And now I will describe in a figure the enlightenment or unenlightenment of our nature:— Imagine human beings living in an underground den which is open towards the light; they have been there from childhood, having their necks and legs chained, and can only see into the den. At a distance there is a fire, and between the fire and the prisoners a raised way, and a low wall is built along the way, like the screen over which marionette players show their puppets. Behind the wall appear moving figures, who hold in their hands various works of art, and among them images of men and animals, wood and stone, and some of the passers-by are talking and others silent. ‘A strange parable,’ he said, ‘and strange captives.’ They are ourselves, I replied; and they see only the shadows of the images which the fire throws on the wall of the den; to these they give names, and if we add an echo which returns from the wall, the voices of the passengers will seem to proceed from the shadows. Suppose now that you suddenly turn them round and make them look with pain and grief to themselves at the real images; will they believe them to be real? Will not their eyes be dazzled, and will they not try to get away from the light to something which they are able to behold without blinking? And suppose further, that they are dragged up a steep and rugged ascent into the presence of the sun himself, will not their sight be darkened with the excess of light? Some time will pass before they get the habit of perceiving at all; and at first they will be able to perceive only shadows and reflections in the water; then they will recognize the moon and the stars, and will at length behold the sun in his own proper place as he is. Last of all they will conclude:— This is he who gives us the year and the seasons, and is the author of all that we see. How will they rejoice in passing from darkness to light! How worthless to them will seem the honours and glories of the den! But now imagine further, that they descend into their old habitations; — in that underground dwelling they will not see as well as their fellows, and will not be able to compete with them in the measurement of the shadows on the wall; there will be many jokes about the man who went on a visit to the sun and lost his eyes, and if they find anybody trying to set free and enlighten one of their number, they will put him to death, if they can catch him. Now the cave or den is the world of sight, the fire is the sun, the way upwards is the way to knowledge, and in the world of knowledge the idea of good is last seen and with difficulty, but when seen is inferred to be the author of good and right — parent of the lord of light in this world, and of truth and understanding in the other. He who attains to the beatific vision is always going upwards; he is unwilling to descend into political assemblies and courts of law; for his eyes are apt to blink at the images or shadows of images which they behold in them — he cannot enter into the ideas of those who have never in their lives understood the relation of the shadow to the substance. But blindness is of two kinds, and may be caused either by passing out of darkness into light or out of light into darkness, and a man of sense will distinguish between them, and will not laugh equally at both of them, but the blindness which arises from fulness of light he will deem blessed, and pity the other; or if he laugh at the puzzled soul looking at the sun, he will have more reason to laugh than the inhabitants of the den at those who descend from above. There is a further lesson taught by this parable of ours. Some persons fancy that instruction is like giving eyes to the blind, but we say that the faculty of sight was always there, and that the soul only requires to be turned round towards the light. And this is conversion; other virtues are almost like bodily habits, and may be acquired in the same manner, but intelligence has a diviner life, and is indestructible, turning either to good or evil according to the direction given. Did you never observe how the mind of a clever rogue peers out of his eyes, and the more clearly he sees, the more evil he does? Now if you take such an one, and cut away from him those leaden weights of pleasure and desire which bind his soul to earth, his intelligence will be turned round, and he will behold the truth as clearly as he now discerns his meaner ends. And have we not decided that our rulers must neither be so uneducated as to have no fixed rule of life, nor so over-educated as to be unwilling to leave their paradise for the business of the world? We must choose out therefore the natures who are most likely to ascend to the light and knowledge of the good; but we must not allow them to remain in the region of light; they must be forced down again among the captives in the den to partake of their labours and honours. ‘Will they not think this a hardship?’ You should remember that our purpose in framing the State was not that our citizens should do what they like, but that they should serve the State for the common good of all. May we not fairly say to our philosopher — Friend, we do you no wrong; for in other States philosophy grows wild, and a wild plant owes nothing to the gardener, but you have been trained by us to be the rulers and kings of our hive, and therefore we must insist on your descending into the den. You must, each of you, take your turn, and become able to use your eyes in the dark, and with a little practice you will see far better than those who quarrel about the shadows, whose knowledge is a dream only, whilst yours is a waking reality. It may be that the saint or philosopher who is best fitted, may also be the least inclined to rule, but necessity is laid upon him, and he must no longer live in the heaven of ideas. And this will be the salvation of the State. For those who rule must not be those who are desirous to rule; and, if you can offer to our citizens a better life than that of rulers generally is, there will be a chance that the rich, not only in this world’s goods, but in virtue and wisdom, may bear rule. And the only life which is better than the life of political ambition is that of philosophy, which is also the best preparation for the government of a State.

