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1 The image of the cave illustrates by another proportion the contrast between the world of sense-perception and the world of thought. Instead of going above the plane of ordinary experience for the other two members of the proportion, Plato here goes below and invents a fire and shadows cast from it on the walls of a cave to correspond to the sun and the “real” objects of sense. In such a proportion our “real” world becomes the symbol of Plato's ideal world. Modern fancy may read what meanings it pleases into the Platonic antithesis of the “real” and the “ideal.” It has even been treated as an anticipation of the fourth dimension. But Plato never leaves an attentive and critical reader in doubt as to his own intended meaning. there may be at the most a little uncertainty as to which are merely indispensable parts of the picture. The source and first suggestion of Plato's imagery is an interesting speculation, but it is of no significance for the interpretation of the thought. Cf. John Henry Wright, “The Origin of Plato's Cave” in Harvard Studies in Class. Phil. xvii. (1906) pp. 130-142. Burnet, Early Greek Philosophy, pp. 89-90, thinks the allegory Orphic. Cf. also Wright, loc. cit. pp. 134-135. Empedocles likens our world to a cave, Diels i.3 269. Cf. Wright, loc. cit. Wright refers it to the Cave of Vari in Attica, pp. 140-142. Others have supposed that Plato had in mind rather the puppet and marionette shows to which he refers. Cf. Diès in Bulletin Budé,No. 14 (1927) pp. 8 f. The suggestiveness of the image has been endless. The most eloquent and frequently quoted passage of Aristotle's early writings is derived from it, Cic.De nat.deor. ii. 37. It is the source of Bacon's “idols of the den.” Sir Thomas Browne writes in Urne-Buriall: “We yet discourse in Plato's den and are but embryo philosophers.” Huxley's allegory of “Jack and the Beanstalk” in Evolution and Ethics, pp. 47 ff. is a variation on it. Berkeley recurs to it, Siris, 263. The Freudians would have still more fantastic interpretations. Cf. Jung, Analytic Psych. p. 232. Eddington perhaps glances at it when he attributes to the new physics the frank realization that physical science is concerned with a world of shadows
3 Cf. Phaedo 67 E.
4 H. Rackham, CIass. Rev. xxix. pp. 77-78, suggests that the τοῖς θαυματοποιοῖς should be translated “at the marionettes” and be classed with καινοῖς τραγῳδοῖς(Pseph.ap.Dem. xviii. 116). For the dative he refers to Kuehner-Gerth, II. i. p. 445.
5 The men are merely a part of the necessary machinery of the image. Their shadows are not cast on the wall. The artificial objects correspond to the things of sense and opinion in the divided line, and the shadows to the world of reflections,εἰκόνες.
6 Cf. Parmen. 130 c, Tim. 51 B, 52 A, and my De Platonis Idearum doctrina, pp. 24-25; also E. Hoffmann in Wochenschrift f. klass. Phil. xxxvi. (1919) pp. 196-197. As we use the word tree of the trees we see, though the reality (αὐτὸ ὃ ἔστι) is the idea of a tree, so they would speak of the shadows as the world, though the real reference unknown to them would be to the objects that cause the shadows, and back of the objects to the things of the “real” world of which they are copies. The general meaning, which is quite certain, is that they wold suppose the shadows to be the realities. The text and the precise turn of expression are doubtful. See crit. note.παριόντα is intentionally ambiguous in its application to the shadows or to the objects which cast them. They suppose that the names refer to the passing shadows, but (as we know) they really apply to the objects. Ideas and particulars are homonymous. Assuming a slight illogicality we can get somewhat the same meaning from the text ταὐτά. “Do you not think that they would identify the passing objects (which strictly speaking they do not know) with what they saw?” Cf. also P. Corssen, Philologische Wochenschrift, 1913, p. 286. He prefers οὐκ αὐτά and renders: “Sie würden in dem, was sie sähen, das Vorübergehende selbst zu benennen glauben.”
7 The echo and the voices (515 A) merely complete the picture.
10 The entire passage is an obvious allegory of the painful experience of one whose false conceit of knowledge is tested by the Socratic elenchus. Cf. Soph. 230 B-D, and for ἀπορεῖνMeno 80 A, 84 B-C, Theaet. 149 A, Apol. 23 D. Cf. also What Plato Said, p. 5123 on Meno 80 A, Eurip.Hippol. 247τὸ γὰρ ὀρθοῦσθαι γνώμαν ὀδυνᾷ, “it is painful to have one's opinions set right,” and 517 A, 494 D.
11 Cf. Theaet. 175 B, Boethius, Cons. iii. 12 “quicunque in superum diem mentem ducere quaeritis”; 529 A, 521 C, and the Neoplatonists' use of ἀνάγειν and their “anagogical” virtue and interpretation. Cf. Leibniz, ed. Gerhardt, vii. 270.
12 Cf. Laws 897 D, Phaedo 99 D.
13 Cf. Phaedo 99 D. Stallbaum says this was imitated by Themistius, Orat. iv. p. 51 B.
14 It is probably a mistake to look for a definite symbolism in all the details of this description. There are more stages of progress than the proportion of four things calls for. all that Plato's thought requires is the general contrast between an unreal and a real world, and the goal of the rise from one to the other in the contemplation of the sun, or the idea of good, Cf. 517 B-C.
15 i.e. a foreign medium.
16 Cf. 508 B, and for the idea of good as the cause of all things cf. on 509 B, and Introd. pp. xxxv-xxxvi. P. Corssen, Philol. Wochenschrift, 1913, pp. 287-299, unnecessarily proposes to emend ὧν σφεῖς ἑώρων to ὧν σκιὰς ἑ. or ὧν σφεῖς σκιὰς ἑ., “ne sol umbrarum, quas videbant, auctor fuisse dicatur, cum potius earum rerum, quarum umbras videbant, fuerit auctor.”
17 Cf. on 486 a, p. 10, note a.
18 Another of Plato's anticipations of modern thought. This is precisely the Humian, Comtian, positivist, pragmatist view of causation. Cf. Gorg. 501 Aτριβῇ καὶ ἐμπειρίᾳ μνήμην μόνον σωζομένη τοῦ εἰθότος γίγνεσθαι“relying on routine and habitude for merely preserving a memory of what is wont to result.” (Loeb tr.)
19 The quotation is almost as apt as that at the beginning of the Crito.
20 On the metaphor of darkness and light cf. also Soph. 254 A.
21 Like the philosopher in the court-room. Cf. Theaet. 172 C, 173 C ff., Gorg.. 484 D-e. Cf. also on 387 C-D. 515 D, 517 D, Soph. 216 D, Laches 196 B, Phaedr. 249 D.
22 An obvious allusion to the fate of Socrates. For other stinging allusions to this Cf. Gorg. 486 B, 521 C, Meno 100 B-C. Cf. Hamlet's “Wormwood, wormwood” (III. ii. 191). The text is disputed. See crit. note. A. Drachmann, “Zu Platons Staat,”Hermes, 1926, p. 110, thinks that an οἴει or something like it must be understood as having preceded, at least in Plato's thought, and that ἀποκτείνειν can be taken as a gloss or variant of ἀποκτεινύναι and the correct reading must be λαβεῖν, καὶ ἀποκτεινύναι ἄν. See also Adam ad loc.
23 Cf. 508 B-C, where Arnou (Le Désir de dieu dans la philos. de Plotin, p. 48 and Robin (La Théorie plat. de l'amour, pp. 83-84) make τόπος νοητός refer to le ciel astronomique as opposed to the ὑπερουράνιος τόπος of the Phaedrus 247 A-E, 248 B, 248 D-249 A. The phrase νοητὸς κόσμος, often attributed to Plato, does not occur in his writings.
24 Plato was much less prodigal of affirmation about metaphysical ultimates than interpreters who take his myths literally have supposed. Cf. What Plato Said, p. 515, on Meno 86 B.
25 Cf. 506 E.
26 This is the main point for the Republic. The significance of the idea of good for cosmogony is just glanced at and reserved for the Timaeus. Cf. on 508 B, p. 102, note a and p. 505-506. For the practical application Cf. Meno 81 D-E. See also Introd. pp. xxxv-xxxvi.
27 Cf. 521 A, 345 E, and Vol. I. on 347 D, p. 81, note d.
28 Cf. 346 E.
30 For the contrast between the philosophical and the pettifogging soul Cf. Theaet. 173 C-175 E. Cf. also on 517 A, p 128, note b.
33 Cf. Theaet. 175 D-E.
34 Lit. “or whether coming from a deeper ignorance into a more luminous world, it is dazzled by the brilliance of a greater light.”
36 ἐπαγγελλόμενοι connotes the boastfulness of their claims. Cf. Protag. 319 A, Gorg. 447 c, Laches 186 C, Euthyd. 273 E, Isoc.Soph. 1, 5, 9, 10, Antid. 193, Xen.Mem. iii. 1. 1, i. 2. 8, Aristot.Rhet. 1402 a 25.
37 Cf. Theognis 429 ff. Stallbaum compares Eurip.Hippol. 917 f. Similarly Anon. Theaet. Comm.(Berlin, 1905), p. 32, 48. 4καὶ δεῖν αὐτῇ οὐκ ἐνθέσεως μαθημάτων, ἀλλὰ ἀναμνήσεως. Cf. also St. Augustine: “Nolite putare quemquam hominem aliquid discere ab homine. Admonere possumus per strepitum vocis nostrae;” and Emerson's “strictly speaking, it is not instruction but provocation that I can receive from another soul.”
