Plato Republic 7.531

τὰς γὰρ ἀκουομένας κτλ. The intervals reckoned as consonant ( σύμφωνα) were such as the octave, double octave, fifth and fourth: see on IV 430 E. These the Pythagoreans ‘measure by’ (or ‘against’) ‘one another,’ by comparing the lengths of vibrating strings of the same material, thickness and tension. It is thus found that the octave is 2 : 1, the double octave 4 : 1, the fifth 3 : 2, and the fourth 4 : 3. See Dict. of Ant. II p. 193 with Theo Smyrn. pp. 48—51, 56—61 Hiller, and Aristox. Harm. 20 ff. Marquard. Richards proposes <ἐν> ἀλλήλοις, but the dative is strictly accurate: cf. Tim. 39 D τῷ τοῦ ταὐτοῦ καὶ ὁμοίως ἰόντος ἀναμετ ρηθέντα κύκλῳ.

ὥσπερ οἱ ἀστρονόμοι . The parallel is exact: as the astronomers studied visible, so the Pythagoreans investigated audible φοραί (Theo l.c.). To Plato, on the other hand, ἁρμονίη ἀφανὴς φανερῆς κρείσσων (Heracl. Fr. 47 B ywater). ‘Heard harmonies are sweet, but those unheard are sweeter.’ See above on 530 C.

νὴ τοὺς θεοὺς κτλ. There were two rival schools of musical theory in Greece, viz. “(1) the Pythagorean or mathematical, who identified each interval with a ratio, (2) the ‘musical’ ( μουσικοί), who measured all intervals as multiples or fractions of the Tone” (Monro in Dict. Ant. II p. 193). Cf. Modes of Anc. Gk. Mus. p. 124. Plato's criticism was intended to apply to the first school; but Glauco erroneously understands it of the second.

πυκνώματα κτλ . ἄττα ( nescio quae) and ὀνομάζοντες shew that πυκνώματα is a technical term. The word πύκνωμα does not appear to occur elsewhere in this sense, but πυκνόν was a favourite word with writers of the ‘musical’ school, as may be seen from its constant employment by Aristoxenus. πυκνόν is thus defined: τὸ ἐκ δύο διαστημάτων συνεστηκὸς ἃ συντεθέντα ἔλαττον διάστημα περιέξει τοῦ λειπομένου διαστήματος ἐν τῷ διὰ τεσσάρων (Aristox. Harm. 24. 10 ff. Marquard) i.e. any combination of two intervals which are together less than the interval remaining in the Fourth when the πυκνόν is subtracted from the Fourth, e.g. two quarter tone intervals, or even two semitone intervals (but not more): see Aristox. l.c. 50. 15 ff. The definition in Bacchius Isag. 20 von Jan τὸ ἐκ δύο διαστημάτων ἐλαχίστων συγκείμενον ἐν ἑκάστῳ γένει is less exact, but not, so far as it goes, inconsistent with that of Aristoxenus. Plato's πυκνώματα must be “haec ipsa πυκνά vel alia parva et tamen composita intervalla,” so called “propter sonorum in angusto spatio quasi confertorum frequentiam” (Schneider). Cf. πυκνότης in Laws 812 D, καταπυκνοῦσθαι, καταπύκνωσις etc. in Theo 91 and often in Aristoxenus, and see generally Westphal and Rossbach Gr. Harm. etc. pp. 105 ff. It is possible that the musical application of these terms was originally a metaphor borrowed from the art of weaving: for “vestes spatha textae, ob densitatem, quam inde consequebantur, πυκνώματα dictae ap. Aesch. Suppl. 235 πέπλοισι βαρβάροισι, καὶ πυκνώμασι” (Stephanus-Hase s.v. πύκνωμα, where reference is made also to Hesych. s.v. σπάθημα and a Scholiast on Ar. Ach. 180 ). I agree with Schneider in doubting whether Gellius' “frequentamenta” (I 11. 12, V 1. 1) are the same as Plato's πυκνώματα.

