Republic

Next, said I, “compare our nature in respect of education and its lack to such an experience as this. Picture men dwelling in a sort of subterranean cavern[*](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) with a long entrance open[*](Cf. Phaedo 111 C ἀναπεπταμένους) to the light on its entire width. Conceive them as having their legs and necks fettered[*](Cf. Phaedo 67 E.) from childhood, so that they remain in the same spot, able to look forward only, and prevented by the fetters from turning their heads. Picture further the light from a fire burning higher up and at a distance behind them, and between the fire and the prisoners and above them a road along which a low wall has been built, as the exhibitors of puppet-shows[*](H. Rackham, Class. 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.) have partitions before the men themselves, above which they show the puppets.” “All that I see,” he said. “See also, then, men carrying[*](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.) past the wall implements of all kinds that rise above the wall, and human images and shapes of animals as well, wrought in stone and wood and every material, some of these bearers presumably speaking and others silent.”

“A strange image you speak of,” he said, “and strange prisoners.” “Like to us,” I said; “for, to begin with, tell me do you think that these men would have seen anything of themselves or of one another except the shadows cast from the fire on the wall of the cave that fronted them?” “How could they,” he said, “if they were compelled to hold their heads unmoved through life?” “And again, would not the same be true of the objects carried past them?” Surely. “If then they were able to talk to one another, do you not think that they would suppose that in naming the things that they saw[*](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.) they were naming the passing objects?” Necessarily. “And if their prison had an echo[*](The echo and the voices (515 A) merely complete the picture.) from the wall opposite them, when one of the passersby uttered a sound, do you think that they would suppose anything else than the passing shadow to be the speaker?” “By Zeus, I do not,” said he. “Then in every way such prisoners would deem reality to be nothing else than the shadows of the artificial objects.” “Quite inevitably,” he said. “Consider, then, what would be the manner of the release[*](Phaedo 67 D λύειν, and 82 D λύσει τε καὶ καθαρμῷ. λύσις became technical in Neoplatonism.) and healing from these bonds and this folly if in the course of nature[*](Lit. by nature. φύσις in Plato often suggests reality and truth.) something of this sort should happen to them: When one was freed from his fetters and compelled to stand up suddenly and turn his head around and walk and to lift up his eyes to the light, and in doing all this felt pain and, because of the dazzle and glitter of the light, was unable to discern the objects whose shadows he formerly saw, what do you suppose would be his answer if someone told him that what he had seen before was all a cheat and an illusion, but that now, being nearer to reality and turned toward more real things, he saw more truly? And if also one should point out to him each of the passing objects and constrain him by questions to say what it is, do you not think that he would be at a loss[*](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 ἀπορεῖν Meno 80 A, 84 B-C, Theaet. 149 A, Apol. 23 D. Cf. also What Plato Said, p. 5123 on Meno 80 A, Eurip. Hippol. 247 τὸ γὰρ ὀρθοῦσθαι γνώμαν ὀδυνᾷ, it is painful to have one’s opinions set right, and 517 A, 494 D.) and that he would regard what he formerly saw as more real than the things now pointed out to him?” “Far more real,” he said. “And if he were compelled to look at the light itself, would not that pain his eyes, and would he not turn away and flee to those things which he is able to discern and regard them as in very deed more clear and exact than the objects pointed out?” “It is so,” he said.

“And if,” said I, “someone should drag him thence by force up the ascent[*](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.) which is rough and steep, and not let him go before he had drawn him out into the light of the sun, do you not think that he would find it painful to be so haled along, and would chafe at it, and when he came out into the light, that his eyes would be filled with its beams so that he would not be able to see[*](Cf. Laws 897 D, Phaedo 99 D.) even one of the things that we call real?” “Why, no, not immediately,” he said. “Then there would be need of habituation, I take it, to enable him to see the things higher up. And at first he would most easily discern the shadows and, after that, the likenesses or reflections in water[*](Cf. Phaedo 99 D. Stallbaum says this was imitated by Themistius, Orat. iv. p. 51 B.) of men and other things, and later, the things themselves, and from these he would go on to contemplate the appearances in the heavens and heaven itself, more easily by night, looking at the light of the stars and the moon, than by day the sun and the sun’s light.[*](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.)” Of course. “And so, finally, I suppose, he would be able to look upon the sun itself and see its true nature, not by reflections in water or phantasms of it in an alien setting,[*](i.e. a foreign medium.) but in and by itself in its own place.” Necessarily, he said. “And at this point he would infer and conclude that this it is that provides the seasons and the courses of the year and presides over all things in the visible region, and is in some sort the cause[*](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.) of all these things that they had seen.” Obviously, he said, “that would be the next step.” “Well then, if he recalled to mind his first habitation and what passed for wisdom there, and his fellow-bondsmen, do you not think that he would count himself happy in the change and pity them[*](Cf. on 486 a, p. 10, note a.)?” “He would indeed.” “And if there had been honors and commendations among them which they bestowed on one another and prizes for the man who is quickest to make out the shadows as they pass and best able to remember their customary precedences, sequences and co-existences,[*](Another of Plato’s anticipations of modern thought. This is precisely the Humian, Comtian, positivist, pragmatist view of causation. Cf. Gorg. 501 A τριβῇ 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.)) and so most successful in guessing at what was to come, do you think he would be very keen about such rewards, and that he would envy and emulate those who were honored by these prisoners and lorded it among them, or that he would feel with Homer[*](The quotation is almost as apt as that at the beginning of the Crito. ) and

greatly prefer while living on earth to be serf of another, a landless man,

“Now if he should be required to contend with these perpetual prisoners in evaluating these shadows while his vision was still dim and before his eyes were accustomed to the dark—and this time required for habituation would not be very short—would he not provoke laughter,[*](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.) and would it not be said of him that he had returned from his journey aloft with his eyes ruined and that it was not worth while even to attempt the ascent? And if it were possible to lay hands on and to kill the man who tried to release them and lead them up, would they not kill him[*](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.)?” “They certainly would,” he said. “This image then, dear Glaucon, we must apply as a whole to all that has been said, likening the region revealed through sight to the habitation of the prison, and the light of the fire in it to the power of the sun. And if you assume that the ascent and the contemplation of the things above is the soul’s ascension to the intelligible region,[*](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.) you will not miss my surmise, since that is what you desire to hear. But God knows[*](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.) whether it is true. But, at any rate, my dream as it appears to me is that in the region of the known the last thing to be seen and hardly seen is the idea of good, and that when seen it must needs point us to the conclusion that this is indeed the cause for all things of all that is right and beautiful, giving birth[*](Cf. 506 E.) in the visible world to light, and the author of light and itself in the intelligible world being the authentic source of truth and reason, and that anyone who is to act wisely[*](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.) in private or public must have caught sight of this.” “I concur,” he said, “so far as I am able.” “Come then,” I said, “and join me in this further thought, and do not be surprised that those who have attained to this height are not willing[*](Cf. 521 A, 345 E, and Vol. I. on 347 D, p. 81, note d.) to occupy themselves with the affairs of men, but their souls ever feel the upward urge and the yearning for that sojourn above. For this, I take it, is likely if in this point too the likeness of our image holds” “Yes, it is likely.” “And again, do you think it at all strange,” said I, “if a man returning from divine contemplations to the petty miseries[*](Cf. 346 E.) of men cuts a sorry figure[*](Cf. Theaet. 174 C ἀσχημοσύνη.) and appears most ridiculous, if, while still blinking through the gloom, and before he has become sufficiently accustomed to the environing darkness, he is compelled in courtrooms[*](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.) or elsewhere to contend about the shadows of justice or the images[*](For ἀγαλμάτων cf. my Idea of Good in Plato’s Republic, p. 237, Soph. 234 C, Polit. 303 C.) that cast the shadows and to wrangle in debate about the notions of these things in the minds of those who have never seen justice itself?” “It would be by no men strange,” he said.