38 περιακτέον is probably a reference to the περίακτοι or triangular prisms on each side of the stage. They revolved on an axis and had different scenes painted on their three faces. Many scholars are of the opinion that they were not known in the classical period, as they are mentioned only by late writers; but others do not consider this conclusive evidence, as a number of classical plays seem to have required something of the sort. Cf. O. Navarre in Daremberg-Saglio s.v. Machine, p. 1469.
39 Hard-headed distaste for the unction or seeming mysticism of Plato's language should not blind us to the plain meaning. Unlike Schopenhauer, who affirms the moral will to be unchangeable, Plato says that men may be preached and drilled into ordinary morality, but that the degree of their intelligence is an unalterable endowment of nature. Some teachers will concur.
40 Plato often distinguishes the things that do or do not admit of reduction to an art or science. Cf. on 488 E p. 22, note b. Adam is mistaken in taking it “Education (ἡ παιδεία) would be an art,” etc.
41 This then is Plato's answer (intended from the first) to the question whether virtue can be taught, debated in the Protagoras and Meno. The intellectual virtues (to use Aristotle's term), broadly speaking, cannot be taught; they are a gift. And the highest moral virtue is inseparable from rightly directed intellectual virtue. Ordinary moral virtue is not rightly taught in democratic Athens, but comes by the grace of God. In a reformed state it could be systematically inculcated and “taught.” Cf. What Plato Said, pp. 51-512 on Meno 70 A. but we need not infer that Plato did not believe in mental discipline. cf. Charles Fox, Educational Psychology, p. 164 “The conception of mental discipline is a least as old as Plato, as may be seen from the seventh book of the Republic . . .”
43 Plato uses such synonyms as φρόνησις, σοφία, νοῦς, διάνοια, etc., as suits his purpose and context. He makes no attempt to define and discriminate them with impracticable Aristotelian meticulousness.
44 Cf. Theaet. 176 D, Laws 689 C-D, Cic.De offic. i. 19, and also Laws 819 A.
45 Cf. Theaet. 195 A, ibid. 173 Aσμικροὶ . . . τὰς ψυχάς, Marcus Aurelius’ψυχάριον εἶ βαστάζων νεκρόν, Swinburne's “A little soul for a little bears up this corpse which is man” (“Hymn to Proserpine,” in fine), Tennyson's “If half the little soul is dirt.”
46 Lit. “Toward which it is turned.”
47 The meaning is plain, the precise nature of the image that carries it is doubtful. Jowett's “circumcision” was suggested by Stallbaum's “purgata ac circumcisa,” but carries alien associations. The whole may be compared with the incrustation of the soul, 611 C-D, and with Phaedo 81 B f.
48 Or “eye of the mind.” Cf. 533 D, Sym. 219 A, Soph. 254 A, Aristot.Eth. 1144 a 30 , and the parallels and imitations collected by Gomperz, Apol. der Heilkunst, 166-167. cf. also What Plato Said, p. 534, on Phaedo 99 E, Ovid, Met. 15.64: “. . . quae natura negabat Visibus humanis, oculis ea pectoris hausit.” Cf. Friedlander, Platon, i. pp. 12-13, 15, and perhaps Odyssey, i. 115, Marc. Aurel. iv. 29καταμύειν τῷ νοερῷ ὄμματι.
49 For likely and necessary cf. on 485 C, p. 6, note c.
52 Cf. 539 E and Laws 803 B-C, and on 520 C, Huxley, Evolution and Ethics, p. 53 “the hero of our story descended the bean-stalk and came back to the common world,” etc.
53 Cf. Vol. I. pp. 314-315 on 419.
54 i.e. happiness, not of course exceptional happiness.
55 Persuasion and compulsion are often bracketed or contrasted. Cf. also Laws 661 C, 722 B, 711 C, Rep. 548 B.
56 Cf. 369 C ff. The reference there however is only to the economic division of labor. For the idea that laws should be for the good of the whole state cf. 420 B ff., 466 A, 341-342, Laws 715 B, 757 D, 875 A.
57 Noblesse oblige. This idea is now a commonplace of communist orations.
60 Cf. Polit. 301 D-E, Xen.Cyr. v.1.24, Oecon. 7.32-33.
62 They must descend into the cave again. Cf. 539 E and Laws 803 B-C. Cf. Burnet, Early Greek Philos. 89-90: “it was he alone, so far as we know, that insisted on philosophers descending by turns into the cave from which they had been released and coming to the help of their former fellow-prisoners.” He agrees with Stewart (Myths of Plato, p. 252, n. 2) that Plato had in mind the Orphic κατάβασις εἰς Ἅιδου to “rescue the spirits in prison.” Cf. Wright, Harvard Studies, xvii. p. 139 and Complete Poems of Henry More, pp. xix-xx “All which is agreeable to that opinion of Plato: That some descend hither to declare the Being and Nature of the Gods; and for the greater Health, Purity and Perfection of this Lower World.” This is taking Plato somewhat too literally and confusing him with Plotinus.
64 i.e. images, Bacon's “idols of the den.”
66 Cf. on 586 C, p. 393.
67 Cf. on 517 C, p. 131, note 3.
68 The world of ideas, the upper world as opposed to that of the cave. Cf. Stallbaum ad loc.
69 Cf. Vol. I. p. 80, note b on 347 C.
70 Cf. Phaedrus in fine, supra 416 E-417 A, 547 B.
71 Stallbaum refers to Xen.Cyr. viii. 3. 39οἴομαί σε καὶ διὰ τοῦτο ἥδιον πλουτεῖν, ὅτι πεινήσας χρημάτων πεπλούτηκας, “for you must enjoy tour riches much more, I think, for the very reason that it was only after being hungry for wealth that you became rich.” (Loeb tr.) Cf. also 577 E-578 A, and Adam ad loc.
72 Cf. 347 D, Laws 715 A, also 586 C and What Plato Said, p. 627, on Laws 678 E, Isoc.Areop. 24, Pan. 145 and 146.
74 Cf. 580 d ff., pp. 370 ff.
76 Cf. on 515 E, p. 124, note b.
77 This has been much debated. Cf. Adam ad loc.Professor Linforth argues from Pausanias i. 34 that Amphiaraus is meant.
78 Cf. Phaedr. 241 B; also the description of the game in Plato Comicus, Fr. 153 apud Norwood, Greek Comedy, p. 167. The players were divided into two groups. A shell or potsherd, black on one side and white on the other, was thrown, and according to the face on which it fell one group fled and the other pursued. Cf. also commentators on Aristoph.Knights 855.
79 Much quoted by Neoplatonists and Christian Fathers. Cf. Stallbaum ad loc. Again we need to remember that Plato's main and explicitly reiterated purpose is to describe a course of study that will develop the power of consecutive consistent abstract thinking. All metaphysical and mystical suggestions of the imagery which conveys this idea are secondary and subordinate. So, e.g. Urwick, The Message of Plato, pp. 66-67, is mistaken when he says “ . . . Plato expressly tells us that his education is designed simply and solely to awaken the spiritual faculty which every soul contains, by ‘wheeling the soul round and turning it away from the world of change and decay.’ He is not concerned with any of those ‘excellences of mind’ which may be produced by training and discipline, his only aim is to open the eye of the soul . . . “ The general meaning of the sentence is plain but the text is disputed. See crit. note.
80 A frequent pretence in Plato. Cf. 370 A, 525 C, Euthyphro 9 C, Laws 686 C, 702 B, Phaedr. 262 C with Friedländer, Platon, ii. p. 498, Laws 888 D with Tayler Lewis, Plato against the Atheists, pp. 118-119. Cf. also Vol. I. on 394 D-E, and Isoc.Antid. 159ἐνθυμοῦμαι δὲ μεταξὺ λέγων, Panath. 127.
81 Cf. 416 D, 422 B, 404 A, and Vol. I. p. 266, note a, on 403 E.
83 This further prerequisite of the higher education follows naturally from the plan of the Republic; but it does not interest Plato much and is, after one or two repetitions, dropped.
84 Cf. 376 E ff.
86 Cf. 376 E. This is of course no contradiction of 410 C.
87 The ordinary study of music may cultivate and refine feeling. Only the mathematics of music would develop the power of abstract thought.
88 Knowledge in the true sense, as contrasted with opinion or habit.
89 Cf. supra, p. 49 note e on 495 E. This idea is the source of much modern prejudice against Plato.
92 A playful introduction to Plato's serious treatment of the psychology of number and the value of the study of mathematics.
93 Palamedes, like Prometheus, is a “culture hero,” who personifies in Greek tragedy the inventions and discoveries that produced civilization. Cf. the speech of Prometheus in Aesch.Prom. 459 ff. and Harvard Studies, xii. p. 208, n. 2.
94 Quoted by later writers in praise of mathematics. Cf. Theo Smyrn. p. 7 ed. Gelder. For the necessity of mathematics Cf. Laws 818 C.
95 Cf. Laws 819 D.
96 Plato's point of view here, as he will explain, is precisely the opposite of that of modern educators who would teach mathematics concretely and not puzzle the children with abstract logic. But in the Laws where he is speaking of primary and secondary education for the entire population he anticipates the modern kindergarten ideas (819 B-C).
98 Cf. Phileb. 38 C.Unity of Plato's Thought, n. 337.
101 The most obvious cause of errors of judgement. Cf. Laws 663 B.
102 Cf. Vol. I. p. 137 on 365 C.
103 The dramatic misapprehension by the interlocutor is one of Plato's methods for enforcing his meaning. Cf. on 529 A, p. 180, note a, Laws 792 B-C.
