Jowett’s translation of Plato’s Republic, 3rd ed.

2 In allusion to a game in which two parties fled or pursued according as an oyster-shell which was thrown into the air fell with the dark or light side uppermost.

3 Reading οὖσαν ἐπάνοδον.

And should we not enquire what sort of knowledge has the Dpower of effecting such a change?

What knowledge will draw the soul upwards? What sort of knowledge is there which would draw the soul from becoming to being? And another consideration has just occurred to me: You will remember that our young men are to be warrior athletes?

Recapitulation. There were two parts in our former scheme of education, Ewere there not?

There were two parts in our former scheme of education, were there not? Just so.

There was gymnastic which presided over the growth and decay of the body, and may therefore be regarded as having to do with generation and corruption?

You are most accurate, I said, in your recollection; in music there certainly was nothing of the kind. But what branch of knowledge is there, my dear Glaucon, which is of the desired nature; since all the useful arts were reckoned mean by us?

Undoubtedly; and yet if music and gymnastic are excluded, and the arts are also excluded, what remains?

Well, I said, there may be nothing left of our special subjects; and then we shall have to take something which is not special, but of universal application.

C There remains for the second education, arithmetic; A something which all arts and sciences and intelligences use in common, and which every one first has to learn among the elements of education.

The little matter of distinguishing one, two, and three—in a word, number and calculation:—do not all arts and sciences necessarily partake of them?

D Then Palamedes, whenever he appears in tragedy, proves Agamemnon ridiculously unfit to be a general. Did you never remark how he declares that he had invented number, and had numbered the ships and set in array the ranks of the army at Troy; which implies that they had never been numbered before, and Agamemnon must be supposed literally to have been incapable of counting his own feet—how could he if he was ignorant of number? And if that is true, what sort of general must he have been? 224

Certainly he should, if he is to have the smallest understanding of military tactics, or indeed, I should rather say, if he is to be a man at all.

I should like to know whether you have the same notion which I have of this study?

that being a study which leads naturally to reflection, for It appears to me to be a study of the kind which we are 523seeking, and which leads naturally to reflection, but never to have been rightly used; for the true use of it is simply to draw the soul towards being.

I will try, I said; and I wish you would share the enquiry with me, and say ‘yes’ or ‘no’ when I attempt to distinguish in my own mind what branches of knowledge have this attracting power, in order that we may have clearer proof that arithmetic is, as I suspect, one of them.

reflection is aroused by contradictory impressions of sense. I mean to say that objects of sense are of two kinds; some Bof them do not invite thought because the sense is an adequate judge of them; while in the case of other objects sense is so untrustworthy that further enquiry is imperatively demanded.

You are clearly referring, he said, to the manner in which the senses are imposed upon by distance, and by painting in light and shade.

When speaking of uninviting objects, I mean those which Cdo not pass from one sensation to the opposite; inviting objects are those which do; in this latter case the sense coming upon the object, whether at a distance or near, gives no more vivid idea of anything in particular than of its opposite. An illustration will make my meaning clearer:—here are three fingers—a little finger, a second finger, and a middle finger.

No difficulty in simple perception. Each of them equally appears a finger, whether seen in the Dmiddle or at the extremity, whether white or black, or thick or thin—it makes no difference; a finger is a finger all the same. In these cases a man is not compelled to ask of thought the question what is a finger? for the sight never intimates to the mind that a finger is other than a finger.

And therefore, I said, as we might expect, there is nothing Ehere which invites or excites intelligence.

But the same senses at the same time give different impressions which are at first indistinct and have to be distinguished by the mind. But is this equally true of the greatness and smallness of the fingers? Can sight adequately perceive them? and is no difference made by the circumstance that one of the fingers is in the middle and another at the extremity? And in like manner does the touch adequately perceive the qualities of thickness or thinness, of softness or hardness? And so of the other senses; do they give perfect intimations of such matters? 524Is not their mode of operation on this wise—the sense which is concerned with the quality of hardness is necessarily concerned also with the quality of softness, and only intimates to the soul that the same thing is felt to be both hard and soft?