οἷον ἐκ γειτόνων κτλ. : ‘as if they were trying to catch a sound in the neighbourhood.’ Cf. Heliod. I 17 πίνει δὲ ἐνταῦθα ἐκ γειτόνων and Blaydes on Ar. Plut. 435 or Stephanus-Hase Thes. s.v. γείτων, where numerous examples of this highly idiomatic phrase are quoted. J. and C.'s translation “from a neighbour's house” is incorrect and pointless: still worse is Westphal's “als ob sie die Intervallgrösse dem Nachbarton ablauschen wollen.” The idiom was understood by Ficinus, who translates it by “viciniore loco.”

οἱ μέν φασιν κτλ. Some will have it that they overhear a note between (let us say) B and C, and that this is the smallest interval, and should be the unit of measurement: others say ‘No! it is not different from B.’ Plato (who is all for simplicity in music Laws 812 C) here satirises the μουσικοί, who made the quartertone or δίεσις their unit: see Theo 55 δίεσιν δὲ καλοῦσιν ἐλαχίστην οἱ περὶ Ἀριστόξενον τὸ τεταρτημόριον τοῦ τόνου, ἥμισυ δὲ ἡμιτονίου, ὡς ἐλάχιστον μελῳδητὸν διάστημα, and on the ἐναρμόνιον γένος generally, which Plato strongly disliked (Theo 56; cf. also Procl. in Tim. 191 E), and in which the δίεσις played a large part, Dict. of Ant. l.c. and Westphal and Rossbach l.c.

ἀμφισβητοῦντες . We should expect ἀμφισβητοῦσιν (so Theo 6) or else φάσκοντες instead of φασιν above. Cobet would emend, but the anacoluthon is not difficult in a writer like Plato: see on VI 488 C, D and supra 519 A note

φθεγγομένων : sc. τῶν χορδῶν, omitted as in ἡ διὰ πασῶν.

ὦτα κτλ. This bitter epigram was applied by Adrastus to Aristoxenus (Procl. in Tim. 192 B). The cap fits admirably; for Aristoxenus was afterwards the leader of the μουσικοί whose principle is here ridiculed. With the expression itself cf. Pliny Epp. VII 27, 8 sed offirmare animum auribusque praetendere.

σὺ μὲν κτλ. Socrates now corrects Glauco's error: see on νὴ τοὺς θεοὺς κτλ. 531 A. τοὺς χρηστούς is of course contemptuous. Plato has no sympathy with the ‘ μουσικοί.’

τοὺς ταῖς χορδαῖς κτλ. : ‘who persecute and torture the strings, racking them upon the pegs. But lest my figure become somewhat tedious if I dwell upon the blows delivered with the plectrum, and the accusations brought against the strings, as well as their denials and braggadocio behaviour’ etc. The figure ( εἰκών) is from torturing and beating slaves, as βασανίζοντας, στρεβλοῦντας and πληγῶν shew: even πράγματα παρέχοντας suggests a court of law (cf. Crit. 44 E ). The strings are the victims, while the pegs are the pulleys by which they were racked upon the τροχός (see Dict. Ant. s. v. eculeus). For ἐπί Herwerden proposes ὑπό: but the strings are racked by the musicians upon the pegs.

πλήκτρῳ τε πληγῶν κτλ. The etymological meaning of πλῆκτρον adds point to this part of the comparison.

πέρι from its position divides πληγῶν and κατηγορίας, which refer to the behaviour of the musicians, from ἐξαρνήσεως καὶ ἀλαζονείας, in which the behaviour of the strings is described. For the anastrophe of πέρι see Lina de praeposit. usu Plat. pp. 26—30. The angry musician is like the prosecutor, and blames the strings, which in their turn repudiate the charge and swagger away like a stubborn slave however savagely the screw is turned. For a further discussion of this passage see App. XI.