104 Cf. Jacks, Alchemy of Thought, p. 29: “The purpose of the world, then, being to attain consciousness of itself as a rational or consistent whole, is it not a little strange that the first step, so to speak, taken by the world for the attainment of this end is that of presenting itself in the form of contradictory experience?” αἴσθησις is not to be pressed. Adam's condescending apology for the primitive character of Plato's psychology here is as uncalled-for as all such apologies. Plato varies the expression, but his meaning is clear. Cf. 524 D. No modern psychologists are able to use “sensation,” “perception,” “judgement,” and similar terms with perfect consistency.
105 For προσπίπτουσα Cf. Tim. 33 A, 44 A, 66 A, Rep. 515 A, 561 C, Laws 791 C, 632 A, 637 A, Phileb. 21 C; also “accidere” in Lucretius, e.g. iv. 882, ii. 1024-1025, iv. 236 and iii. 841, and Goethe's “Das Blenden der Erscheinung, die sich an unsere Sinne drängt.”
106 This anticipates Aristotle's doctrine that “substances” do not, as qualities do, admit of more or less.
109 Cf. Theaet. 186 ff., Tim. 62 B, Taylor, Timaeus, p. 233 on 63 D-E, Unity of Plato's Thought, nn. 222 and 225, Diels, Dialex. 5 (ii.3 p. 341). Protag. 331 D anticipates this thought, but Protagoras cannot follow it out. Cf. also Phileb. 13 A-B. Stallbaum also compares Phileb. 57 D and 56 C f.
110 Plato gives a very modern psychological explanation. Thought is provoked by the contradictions in perceptions that suggest problems. The very notion of unity is contradictory of uninterpreted experience. This use of ἀπορεῖν(Cf. 515 D) anticipates much modern psychology supposed to be new. Cf. e.g. Herbert Spencer, passim, and Dewey, How We Think, p. 12 “we may recapitulate by saying that the origin of thinking is some perplexity, confusion, or doubt”; also ibid, p. 62. Meyerson, Déduction relativiste p. 142, says “Mais Platon . . . n'avait-il pas dit qu'il était impossible de raisonner si ce n'est en partant d'une perception?” citing Rep. 523-524, and Rodier, Aristot. De anima, i. p. 191. But that is not Plato's point here. Zeller, Aristot. i. p. 166 (Eng.), also misses the point when he says “Even as to the passage from the former to the latter he had only the negative doctrine that the contradictions of opinion and fancy ought to lead us to go further and to pass to the pure treatment of ideas.”
113 Cf. Theaet. 185 B, Laws 963 C, Sophist 254 D, Hipp. Major 301 D-E, and, for the dialectic here, Parmen. 143 D.
117 Plato's aim is the opposite of that of the modern theorists who say that teaching should deal integrally with the total experience and not with the artificial division of abstraction.
118 The final use of διά became more frequent in later Greek. Cf. Aristot.Met. 982 b 20, Eth. Nic. 1110 a 4.Gen. an. 717 a 6, Poetics 1450 b 3, 1451 b 37. Cf. Lysis 218 B, Epin. 975 A, Olympiodorus, Life of Plato,Teubner vi. 191, ibid. p. 218, and schol.passim,Apsines, Spengel i. 361, line 18.
119 Plato merely means that this is the psychological origin of our attempt to form abstract and general ideas. My suggestion that this passage is the probable source of the notion which still infests the history of philosophy, that the great-and-the-small was a metaphysical entity or principle in Plato's later philosophy, to be identified with indeterminate dyad, has been disregarded. Cf. Unity of Plato's Thought, 84. But it is the only plausible explanation that has ever been proposed of the attribution of that “clotted nonsense” to Plato himself. For it is fallacious to identify μᾶλλον καὶ ἦττον in Philebus 24 C, 25 C, 21 E, and elsewhere with the μέγα καὶ σμικρόν. But there is no limit to the misapprehension of texts by hasty or fanciful readers in any age.
120 To waive metaphysics, unity is, as modern mathematicians say, a concept of the mind which experience breaks up. The thought is familiar to Plato from the Meno to the Parmenides. But it is not true that Plato derived the very notion of the concept from the problem of the one and the many. Unity is a typical concept, but the consciousness of the concept was developed by the Socratic quest for the definition.
121 Cf. 523 B. The meaning must be gathered from the context.
122 See crit. note and Adam ad loc.
123 This is the problem of the one and the many with which Plato often plays, which he exhaustively and consciously illustrates in the Parmenides, and which the introduction to the Philebus treats as a metaphysical nuisance to be disregarded in practical logic. We have not yet got rid of it, but have merely transferred it to psychology.
124 Cf. Gorg. 450 D, 451 B-C.
125 Cf. my review of Jowett, A.J.P. xiii. p. 365. My view there is adopted by Adam ad loc., and Apelt translates in the same way.
126 It is not true as Adam says that “the nature of numbers cannot be fully seen except in their connection with the Good.” Plato never says that and never really meant it, though he might possibly have affirmed it on a challenge. Numbers are typical abstractions and educate the mind for the apprehension of abstractions if studied in their nature, in themselves, and not in the concrete form of five apples. There is no common sense nor natural connection between numbers and the good, except the point made in the Timaeus 53 B, and which is not relevant here, that God used numbers and forms to make a cosmos out of a chaos.
127 Instead of remarking on Plato's scorn for the realities of experience we should note that he is marking the distinctive quality of the mind of the Greeks in contrast with the Egyptians and orientals from whom they learned and the Romans whom they taught. Cf. 525 Dκαπηλεύειν, and Horace, Ars Poetica 323-332, Cic.Tusc. i. 2. 5. Per contraXen. Mem. iv. 7, and Libby, Introduction to History of Science, p. 49: “In this the writer did not aim at the mental discipline of the students, but sought to confine himself to what is easiest and most useful in calculation, ‘such as men constantly require in cases of inheritance, legacies, partition, law-suits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other objects of various sorts and kinds are concerned.’”
128 Cf. on 521 D, p. 147, note e.
129 Cf. Aristot. Met. 982 a 15τοῦ εἰδέναι χάριν, and Laws 741 C. Montesquieu apud Arnold, Culture and Anarchy, p. 6: “The first motive which ought to impel us to study is the desire to augment the excellence of our nature and to render an intelligent being more intelligent.”
130 Lit. “numbers (in) themselves,” i.e. ideal numbers or the ideas of numbers. For this and the following as one of the sources of the silly notion that mathematical numbers are intermediate between ideal and concrete numbers, cf. my De Platonis Idearum Doctrina, p. 33, Unity of Plato's Thought, pp. 83-84, Class. Phil. xxii. (1927) pp. 213-218.
131 Cf. Meno 79 Cκατακερματίζῃς, Aristot.Met. 1041 a 19ἀδιαίρετον πρὸς αὑτὸ ἕκαστον: τοῦτο δ᾽ ἦν τὸ ἑνὶ εἶναι, Met. 1052 b a ff., 15 ff. and 1053 a 1τὴν γὰρ μονάδα τιθέασι πάντῃ ἀδιαίρετον. κερματίζειν is also the word used of breaking money into small change.
132 Numbers are the aptest illustration of the principle of the Philebus and the Parmenides that thought has to postulate unities which sensation (sense perception) and also dialectics are constantly disintegrating into pluralities. Cf. my Ideas of Good in Plato's Republic, p. 222. Stenzel, Dialektik, p. 32, says this dismisses the problem of the one and the many “das ihn (Plato) später so lebhaft beschäftigen sollte.” But that is refuted by Parmen. 159 Cοὐδὲ μὴν μόριά γε ἔχειν φαμὲν τὸ ὡς ἀληθῶς ἕν. The “problem” was always in Plato's mind. He played with it when it suited his purpose and dismissed it when he wished to go on to something else. Cf. on 525 A, Phaedr. 266 B, Meno 12 C, Laws 964 A, Soph. 251.
133 This is one of the chief sources of the fancy that numbers are intermediate entities between ideas and things. Cf. Alexander, Space, Time, and Deity, i. p. 219: “Mathematical particulars are therefore not as Plato thought intermediate between sensible figures and universals. Sensible figures are only less simple mathematical ones.” Cf. on 525 D. Plato here and elsewhere simply means that the educator may distinguish two kinds of numbers—five apples, and the number five as an abstract idea. Cf. Theaet. 19 E: We couldn't err about eleven which we only think, i.e. the abstract number eleven. Cf. also Berkeley, Siris, 288.
134 Cf. Isoc.Antid. 267αὐτοὶ δ᾽ αὑτῶν εὐμαθέστεροι. For the idiom αὐτοὶ αὑτῶν cf. also 411 C. 421 D, 571 D, Prot. 350 A and D, Laws 671 B, Parmen. 141 A, Laches 182 C. “Educators” have actually cited him as authority for the opposite view. On the effect of Mathematical studies cf. also Laws 747 B, 809 C-D, 810 C, Isoc.Antid. 276. Cf. Max Tyr. 37 7ἀλλὰ τοῦτο μὲν εἴη ἄν τι ἐν γεωμετρίᾳ τὸ φαυλότατον. Mill on Hamilton ii. 311 “If the Practice of mathematical reasoning gives nothing else it gives wariness of mind.” Ibid. 312.