And must not the soul be perplexed at this intimation which the sense gives of a hard which is also soft? What, again, is the meaning of light and heavy, if that which is light is also heavy, and that which is heavy, light?

B Yes, he said, these intimations which the soul receives are very curious and require to be explained.

The aid of numbers is invoked in order to remove the confusion. Yes, I said, and in these perplexities the soul naturally summons to her aid calculation and intelligence, that she may see whether the several objects announced to her are one or two.

The eye certainly did see both small and great, but only in a confused manner; they were not distinguished.

The chaos then begins to be defined. Whereas the thinking mind, intending to light up the chaos, was compelled to reverse the process, and look at small and great as separate and not confused.

Was not this the beginning of the enquiry ‘What is great?’ and ‘What is small?’

The parting of the visible and intelligible. And thus arose the distinction of the visible and the intelligible.

This was what I meant when I spoke of impressions which invited the intellect, or the reverse—those which are simultaneous with opposite impressions, invite thought; those which are not simultaneous do not.

Thought is aroused by the contradiction of the one and many. Think a little and you will see that what has preceded will supply the answer; for if simple unity could be adequately perceived by the sight or by any other sense, then, Eas we were saying in the case of the finger, there would be nothing to attract towards being; but when there is some contradiction always present, and one is the reverse of one and involves the conception of plurality, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks ‘What is absolute unity?’ This 525is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of true being.

And surely, he said, this occurs notably in the case of one; for we see the same thing to be both one and infinite in multitude?

Arithmetic has a practical and also a philosophical use, the latter the higher. Then this is knowledge of the kind for which we are seeking, having a double use, military and philosophical; for the man of war must learn the art of number or he will not know how to array his troops, and the philosopher also, because he has to rise out of the sea of change and lay hold of true being, and therefore he must be an arithmetician.

Then this is a kind of knowledge which legislation may fitly prescribe; and we must endeavour to persuade those Cwho are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or retail-traders, with a view to buying or selling, but for the sake of their military use, and of the soul herself; and because this will be the easiest way for her to pass from becoming to truth and being.

Yes, I said, and now having spoken of it, I must add Dhow charming the science is! and in how many ways it conduces to our desired end, if pursued in the spirit of a philosopher, and not of a shopkeeper!

The higher arithmetic is concerned, not with visible or tangible objects, but with abstract numbers. I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. You know Ehow steadily the masters of the art repel and ridicule any one who attempts to divide absolute unity when he is calculating, and if you divide, they multiply4, taking care that one shall continue one and not become lost in fractions. 228

4 Meaning either (1) that they integrate the number because they deny the possibility of fractions; or (2) that division is regarded by them as a process of multiplication, for the fractions of one continue to be units.

526 Now, suppose a person were to say to them: O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you demand, and each unit is equal, invariable, indivisible,—what would they answer?

They would answer, as I should conceive, that they were speaking of those numbers which can only be realized in thought.

Then you see that this knowledge may be truly called Bnecessary, necessitating as it clearly does the use of the pure intelligence in the attainment of pure truth?

The arithmetician is naturally quick, and the study of arithmetic gives him still greater quickness. And have you further observed, that those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been.

C And indeed, you will not easily find a more difficult study, and not many as difficult.

And, for all these reasons, arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.

Let this then be made one of our subjects of education. And next, shall we enquire whether the kindred science also concerns us?

D Geometry has practical applications; Clearly, he said, we are concerned with that part of geometry which relates to war; for in pitching a camp, or taking up a position, or closing or extending the lines of an army, or any other military manoeuvre, whether in actual battle or on a march, it will make all the difference whether a general is or is not a geometrician.

these however are trifling in comparison with that greater part of the science which tends towards the good, Yes, I said, but for that purpose a very little of either geometry or calculation will be enough; the question relates 229 rather to the greater and more advanced part of geometry—Ewhether that tends in any degree to make more easy the vision of the idea of good; and thither, as I was saying, all things tend which compel the soul to turn her gaze towards that place, where is the full perfection of being, which she ought, by all means, to behold.

Then if geometry compels us to view being, it concerns us; if becoming only, it does not concern us?

Yet anybody who has the least acquaintance with geometry will not deny that such a conception of the science is in flat contradiction to the ordinary language of geometricians.