“But a sensible man,” I said, “would remember that there are two distinct disturbances of the eyes arising from two causes, according as the shift is from light to darkness or from darkness to light,[*](Aristotle, De an. 422 a 20 f. says the over-bright is ἀόρατον but otherwise than the dark.) and, believing that the same thing happens to the soul too, whenever he saw a soul perturbed and unable to discern something, he would not laugh[*](Cf. Theaet. 175 D-E.) unthinkingly, but would observe whether coming from a brighter life its vision was obscured by the unfamiliar darkness, or whether the passage from the deeper dark of ignorance into a more luminous world and the greater brightness had dazzled its vision.[*](Lit. or whether coming from a deeper ignorance into a more luminous world, it is dazzled by the brilliance of a greater light.) And so[*](i.e. only after that. For οὕτω δή in this sense cf. 484 D, 429 D, 443 E, Charm. 171 E.) he would deem the one happy in its experience and way of life and pity the other, and if it pleased him to laugh at it, his laughter would be less laughable than that at the expense of the soul that had come down from the light above.” “That is a very fair statement,” he said. “Then, if this is true, our view of these matters must be this, that education is not in reality what some people proclaim it to be in their professions.[*](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.) What they aver is that they can put true knowledge into a soul that does not possess it, as if they were inserting[*](Cf. Theognis 429 ff. Stallbaum compares Eurip. Hippol. 917 f. Similarly Anon. Theaet. Comm. (Berlin, 1905), p. 32, 48. 4 καὶ 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.) vision into blind eyes.” “They do indeed,” he said. “But our present argument indicates,” said I, “that the true analogy for this indwelling power in the soul and the instrument whereby each of us apprehends is that of an eye that could not be converted to the light from the darkness except by turning the whole body. Even so this organ of knowledge must be turned around from the world of becoming together with the entire soul, like the scene-shifting periact[*](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.) in the theater, until the soul is able to endure the contemplation of essence and the brightest region of being. And this, we say, is the good,[*](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.) do we not?” Yes. “Of this very thing, then,” I said, “there might be an art,[*](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.) an art of the speediest and most effective shifting or conversion of the soul, not an art of producing vision in it, but on the assumption that it possesses vision but does not rightly direct it and does not look where it should, an art of bringing this about.” “Yes, that seems likely,” he said. “Then the other so-called virtues[*](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 . . .) of the soul do seem akin to those of the body. For it is true that where they do not pre-exist, they are afterwards created by habit[*](Cf. Aristot. Eth. Nic. 1103 a 14-17 ἡ δὲ ἠθικὴ ἐξ ἔθους. Plato does not explicitly name ethical and intellectual virtues. Cf. Fox, op. cit. p. 104 Plato correctly believed . . . ) and practice. But the excellence of thought,[*](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.) it seems, is certainly of a more divine quality, a thing that never loses its potency, but, according to the direction of its conversion, becomes useful and beneficent, or, again, useless and harmful.

Have you never observed in those who are popularly spoken of as bad, but smart men,[*](Cf. Theaet. 176 D, Laws 689 C-D, Cic. De offic. i. 19, and also Laws 819 A.) how keen is the vision of the little soul,[*](Cf. Theaet. 195 A, ibid. 173 A σμικροὶ . . . 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.) how quick it is to discern the things that interest it,[*](Lit. Toward which it is turned.) a proof that it is not a poor vision which it has, but one forcibly enlisted in the service of evil, so that the sharper its sight the more mischief it accomplishes?” “I certainly have,” he said. “Observe then,” said I, “that this part of such a soul, if it had been hammered from childhood, and had thus been struck free[*](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.) of the leaden weights, so to speak, of our birth and becoming, which attaching themselves to it by food and similar pleasures and gluttonies turn downwards the vision of the soul[*](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. 29 καταμύειν τῷ νοερῷ ὄμματι.)—If, I say, freed from these, it had suffered a conversion towards the things that are real and true, that same faculty of the same men would have been most keen in its vision of the higher things, just as it is for the things toward which it is now turned.” “It is likely,” he said. “Well, then,” said I, “is not this also likely[*](For likely and necessary cf. on 485 C, p. 6, note c.) and a necessary consequence of what has been said, that neither could men who are uneducated and inexperienced in truth ever adequately preside over a state, nor could those who had been permitted to linger on to the end in the pursuit of culture—the one because they have no single aim[*](σκοπόν: this is what distinguishes the philosophic statesman from the opportunist politician. Cf. 452 E, Laws 962 A-B, D, Unity of Plato’s Thought, p. 18 n. 102.) and purpose in life to which all their actions, public and private, must be directed, and the others, because they will not voluntarily engage in action, believing that while still living they have been transported to the Islands of the Blest.[*]( Cf. 540 B, Gorg. 526 C, 520 D ἐν τῷ καθαρῷ and Phaedo 114 C, 109 B. Because they will still suppose that they are building Jerusalem in England’s green and pleasant land (Blake).)” True, he said. “It is the duty of us, the founders, then,” said I, “to compel the best natures to attain the knowledge which we pronounced the greatest, and to win to the vision of the good, to scale that ascent, and when they have reached the heights and taken an adequate view, we must not allow what is now permitted.” “What is that?” “That they should linger there,” I said, “and refuse to go down again[*](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.) among those bondsmen and share their labors and honors, whether they are of less or of greater worth.” “Do you mean to say that we must do them this wrong, and compel them to live an inferior life when the better is in their power?” “You have again forgotten,[*](Cf. Vol. I. pp. 314-315 on 419.) my friend,” said I, “that the law is not concerned with the special happiness of any class in the state, but is trying to produce this condition[*](i.e. happiness, not of course exceptional happiness.) in the city as a whole, harmonizing and adapting the citizens to one another by persuasion and compulsion,[*](Persuasion and compulsion are often bracketed or contrasted. Cf. also Laws 661 C, 722 B, 711 C, Rep. 548 B.) and requiring them to impart to one another any benefit[*](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.) which they are severally able to bestow upon the community, and that it itself creates such men in the state, not that it may allow each to take what course pleases him, but with a view to using them for the binding together of the commonwealth.”