135 The translation is, I think, right. Cf. A.J.P. xiii. p. 365, and Adam ad loc.
136 Cf. Burnet, Early Greek Philosophy, p. 111: “Even Plato puts arithmetic before geometry in the Republic in deference to tradition.” For the three branches of higher learning, arithmetic, geometry, and astronomy, Cf. Laws 811 E-818 A, Isoc.Antid. 261-267, Panath. 26, Bus. 226; Max, Tyr. 37 7.
137 Cf. Basilicon Doron(Morley, A Miscellany, p. 144): “I grant it is meete yee have some entrance, specially in the Mathematickes, for the knowledge of the art militarie, in situation of Campes, ordering of battels, making fortifications, placing of batteries, or such like.”
138 This was Xenophon's view, Mem. vi. 7. 2. Whether it was Socrates' nobody knows. Cf. pp. 162-163 on 525 C, Epin. 977 E, Aristoph.Clouds 202.
139 Because it develops the power of abstract thought. Not because numbers are deduced from the idea of good. Cf. on 525, p. 162, note b.
140 Cf. 518 C. Once more we should remember that for the practical and educational application of Plato's main thought this and all similar expressions are rhetorical surplusage or “unction,” which should not be pressed, nor used e.g. to identify the idea of good with god. Cf. Introd. p. xxv.
141 Or “becoming.” Cf. 485 B, 525 B.
143 Geometry (and mathematics) is inevitably less abstract than dialectics. But the special purpose of the Platonic education values mathematics chiefly as a discipline in abstraction. Cf. on 523 A, p. 152, note b; and Titchener, A Beginner's Psychology, pp. 265-266: “There are probably a good many of us whose abstract idea of ‘triangle’ is simply a mental picture of the little equilateral triangle that stands for the word in text-books of geometry.” There have been some attempts to prove (that of Mr. F. M. Cornford in Mind,April 1932, is the most recent) that Plato, if he could not anticipate in detail the modern reduction of mathematics to logic, did postulate something like it as an ideal, the realization of which would abolish his own sharp distinction between mathematics and dialectic. The argument rests on a remote and strained interpretation of two or three texts of the Republic(cf. e.g. 511 and 533 B-D) which, naturally interpreted, merely affirm the general inferiority of the mathematical method and the intermediate position for education of mathematics as a propaedeutic to dialectics. Plato's purpose throughout is not to exhort mathematicians as such to question their initiatory postulates, but to mark definitely the boundaries between the mathematical and other sciences and pure dialectics or philosophy. The distinction is a true and useful one today. Aristotle often refers to it with no hint that it could not be abolished by a new and different kind of mathematics. And it is uncritical to read that intention into Plato's words. He may have contributed, and doubtless did contribute, in other ways to the improvement and precision of mathematical logic. But he had no idea of doing away with the fundamental difference that made dialectics and not mathematics the coping-stone of the higher education—science as such does not question its first principles and dialectic does. Cf. 533 B-534 E.
145 Cf. Polit. 302 E, Laws 757 E, 818 B, Phileb. 62 B, Tim. 69 D, and also on 494 A. The word ἀναγκαίως has been variously misunderstood and mistranslated. It simply means that geometers are compelled to use the language of sense perception though they are thinking of abstractions (ideas) of which sense images are only approximations.
146 Cf. Aristot.Met. 1051 a 22εὑρίσκεται δὲ καὶ τὰ διαγράμματα ἐνεργείᾳ: διαιροῦντες γὰρ εὑρίσκουσιν, “geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them.” (Loeb tr.)
148 Cf. Thompson on Meno 87 A.
149 E. Hoffmann, Der gegenwärtige Stand der Platonforschung, p. 1091 (Anhang, Zeller, Plato, 5th ed.), misunderstands the passage when he says: “Die Abneigung Platons, dem Ideellen irgendwie einen dynamischen Charakter zuzuschreiben, zeigt sich sogar in terminologischen Andeutungen; so verbietet er Republ. 527 A für die Mathematik jede Anwendung dynamischer Termini wie τετραγωνίζειν, παρατείνειν, προστιθέναι” Plato does not forbid the use of such terms but merely recognizes their inadequacy to express the true nature and purpose of geometry.
150 Cf. Meyerson, De l'explication dans les sciences, p. 33: “En effet, Platon déjà fait ressortir que Ia géométrie, en dépit de l'apparence, ne poursuit aucun but pratique et n'a tout entière d'autre objet que Ia connaissance.
151 i.e. mathematical ideas are (Platonic) ideas like other concepts. Cf. on 525 D, p. 164, note a.
152 καλλιπόλει: Plato smiles at his own Utopia. There were cities named Callipolis, e.g. in the Thracian Chersonese and in Calabria on the Gulf of Tarentum. Cf. also Herod. vii. 154. fanciful is the attempt of some scholars to distinguish the Callipolis as a separate section of the Republic, or to take it as the title of the Republic.
153 Plato briefly anticipates much modern literature on the value of the study of mathematics. Cf. on 526 B, p. 166, note a. Olympiodorus says that when geometry deigns to enter into matter she creates mechanics which is highly esteemed.
155 Xen.Mem. iv. 7. 3 ff. attributes to Socrates a similar utilitarian view of science.
157 Cf. on 499 D-E, p. 66, note a.
158 Again Plato anticipates much modern controversy.
162 This is the thought more technically expressed in the “earlier” work, Crito 49 D. Despite his faith in dialectics Plato recognizes that the primary assumptions on which argument necessarily proceeds are irreducible choices of personality. Cf. What Plato Said, p. 478, Class. Phil. ix. (1914) p. 352.
163 Cf. Charm. 166 D, Phaedo 64 C, Soph. 265 A, Apol. 33 A.
166 Lit. “increase” Cf. Pearson, The Grammar of Science, p. 411: “He proceeds from curves of frequency to surfaces of frequency, and then requiring to go beyond these he finds his problem lands him in space of many dimensions.”
167 This is not to be pressed. Plato means only that the progress of solid geometry is unsatisfactory. Cf. 528 D. There may or may not be a reference here to the “Delian problem” of the duplication of the cube (cf. Wilamowitz, Platon, i. p. 503 for the story) and other specific problems which the historians of mathematics discuss in connection with this passage. Cf. Adam ad loc. To understand Plato we need only remember that the extension of geometry to solids was being worked out in his day, perhaps partly at his suggestion, e.g. by Theaetetus for whom a Platonic dialogue is named, and that Plato makes use of the discovery of the five regular solids in his theory of the elements in the Timaeus. Cf. also Laws 819 E ff. for those who wish to know more of the ancient traditions and modern conjectures I add references: Eva Sachs, De Theaeteto Ath. Mathematico,Diss. Berlin, 1914, and Die fünf platonischen Körper(Philolog. Untersuch. Heft 24), Berlin, 1917; E. Hoppe, Mathematik und Astronomie im klass. Altertum, pp. 133 ff.; Rudolf Eberling, Mathematik und Philosophie bei Plato,Münden, 1909, with my review in Class. Phil. v. (1910) p. 114; Seth Demel, Platons Verhältnis zur Mathematik,Leipzig, with my review, Class. Phil. xxiv. (1929) pp. 312-313; and, for further bibliography on Plato and mathematics, Budé, Rep.Introd. pp. lxx-lxxi.
168 Plato is perhaps speaking from personal experience as director of the Academy. Cf. the hint in Euthydem. 290 C.
169 i.e. the mathematicians already feel themselves to be independent specialists.
170 This interpretation is, I think, correct. For the construction of this sentence cf. Isoc. xv. 84. The text is disputed; see crit. note.
172 An eminent modern psychologist innocently writes: “The problem of why geometry gives pleasure is therefore a deeper problem than the mere assertion of the fact. Furthermore, there are many known cases where the study of geometry does not give pleasure to the student.” Adam seems to think it may refer to the personality of Eudoxus.
174 An obvious allusion to the proverb found in many forms in many languages. Cf. also Polit. 277 A-B, 264 B, Soph.Antig. 231σχολῇ ταχύς, Theognis 335, 401μηδὲν ἄγαν σπεύδειν, Suetonius, Augustus 25, Aulus Gellius x. 11. 4, Macrob.Sat. vi. 8. 9, “festina lente,” “hâtez-vous lentement” (Boileau, Art poétique, i. 171), “Chi va piano va sano e va lontano” (Goldoni, I volponi,I. ii.), “Eile mit Weile” and similar expressions; Franklin's “Great haste makes great waste,” etc.
176 This is the meaning. Neither Stallbaum's explanation, “quia ita est comparata, ut de ea quaerere ridiculum sit,” nor that accepted by Adam, “quia ridicule tractatur,” is correct, and 529 E and 521 A are not in point. Cf. 528 B p. 176, note a.
177 Cf. Laws 822 A ff.
178 i.e. “assuming this to exist,” “vorhanden sein,” which is the usual meaning of ὑπάρχειν in classical Greek. The science, of course, is solid geometry, which is still undeveloped, but in Plato's state will be constituted as a regular science through endowed research.
