅμα εἰς τὸν Ἱππίαν ἀπέβλεψεν. If we can understand μουσικήν as ‘theory of Music,’ Hippias' quadrivium is identical with Plato's, except that Plato would like to add Stereometry. Cf. also Theaet. 145 A, B and see Tannery L'Éducation Platonicienne in Rev. Philos. X p. 523, the Appendix to Book VII On the propaedeutic studies of the Republic and my article in Cl. Rev. XV p. 220, where I have tried to shew that our use of the word ‘Arts’ in ‘Bachelor of Arts’ etc. is an inheritance from the Platonic Academy. καὶ -- θεώμενοι. The relative sentence passes into a main clause, as in II 357 B, where see note. αὐτά: viz. the subject-matter of the so-called ‘Arts’: cf. VII 518 B.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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