Plato Republic 7.527

αὕτη ἡ ἐπιστήμη κτλ. : ‘the nature of this science is in precise contradiction to’ etc. πᾶν τοὐναντίον is adverbial, and ἔχει intransitive. In what follows Plato is not (as Stallbaum strangely supposes) censuring contemporary geometricians, “sed vitium quoddam ipsius scientiae” (Schneider, who refers to VI 510 B—511 A), for even those ὅσοι καὶ σμικρὰ γεωμετρίας ἔμπειροι agree with him. It is however probable on other grounds that Plato himself was afraid lest his pupils should depend too much on geometrical figures and instruments; and Plutarch tells us that he reproved Eudoxus and others for this very fault: ἀπόλλυσθαι γὰρ οὕτω καὶ διαφθείρεσθαι τὸ γεωμετρίας ἀγαθὸν αὖθις ἐπὶ τὰ αἰσθητὰ παλινδρομούσης, καὶ μὴ φερομένης ἄνω μηδὲ ἀντιλαμβανομένης τῶν ἀϊδίων καὶ ἀσωμάτων εἰκόνων, πρὸς οἷσπερ ὢν ὁ θεὸς ἀεὶ θεός ἐστι ( Conv. Disp. VIII 2. 718 F: cf. also Vit. Marc. 14. 5—7. The anecdote refers in particular to stereometrical instruments, but its moral applies equally to the study of plane geometry). See Rothlauf l.c. pp. 66 ff. and Gow Gk Math. p. 181.

ἀναγκαίως ‘in beggarly fashion’ (“nothgedrungenen Weise” Prantl). They are ‘hard up’ for words to express their meaning, and must consequently use language which does not: cf. VI 510 D. J. and C.'s explanation “with merely practical needs in view” is quite wrong; nor does the word appear to me to contain “a facetious allusion to geometrical necessity” (in the sense of V 458 D), as they assert. Madvig's ἀκάκως for ἀναγκαίως is a singularly unhappy suggestion.

παρατείνειν = ‘to apply,’ e.g. a parallelogram to a given line: cf. Men. 87 A ( παρὰ τὴν δοθεῖσαν—γραμμὴν παρατείναντα κτλ.) with E. S. Thompson's note. Blass takes the same view ( de Pl. math. p. 19). Euclid's expression for this is παραβάλλειν (X 18 ff. and passim: cf. Cantor l.c. p. 145). The ordinary translation ‘produce’ (as e.g. a line) has no authority, and Euclid's word for ‘producing’ a line is ἐκβάλλειν or προσεκβάλλειν (I 5, 17 and passim. So also in Aristotle: see the Ind. Arist. s.v.).

προστιθέναι : ‘to add,’ sc. one μέγεθος to another in any geometrical construction: cf. Nicom. Introd. Ar. II 12. 2. Euclid uses συντιθέναι, σύγκειμαι (X 16 and passim) of such an operation.

φθεγγόμενοι is said “non sine eleganti quadam irrisione” (Stallbaum): cf. VI 505 C note

τὸ δέ : ‘whereas’: cf. I 340 D note

τοῦ ἀεὶ ὄντος . Plato held the objects of mathematical study to be ἀΐδια καὶ ἀκίνητα ‘eternal and unchangeable’ (Arist. Met. A 6. 987^{b} 16: cf. VI 510 C ff., VII 526 A note), but not Ideas. The Platonic meaning of τοῦ ἀεὶ ὄντος is certainly not exhausted by the observation that “the truths of every science are always true” (Bosanquet). ὄντος implies substantial existence, independently of our thoughts, and independently also of particulars. The existence of τὰ μαθηματικά as μιμήματα τῶν ὄντων or copies of the Ideas, ‘moving in and out of’ the material substance of the Universe, which they stamp with an infinite diversity of forms and shapes, is a cardinal doctrine of Plato's physics ( Tim. 50 C al.), and Bosanquet appears to me to rob the words of Plato of half their significance, in the fruitless attempt to find in his ontology nothing but what commends itself to certain schools of philosophy in the present day. See V 476 E and App. I.