179 Cf. Vol. I. p. 410, note c, on 442 E, Gorg. 482 E, Rep. 581 D, Cratyl. 400 A, Apol. 32 A, Aristot.Pol. 1333 b 9.
180 Cf. my review if Warburg, Class. Phil. xxiv. (1929) p. 319. The dramatic misunderstanding forestalls a possible understanding by the reader. Cf. on 523 B. The misapprehension is typical of modern misunderstandings. Glaucon is here the prototype of all sentimental Platonists or anti-Platonists. The meaning of “higher” things in Plato's allegory is obvious. But Glaucon takes it literally. Similarly, modern critics, taking Plato's imagery literally and pressing single expressions apart from the total context, have inferred that Plato would be hostile to all the applications of modern science to experience. They refuse to make allowance for his special and avowed educational purpose, and overlook the fact that he is prophesying the mathematical astronomy and science of the future. The half-serious exaggeration of his rhetoric can easily be matched by similar utterances of modern thinkers of the most various schools, from Rousseau's “écarter tous les faits” to Judd's “Once we acquire the power to neglect all the concrete facts . . . we are free from the incumbrances that come through attention to the concrete facts.” Cf. also on 529 B, 530 B and 534 A.
181 ἀνάγοντες is tinged with the suggestions of 517 A, but the meaning here is those who use astronomy as a part of the higher education. φιλοσοφία is used in the looser sense of Isocrates. Cf. A.J.P. xvi. p. 237.
183 The humorous exaggeration of the language reflects Plato's exasperation at the sentimentalists who prefer star-gazing to mathematical science. Cf. Tim. 91 D on the evolution of birds from innocents who supposed that sight furnished the surest proof in such matters. Yet such is the irony of misinterpretation that this and the following pages are the chief support of the charge that Plato is hostile to science. Cf. on 530 B, p. 187, note c.
185 Cf. Aristoph.Clouds 172.
187 Cf. Phaedr. 264 A, and Adam in Class. Rev. xiii. p. 11.
188 Or rather, “serves me right,” or, in the American language, “I’ve got what's coming to me.” The expression is colloquial. Cf. Epist. iii. 319 E, Antiphon cxxiv. 45. But δίκην ἔχει in 520 B = “it is just.”
189 Cf. Tim. 40 Aκόσμον ἀληθινὸν αὐτῷ πεποικιλμένον, Eurip.Hel. 1096ἀστέρων ποικίλματα, Critias, Sisyphus,Diels ii.3 p. 321, lines 33-34τό τ᾽ ἀστερωπὸν οὐρανοῦ δέμας χρόνου καλὸν ποίκιλμα τέκτονος σοφοῦ. Cf. also Gorg. 508 A, Lucretius v. 1205 “stellis micantibus aethera fixum,” ii. 1031 ff., Aeneid iv. 482 “stellis ardentibus aptum,” vi. 797, xi. 202, Ennius, Ann. 372. The word ποικίλματα may further suggest here the complication of the movements in the heavens
190 The meaning of this sentence is certain, but the expression will no more bear a matter-of-fact logical analysis than that of Phaedo 69 A-B, or Rep. 365 C, or many other subtle passages in Plato. No material object perfectly embodies the ideal and abstract mathematical relation. These mathematical ideas are designated as the true,ἀληθινῶν, and the real,ὄν. As in the Timaeus(38 C, 40 A-B, 36 D-E) the abstract and ideal has the primacy and by a reversal of the ordinary point of view is said to contain or convey the concrete. The visible stars are in and are carried by their invisible mathematical orbits. By this way of speaking Plato, it is true, disregards the apparent difficulty that the movement of the visible stars then ought to be mathematically perfect. But this interpretation is, I think, more probable for Plato than Adam's attempt to secure rigid consistency by taking τὸ ὂν τάχος etc., to represent invisible and ideal planets, and τὰ ἐνόντα to be the perfect mathematical realities, which are in them. ἐνόντα would hardly retain the metaphysical meaning of ὄντα. For the interpretation of 529 D cf. also my “Platonism and the History of Science,”Am. Philos. Soc, Proc. lxvi. p. 172.
192 Cf. Bruno apudHöffding, History of Modern Philosophy, i. 125 and 128, and Galileo, ibid. i. 178; also Lucretius v. 302-305.
193 Plato was right against the view that Aristotle imposed on the world for centuries. We should not therefore say with Adam that he would have attached little significance to the perturbations of Neptune and the consequent discovery of Uranus. It is to Plato that tradition attributes the problem of accounting by the simplest hypothesis for the movement of the heavenly bodies and “saving the phenomena.” The alleged contradiction between this and Laws 821 B ff. and Tim. 41 A is due to a misapprehension. That the stars in their movements do not perfectly express the exactness of mathematical conceptions is no more than modern astronomers say. In the Laws passage Plato protests against the idea that there is no law and order governing the movement of the planets, but that they are “wandering stars,” as irregular in their movements as they seem. In the Timaeus he is saying that astronomy or science took its beginning from the sight and observation of the heavenly bodies and the changing seasons. In the RepublicPlato's purpose is to predict and encourage a purely mathematical astronomy and the indicate its place in the type of education which he wishes to give his guardians. There is not the slightest contradiction or change of opinion in the three passages if interpreted rightly in their entire context.
194 The meaning is not appreciably affected by a slight doubt as to the construction of ζητεῖν. It is usually taken with ἄτοπον(regarded as neuter), the meaning being that the Philosophic astronomer will think it strange to look for the absolute truth in these things. This double use of ἄτοπον is strained and it either makes παντὶ τρόπῳ awkward or attributes to Plato the intention of decrying the concrete study of astronomy. I think ζητεῖν etc. are added by a trailing anacoluthon such as occurs elsewhere in the Republic. Their subject is the real astronomer who, using the stars only as “diagrams” or patterns (529 D), seeks to learn a higher exacter mathematical truth than mere observation could yield. Madvig's ζητήσει implies a like view of the meaning but smooths out the construction. But my interpretation of the passage as a whole does not depend on this construction. If we make ζητεῖν depend on ἄτοπον(neuter)ἡγήσεται, the meaning will be that he thinks it absurd to expect to get that higher truth from mere observation. At all events Plato is not here objecting to observation as a suggestion for mathematical studies but to its substitution for them, as the next sentence shows.
195 That is just what the mathematical astronomy of today does, and it is a πολλαπλάσιον ἔργον compared with the merely observational astronomy of Plato's day. Cf. the interesting remarks of Sir James Jeans, apudS. J. Woolf, Drawn from Life, p. 74: “The day is gone when the astronomer's work is carried on only at the eyepiece of a telescope. Naturally, observations must be made, but these must be recorded by men who are trained for that purpose, and I am not one of them,” etc. Adam's quotation of Browning's “Abt Vogler” in connection with this passage will only confirm the opinion of those who regard Plato as a sentimental enemy of science.
196 Cf. also Phileb. 59 A, Aristot.Met. 997 b 35οὐδὲ περὶ τὸν οὐρανὸν ἡ ἀστρολογία τόνδε. This intentional Ruskinian boutade has given great scandal. The Platonist, we are told ad nauseam, deduces the world from his inner consciousness. This is of course not true (Cf. Unity of Plato's Thought, p. 45). But Plato, like some lesser writers, loves to emphasize his thought by paradox and surprise, and his postulation and of a mathematical astronomy required emphasis. Cf. my Platonism and the History of Science, pp. 171-174. This and similar passages cannot be used to prove that Plato was unscientific, as many hostile or thoughtless critics have attempted to do. Cf. e.g. the severe strictures of Arthur Platt, Nine Essays,Cambridge Univ. Press, 1921, pp. 12-16, especially p. 16: “Plato being first and foremost a metaphysician with a sort of religious system would not have us study anything but metaphysics and a kind of mystic religion.” Woodbridge Riley, From Myth to Reason, p. 47: “ . . . Plato...was largely responsible for turning back the clock of scientific progress. To explain the wonders of the world he preferred imagination to observation.” Cf. also Benn, Greek Philosophers, vol. i. pp. 173 and 327, Herrick, The Thinking Machine, p. 335, f. C. s. Schiller, Plato and he Predecessors, p. 81: “ . . . that Plato's anti-empirical bias renders him profoundly anti-scientific, and that his influence has always, openly or subtly, counteracted and thwarted the scientific impulse, or at least diverted it into unprofitable channels.” Dampier-Whetham, A History of Science, pp. 27-28: “Plato was a great philosopher but in the history of experimental science he must be counted a disaster.” Such statements disregard the entire context of the Platonic passages they exploit, and take no account of Plato's purpose or of other passages which counteract his seemingly unscientific remarks. Equally unfair is the practice of comparing Plato unfavorably with Aristotle in this respect, as Grote e.g. frequently does (Cf. Aristotle, p. 233). Plato was an artist and Aristotle an encyclopaedist; but Plato as a whole is far nearer the point of view of recent science than Aristotle. Cf. my Platonism and the History of Science, p. 163; also 532 A and on 529 A, p. 180, note a and What Plato Said, p. 236.
198 Plato here generalizes motion as a subject of science.
199 The modesty is in the tone of the Timaeus.
201 The similar statement attributed to Archytas, Diels i.3 p. 331, is probably an imitation of this.
202 Pythagoras is a great name, but little is known of him. “Pythagoreans” in later usage sometimes means mystics, sometimes mathematical physicists, sometimes both. Plato makes use of both traditions but is dominated by neither. For Erich Frank's recent book, Plato und die sogenannten Pythagoreer, cf. my article in Class. Phil. vol. xxiii. (1928） pp. 347 ff. The student of Plato will do well to turn the page when he meets the name Pythagoras in a commentator.