True, he said, “I did forget it.” “Observe, then, Glaucon,” said I, “that we shall not be wronging, either, the philosophers who arise among us, but that we can justify our action when we constrain them to take charge of the other citizens and be their guardians.[*](Noblesse oblige. This idea is now a commonplace of communist orations.) For we will say to them that it is natural that men of similar quality who spring up in other cities should not share in the labors there. For they grow up spontaneously[*](αὐτόματοι Cf. Protag. 320 A, Euthyd. 282 C. For the thought that there are a few men naturally good in any state cf. also Laws 951 B, 642 C-D.) from no volition of the government in the several states, and it is justice that the self-grown, indebted to none for its breeding, should not be zealous either to pay to anyone the price of its nurture.[*](Cf. Isoc. Archidamus 108 ἀποδῶμεν τὰ τροφεῖα τῇ πατρίδι. Stallbaum refers also to Phoenissae 44. For the country as τροφός see Vol. I. p. 303, note e on 414 E.) But you we have engendered for yourselves and the rest of the city to be, as it were, king-bees[*](Cf. Polit. 301 D-E, Xen. Cyr. v.1.24, Oecon. 7.32-33.) and leaders in the hive. You have received a better and more complete education[*](For τελεώτερον . . . πεπαιδευμένους Cf. Prot. 342 E τελέως πεπαιδευμένου.) than the others, and you are more capable of sharing both ways of life. Down you must go[*](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.) then, each in his turn, to the habitation of the others and accustom yourselves to the observation of the obscure things there. For once habituated you will discern them infinitely[*](For μυρίῳ cf. Eurip. Androm. 701.) better than the dwellers there, and you will know what each of the idols[*](i.e. images, Bacon’s idols of the den.) is and whereof it is a semblance, because you have seen the reality of the beautiful, the just and the good. So our city will be governed by us and you with waking minds, and not, as most cities now which are inhabited and ruled darkly as in a dream[*](Plato is fond of the contrast, ὕπαρ . . . ὄναρ. Cf. 476 C, Phaedr. 277 D, Phileb. 36 E, 65 E, Polit. 277 D, 278 E, Theaet. 158 B, Rep. 574 D, 576 B, Tim. 71 E, Laws 969 B, also 533 B-C.) by men who fight one another for shadows[*](Cf. on 586 C, p. 393.) and wrangle for office as if that were a great good, when the truth is that the city in which those who are to rule are least eager to hold office[*](Cf. on 517 C, p. 131, note 3.) must needs be best administered and most free from dissension, and the state that gets the contrary type of ruler will be the opposite of this.” “By all means,” he said. “Will our alumni, then, disobey us when we tell them this, and will they refuse to share in the labors of state each in his turn while permitted to dwell the most of the time with one another in that purer world[*](The world of ideas, the upper world as opposed to that of the cave. Cf. Stallbaum ad loc.)?” Impossible, he said: “for we shall be imposing just commands on men who are just. Yet they will assuredly approach office as an unavoidable necessity,[*](Cf. Vol. I. p. 80, note b on 347 C.) and in the opposite temper from that of the present rulers in our cities.”

“For the fact is, dear friend,” said I, “if you can discover a better way of life than office-holding for your future rulers, a well-governed city becomes a possibility. For only in such a state will those rule who are really rich,[*](Cf. Phaedrus in fine, ibid 416 E-417 A, 547 B.) not in gold, but in the wealth that makes happiness—a good and wise life. But if, being beggars and starvelings[*](Stallbaum refers to Xen. Cyr. viii. 3. 39 οἴομαί 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.) from lack of goods of their own, they turn to affairs of state thinking that it is thence that they should grasp their own good, then it is impossible. For when office and rule become the prizes of contention,[*](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.) such a civil and internecine strife[*](Cf. Eurip. Heracleidae 415 οἰκεῖος ἤδη πόλεμος ἐξαρτεύεται.) destroys the office-seekers themselves and the city as well.” “Most true,” he said. “Can you name any other type or ideal of life that looks with scorn on political office except the life of true philosophers[*](Cf. 580 d ff., pp. 370 ff.)?” I asked. “No, by Zeus,” he said. “But what we require,” I said, “is that those who take office[*](ἰέναι ἐπί in erotic language means to woo. Cf. on 489 C, p. 26, note b, also 347 C, 588 B, 475 C.) should not be lovers of rule. Otherwise there will be a contest with rival lovers.” Surely. “What others, then, will you compel to undertake the guardianship of the city than those who have most intelligence of the principles that are the means of good government and who possess distinctions of another kind and a life that is preferable to the political life?” “No others,” he said. “Would you, then, have us proceed to consider how such men may be produced in a state and how they may be led upward[*](Cf. on 515 E, p. 124, note b.) to the light even as some[*](This has been much debated. Cf. Adam ad loc. Professor Linforth argues from Pausanias i. 34 that Amphiaraus is meant.) are fabled to have ascended from Hades to the gods?” “Of course I would.” “So this, it seems, would not be the whirling of the shell[*](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.) in the children’s game, but a conversion and turning about of the soul from a day whose light is darkness to the veritable day—that ascension[*](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.) to reality of our parable which we will affirm to be true philosophy.” “By all means.” “Must we not, then, consider what studies have the power to effect this?” Of course. “What, then, Glaucon, would be the study that would draw the soul away from the world of becoming to the world of being? A thought strikes me while I speak[*](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. 159 ἐνθυμοῦμαι δὲ μεταξὺ λέγων, Panath. 127.): Did we not say that these men in youth must be athletes of war[*](Cf. 416 D, 422 B, 404 A, and Vol. I. p. 266, note a, on 403 E.)” “We did.” “Then the study for which we are seeking must have this additional[*](προσέχειν is here used in its etymological sense. Cf. pp. 66-67 on 500 A.) qualification.” “What one?” “That it be not useless to soldiers.[*](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.)” “Why, yes, it must,” he said, “if that is possible.” “But in our previous account they were educated in gymnastics and music.[*](Cf. 376 E ff.)” “They were, he said. “And gymnastics, I take it, is devoted[*](For τετεύτακε Cf. Tim. 90 B τετευτακότι ) to that which grows and perishes; for it presides over the growth and decay of the body.[*](Cf. 376 E. This is of course no contradiction of 410 C.)” Obviously. “Then this cannot be the study that we seek.”