τοῦ ποτέ κτλ. : ‘that which at some particular time is a particular instance of becoming and perishing.’ τι γιγνομένου= ὄντος (the copula) γιγνομένου τινός, but γιγνομένου itself involves the copula, the presence of which would here be intolerable. Cf. V 473 D note and Euthyph. 10 C εἴ τι γίγνεται ἤ τι πάσχει, οὐχ ὅτι γιγνόμενόν ἐστι, γίγνεται, ἀλλ’ ὅτι γίγνεται, γιγνόμενόν ἐστι. Here τι is indeclinable like τι in Lach. 200 B , Menex. 247 B ( οἰομένῳ τι εἶναι), Euthyd. 303 C ( δοκούντων τι εἶναι), οὐδέν, μηδέν etc. tolerably often in tragedy, and the adverbial use of ἀμφότερα and τἀναντία (e.g. Lach. 185 A ὑέων γὰρ που ἢ χρηστῶν ἢ τἀναντία γενομένων κτλ.): cf. also (with Schneider Addit. p. 57) Procl. in Tim. 136 E τοῦ—ἀδιαιρέτως πάντα ὄντος et al. The indeclinable form adds to the emphasis, and indeed τινὸς (if placed after ποτέ) could hardly stand at all. Schneider translates “des etwas werdenden und vergehenden,” apparently taking τι predicatively with γιγνομένου. But the expression ‘that which becomes something’ suggests a substratum underlying γιγνόμενον, whereas the only correct antithesis to ὄν ( τοῦ ἀεὶ ὄντος) is γιγνόμενον itself. Stallbaum wrongly explains τι as “aliqua ratione.” A few inferior MSS omit the word. I believe the text is sound, though possibly τι should be accented, as in the exactly similar Aristotelian usage of τις “ad significandam τὴν ἀτομότητα” (Bonitz Ind. Ar. p. 763) e.g. ὁ τὶς ἄνθρωπος. The use of ποτέ also reminds us of the ποτέ of the Categories.

γεωμετρική is an adjective (Schneider).

σχεῖν . The tense is inchoative or ingressive, as usual: see 516 E note

καλλιπόλει . Socrates rallies Glauco on his ‘braif toun.’ The word, as J. and C. point out, is full of tenderness and affection. Callipolis was the name of several cities in Greece (PapeBenseler Gr. Eigennam. s.v.), a fact which sufficiently refutes Herwerden's doubts as to the formation of the word: see also (with Schneider) Lobeck's Phrynichus pp. 600—607. Herwerden ought not to have revived the tasteless and prosaic conjectures καλῇ πόλει ( Π^{2}) and καλλίστῃ πόλει ( Ξ).

αὐτοῦ : viz. τοῦ μαθήματος.

καὶ δὴ καὶ κτλ. See on 526 B.

ἡμμένος τε . Herwerden excises τε, comparing 526 D; but the MSS are a safer guide.

ἐμοὶ γοῦν . Schneider and others write ἔμοιγ’ οὖν (see cr. n.), but οὖν is too strongly illative for this passage. Cf. I 335 E note

τὸ γὰρ περὶ κτλ. Cf. 526 C note and Xenophon there quoted, esp. § 4 ἐκέλευε δὲ καὶ ἀστρολογίας ἐμπείρους γίγνεσθαι, καὶ ταύτης μέντοι μέχρι τοῦ νυκτός τε ὥραν καὶ μηνὸς καὶ ἐνιαυτοῦ δύνασθαι γιγνώσκειν κτλ. and infra τὰς ὥρας τῶν εἰρημένων διαγιγνώσκοντες. The ana logy of this passage suggests that in Plato καὶ (‘both’) μηνῶν καὶ ἐνιαυτῶν depends on ὥρας, which is the accusative plural: cf. Laws 812 B εὐαισθήτους δεῖν γεγονέναι περί τε τοὺς ῥυθμοὺς κτλ. Practical astronomy will enable one to tell both the time of month and the time of year by looking at the moon and the sun. For ὥρας μηνῶν cf. also, besides the passage of Xenophon just quoted, Eur. Alc. 449 f. Σπάρτᾳ κυκλὰς ἁνίκα Καρνείου περινίσσεται ὥρα | μηνός κτλ. Schneider and the English translators take ὥρας as genitive and parallel with μηνῶν κτλ., but it is difficult to see what εὐαισθητοτέρως ἔχειν περὶ ἐνιαυτῶν can mean: for ἐπιμέλειαν ποιεῖσθαι ἐνιαυτοῦ καὶ ὡρῶν in VI 488 D is quite different. Schleiermacher translates the passage correctly.

εὐαισθητοτέρως . For this form of the comparative adverb see I 343 E note

ἡδὺς εἶ : ‘you amuse me.’ See I 337 D note

μὴ δοκῇς κτλ. The usefulness of ‘useless’ studies is a fundamental principle in Plato's theory; and (as Schneider points out) ὅτι ἐν τούτοις κτλ. is intended to shew that liberal studies are in the highest and truest sense useful.