They have in view practice only, and are always speaking, in a narrow and ridiculous manner, of squaring and extending and applying and the like—they confuse the necessities of geometry with those of daily life; whereas knowledge is the Breal object of the whole science.

and is concerned with the eternal. That the knowledge at which geometry aims is knowledge of the eternal, and not of aught perishing and transient.

Then, my noble friend, geometry will draw the soul towards truth, and create the spirit of philosophy, and raise up that which is now unhappily allowed to fall down.

C Then nothing should be more sternly laid down than that the inhabitants of your fair city should by all means learn geometry. Moreover the science has indirect effects, which are not small.

There are the military advantages of which you spoke, I said; and in all departments of knowledge, as experience proves, any one who has studied geometry is infinitely quicker of apprehension than one who has not.

Astronomy, like the previous sciences, is at first praised by Glaucon for its practical uses. I am strongly inclined to it, he said; the observation of the seasons and of months and years is as essential to the general as it is to the farmer or sailor.

I am amused, I said, at your fear of the world, which makes you guard against the appearance of insisting upon useless studies; and I quite admit the difficulty of believing that in every man there is an eye of the soul which, when by Eother pursuits lost and dimmed, is by these purified and re-illumined; and is more precious far than ten thousand bodily eyes, for by it alone is truth seen. Now there are two classes of persons: one class of those who will agree with you and will take your words as a revelation; another class 528to whom they will be utterly unmeaning, and who will naturally deem them to be idle tales, for they see no sort of profit which is to be obtained from them. And therefore you had better decide at once with which of the two you are proposing to argue. You will very likely say with neither, and that your chief aim in carrying on the argument is your own improvement; at the same time you do not grudge to others any benefit which they may receive.

Correction of the order. Then take a step backward, for we have gone wrong in the order of the sciences.

After plane geometry, I said, we proceeded at once to Bsolids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed.

That is true, Socrates; but so little seems to be known as yet about these subjects.

The pitiable condition of solid geometry. Why, yes, I said, and for two reasons:—in the first place, no government patronises them; this leads to a want of energy in the pursuit of them, and they are difficult; in the 231 second place, students cannot learn them unless they have a director. But then a director can hardly be found, and even Cif he could, as matters now stand, the students, who are very conceited, would not attend to him. That, however, would be otherwise if the whole State became the director of these studies and gave honour to them; then disciples would want to come, and there would be continuous and earnest search, and discoveries would be made; since even now, disregarded as they are by the world, and maimed of their fair proportions, and although none of their votaries can tell the use of them, still these studies force their way by their natural charm, and very likely, if they had the help of the State, they would some day emerge into light.

D Yes, he said, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces?

The motion of solids. Yes, and I have delayed you by my hurry; the ludicrous state of solid geometry, which, in natural order, should have followed, made me pass over this branch and go on to Eastronomy, or motion of solids.

Then assuming that the science now omitted would come into existence if encouraged by the State, let us go on to astronomy, which will be fourth.

Glaucon grows sentimental about astronomy. The right order, he replied. And now, Socrates, as you rebuked the vulgar manner in which I praised astronomy 529before, my praise shall be given in your own spirit. For every one, as I think, must see that astronomy compels the soul to look upwards and leads us from this world to another.

Every one but myself, I said; to every one else this may be clear, but not to me.

I should rather say that those who elevate astronomy into philosophy appear to me to make us look downwards and not upwards.

He is rebuked by Socrates, You, I replied, have in your mind a truly sublime conception of our knowledge of the things above. And I dare Bsay that if a person were to throw his head back and study the fretted ceiling, you would still think that his mind was the percipient, and not his eyes. And you are very likely right, and I may be a simpleton: but, in my opinion, that knowledge only which is of being and of the unseen can make the soul look upwards, and whether a man gapes at the heavens or blinks on the ground, seeking to learn some particular of sense, I would deny that he can learn, for Cnothing of that sort is matter of science; his soul is looking downwards, not upwards, whether his way to knowledge is by water or by land, whether he floats, or only lies on his back.

who explains that the higher astronomy is an abstract science. I acknowledge, he said, the justice of your rebuke. Still, I should like to ascertain how astronomy can be learned in any manner more conducive to that knowledge of which we are speaking?