203 For this turn of phrase cf. Vol. I. p. 333, 424 C, Protag. 316 A, Symp. 186 E.
204 For the reference to experts Cf. 400 B, 424 C. Cf. also What Plato Said, p. 484, on Laches 184 D-E.
207 This passage is often taken as another example of Plato's hostility to science and the experimental method. It is of course not that, but the precise interpretation is difficult. Glaucon at first misapprehends (cf. p. 180, note a, on 529 A) and gives an amusing description of the mere empiricist in music. But Socrates says he does not mean these, but those who try to apply mathematics to the perception of sound instead of developing a (Kantian)a priori science of harmony to match the mathematical science of astronomy. Cf. also p. 193, note g, on 531 B, W. Whewell, Transaction of the Cabridge Philos. Soc. vol. ix. p. 389, and for music A. Rivaud, “Platon et la musique,”Rev. d’Histoire de la Philos. 1929, pp. 1-30; also Stallbaum ad loc., and E. Frank, Platon u. d. sog. Pyth.,Anhang, on the history of Greek music. He expresses surprise (p. 199) that Glaucon knows nothing of Pythagorean theories of music. Others use this to prove Socrates' ignorance of music.
208 This hints at the distinction developed in the Politicus between relative measurement of one thing against another and measurement by a standard. Cf. Polit. 283 E, 284 B-C, Theat. 186 A.
209 πυκνώματα(condensed notes). The word is technical. Cf. Adam ad loc.But, as ἄττα shows, Plato is using it loosely to distinguish a measure of sense perception from a mathematically determined interval.
210 Cf. Pater, Renaissance, p. 157. The phrase,ἐκ γειτόνων, is colloquial and, despite the protest of those who insist that it only means in the neighborhood, suggests overhearing what goes on next door—as often in the New Comedy.
211 Cf. Aldous Huxley, Jesting Pilate, p. 152: “Much is enthusiastically taught about the use of quarter tones in Indian music. I listened attentively at Lucknow in the hope of hearing some new and extraordinary kind of melody based on these celebrated fractions. But I listened in vain.” Gomprez, Greek Thinkers, iii. pp. 334-335, n. 85, thinks that Plato “shrugs his shoulders at experiments.” He refers to Plutarch, Life of Marcellus, xiv. 65, and Quaest. Conv. viii. 2. 1, 7, where Plato is represented as “having been angry with Eudoxus and Archytas because they employed instruments and apparatus for the solution of a problem, instead of relying solely on reasoning.”
212 So Malebranche, Entretiens sur la métaphysique, 3, x.: “Je pense que nous vous moquez de moi. C’est la raison et non les sens qu'il faut consulter.”
214 The language of the imagery confounds the torture of slaves giving evidence on the rack with the strings and pegs of a musical instrument. For the latter cf. Horace, A.P. 348, “nam neque chorda sonum reddit quem vult manus et mens Poscentique gravem persaepe remittit acutum.” Stallbaum says that Plato here was imitated by Aristaenetus, Epist. xiv. libr. 1τί πράγματα παρέχετε χορδαῖς;
215 This also may suggest a reluctant and a too willing witness.
216 Cf. on 489 A, p. 23, note d.
217 He distinguishes from the pure empirics just satirized those who apply their mathematics only to the data of observation. This is perhaps one of Plato's rare errors. For though there may be in some sense a Kantian a priori mechanics of astronomy, there can hardly be a purely a priori mathematics of acoustics. What numbers are consonantly harmonious must always remain a fact of direct experience. Cf. my Platonism and the History of Science, p. 176.
218 Cf. Friedländer, Platon, p. 108, n. 1.
219 Cf. Tim. 47 C-D. Plato always keeps to his point—cf. 349 B-C, 564 A-B—or returns to it after a digression. Cf. on 572 B, p. 339, note e.
220 Cf. on 505 B, p. 88, note a.
222 Cf. on 537 C, Epin. 991 E.
223 Plato is fond of this image. It suggests here also the preamble of a law, as the translation more explicitly indicates. Cf. 532 D, anticipated in 457 C, and Laws 722 D-E, 723 A-B and E, 720 D-E, ;772 E, 870 D, 854 A, 932 A and passim.
224 Cf. Theaet. 146 B, and perhaps Euthyd. 290 C. Though mathematics quicken the mind of the student, it is, apart from metaphysics, a matter of common experience that mathematicians are not necessarily good reasoners on other subjects. Jowett's wicked jest, “I have hardly ever known a mathematician who could reason,” misled an eminent professor of education who infers that Plato disbelieved in “mental discipline” (Yale Review,July 1917). Cf. also Taylor, Note in Reply to Mr. A. W. Benn, Mind, xii. (1903) p. 511; Charles Fox, Educational Psychology pp. 187-188: “ . . . a training in the mathematics may produce exactness of thought . . . provided that the training is of such a kind as to inculcate an ideal which the pupil values and strives to attain. Failing this, Glaucon's observation that he had ‘hardly ever known a mathematician who was capable of reasoning’ is likely to be repeated.” On the text cf. Wilamowitz, Platon, ii. pp. 384-385, and Adam ad loc.
225 λόγον . . . δοῦναιA commonplace Platonic plea for dialectics. Cf. 534 B, Prot. 336 C, Polit. 286 A, Theaet. 202 C, 175 C, 183 D, Soph. 230 A, Phaedo 78 C-D, 95 D, Charm. 165 B, Xen.Oecon. 11. 22. Cf. also λόγον λαβεῖνRep. 402 A, 534 B, Soph. 246 C, Theaet. 208 D, and Thompson on Meno 76 D.
226 Cf. Phileb. 58 D, Meno 75 C-D, Charm. 155 A, Cratyl. 390 C, and on 533 B, pp. 200 f., note f.
227 This is not a literal rendering, but gives the meaning.
228 Cf. 516 A-B. Plato interprets his imagery again here and in B infra.
229 Cf. p. 180, note a, and p. 187, note c. Cf. also 537 D, and on 476 A ff. Cf. Bergson, Introduction to Metaphysics, p. 9: “Metaphysics, then, is the science which claims to dispense with symbols”; E. S. Robinson, Readings in General Psych. p. 295: “A habit of suppressing mental imagery must therefore characterize men who deal much with abstract ideas; and as the power of dealing easily and firmly with these ideas is the surest criterion of a high order if intellect . . . “; Pear, Remembering and Forgetting, p. 57: “He (Napoleon) is reported to have said that ‘there are some who, from some physical or moral peculiarity of character, form a picture (tableau) of everything. No matter what knowledge, intellect, courage, or good qualities they may have, these men are unfit to command”; A. Bain, Mind, 1880, p. 570: “Mr. Galton is naturally startled at finding eminent scientific men, by their own account, so very low in the visualizing power. His explanation, I have no doubt, hits the mark; the deficiency is due to the natural antagonism of pictorial aptitude and abstract thought.”; Judd, Psychology of High School Subjects, p.921: “It did not appear on superficial examination of the standings of students that those who can draw best are the best students from the point of view of the teacher of science.”
232 Lit. “sun,” i.e. the world illumined by the sun, not by the fire in the cave.
233 See crit. note. The text of Iamblichus is the only reasonable one. The reading of the manuscripts is impossible. For the adverb modifying a noun cf. 558 Bοὐδ᾽ ὁπωστιοῦν σμικρολογία, Laws 638 Bσφόδρα γυναικῶν, with England's note, Theaet. 183 Eπάνυ πρεσβύτης, Laws 791 Cπαντελῶς παίδων, 698 Cσφόδρα φιλία, Rep. 564 Aἄγαν δουλείαν, with Stallbaum's note.
234 θεῖα because produced by God or nature and not by man with a mirror or a paintbrush. See crit. note and CIass. Review, iv. p. 480. I quoted Sophist 266 B-D, and Adam with rare candor withdrew his emendation in his Appendix XIII. to this book. Apelt still misunderstands and emends, p.296 and note.
235 This sentence is fundamental for the understanding of Plato's metaphysical philosophy generally. Cf. Unity of Plato's Thought, p. 30, n. 192, What Plato Said, p. 268 and 586 on Parmen. 135 C. So Tennyson says it is hard to believe in God and hard not to believe.
236 This is not mysticism or secret doctrine. It is, in fact, the avoidance of dogmatism. but that is not all. Plato could not be expected to insert a treatise on dialectical method here, or risk an absolute definition which would only expose him to misinterpretation. The principles and methods of such reasoning, and the ultimate metaphysical conclusions to which they may lead, cannot be expounded in a page or a chapter. They can only be suggested to the intelligent, whose own experience will help them to understand. As the Republic and Laws entire explain Plato's idea of social good, so all the arguments in the dialogues illustrate his conception of fair and unfair argument. Cf. What Plato Said,Index s.v.Dialectics, and note f below.
238 On Plato's freedom from the dogmatism often attributed to him Cf. What Plato Said, p. 515 on Meno 86 B.
239 On Plato's freedom from the dogmatism often attributed to him Cf. What Plato Said, p. 515 on Meno 86 B.
240 The mystical implications of φήνειεν are not to be pressed. It is followed, as usual in Plato, by a matter-of-fact statement of the essential practical conclusion (γοῦν)that no man can be trusted to think straight in large matters who has not been educated to reason and argue straight.
241 Plato anticipates the criticism that he neglects experience.
242 i.e. dispute our statement and maintain. The meaning is plain. It is a case of what I have called illogical idiom. Cf. T.A.P.A. vol. xlvii. pp. 205-234. The meaning is that of Philebus 58 E, 59 A. Other “science” may be more interesting or useful, but sound dialectics alone fosters the disinterested pursuit of truth for its own sake. Cf. Soph. 295 C, Phaedr. 265-266. Aristotle, Topics i. 2. 6, practically comes back to the Platonic conception of dialectics. The full meaning of dialectics in Plato would demand a treatise. It is almost the opposite of what Hegelians call by that name, which is represented in Plato by the second part of the Parmenides. The characteristic Platonic dialectic is the checking of the stream of thought by the necessity of securing the understanding and assent of an intelligent interlocutor at every step, and the habit of noting all relevant distinctions, divisions, and ambiguities, in ideas and terms. When the interlocutor is used merely to relieve the strain on the leader's voice or the reader's attention, as in some of the later dialogues, dialectic becomes merely a literary form.