Then now comes the question — How shall we create our rulers; what way is there from darkness to light? The change is effected by philosophy; it is not the turning over of an oyster-shell, but the conversion of a soul from night to day, from becoming to being. And what training will draw the soul upwards? Our former education had two branches, gymnastic, which was occupied with the body, and music, the sister art, which infused a natural harmony into mind and literature; but neither of these sciences gave any promise of doing what we want. Nothing remains to us but that universal or primary science of which all the arts and sciences are partakers, I mean number or calculation. ‘Very true.’ Including the art of war? ‘Yes, certainly.’ Then there is something ludicrous about Palamedes in the tragedy, coming in and saying that he had invented number, and had counted the ranks and set them in order. For if Agamemnon could not count his feet (and without number how could he?) he must have been a pretty sort of general indeed. No man should be a soldier who cannot count, and indeed he is hardly to be called a man. But I am not speaking of these practical applications of arithmetic, for number, in my view, is rather to be regarded as a conductor to thought and being. I will explain what I mean by the last expression:— Things sensible are of two kinds; the one class invite or stimulate the mind, while in the other the mind acquiesces. Now the stimulating class are the things which suggest contrast and relation. For example, suppose that I hold up to the eyes three fingers — a fore finger, a middle finger, a little finger — the sight equally recognizes all three fingers, but without number cannot further distinguish them. Or again, suppose two objects to be relatively great and small, these ideas of greatness and smallness are supplied not by the sense, but by the mind. And the perception of their contrast or relation quickens and sets in motion the mind, which is puzzled by the confused intimations of sense, and has recourse to number in order to find out whether the things indicated are one or more than one. Number replies that they are two and not one, and are to be distinguished from one another. Again, the sight beholds great and small, but only in a confused chaos, and not until they are distinguished does the question arise of their respective natures; we are thus led on to the distinction between the visible and intelligible. That was what I meant when I spoke of stimulants to the intellect; I was thinking of the contradictions which arise in perception. The idea of unity, for example, like that of a finger, does not arouse thought unless involving some conception of plurality; but when the one is also the opposite of one, the contradiction gives rise to reflection; an example of this is afforded by any object of sight. All number has also an elevating effect; it raises the mind out of the foam and flux of generation to the contemplation of being, having lesser military and retail uses also. The retail use is not required by us; but as our guardian is to be a soldier as well as a philosopher, the military one may be retained. And to our higher purpose no science can be better adapted; but it must be pursued in the spirit of a philosopher, not of a shopkeeper. It is concerned, not with visible objects, but with abstract truth; for numbers are pure abstractions — the true arithmetician indignantly denies that his unit is capable of division. When you divide, he insists that you are only multiplying; his ‘one’ is not material or resolvable into fractions, but an unvarying and absolute equality; and this proves the purely intellectual character of his study. Note also the great power which arithmetic has of sharpening the wits; no other discipline is equally severe, or an equal test of general ability, or equally improving to a stupid person.

Let our second branch of education be geometry. ‘I can easily see,’ replied Glaucon, ‘that the skill of the general will be doubled by his knowledge of geometry.’ That is a small matter; the use of geometry, to which I refer, is the assistance given by it in the contemplation of the idea of good, and the compelling the mind to look at true being, and not at generation only. Yet the present mode of pursuing these studies, as any one who is the least of a mathematician is aware, is mean and ridiculous; they are made to look downwards to the arts, and not upwards to eternal existence. The geometer is always talking of squaring, subtending, apposing, as if he had in view action; whereas knowledge is the real object of the study. It should elevate the soul, and create the mind of philosophy; it should raise up what has fallen down, not to speak of lesser uses in war and military tactics, and in the improvement of the faculties.