I will tell you, I said: The starry heaven which we behold is wrought upon a visible ground, and therefore, Dalthough the fairest and most perfect of visible things, must necessarily be deemed inferior far to the true motions of absolute swiftness and absolute slowness, which are relative to each other, and carry with them that which is contained in them, in the true number and in every true figure. Now, these are to be apprehended by reason and intelligence, but not by sight.

The spangled heavens should be used as a pattern and with a view to that higher knowledge; their beauty is like Ethe beauty of figures or pictures excellently wrought by the hand of Daedalus, or some other great artist, which we may chance to behold; any geometrician who saw them would appreciate the exquisiteness of their workmanship, but he would never dream of thinking that in them he could find the true equal or the true double, or the truth of any 530other proportion.

The real knowledge of astronomy or geometry is to be attained by the use of abstractions. Then, I said, in astronomy, as in geometry, we should employ problems, and let the heavens alone if we would approach the subject in the right way and so make the Cnatural gift of reason to be of any real use.

Yes, I said; and there are many other things which must also have a similar extension given to them, if our legislation is to be of any value. But can you tell me of any other suitable study?

Motion, I said, has many forms, and not one only; two of Dthem are obvious enough even to wits no better than ours; and there are others, as I imagine, which may be left to wiser persons.

What astronomy is to the eye, harmonics are to the ear. The second, I said, would seem relatively to the ears to be what the first is to the eyes; for I conceive that as the eyes are designed to look up at the stars, so are the ears to hear harmonious motions; and these are sister sciences—as the Pythagoreans say, and we, Glaucon, agree with them?

E But this, I said, is a laborious study, and therefore we had better go and learn of them; and they will tell us whether there are any other applications of these sciences. At the same time, we must not lose sight of our own higher object.

They must be studied with a view to the good and not after the fashion of the empirics or even of the Pythagoreans. There is a perfection which all knowledge ought to reach, 234 and which our pupils ought also to attain, and not to fall short of, as I was saying that they did in astronomy. 531For in the science of harmony, as you probably know, the same thing happens. The teachers of harmony compare the sounds and consonances which are heard only, and their labour, like that of the astronomers, is in vain.

Yes, by heaven! he said; and ’tis as good as a play to hear them talking about their condensed notes, as they call them; they put their ears close alongside of the strings like persons catching a sound from their neighbour’s wall5—one set of them declaring that they distinguish an intermediate note and have found the least interval which should be the unit of measurement; the others insisting that the two sounds have passed into the same—either party setting Btheir ears before their understanding.

5 Or, ‘close alongside of their neighbour’s instruments, as if to catch a sound from them.’

You mean, I said, those gentlemen who tease and torture the strings and rack them on the pegs of the instrument: I might carry on the metaphor and speak after their manner of the blows which the plectrum gives, and make accusations against the strings, both of backwardness and forwardness to sound; but this would be tedious, and therefore I will only say that these are not the men, and that I am referring to the Pythagoreans, of whom I was just now proposing to enquire about harmony. For they too are in error, like the Castronomers; they investigate the numbers of the harmonies which are heard, but they never attain to problems—that is to say, they never reach the natural harmonies of number, or reflect why some numbers are harmonious and others not.

A thing, I replied, which I would rather call useful; that is, if sought after with a view to the beautiful and good; but if pursued in any other spirit, useless.

All these studies must be correlated with one another. Now, when all these studies reach the point of inter-communion Dand connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects; otherwise there is no profit in them. 235

Want of reasoning power in mathematicians. Assuredly not, he said; I have hardly ever known a mathematician who was capable of reasoning.

But do you imagine that men who are unable to give and take a reason will have the knowledge which we require of them?

532 Dialectic proceeds by reason only, without any help of sense. And so, Glaucon, I said, we have at last arrived at the hymn of dialectic. This is that strain which is of the intellect only, but which the faculty of sight will nevertheless be found to imitate; for sight, as you may remember, was imagined by us after a while to behold the real animals and stars, and last of all the sun himself. And so with dialectic; when a person starts on the discovery of the absolute by the light of reason only, and without any assistance of sense, and perseveres Buntil by pure intelligence he arrives at the perception of the absolute good, he at last finds himself at the end of the intellectual world, as in the case of sight at the end of the visible.