243 Cicero's “via et ratione.”περὶ παντός is virtually identical with αὐτοῦ γε ἑκάστου πέρι. It is true that the scientific specialist confines himself to his specialty. The dialectician, like his base counterfeit the sophist (Soph. 231 A), is prepared to argue about anything, Soph. 232 cf., Euthyd. 272 A-B.
244 Cf. 525 C, 527 B.
245 The interpreters of Plato must allow for his Emersonian habit of hitting each nail in turn as hard as he can. There is no real contradiction between praising mathematics in comparison with mere loose popular thinking, and disparaging it in comparison with dialectics. There is no evidence and no probability that Plato is here proposing a reform of mathematics in the direction of modern mathematical logic, as has been suggested. Cf. on 527 A. It is the nature of mathematics to fall short of dialectics.
246 Cf. Phileb. 20 B and on 520 C, p. 143, note g.
247 Cf. on 531 E.
248 The touch of humor is the expression may be illustrated by Lucian, Hermotimus 74, where it is used to justify Lucian's skepticism even of mathematics, and by Hazlitt's remark on Coleridge, “Excellent talker if you allow him to start from no premises and come to no conclusion.”
249 Or “admission.” Plato thinks of even geometrical reasoning as a Socratic dialogue. Cf. the exaggeration of this idea by the Epicureans in Cic.De fin. i. 21 “quae et a falsis initiis profecta, vera esse non possunt: et si essent vera nihil afferunt quo iucundius, id est, quo melius viveremus.” Dialectic proceeds διὰ συγχωρήσεων, the admission of the interlocutor. Cf. Laws 957 D, Phaedr. 237 C-D, Gorg. 487 E, Lysis 219 C, Prot. 350 E, Phileb. 12 A, Theaet. 162 A, 169 D-E, I 64 C, Rep. 340 B. But such admissions are not valid unless when challenged they are carried back to something satisfactory—ἱκανόν—(not necessarily in any given case to the idea of good). But the mathematician as such peremptorily demands the admission of his postulates and definitions. Cf. 510 B-D, 511 B.
250 Cf. on 519 B, p. 138, note a.
251 Orphism pictured the impious souls as buried in mud in the world below; cf. 363 D. Again we should not press Plato's rhetoric and imagery either as sentimental Platonists or hostile critics. See Newman, Introd. Aristot.Pol. p. 463, n. 3.
252 All writers and philosophers are compelled to “speak with the vulgar.” Cf. e.g. Meyerson, De l'explication dans les sciences, i. p. 329: “Tout en sachant que la couleur n'est pas réellement une qualité de l'object, à se servir cependant, dans la vie de tous les jours, d'une locution qui l'affirme.”
253 Cf. on 511 D, pp. 116-117, note c.
254 This unwillingness to dispute about names when they do not concern the argument is characteristic of Plato. Cf. What Plato Said, p. 516 on Meno 78 B-C for numerous instances. Stallbaum refers to Max. Tyr.Diss. xxvii. p. 40ἐγὼ γάρ τοι τά τε ἄλλα, καὶ ἐν τῇ τῶν ὀνομάτων ἐλευθερίᾳ πείθομαι Πλάτωνι.
255 The next sentence is hopelessly corrupt and is often considered an interpolation. The translation omits it. See Adam, Appendix XVI. to Bk. VII., Bywater, Journal of Phil.(Eng.) v. pp. 122-124.
256 Supra 511 D-E.
257 Always avoid “faith” in translating Plato.
258 Cf. on 508 C, p. 103, note b.
259 That is the meaning, though some critics will object to the phrase. Lit. “the things over which these (mental states) are set, or to which they apply.”
260 There are two probable reasons for this: (1) The objective classification is nothing to Plato's present purpose; (2) The second member of the proportion is lacking in the objective correlates. Numbers are distinguished from ideas not in themselves but only by the difference of method in dialectics and in mathematics. Cf. on 525 D, 526 A, Unity of Plato's Thought, pp. 83-84, and Class. Phil. xxii. (1927) pp. 213-218. The explicit qualifications of my arguments there have been neglected and the arguments misquoted but not answered. They can be answered only by assuming the point at issue and affirming that Plato did assign an intermediate place to mathematical conceptions, for which there is no evidence in Plato's own writings.
261 Cf. on 531 E, p. 195, note f.
262 Cf. on 511 D, p. 117, note a.
263 This would be superfluous on the interpretation that the ἱκανόν must always be the idea of good. What follows distinguishes the dialectician from the the eristic sophist. For the short cut,καὶ . . . ὡσαύτως, cf. 523 E, 580 D, 585 D, 346 A, etc.
264 It imports little whether the objections are in his own mind or made by others. Thought is a discussion of the soul with itself (Cf. Theaet. 189 E, Phileb. 38 E, Soph. 263 E), and when the interlocutor refuses to proceed Socrates sometimes continues the argument himself by supplying both question and answer, e.g.Gorg. 506 C ff. Cf. further Phaedrus 278 C, Parman. 136 D-E, Unity of Plato's Thought, p. 17.
265 Cf. Theaet. 160 D, Phileb. 45 A. The practical outcome=Laws 966 A-B, Phaedr. 278 C, Soph. 259 B-C. Cf. Mill, Diss. and Disc. iv. p. 283: “There is no knowledge and no assurance of right belief but with him who can both confute the opposite opinion and successfully defend his own against confutation.”
267 For Platonic intellectualism the life of the ordinary man is something between sleep and waking. Cf. Apol. 31 A. Note the touch of humor in τελέως ἐπικαταδαρθάνειν. Cf. Bridges, Psychology, p. 382: “There is really no clear-cut distinction between what is usually called sleeping and waking. In sleep we are less awake than in the waking hours, and in waking life we are less asleep than in sleep.”
268 Plato likes to affirm his ideal only of the philosophic rulers.
269 Cf. 376 D, 369 C, 472 E, Critias 106 A.
270 A slight touch of humor. Cf. the schoolgirl who said, “These equations are inconsiderate and will not be solved.”
273 Cf. 541 B.
274 Cf. 412 D-E, 485-487, 503 A, C-E.
275 Intellectually as well as physically. Cf. 357 A, Prot. 350 B f.
276 Cf. Symp. 209 B-C, Phaedr. 252 E and Vol. I. p. 261 on 402 D. Ascham, The Schoolmaster,Bk. I. also approves of this qualification.
278 Cf. 504 A, 364 E, Gorg. 480 C, Protag. 326 C, Euthyphro 15 C.
279 The qualities of the ideal student again. Cf. on 487 A.
280 Cf. 495 C ff., pp. 49-51.
281 Montaigne, i. 24 (vol. i. p. 73), “les âmes boiteuses, les bastardes et vulgaires, sont indignes de Ia philosophie.”
282 Cf. Laws 634 A, Tim. 44 C.
283 Cf. 548 E, Lysis 206 C, Euthyd. 274 C, 304 C, and Vol. I. p. 515 on 475 D.
284 Cf. 382 A-B-C.
285 Cf. Laws 819 D, Rep. 372 D, Politicus 266 C, and my note in Class. Phil. xii. (1917) pp. 308-310. Cf. too the proverbial ὗς γνοίη, Laches 196 D and Rivals 134 A; and Apelt's emendation of Cratyl. 393 C, Progr. Jena, 1905, p. 19.
286 Cf. 487 A and vol. I. p. 261, note c on 402 C. The cardinal virtues are not rigidly fixed in Plato. Cf. on 427 E, vol. I. p. 346.
287 Plato is using ordinary language and not troubling himself with the problem of Protag. 329 D (What Plato Said, p. 497) and Laws 633 A (What Plato Said, p. 624). Cf. also on 533 D.
288 πρὸς ὅ τι ἂν τύχωσι lit. “for whatsoever they happen to of these (services).” Cf. Symp. 181 B, Prot. 353 A, Crito 44 D and 45 D, Gorg. 522 C, Laws 656 C, Rep. 332 B, 561 D, Dem. iv. 46, Isoc.Panath. 25, 74, 239, Aristot.Mat. 1013 a 6.
291 Jest and earnest are never far apart in Plato. Fabling about justice is an old man's game, Laws 685 A, 769 A. Life itself is best treated as play, Laws 803 C. Science in Tim. 59 D is παιδιά, like literature in the Phaedrus 276 D-E, ibid. 278 B. Cf. Friedländer, Platon, i. pp. 38 and 160, and What Plato Said, pp. 553 and 601.
293 Cf. Isoc.Busiris 49. Whatever the difficulties of the chronology it is hard to believe that this is not one of Isocrates' many endeavors to imitate Platonic effects.
294 Cf. Soph. 226 C, Sophocles, Ajax 397.
296 Cf. Theaet. 146 B. This has been misquoted to the effect that Plato said the young are the best philosophers.
298 Newman, Introd. Aristot.Pol. 358, says Aristotle rejects this distinction, Pol. 1338 b 40μέχρι μὲν γὰρ ἥβης κουφότερα γυμνάσια προσοιστέον, τὴν βίαιον τροφὴν καὶ τοὺς πρὸς ἀνάγκην πόνους ἀπείργοντας, ἵνα μηδὲν ἐμπόδιον ᾖ πρὸς τὴν αὔξησιν.