τὸ δ’ ἔστιν . I 340 D note

χαλεπόν . Cobet's παγχάλεπον (after Nicom. Introd. Ar. III 7) is a wholly gratuitous change: see App. VII.

ἑκάστου . Every human being has an ὄργανον ψυχῆς viz. νοῦς: it is indeed the possession of νοῦς which makes him at once truly human and therewithal divine (VI 501 B note). The genitive is much more expressive than ἑκάστῳ, which Herwerden proposes: cf. 518 C note, and for the combination of genitives V 449 A note

ἐκκαθαίρεται κτλ. : ‘is purged and rekindled.’ In passages like this Plato hurls his metaphors about with Shakespearian vehemence and profusion. Cf. II 365 C note, and see the admirable remarks on metaphor by the author of the treatise περὶ ὕψους 32. 4 πλήθους καὶ τόλμης μεταφορῶν—τὰ εὔκαιρα καὶ σφοδρὰ πάθη καὶ τὸ γενναῖον ὕψος εἶναί φημι ἴδιά τινα ἀλεξιφάρμακα, ὅτι τῷ ῥοθίῳ τῆς φορᾶς ταυτὶ πέφυκεν ἅπαντα τἄλλα παρασύρειν καὶ προωθεῖν, μᾶλλον δὲ καὶ ὡς ἀναγκαῖα πάντως εἰσπράττεσθαι τὰ παράβολα, καὶ οὐκ ἐᾷ τὸν ἀκροατὴν σχολάζειν περὶ τὸν τοῦ πλήθους ἔλεγχον διὰ τὸ συνενθουσιᾶν τῷ λέγοντι. The eye of soul is purged of its blindness: its smouldering fires flame forth afresh. To translate “‘is polished’ like a soiled mirror” (J. and C.), besides being wrong, falls far below the level of Plato's ὕψος. The chiasmus in ἐκκαθαίρεται—τυφλούμενον adds to the literary effect. On other readings in this passage see App. VII.

οἷς μὲν οὖν κτλ. The logical sequence is somewhat difficult. Do not (says Socrates) be so anxious to persuade οἱ πολλοί of the usefulness of our curriculum. Its true utility is difficult to understand, and οἱ πολλοί will not easily be persuaded of it. Those who agree with us about its true utility will highly approve of your proposals; but οἱ πολλοί will not, for they can see no practical advantage (worthy of mention) accruing from them. δόξεις λέγειν attributes the proposals to Glauco as in D μὴ δοκῇς—προστάττειν, and ἄλλην is said with reference to τούτου. To the ὠφελία of intellectual salvation such persons are blind; and they cannot see any other, i.e. any practical ὠφελία worth mentioning in Plato's studies. ἄλλην cannot be understood as “beyond their practical applications” (D. and V.) unless we refer it to Glauco's remark τὸ γὰρ περὶ κτλ. in D, to the detriment both of grammar and of sense.

σκόπει οὖν κτλ. ‘Very well: make up your mind once for all with which of these parties you are discoursing: or are you not addressing your remarks to either, but’ etc.? Glauco's insistence on the practical uses of astronomy may be all very well with a popular audience, but are out of place in a philosophical discussion. For this peremptory αὐτόθεν cf. Symp. 213 A. οὐ πρὸς οὐδετέρους lit. ‘not to neither’: cf. the familiar μᾶλλον ἢ οὐ for μᾶλλον ἤ (Kühner Gr. Gr. II pp. 771—773). I understand ἢ—ὄνασθαι (with Ast) as an independent question: for it is difficult to supply ‘whether.’ Schneider's objections to this view are based on the idea that ἢ οὐ (if interrogative) must have an affirmative answer; but οὐ has nothing to do with ἤ, and only balances ἀλλά: cf. Ar. Plut. 372 μῶν οὐ κέκλοφας, ἀλλ’ ἥρπακας; Plato makes this clear by placing the two contrasting clauses in close juxtaposition. οὐ is omitted by Ξ and some inferior MSS. The text is, however, sound, and none of the proposed corrections— σὺ for οὐ (Schneider), εἰ πρὸς οὐδετέρους (Madvig), οὐδὲ πρὸς ἑτέρους (Cobet), εἰ οὐδὲ πρὸς ἑτέρους (Baiter), ἦ που πρὸς οὐδετέρους (Liebhold)—will bear examination, though Cobet's deserves the praise of elegance.