No. “Is it, then, music, so far as we have already described it?[*](The ordinary study of music may cultivate and refine feeling. Only the mathematics of music would develop the power of abstract thought.)” “Nay, that,” he said, “was the counterpart of gymnastics, if you remember. It educated the guardians through habits, imparting by the melody a certain harmony of spirit that is not science,[*](Knowledge in the true sense, as contrasted with opinion or habit.) and by the rhythm measure and grace, and also qualities akin to these in the words of tales that are fables and those that are more nearly true. But it included no study that tended to any such good as you are now seeking.” “Your recollection is most exact,” I said; “for in fact it had nothing of the kind. But in heaven’s name, Glaucon, what study could there be of that kind? For all the arts were in our opinion base and mechanical.[*](Cf. ibid, p. 49 note e on 495 E. This idea is the source of much modern prejudice against Plato.)” “Surely; and yet what other study is left apart from music, gymnastics and the arts?” Come, said I, “if we are unable to discover anything outside of these, let us take something that applies to all alike.[*](Cf. Symp. 186 B ἐπὶ πᾶν τείνει.)” What? “Why, for example, this common thing that all arts and forms of thought[*](διάνοιαι is not to be pressed in the special sense of 511 D-E.) and all sciences employ, and which is among the first things that everybody must learn.” What? he said. “This trifling matter,[*](A playful introduction to Plato’s serious treatment of the psychology of number and the value of the study of mathematics.)” I said, “of distinguishing one and two and three. I mean, in sum, number and calculation. Is it not true of them that every art and science must necessarily partake of them?” “Indeed it is,” he said. “The art of war too?” said I. “Most necessarily,” he said. “Certainly, then,” said I, “Palamedes[*](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.) in the play is always making Agamemnon appear a most ridiculous[*](Quoted by later writers in praise of mathematics. Cf. Theo Smyrn. p. 7 ed. Gelder. For the necessity of mathematics Cf. Laws 818 C.) general. Have you not noticed that he affirms that by the invention of number he marshalled the troops in the army at Troy in ranks and companies and enumerated the ships and everything else as if before that they had not been counted, and Agamemnon apparently did not know how many feet he had if he couldn’t count? And yet what sort of a General do you think he would be in that case?” “A very queer one in my opinion,” he said, “if that was true.” “Shall we not, then,” I said, “set down as a study requisite for a soldier the ability to reckon and number?” “Most certainly, if he is to know anything whatever of the ordering of his troops—or rather if he is to be a man at all.[*](Cf. Laws 819 D.)” “Do you observe then,” said I, “in this study what I do?” What?

“It seems likely that it is one of those studies which we are seeking that naturally conduce to the awakening of thought, but that no one makes the right use[*](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).) of it, though it really does tend to draw the mind to essence and reality.” “What do you mean?” he said. “I will try,” I said, “to show you at least my opinion. Do you keep watch and observe the things I distinguish in my mind as being or not being conducive to our purpose, and either concur or dissent, in order that here too we may see more clearly[*](For σαφέστερον cf. 523 C. Cf. Vol. I. p. 47, note f, on 338 D, and What Plato Said, p. 503, on Gorg. 463 D.) whether my surmise is right.” “Point them out,” he said. “I do point them out,” I said, “if you can discern that some reports of our perceptions do not provoke thought to reconsideration because the judgement[*](Cf. Phileb. 38 C. Unity of Plato’s Thought, n. 337.) of them by sensation seems adequate,[*](ἱκανῶς is not to be pressed here.) while others always invite the intellect to reflection because the sensation yields nothing that can be trusted.[*](For οὐδὲν ὑγιές cf. 496 C, 584 A, 589 C, Phaedo 69 B, 89 E, 90 E, Gorg. 524 E, Laws 776 E, Theaet. 173 B, Eurip. Phoen. 201, Bacch. 262, Hel.. 746, etc.)” “You obviously mean distant[*](The most obvious cause of errors of judgement. Cf. Laws 663 B.) appearances,” he said, “and shadow-painting.[*](Cf. Vol. I. p. 137 on 365 C.)” “You have quite missed my meaning,[*](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.)” said I. “What do you mean?” he said. “The experiences that do not provoke thought are those that do not at the same time issue in a contradictory perception.[*](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.) Those that do have that effect I set down as provocatives, when the perception no more manifests one thing than its contrary, alike whether its impact[*](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.) comes from nearby or afar. An illustration will make my meaning plain. Here, we say, are three fingers, the little finger, the second and the middle.” “Quite so,” he said. “Assume that I speak of them as seen near at hand. But this is the point that you are to consider.” What? “Each one of them appears to be equally a finger,[*](This anticipates Aristotle’s doctrine that substances do not, as qualities do, admit of more or less.) and in this respect it makes no difference whether it is observed as intermediate or at either extreme, whether it is white or black, thick or thin, or of any other quality of this kind. For in none of these cases is the soul of most men impelled to question the reason and to ask what in the world is a finger, since the faculty of sight never signifies to it at the same time that the finger is the opposite of a finger.” “Why, no, it does not,” he said. Then, said I, “it is to be expected that such a perception will not provoke or awaken[*](We should never press synonyms which Plato employs for ποικιλία of style or to avoid falling into a rut of terminology.) reflection and thought.” “It is.” “But now, what about the bigness and the smallness of these objects? Is our vision’s view of them adequate, and does it make no difference to it whether one of them is situated[*](κεῖσθαι perhaps anticipates the Aristotelian category.) outside or in the middle; and similarly of the relation of touch, to thickness and thinness, softness and hardness? And are not the other senses also defective in their reports of such things?

Or is the operation of each of them as follows? In the first place, the sensation that is set over the hard is of necessity related also to the soft,[*](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.) and it reports to the soul that the same thing is both hard and soft to its perception.” “It is so,” he said. Then, said I, “is not this again a case where the soul must be at a loss[*](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.) as to what significance for it the sensation of hardness has, if the sense reports the same thing as also soft? And, similarly, as to what the sensation of light and heavy means by light and heavy, if it reports the heavy as light, and the light as heavy?” “Yes, indeed,” he said, “these communications[*](For ἑρμηνεῖαι Cf. Theaet. 209 A.) to the soul are strange and invite reconsideration.” “Naturally, then,” said I, “it is in such cases as these that the soul first summons to its aid the calculating reason[*](Cf. Parmen. 130 A τοῖς λογισμῷ λαμβανομένοις.) and tries to consider whether each of the things reported to it is one or two.[*](Cf. Theaet. 185 B, Laws 963 C, Sophist 254 D, Hipp. Major 301 D-E, and, for the dialectic here, Parmen. 143 D.)” Of course. “And if it appears to be two, each of the two is a distinct unit.[*](Or, as the Greek puts it, both one and other. Cf. Vol. 1. p. 516, note f on 416 A. For ἕτερον Cf. What Plato Said, pp. 522, 580, 587-588.)” Yes. “If, then, each is one and both two, the very meaning[*](γεvi termini Cf. 379 B, 576 C, Parmen. 145 A, Protag. 358 C.) of two is that the soul will conceive them as distinct.[*](κεχωρισμένα and ἀχώριστα suggest the terminology of Aristotle in dealing with the problem of abstraction.) For if they were not separable, it would not have been thinking of two, but of one.” Right. “Sight too saw the great and the small, we say, not separated but confounded.[*](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.) “Is not that so?” Yes. “And for[*](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.) the clarification of this, the intelligence is compelled to contemplate the great and small,[*](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.) not thus confounded but as distinct entities, in the opposite way from sensation.” True. “And is it not in some such experience as this that the question first occurs to us, what in the world, then, is the great and the small?” “By all means.” “And this is the origin of the designation intelligible for the one, and visible for the other.” “Just so,” he said. “This, then, is just what I was trying to explain a little while ago when I said that some things are provocative of thought and some are not, defining as provocative things that impinge upon the senses together with their opposites, while those that do not I said do not tend to awaken reflection.” “Well, now I understand,” he said, “and agree.” “To which class, then, do you think number and the one belong[*](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.)?” “I cannot conceive,” he said. “Well, reason it out from what has already been said. For, if unity is adequately[*](Cf. 523 B. The meaning must be gathered from the context.) seen by itself or apprehended by some other sensation, it would not tend to draw the mind to the apprehension of essence, as we were explaining in the case of the finger.