299 Cf. 424 E-425 A, Laws 819 B-C, 643 B-D, 797 A-B, Polit. 308 D. Cf. the naive statement in Colvin And Bagley, Human Behavior, p. 41: “The discovery [sic !] by Karl Groos that play was actually a preparation for the business of later life was almost revolutionary from the standpoint of educational theory and practice.”
300 Cf. 467, vol. I. pp. 485-487.
302 Cf. Aristot.Pol. 1339 a 7 f.ἅμα γὰρ τῇ τε διανοίᾳ καὶ τῷ σώματι διαπονεῖν οὐ δεῖ, etc.; Plut.De Ed. Puer. 11, De Tuenda San.C. 25, quoted by Newman, Aristot.Pol.I. p. 359, are irrelevant to this passage, but could be referred to the balancing of music and gymnastics in 410-412.
303 Cf. Laws 829 B-C.
304 σύνοψιν: cf. 531 D. This thought is endlessly repeated by modern writers on education. Cf. Mill, Diss. and Disc. iv. 336; Bagley, The Educative Process, p. 180: “The theory of concentration proposed by Ziller . . . seeks to organize all the subject matter of instruction into a unifies system, the various units of which shall be consciously related to one another in the minds of the pupils”; Haldane, The Philosophy of Humanism, p. 94: “There was a conference attended by representatives of various German Universities . . . which took place at Hanstein, not far from Göttingen in May 1921. . . . The purpose of the movement is nominally the establishment of a Humanistic Faculty. But in this connection ‘faculty’ does not mean a separate faculty of humanistic studies. . . . The real object is to bring these subjects into organic relation to one another.” Cf. Alexander, Space, Time, and Deity, vol. i. p. 4 “So true is it that, as Plato puts it, the metaphysician is a ‘synoptical’ man.” Cf. also Aristot.Soph. El. 167 a 38διὰ τὸ μὴ δύνασθαι συνορᾶν τὸ ταὐτὸν καὶ τὸ ἕτερον. Stenzel, Dialektik, misuses the passage to support the view that Plato's dialectic still looks for unity and not for divisions and distinctions, as in the Sophist. Cf. also ibid. p.72.
306 For this periphrasis Cf. Phaedr. 246 D, Tim. 85 E. Cf. also on 509 A.
307 The reader of Plato ought not to misunderstand this now. Cf. on 532 A, pp. 196 f., note d, and 530 p. 187, note c.
308 Plato returns to an idea suggested in 498 A, and warns against the mental confusion and moral unsettlement that result from premature criticism of life by undisciplined minds. In the terminology of modern education, he would not encourage students to discuss the validity of the Ten commandments and the Constitution of the United States before they could spell, construe, cipher, and had learned to distinguish an undistributed middle term from a petitio principii. Cf. Phaedo 89 D-E. We need not suppose with Grote and others that this involves any “reaction” or violent change of the opinion he held when he wrote the minor dialogues that portray such discussions. In fact, the still later Sophist, 230 B-C-D, is more friendly to youthful dialectics. Whatever the effect of the practice of Socrates or the Sophists, Plato himself anticipates Grote's criticism in the Republic by representing Socrates as discoursing with ingenuous youth in a more simple and edifying style. Cf. Lysis 207 D ff., Euthydem. 278 E-282 C, 288 D-290 D. Yet again the Charmides might be thought an exception. Cf. also Zeller, Phil. d. Griechen, ii. 1, p. 912, who seems to consider the Sophist earlier than the Republic.
309 i.e. they call all restrictions on impulses and instincts tyrannical conventions. Cf. Gorg. 483-484, Aristoph.Clouds, passim, and on nature and law cf. Vol. I. p. 116, note a, on 359 C.
310 Cf. on 494 A, p. 43, note c.
313 That is the meaning. Lit. “those who lay hold on discourse.”
314 Plato's warning apples to our day no less than to his own. Like the proponents of ethical nihilism in Plato's Athens, much of our present-day literature and teaching questions all standards of morality and aesthetics, and confuses justice and injustice, beauty and ugliness. Cf. also on 537 D, p. 220, note a.
319 Cf. Laws 633 E and 442 A-B. Others render it, “than the life of the flatterers (parasites).” Why not both?
320 See on 498 A-B. Cf. Richard of Bury, Philobiblon(Morley, A Miscellany, pp. 49-50): “But the contemporaries of our age negligently apply a few years of ardent youth, burning by turns with the fire of vice; and when they have attained the acumen of discerning a doubtful truth, they immediately become involved in extraneous business, retire, and say farewell to the schools of philosophy; they sip the frothy must of juvenile wit over the difficulties of philosophy, and pour out the purified old wine with economical care.”
321 Cf. Apol. 23 C, Phileb. 15 E, Xen.Mem. i. 2. 46, Isoc. xii. 26 and x. 6; also Friedländer, Platon, ii. p. 568.
322 But in another mood or from another angle this is the bacchic madness of philosophy which all the company in the Symposium have shared, 218 A-B. Cf. also Phaedr. 245 B-C, 249 C-E, Sophist 216 D, Phileb. 15 D-E, and What Plato Said, p. 493 on Protag. 317 D-E.
323 Cf. Gorg. 500 B-C. Yet the prevailing seriousness of Plato's own thought does not exclude touches of humor and irony, and he vainly warns the modern reader to distinguish between jest and earnest in the drama of disputation in his dialogues. Many misinterpretations of Plato's thought are due to the failure to heed this warning. Cf. e.g .Gorgias 474 A (What Plato Said, p. 504), which Robin, L’Année Philos. xxi. p. 29, and others miss, Rep. 376 B, Symp. 196 C, Protag. 339 f., Theaet. 157 A-B, 160 B,165 B,and passim. Cf. also on 536 C, p. 214, note b.
324 For the idiom μὴ ὡς νῦν etc. Cf. on 410 Bοὐχ ὥσπερ; also 610 D, Gorg. 522 A, Symp. 179 E, 189 C, Epist. vii. 333 A, Aristoph.Knights 784, Eurip.Bacchae 929, Il. xix. 493, Od. xxiv. 199, xxi. 427, Dem. iv. 34, Aristot.De an. 414 A 22.
325 It is very naive of modern commentators to cavil at the precise time allotted to dialectic, and still more so to infer that there was not much to say about the ideas. Dialectic was not exclusively or mainly concerned with the metaphysics of the ideas. It was the development of the reasoning powers by rational discussion.
326 Cf. 519 C ff., pp. 139-145.
327 Xen.Cyrop. i. 2. 13 seems to copy this. Cf. on 484 D. Critics of Plato frequently overlook the fact that he insisted on practical experience in the training of his rulers. Newman, Aristot.Pol. i. p. 5 points out that this experience takes the place of special training in political science.
329 An eminent scholar quaintly infers that Plato could not have written this page before he himself was fifty years old.
330 Plato having made his practical meaning quite clear feels that he can safely permit himself the short cut of rhetoric and symbolism in summing it up. He reckoned without Neoplatonists ancient and modern. Cf. also on 519 B, p. 138, note a.
332 Cf. 520 D.
333 Cf. 347 C-D, 520 E.
334 Plato's guardians, unlike Athenian statesmen, could train their successors. Cf. Protag. 319 E-320 B, Meno 99 B. Also ἄλλους ποιεῖνMeno 100 A, Gorg. 449 B, 455 C, Euthyph. 3 C, Phaedr. 266 C, 268 B, Symp. 196 E, Protag. 348 E, Isoc.Demon. 3, Panath. 28, Soph. 13, Antid. 204, Xen.Oecon. 15. 10, and παιδεύειν ἀνθρώπους, generally used of the sophists, Gorg. 519 E, Protag. 317 B, Euthyd. 306 E, Laches 186 D, Rep. 600 C.
335 Cf. p. 139, note d. Plato checks himself in mid-flight and wistfully smiles at his own idealism. Cf. on 536 B-C, also 540 C and 509 C. Frutiger, Mythes de Platon, p. 170.
336 Cf. Symp. 209 E.
337 For this caution cf. 461 E and Vol. I. p. 344, note c, on 427 C.
339 Cf. 361 D.
340 Lit. “female rulers.”
341 Cf. on 450 D and 499 C.
342 Cf. 499 D.
343 Cf. What Plato Said, p. 564 on Rep. 472 B-E, and p. 65, not h, on 499 D.
344 Cf. 463 C-D, 499 B-C.
345 Cf. 521 B, 516 C-D.
347 This is another of the passages in which Plato seems to lend support to revolutionaries. Cf. p. 71, note g. Cf. Laws 752 C, where it is said that the children would accept the new laws if the parents would not. Cf. 415 D, and also What Plato Said, p. 625, on Laws 644 A and p. 638, on 813 D. There is some confusion in this passage between the inauguration and the normal conduct of the ideal state, and Wilamowitz, Platon, i. p. 439 calls the idea “ein hingeworfener Einfall.” But Plato always held that the reformer must have or make a clean slate. Cf. 501 A, Laws 735 E. And he constantly emphasizes the supreme importance of education;Rep. 377 A-B, 423 E, 416 C, Laws 641 B, 644 A-B, 752 C, 765 E-766 A, 788 C, 804 D. For παραλαβόντες Cf. Phaedo 82 Eπαραλαβοῦσα.
348 Cf. 535 A.
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