Republic

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.)”