But if some contradiction is always seen coincidentally with it, so that it no more appears to be one than the opposite, there would forthwith be need of something to judge between them, and it would compel the soul to be at a loss and to inquire, by arousing thought in itself, and to ask, whatever then is the one as such, and thus the study of unity will be one of the studies that guide and convert the soul to the contemplation of true being.” “But surely,” he said, “the visual perception of it[*](See crit. note and Adam ad loc.) does especially involve this. For we see the same thing at once as one and as an indefinite plurality.[*](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.)” “Then if this is true of the one,” I said, “the same holds of all number, does it not?” Of course. “But, further, reckoning and the science of arithmetic[*](Cf. Gorg. 450 D, 451 B-C.) are wholly concerned with number.” “They are, indeed.” “And the qualities of number appear to lead to the apprehension of truth.” “Beyond anything,” he said. “Then, as it seems, these would be among the studies that we are seeking. For a soldier must learn them in order to marshal his troops, and a philosopher, because he must rise out of the region of generation and lay hold on essence or he can never become a true reckoner.[*](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.)” “It is so,” he said. “And our guardian is soldier and philosopher in one.” Of course. “It is befitting, then, Glaucon, that this branch of learning should be prescribed by our law and that we should induce those who are to share the highest functions of state to enter upon that study of calculation and take hold of it, not as amateurs, but to follow it up until they attain to the contemplation of the nature of number,[*](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.) by pure thought, not for the purpose of buying and selling,[*](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 D καπηλεύειν, and Horace, Ars Poetica 323-332, Cic. Tusc. i. 2. 5. Per contra Xen. 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.) as if they were preparing to be merchants or hucksters, but for the uses of war and for facilitating the conversion of the soul itself from the world of generation to essence and truth.” “Excellently said,” he replied. “And, further,” I said, “it occurs to me,[*](Cf. on 521 D, p. 147, note e.) now that the study of reckoning has been mentioned, that there is something fine in it, and that it is useful for our purpose in many ways, provided it is pursued for the sake of knowledge[*](Cf. Aristot. Met. 982 a 15 τοῦ 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.) and not for huckstering.” “In what respect?” he said. “Why, in respect of the very point of which we were speaking, that it strongly directs the soul upward and compels it to discourse about pure numbers,[*](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.) never acquiescing if anyone proffers to it in the discussion numbers attached to visible and tangible bodies. For you are doubtless aware that experts in this study, if anyone attempts to cut up the one in argument, laugh at him and refuse to allow it; but if you mince it up,[*](Cf. Meno 79 C κατακερματίζῃς, Aristot. Met. 1041 a 19 ἀδιαίρετον πρὸς αὑτὸ ἕκαστον· τοῦτο δ’ ἦν τὸ ἑνὶ εἶναι, Met. 1052 b a ff., 15 ff. and 1053 a 1 τὴν γὰρ μονάδα τιθέασι πάντῃ ἀδιαίρετον. κερματίζειν is also the word used of breaking money into small change.) they multiply, always on guard lest the one should appear to be not one but a multiplicity of parts.[*](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 C οὐδὲ 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.)” “Most true,” he replied.

“Suppose now, Glaucon, someone were to ask them, My good friends, what numbers[*](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.) are these you are talking about, in which the one is such as you postulate, each unity equal to every other without the slightest difference and admitting no division into parts? What do you think would be their answer?” “This, I think—that they are speaking of units which can only be conceived by thought, and which it is not possible to deal with in any other way.” “You see, then, my friend,” said I, “that this branch of study really seems to be indispensable for us, since it plainly compels the soul to employ pure thought with a view to truth itself.” “It most emphatically does.” “Again, have you ever noticed this, that natural reckoners are by nature quick in virtually all their studies? And the slow, if they are trained and drilled in this, even if no other benefit results, all improve and become quicker than they were[*](Cf. Isoc. Antid. 267 αὐτοὶ 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 7 ἀλλὰ 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.)?” “It is so,” he said. “And, further, as I believe, studies that demand more toil in the learning and practice than this we shall not discover easily nor find many of them.[*](The translation is, I think, right. Cf. A.J.P. xiii. p. 365, and Adam ad loc.)” “You will not, in fact.” “Then, for all these reasons, we must not neglect this study, but must use it in the education of the best endowed natures.” “I agree,” he said. “Assuming this one point to be established,” I said, “let us in the second place consider whether the study that comes next[*](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.) is suited to our purpose.” “What is that? Do you mean geometry,” he said. “Precisely that,” said I. “So much of it,” he said, “as applies to the conduct of war[*](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.) is obviously suitable. For in dealing with encampments and the occupation of strong places and the bringing of troops into column and line and all the other formations of an army in actual battle and on the march, an officer who had studied geometry would be a very different person from what he would be if he had not.” “But still,” I said, “for such purposes a slight modicum[*](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.) of geometry and calculation would suffice. What we have to consider is whether the greater and more advanced part of it tends to facilitate the apprehension of the idea of good.[*](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.) That tendency, we affirm, is to be found in all studies that force the soul to turn its vision round to the region where dwells the most blessed part of reality,[*](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.) which it is imperative that it should behold.” “You are right,” he said. “Then if it compels the soul to contemplate essence, it is suitable; if genesis,[*](Or becoming. Cf. 485 B, 525 B.) it is not.” “So we affirm.[*](γε δή is frequent in confirming answers. Cf. 557 B, 517 C, Symp. 172 C, 173 E, Gorg. 449 B, etc.)”