The gradual acquirement of dialectic by the pursuit of the arts anticipated in the allegory of the den. But the release of the prisoners from chains, and their translation from the shadows to the images and to the light, and the ascent from the underground den to the sun, while in his presence they are vainly trying to look on animals and plants and the light of the sun, but are able to perceive Ceven with their weak eyes the images6 in the water (which are divine), and are the shadows of true existence (not shadows of images cast by a light of fire, which compared with the sun is only an image)—this power of elevating the highest principle in the soul to the contemplation of that which is best in existence, with which we may compare the raising of that 236 faculty which is the very light of the body to the sight of that which is brightest in the material and visible world—this power is given, as I was saying, by all that study and pursuit Dof the arts which has been described.

6 Omitting ἐνταῦθα δὲ πρὸς φαντάσματα. The word θεῖα is bracketed by Stallbaum.

I agree in what you are saying, he replied, which may be hard to believe, yet, from another point of view, is harder still to deny. This, however, is not a theme to be treated of in passing only, but will have to be discussed again and again. And so, whether our conclusion be true or false, let us assume all this, and proceed at once from the prelude or preamble to the chief strain7, and describe that in like manner. Say, then, what is the nature and what are the divisions of Edialectic, and what are the paths which lead thither; for these paths will also lead to our final rest.

7 A play upon the word νόμος, which means both ‘law’ and ‘strain.’

533 The nature of dialectic can only be revealed to those who have been students of the preliminary sciences, Dear Glaucon, I said, you will not be able to follow me here, though I would do my best, and you should behold not an image only but the absolute truth, according to my notion. Whether what I told you would or would not have been a reality I cannot venture to say; but you would have seen something like reality; of that I am confident.

But I must also remind you, that the power of dialectic alone can reveal this, and only to one who is a disciple of the previous sciences.

B And assuredly no one will argue that there is any other method of comprehending by any regular process all true existence or of ascertaining what each thing is in its own nature; for the arts in general are concerned with the desires or opinions of men, or are cultivated with a view to production and construction, or for the preservation of such productions and constructions; and as to the mathematical sciences which, as we were saying, have some apprehension of true being—geometry and the like—they only dream about Cbeing, but never can they behold the waking reality so long as they leave the hypotheses which they use unexamined, and are unable to give an account of them. For when a man knows not his own first principle, and when the conclusion 237 and intermediate steps are also constructed out of he knows not what, how can he imagine that such a fabric of convention can ever become science?

Why indeed, he said, when any name will do which expresses the thought of the mind with clearness?

Two divisions of the mind, intellect and opinion, each having two subdivisions. At any rate, we are satisfied, as before, to have four divisions; two for intellect and two for opinion, and to call the first division science, the second understanding, the third belief, and the fourth perception of shadows, opinion 534 being concerned with becoming, and intellect with being; and so to make a proportion:—

But let us defer the further correlation and subdivision of the subjects of opinion and of intellect, for it will be a long enquiry, many times longer than this has been.

And do you also agree, I said, in describing the dialectician as one who attains a conception of the essence of each thing? And he who does not possess and is therefore unable to impart this conception, in whatever degree he fails, may in that degree also be said to fail in intelligence? Will you admit so much?

No truth which does not rest on the idea of good And you would say the same of the conception of the good? Until the person is able to abstract and define rationally the 238 Cidea of good, and unless he can run the gauntlet of all objections, and is ready to disprove them, not by appeals to opinion, but to absolute truth, never faltering at any step of the argument—unless he can do all this, you would say that he knows neither the idea of good nor any other good; he apprehends only a shadow, if anything at all, which is given by opinion and not by science;—dreaming and slumbering in this life, before he is well awake here, he Darrives at the world below, and has his final quietus.

And surely you would not have the children of your ideal State, whom you are nurturing and educating—if the ideal ever becomes a reality—you would not allow the future rulers to be like posts8, having no reason in them, and yet to be set in authority over the highest matters?