ἐκείνους : i.e. the Pythagoreans, and not the μουσικοί, as Glauco supposed.

τοὺς γὰρ κτλ. It is strange that in spite of οὓς ἔφαμεν νῦν δὴ κτλ. this should have been so frequently understood as referring to the school satirised by Glauco: see for example Susemihl Gen. Entw. II p. 210. Plato is of course, as Schneider pointed out, speaking about the Pythagoreans who investigated the numbers or ratios of audible consonances: see 531 A note and RP.^{7} § 56 C.

ἀλλ’ οὐκ κτλ. Cf. 530 B. ἀνίασιν is undoubtedly present, and not future, here: see on V 473 C.

τίνες ξύμφωνοι κτλ. As the true astronomer should study intelligible stars with the mathematical intelligence, using the visible stars only as imperfect παραδείγματα (529 C, D note), so the true ἁρμονικός must investigate intelligible, and not audible, consonances. In the words of a modern writer, he must “look, not into the tone-world here, but into the world of harmony beyond.” Plato holds that certain mathematical numbers are in themselves ξύμφωνοι, and others not: see Theo 72—75, where examples of both varieties are given. The numbers or ratios of audible consonances are only particular and imperfect embodiments or expressions of these numbers: they may serve as παραδείγματα, but nothing more. In the Timaeus Plato represents the World-soul as the grandest expression of certain ξύμφωνοι ἀριθμοί, so that it is natural enough for him to crown his προπαιδεία with the study of mathematical ξυμφωνία, and say that it is ‘useful in seeking out the beautiful and good.’ It must nevertheless be admitted that Plato's conception of Harmonics as well as of Astronomy is fundamentally different from that of modern science, in spite of the attempts which Bosanquet and others have made to prove their essential harmony. See on 530 C and App. II.

ᾗ ‐‐ 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 ἂν— ὀρθῶς 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.

ὧν . For the attraction see VI 510 B note

ἀλλ’ ἤδη κτλ. ‘Well, did it ever seem to you that persons who are unable’ etc. The subject is μὴ δυνατοί τινες ὄντες— λόγον, and after ἤδη “supplendum est ἔδοξαν, quod ipsum Glauconis verbis magis accommodatum est quam δοκοῦσι” (Schneider). The form of Socrates' question is in fact affected by Glauco's reference to the past in ὧν ἐγὼ ἐντετύχηκα. I formerly, with v and three other MSS, including Vind. F, read ἀλλὰ δή, understanding δοκοῦσι: but ἀλλὰ δή is scarcely appropriate here (see on II 365 C), and Schneider's explanation gives a satisfactory meaning to ἤδη. J. and C. take ἤδη with μὴ δυνατοί τινες ὄντες (‘persons who are as yet unable’ etc.); but the hyperbaton is too difficult, and the meaning (which Plato would rather have expressed by μήπω δυνατοὶ κτλ.) unsuitable. Few will approve of Badham's ἀλλ’ οἱ δὴ κτλ. or even of Burnet's ἀλλὰ δή, εἶπον, μὴ δυνατοὶ οἵτινες δοῦναί τε κτλ. For the sentiment, which is a commonplace of the Socratic school, cf. Xen. Mem. IV 6. 1 , Prot. 336 C , Phaed. 76 B , Crat. 390 C ff. al.

οὐδ’ αὖ κτλ. ‘My answer to this question is also no.’

περαίνει =‘performs’: cf. Plut. Crass. 33. 3 ἀναβακχεύσας ἐπέραινεν ἐκεῖνα τὰ μέλη κτλ., Tim. 29 D τὸ μὲν οὖν προοίμιον θαυμασίως ἀπεδεξάμεθά σου, τὸν δὲ δὴ νόμον ἡμῖν ἐφεξῆς πέραινε, and Laws 723 E. The metaphor is still from music, though D. and V. erroneously translate “of which dialectical reasoning is the consummation.”