“This at least,” said I, “will not be disputed by those who have even a slight acquaintance with geometry, that this science is in direct contradiction with the language employed in it by its adepts.[*](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.)” “How so?” he said. “Their language is most ludicrous,[*](The very etymology of geometry implies the absurd practical conception of the science. Cf. Epin. 990 C γελοῖον ὄνομα.) though they cannot help it,[*](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.) for they speak as if they were doing something[*](Cf. Aristot. Met. 1051 a 22 εὑρίσκεται 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.)) and as if all their words were directed towards action. For all their talk[*](For φθεγγόμενοι cf. on 505 C, p. 89, note g.) is of squaring and applying[*](Cf. Thompson on Meno 87 A.) and adding and the like,[*](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.) whereas in fact the real object of the entire study is pure knowledge.[*](Cf. Meyerson, De l’explication dans les sciences, p. 33: En effet, Platon déjà fait ressortir que la géométrie, en dépit de l’apparence, ne poursuit aucun but pratique et n’a tout entière d’autre objet que Ia connaissance.)” “That is absolutely true,” he said. “And must we not agree on a further point?” What? “That it is the knowledge of that which always is,[*](i.e. mathematical ideas are (Platonic) ideas like other concepts. Cf. on 525 D, p. 164, note a.) and not of a something which at some time comes into being and passes away.” “That is readily admitted,” he said, “for geometry is the knowledge of the eternally existent.” “Then, my good friend, it would tend to draw the soul to truth, and would be productive of a philosophic attitude of mind, directing upward the faculties that now wrongly are turned earthward.” “Nothing is surer,” he said. “Then nothing is surer,” said I, “than that we must require that the men of your Fair City[*](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.) shall never neglect geometry, for even the by-products of such study are not slight.” “What are they?” said he. “What you mentioned,” said I, “its uses in war, and also we are aware that for the better reception of all studies[*](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.) there will be an immeasurable[*](For ὅλῳ καὶ παντί cf. 469 C. Laws 779 B, 734 E, Phaedo 79 E, Crat. 434 A.) difference between the student who has been imbued with geometry and the one who has not.” “Immense indeed, by Zeus,” he said. “Shall we, then, lay this down as a second branch of study for our lads?” “Let us do so,” he said. “Shall we set down astronomy as a third, or do you dissent?” “I certainly agree,” he said; “for quickness of perception about the seasons and the courses of the months and the years is serviceable,[*](Xen. Mem. iv. 7. 3 ff. attributes to Socrates a similar utilitarian view of science.) not only to agriculture and navigation, but still more to the military art.” “I am amused,[*](For ἡδὺς εἶ cf. 337 D, Euthydem. 300 A, Gorg. 491 E ἥδιστε, Rep. 348 C γλυκὺς εἶ, Hipp. Maj. 288 B.)” said I, “at your apparent fear lest the multitude[*](Cf. on 499 D-E, p. 66, note a.) may suppose you to be recommending useless studies.[*](Again Plato anticipates much modern controversy.) It is indeed no trifling task, but very difficult to realize that there is in every soul an organ or instrument of knowledge that is purified[*](Cf. Xen. Symp. 1. 4 ἐκκεκαθαρμένοις τὰς ψυχάς, and Phaedo 67 B-C.) and kindled afresh by such studies when it has been destroyed and blinded by our ordinary pursuits, a faculty whose preservation outweighs ten thousand eyes[*](Another instance of Plato’s unction. Cf. Tim. 47 A-B, Eurip. Orest. 806 μυρίων κρείσσων, and Stallbaum ad loc. for imitations of this passage in antiquity.); for by it only is reality beheld. Those who share this faith will think your words superlatively[*](For ἀμηχάνως ὡς Cf. Charm. 155 D ἀμήχανόν τι οἷον. Cf. 588 A, Phaedo 80 C, 95 C, Laws 782 A, also Rep. 331 A θαυμάστος ὡς, Hipp. Maj. 282 C, Epin. 982 C-E, Aristoph. Birds 427, Lysist. 198, 1148.) true. But those who have and have had no inkling of it will naturally think them all moonshine.[*](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.) For they can see no other benefit from such pursuits worth mentioning.

Decide, then, on the spot, to which party you address yourself. Or are you speaking to neither, but chiefly carrying on the discussion for your own sake,[*](Cf. Charm. 166 D, Phaedo 64 C, Soph. 265 A, Apol. 33 A.) without however judging any other who may be able to profit by it?” “This is the alternative I choose,” he said, “that it is for my own sake chiefly that I speak and ask questions and reply.” “Fall back[*](ἄναγε is a military term. Cf. Aristoph. Birds 383, Xen. Cyr. vii. 1.45, iii. 3. 69.) a little, then,” said I; “for we just now did not rightly select the study that comes next[*](ἑξῆς Cf. Laches 182 B.) after geometry.” “What was our mistake?” he said. “After plane surfaces,” said I, “we went on to solids in revolution before studying them in themselves. The right way is next in order after the second dimension[*](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.) to take the third. This, I suppose, is the dimension of cubes and of everything that has depth.” “Why, yes, it is,” he said; “but this subject, Socrates, does not appear to have been investigated yet.[*](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.)” “There are two causes of that,” said I: “first, inasmuch as no city holds them in honor, these inquiries are languidly pursued owing to their difficulty. And secondly, the investigators need a director,[*](Plato is perhaps speaking from personal experience as director of the Academy. Cf. the hint in Euthydem. 290 C.) who is indispensable for success and who, to begin with, is not easy to find, and then, if he could be found, as things are now, seekers in this field would be too arrogant[*](i.e. the mathematicians already feel themselves to be independent specialists.) to submit to his guidance. But if the state as a whole should join in superintending these studies and honor them, these specialists would accept advice, and continuous and strenuous investigation would bring out the truth. Since even now, lightly esteemed as they are by the multitude and hampered by the ignorance of their students[*](This interpretation is, I think, correct. For the construction of this sentence cf. Isoc. xv. 84. The text is disputed; see crit. note.) as to the true reasons for pursuing them,[*](Lit. in what respect they are useful. Plato is fond of the half legal καθ’ ὅ τι. Cf. Lysis 210 C, Polit. 298 C.) they nevertheless in the face of all these obstacles force their way by their inherent charm[*](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.) and it would not surprise us if the truth about them were made apparent.” “It is true,” he said, “that they do possess an extraordinary attractiveness and charm. But explain more clearly what you were just speaking of. The investigation[*](πραγματείαν: interesting is the development of this word from its use in Phaedo 63 A (interest, zeal, inquiring spirit. Cf. Aristot. Top. 100 a 18, Eth. Nic. 1103 b 26, Polyb. i. 1. 4, etc.) of plane surfaces, I presume, you took to be geometry?” Yes, said I. “And then,” he said, “at first you took astronomy next and then you drew back.” Yes, I said, “for in my haste to be done I was making less speed.[*](An obvious allusion to the proverb found in many forms in many languages. Cf. also Polit. 277 A-B, 264 B, Soph. Antig. 231 σχολῇ ταχύς, Theognis 335, 401 μηδὲν 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.) For, while the next thing in order is the study[*](μέθοδον: this word, like πραγματεία came to mean treatise.) of the third dimension or solids, I passed it over because of our absurd neglect[*](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.) to investigate it, and mentioned next after geometry astronomy,[*](Cf. Laws 822 A ff.) which deals with the movements of solids.” “That is right,” he said. “Then, as our fourth study,” said I, “let us set down astronomy, assuming that this science, the discussion of which has been passed over, is available,[*](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.) provided, that is, that the state pursues it.”

“That is likely,” said he; “and instead of the vulgar utilitarian[*](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.) commendation of astronomy, for which you just now rebuked me, Socrates, I now will praise it on your principles. For it is obvious to everybody, I think, that this study certainly compels the soul to look upward[*](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.) and leads it away from things here to those higher things.” “It may be obvious to everybody except me,” said I, “for I do not think so.” “What do you think?” he said. “As it is now handled by those who are trying to lead us up to philosophy,[*](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.) I think that it turns the soul’s gaze very much downward.” “What do you mean?” he said. “You seem to me in your thought to put a most liberal[*](For οὐκ ἀγεννῶς Gorg. 462 D, where it is ironical, as here, Phaedr. 264 B, Euthyph. 2 C, Theaet. 184 C. In Charm. 158 C it is not ironical.) interpretation on the study of higher things,” I said, “for apparently if anyone with back-thrown head should learn something by staring at decorations on a ceiling, you would regard him as contemplating them with the higher reason and not with the eyes.[*](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.) Perhaps you are right and I am a simpleton. For I, for my part, am unable to suppose that any other study turns the soul’s gaze upward[*](Cf. Theaet. 174 A ἄνω βλέποντα.) than that which deals with being and the invisible. But if anyone tries to learn about the things of sense, whether gaping up[*](Cf. Aristoph. Clouds 172.) or blinking down,[*](συμμύω probably refers to the eyes. But cf. Adam ad loc.) I would never say that he really learns—for nothing of the kind admits of true knowledge—nor would I say that his soul looks up, but down, even though he study floating on his back[*](Cf. Phaedr. 264 A, and Adam in Class. Rev. xiii. p. 11.) on sea or land.” “A fair retort,[*](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.)” he said; “your rebuke is deserved. But how, then, did you mean that astronomy ought to be taught contrary to the present fashion if it is to be learned in a way to conduce to our purpose?” Thus, said I, “these sparks that paint the sky,[*](Cf. Tim. 40 A κόσμον ἀληθινὸν αὐτῷ πεποικιλμένον, Eurip. Hel. 1096 ἀστέρων ποικίλματα, Critias, Sisyphus, Diels ii.3 p. 321, lines 33-34 τό 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) since they are decorations on a visible surface, we must regard, to be sure, as the fairest and most exact of material things but we must recognize that they fall far short of the truth,[*](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.) the movements, namely, of real speed and real slowness in true number and in all true figures both in relation to one another and as vehicles of the things they carry and contain. These can be apprehended only by reason and thought, but not by sight; or do you think otherwise?” “By no means,” he said. Then, said I, “we must use the blazonry of the heavens as patterns to aid in the study of those realities, just as one would do who chanced upon diagrams drawn with special care and elaboration by Daedalus or some other craftsman or painter.

For anyone acquainted with geometry who saw such designs would admit the beauty of the workmanship, but would think it absurd to examine them seriously in the expectation of finding in them the absolute truth with regard to equals or doubles or any other ratio.” “How could it be otherwise than absurd?” he said. “Do you not think,” said I, “that one who was an astronomer in very truth would feel in the same way when he turned his eyes upon the movements of the stars? He will be willing to concede that the artisan[*](δημιουργῷ: an anticipation of the Timaeus.) of heaven fashioned it and all that it contains in the best possible manner for such a fabric; but when it comes to the proportions of day and night, and of their relation to the month, and that of the month to the year, and of the other stars to these and one another, do you not suppose that he will regard as a very strange fellow the man who believes that these things go on for ever without change[*](Cf. Bruno apud Höffding, History of Modern Philosophy, i. 125 and 128, and Galileo, ibid. i. 178; also Lucretius v. 302-305.) or the least deviation[*](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 Republic Plato’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.)—though they possess bodies and are visible objects—and that his unremitting quest[*](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.) the realities of these things?” “I at least do think so,” he said, “now that I hear it from you.” “It is by means of problems,[*](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, apud S. 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.) then,” said I, “as in the study of geometry, that we will pursue astronomy too, and we will let be the things in the heavens,[*](Cf. also Phileb. 59 A, Aristot. Met. 997 b 35 οὐδὲ 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.) if we are to have a part in the true science of astronomy and so convert to right use from uselessness that natural indwelling intelligence of the soul.” “You enjoin a task,” he said, “that will multiply the labor[*](Cf. Phaedr. 272 B καίτοι οὐ σμικρόν γε φαίνεται ἔργον.) of our present study of astronomy many times.” “And I fancy,” I said, “that our other injunctions will be of the same kind if we are of any use as lawgivers. “However, what suitable studies have you to suggest?” Nothing, he said, “thus off-hand.” “Yet, surely,” said I, “motion[*](Plato here generalizes motion as a subject of science.) in general provides not one but many forms or species, according to my opinion. To enumerate them all will perhaps be the task of a wise man,[*](The modesty is in the tone of the Timaeus.) but even to us two of them are apparent.” “What are they?” “In addition to astronomy, its counterpart, I replied.” “What is that?” “We may venture to suppose,” I said, “that as the eyes are framed for astronomy so the ears are framed,[*](For πέπηγεν cf. 605 A.) for the movements of harmony; and these are in some sort kindred sciences,[*](The similar statement attributed to Archytas, Diels i.3 p. 331, is probably an imitation of this.) as the Pythagoreans[*](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.) affirm and we admit,[*](For this turn of phrase cf. Vol. I. p. 333, 424 C, Protag. 316 A, Symp. 186 E.) do we not, Glaucon?” “We do,” he said. Then, said I, since the task is, so great, shall we not inquire of them[*](For the reference to experts Cf. 400 B, 424 C. Cf. also What Plato Said, p. 484, on Laches 184 D-E.) what their opinion is and whether they have anything to add? And we in all this[*](παρά of course here means throughout and not contrary.) will be on the watch for what concerns us.” “What is that?” “To prevent our fosterlings from attempting to learn anything that does not conduce to the end[*](I take the word ἀτελές etymologically (cf. pp. 66-67, note b, on 500 A), with reference to the end in view. Others take it in the ordinary Greek sense, imperfect, incomplete.) we have in view, and does not always come out at what we said ought to be the goal of everything, as we were just now saying about astronomy.

Or do you not know that they repeat the same procedure in the case of harmonies[*](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.)? They transfer it to hearing and measure audible concords and sounds against one another,[*](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.) expending much useless labor just as the astronomers do.” “Yes, by heaven,” he said, “and most absurdly too. They talk of something they call minims[*](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.) and, laying their ears alongside, as if trying to catch a voice from next door,[*](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.) some affirm that they can hear a note between and that this is the least interval and the unit of measurement, while others insist that the strings now render identical sounds,[*](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.) both preferring their ears to their minds.[*](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.)” You, said I, “are speaking of the worthies[*](For χρηστός in this ironical sense cf. also 479 A, Symp. 177 B.) who vex and torture the strings and rack them[*](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. 1 τί πράγματα παρέχετε χορδαῖς;) on the pegs; but—not to draw out the comparison with strokes of the plectrum and the musician’s complaints of too responsive and too reluctant strings[*](This also may suggest a reluctant and a too willing witness.)—I drop the figure,[*](Cf. on 489 A, p. 23, note d.) and tell you that I do not mean these people, but those others[*](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.) whom we just now said we would interrogate about harmony. Their method exactly corresponds to that of the astronomer; for the numbers they seek are those found in these heard concords, but they do not ascend[*](Cf. Friedländer, Platon, p. 108, n. 1.) to generalized problems and the consideration which numbers are inherently concordant and which not and why in each case.” “A superhuman task,” he said. “Say, rather, useful,[*](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.) said I, for the investigation of the beautiful and the good,[*](Cf. on 505 B, p. 88, note a.) but if otherwise pursued, useless.” “That is likely,” he said. “And what is more,” I said, I take it that if the investigation[*](μέθοδος, like πραγματείαν in D, is used almost in the later technical sense of treatise or branch of study. Cf. on 528 D, p. 178, note a.) of all these studies goes far enough to bring out their community and kinship[*](Cf. on 537 C, Epin. 991 E.) with one another, and to infer their affinities, then to busy ourselves with them contributes to our desired end, and the labor taken is not lost; but otherwise it is vain.” “I too so surmise,” said he; “but it is a huge task of which you speak, Socrates.” “Are you talking about the prelude,[*](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.)” I said, “or what? Or do we not know that all this is but the preamble of the law itself, the prelude of the strain that we have to apprehend? For you surely do not suppose that experts in these matters are reasoners and dialecticians[*](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.)? “ “No, by Zeus,” he said, “except a very few whom I have met.” “But have you ever supposed,” I said, “that men who could not render and exact an account[*](λόγον . . . δοῦναι A 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 λαβεῖν Rep. 402 A, 534 B, Soph. 246 C, Theaet. 208 D, and Thompson on Meno 76 D.) of opinions in discussion would ever know anything of the things we say must be known?” “No is surely the answer to that too.”