ἣν ἐλέγομεν κτλ. It follows that the progress of the prisoner after he has begun to look on real objects outside the Cave represents Dialectic: cf. 516 A note and 532 B.

αὐτὰ ἄστρα . I formerly read αὐτὰ <τὰ> ἄστρα with Baiter; but there is no MS authority for the article, and its presence is unnecessary even between αὐτὰ τὰ ζῷα and αὐτὸν τὸν ἥλιον.

οὕτω καὶ κτλ. : ‘so also whenever by means of dialectic one attempts through discourse of reason’ etc. On τοῦ λόγου and ἄνευ πασῶν τῶν αἰσθήσεων see VI 511 B note and App. III. Ast's conjecture ὁρμᾶν (see cr. n.) is supported by Clement Strom. V 112 B Migne (quoted by Schneider) ἐὰν ἐπιχειρῇ τις ἄνευ πασῶν τῶν αἰσθήσεων διὰ τοῦ λόγου ἐπ’ αὐτὸ ὃ ἔστιν ἕκαστον ὁρμᾶν κτλ., and closely corresponds with ἐπιχειρεῖν ἀποβλέπειν in the last sentence. There is no occasion for Stallbaum's professional ridicule of Schneider's view: ‘quasi vero recte dici potuerit: τῷ διαλέγεσθαι ἐπιχειρεῖν διὰ τοῦ λόγου ὁρμᾶν ἐπί τι!’ for οὗ αὐτὸς ὁ λόγος ἅπτεται τῇ τοῦ διαλέγεσθαι δυνάμει in VI 511 B is an exact parallel. On other views see App. XII.

ἕκαστον is omitted in A (see cr. n.) and some other MSS. It is however necessary both in itself, and in order to provide a proper contrast with αὐτὸ ὃ ἔστιν ἀγαθόν. For the process here described see App. III.

τότε . 516 B.

ἡ δέ γε κτλ. Having described διαλεκτική in terms of the cave-simile, Plato now proceeds to describe his προπαιδεία in the same way: cf. 515 C, 516 A notes Bosanquet finds a difficulty in ἡ λύσις—ἐπάνοδος, and thinks it just conceivable that these words describe the training in music and gymnastic and not the προπαιδεία (so also Susemihl Gen. Entw. II p. 201). But Plato's language is perfectly definite; and τῶν τεχνῶν ἂς διήλθομεν (532 C) cannot mean anything beyond or except the five studies just described. Nor is this the only passage where the ‘turning round’ of the prisoners while still in the cave and their gradual ascent are identified with the προπαιδεία, or with part of it: see 521 C. Plato means that the emancipation of the soul is a gradual process, and that we are not to expect our mathematical studies to deliver us from δόξα all at once. ἡ λύσις —εἴδωλα suggests that their first effect will be to loosen our intellectual bonds, and turn us as it were from reflected to original δόξαι—from εἰκασία to πίστις (VI 511 E, VII 517 A notes). The higher we mount, the less of δόξα we retain, and in the higher stages of the προπαιδεία (symbolized by ἐκεῖ—ἀποσκιαζομένας) we escape from δόξα altogether. See App. I.

καὶ ἐκεῖ κτλ. ‘and when there, their inability still to look upon animals and plants and the light of the sun, but upon divine reflections in water and shadows of things real, not, as before, shadows of images thrown by a light which is itself but an image compared with the sun.’ Cf. 516 A, B. ἔτι ἀδυναμία is due to Iamblichus: see cr. n. and cf. Bywater in J. Ph. X p. 78. Nägelsbach also conjectured ἔτ’ ἀδυναμία. The difference between ἔτι and ἐπ in an uncial MS is practically nil. With πρὸς δὲ τὰ κτλ. the positive counterpart of ἀδυναμία ( βλέπειν) is to be supplied: cf. Ap. 36 B (where Schanz's insertion of οὔ after οἱ πολλοί is inelegant and unnecessary) and Kühner Gr. Gr. II p. 1072. For ἔτι with a verbal noun cf. IV 434 C note ‘Divine’ φαντάσματα is a half-technical Platonic phrase for reflections of natural objects produced by natural lights: they are θεῖα because θείας ἔργα ποιήσεως ( Soph. 266 C , where the whole matter is very clearly explained). Even without the aid of the Sophist, we might deduce the meaning from the antithetical clause ἀλλ’ οὐκ —ἀποσκιαζομένας, if we remember that the sun is a θεός (VI 508 A). The adjective is regularly placed after the substantive when two coordinate qualifications have to be expressed (here ἐν τοῖς ὕδασιν and θεῖα): cf. III 397 D τὸν τοῦ ἐπιεικοῦς μιμητὴν ἄκρατον, IX 573 A τῶν ἐν ταῖς τοιαύταις συνουσίαις ἡδονῶν ἀνειμένων. Other examples are given by Jebb on Soph. O. T. 1245 and Sandys on Arist. Ath. Pol. 51. 3: cf. also Stallbaum on Phil. 20 B . The present passage explains why Plato was so careful to make the originals in the Cave σκευαστά and εἴδωλα, and not φυτευτά: see on 514 B. Other views of this sentence are discussed in App. XIII.

πᾶσα κτλ. The anacoluthon is illustrated by Engelhardt Anac. Pl. Spec. III p. 45.

ταύτην τὴν δύναμιν : viz. λύσιν ἀπὸ τῶν δεσμῶν κτλ.

οὐ γὰρ ἐν τῷ νῦν κτλ. We ought not to interpret this as a promise of future dialogues (with Siebeck Unters. z. Phil. d. Griechen p. 118); it is only a way of indicating, before we pass on, that the subject is not exhausted. See on IV 430 C.

οὐκέτι κτλ. With the general tenour and form of the sentence cf. (with Jackson) Symp. 210 A. I can see no reason for suspecting the text (with Madvig, who proposes εἴ γ’ ἔτι, or εἰ σύ γ’ ἔτι, and Badham, who would insert εἰ before οἷός τ’ ἔσει). Glauco has not without difficulty (517 C) followed Socrates thus far: nor is there anything rude in telling him frankly that he has reached his limit, and even if there were, Socrates does not spare Glauco's feelings (cf. 527 D, 529 A). That his audience would not be able to follow a description of the Good, has already been implied in VI 506 E ff. βουλοίμην ἄν, εἶπον, ἐμέ τε δύνασθαι αὐτὴν (the account of the Good itself) ἀποδοῦναι καὶ ὑμᾶς κομίσασθαι. Here Socrates appears to be a trifle more confident of his own expository powers, though he is careful, as before, to avoid the appearance of dogmatism and therefore introduces the expression ὅ γε δή μοι φαίνεται etc. (cf. τοῦ γε δοκοῦντος ἐμοί l.c.) and προθυμίας (cf. προθυμούμενος δὲ κτλ. VI 506 D). Krohn (Pl. St. pp. 179 ff.) bitterly complains of Socrates for drawing back; and Whewell (Phil. of Discovery p. 436) observes “We may venture to say that it does not appear that he had any answer ready.” The dialectical method recommended by Plato in the Republic is doubtless, in its full significance, an unrealised ideal (cf. nn. on ἀρχὴν ἀνυπόθετον VI 510 B and τοῦ ἀνυποθέτου 511 B), just as the ultimate object of Dialectic, the Idea of Good, will still recede as we approach it. The description which follows merely recapitulates the account already given in Book VI, with a few additional characteristics already familiar in the Socratic school: but the majority of the Platonic dialogues furnish practical illustrations of many essential features in Plato's dialectical method: so that it is possible to form a tolerably clear idea of the kind of answer which the Platonic Socrates might have made in reply to Glauco's invitation. See on the whole subject App. III.