“This, then, at last, Glaucon,” I said, “is the very law which dialectics[*](Cf. Phileb. 58 D, Meno 75 C-D, Charm. 155 A, Cratyl. 390 C, and on 533 B, pp. 200 f., note f.) recites, the strain which it executes, of which, though it belongs to the intelligible, we may see an imitation in the progress[*](This is not a literal rendering, but gives the meaning.) of the faculty of vision, as we described[*](Cf. 516 A-B. Plato interprets his imagery again here and in B infra.) its endeavor to look at living things themselves and the stars themselves and finally at the very sun. In like manner, when anyone by dialectics attempts through discourse of reason and apart from all perceptions of sense[*](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.) to find his way to the very essence of each thing and does not desist till he apprehends by thought itself the nature of the good in itself, he arrives at the limit of the intelligible, as the other in our parable, came to the goal of the visible.” “By all means,” he said. “What, then, will you not call this progress of thought dialectic?” Surely. “And the release from bonds,” I said, “and the conversion from the shadows to the images[*](εἴδωλα: cf. my Idea of Good in Plato’s Republic, p. 238; also 516 A, Theaet. 150 C, Soph. 240 A, 241 E, 234 C, 266 B with 267 C, and Rep. 517 D ἀγαλμάτων.) that cast them and to the light and the ascent[*](ἐπάνοδος became almost technical in Neoplatonism. Cf. also 517 A, 529 A, and p. 124, note b.) from the subterranean cavern to the world above,[*](Lit. sun, i.e. the world illumined by the sun, not by the fire in the cave.) and there the persisting inability[*](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 B οὐδ’ ὁπωστιοῦν σμικρολογία, Laws 638 B σφόδρα γυναικῶν, with England’s note, Theaet. 183 E πάνυ πρεσβύτης, Laws 791 C παντελῶς παίδων, 698 C σφόδρα φιλία, Rep. 564 A ἄγαν δουλείαν, with Stallbaum’s note.) to look directly at animals and plants and the light of the sun, but the ability to see the phantasms created by God[*](θεῖα because produced by God or nature and not by man with a mirror or a paintbrush. See crit. note and Class. 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.) in water and shadows of objects that are real and not merely, as before, the shadows of images cast through a light which, compared with the sun, is as unreal as they—all this procedure of the arts and sciences that we have described indicates their power to lead the best part of the soul up to the contemplation of what is best among realities, as in our parable the clearest organ in the body was turned to the contemplation of what is brightest in the corporeal and visible region.” “I accept this,” he said, “as the truth; and yet it appears to me very hard to accept, and again, from another point of view, hard to reject.[*](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.) Nevertheless, since we have not to hear it at this time only, but are to repeat it often hereafter, let us assume that these things are as now has been said, and proceed to the melody itself, and go through with it as we have gone through the prelude. Tell me, then, what is the nature of this faculty of dialectic? Into what divisions does it fall? And what are its ways? For it is these, it seems, that would bring us to the place where we may, so to speak, rest on the road and then come to the end of our journeying.”

“You will not be able, dear Glaucon, to follow me further,[*](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.) though on my part there will be no lack of goodwill.[*](For the idiom οὐδὲν προθυμίας ἀπολίποι Cf. Symp. 210 A, Meno 77 A, Laws 961 C, Aesch. Prom. 343, Thucyd. viii. 22. 1, Eurip. Hippol. 285.) And, if I could, I would show you, no longer an image and symbol of my meaning, but the very truth, as it appears to me—though whether rightly or not I may not properly affirm.[*](On Plato’s freedom from the dogmatism often attributed to him Cf. What Plato Said, p. 515 on Meno 86 B.) But that something like this is what we have to see, I must affirm.[*](On Plato’s freedom from the dogmatism often attributed to him Cf. What Plato Said, p. 515 on Meno 86 B.) Is not that so?” Surely. “And may we not also declare that nothing less than the power of dialectics could reveal[*](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.) this, and that only to one experienced[*](Plato anticipates the criticism that he neglects experience.) in the studies we have described, and that the thing is in no other wise possible?” “That, too,” he said, “we may properly affirm.” “This, at any rate,” said I, “no one will maintain in dispute against us[*](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.): that there is any other way of inquiry[*](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.) that attempts systematically and in all cases to determine what each thing really is. But all the other arts have for their object the opinions and desires of men or are wholly concerned with generation and composition or with the service and tendance of the things that grow and are put together, while the remnant which we said[*](Cf. 525 C, 527 B.) did in some sort lay hold on reality—geometry and the studies that accompany it— are, as we see, dreaming[*](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.) about being, but the clear waking vision[*](Cf. Phileb. 20 B and on 520 C, p. 143, note g.) of it is impossible for them as long as they leave the assumptions which they employ undisturbed and cannot give any account[*](Cf. on 531 E.) of them. For where the starting-point is something that the reasoner does not know, and the conclusion and all that intervenes is a tissue of things not really known,[*](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.) what possibility is there that assent[*](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, 164 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.) in such cases can ever be converted into true knowledge or science?” None, said he. Then, said I, “is not dialectics the only process of inquiry that advances in this manner, doing away with hypotheses, up to the first principle itself in order to find confirmation there? And it is literally true that when the eye of the soul[*](Cf. on 519 B, p. 138, note a.) is sunk in the barbaric slough[*](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.) of the Orphic myth, dialectic gently draws it forth and leads it up, employing as helpers and co-operators in this conversion the studies and sciences which we enumerated, which we called sciences often from habit,[*](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.) though they really need some other designation, connoting more clearness than opinion and more obscurity than science. Understanding,[*](Cf. on 511 D, pp. 116-117, note c.) I believe, was the term we employed. But I presume we shall not dispute about the name[*](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. 40 ἐγὼ γάρ τοι τά τε ἄλλα, καὶ ἐν τῇ τῶν ὀνομάτων ἐλευθερίᾳ πείθομαι Πλάτωνι.) when things of such moment lie before us for consideration.” “No, indeed,” he said.[*](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.)---