Shall we propose, as a third branch of our education, astronomy? ‘Very good,’ replied Glaucon; ‘the knowledge of the heavens is necessary at once for husbandry, navigation, military tactics.’ I like your way of giving useful reasons for everything in order to make friends of the world. And there is a difficulty in proving to mankind that education is not only useful information but a purification of the eye of the soul, which is better than the bodily eye, for by this alone is truth seen. Now, will you appeal to mankind in general or to the philosopher? or would you prefer to look to yourself only? ‘Every man is his own best friend.’ Then take a step backward, for we are out of order, and insert the third dimension which is of solids, after the second which is of planes, and then you may proceed to solids in motion. But solid geometry is not popular and has not the patronage of the State, nor is the use of it fully recognized; the difficulty is great, and the votaries of the study are conceited and impatient. Still the charm of the pursuit wins upon men, and, if government would lend a little assistance, there might be great progress made. ‘Very true,’ replied Glaucon; ‘but do I understand you now to begin with plane geometry, and to place next geometry of solids, and thirdly, astronomy, or the motion of solids?’ Yes, I said; my hastiness has only hindered us.

‘Very good, and now let us proceed to astronomy, about which I am willing to speak in your lofty strain. No one can fail to see that the contemplation of the heavens draws the soul upwards.’ I am an exception, then; astronomy as studied at present appears to me to draw the soul not upwards, but downwards. Star-gazing is just looking up at the ceiling — no better; a man may lie on his back on land or on water — he may look up or look down, but there is no science in that. The vision of knowledge of which I speak is seen not with the eyes, but with the mind. All the magnificence of the heavens is but the embroidery of a copy which falls far short of the divine Original, and teaches nothing about the absolute harmonies or motions of things. Their beauty is like the beauty of figures drawn by the hand of Daedalus or any other great artist, which may be used for illustration, but no mathematician would seek to obtain from them true conceptions of equality or numerical relations. How ridiculous then to look for these in the map of the heavens, in which the imperfection of matter comes in everywhere as a disturbing element, marring the symmetry of day and night, of months and years, of the sun and stars in their courses. Only by problems can we place astronomy on a truly scientific basis. Let the heavens alone, and exert the intellect.

Still, mathematics admit of other applications, as the Pythagoreans say, and we agree. There is a sister science of harmonical motion, adapted to the ear as astronomy is to the eye, and there may be other applications also. Let us inquire of the Pythagoreans about them, not forgetting that we have an aim higher than theirs, which is the relation of these sciences to the idea of good. The error which pervades astronomy also pervades harmonics. The musicians put their ears in the place of their minds. ‘Yes,’ replied Glaucon, ‘I like to see them laying their ears alongside of their neighbours’ faces — some saying, “That’s a new note,” others declaring that the two notes are the same.’ Yes, I said; but you mean the empirics who are always twisting and torturing the strings of the lyre, and quarrelling about the tempers of the strings; I am referring rather to the Pythagorean harmonists, who are almost equally in error. For they investigate only the numbers of the consonances which are heard, and ascend no higher — of the true numerical harmony which is unheard, and is only to be found in problems, they have not even a conception. ‘That last,’ he said, ‘must be a marvellous thing.’ A thing, I replied, which is only useful if pursued with a view to the good.

All these sciences are the prelude of the strain, and are profitable if they are regarded in their natural relations to one another. ‘I dare say, Socrates,’ said Glaucon; ‘but such a study will be an endless business.’ What study do you mean — of the prelude, or what? For all these things are only the prelude, and you surely do not suppose that a mere mathematician is also a dialectician? ‘Certainly not. I have hardly ever known a mathematician who could reason.’ And yet, Glaucon, is not true reasoning that hymn of dialectic which is the music of the intellectual world, and which was by us compared to the effort of sight, when from beholding the shadows on the wall we arrived at last at the images which gave the shadows? Even so the dialectical faculty withdrawing from sense arrives by the pure intellect at the contemplation of the idea of good, and never rests but at the very end of the intellectual world. And the royal road out of the cave into the light, and the blinking of the eyes at the sun and turning to contemplate the shadows of reality, not the shadows of an image only — this progress and gradual acquisition of a new faculty of sight by the help of the mathematical sciences, is the elevation of the soul to the contemplation of the highest ideal of being.

‘So far, I agree with you. But now, leaving the prelude, let us proceed to the hymn. What, then, is the nature of dialectic, and what are the paths which lead thither?’ Dear Glaucon, you cannot follow me here. There can be no revelation of the absolute truth to one who has not been disciplined in the previous sciences. But that there is a science of absolute truth, which is attained in some way very different from those now practised, I am confident. For all other arts or sciences are relative to human needs and opinions; and the mathematical sciences are but a dream or hypothesis of true being, and never analyse their own principles. Dialectic alone rises to the principle which is above hypotheses, converting and gently leading the eye of the soul out of the barbarous slough of ignorance into the light of the upper world, with the help of the sciences which we have been describing — sciences, as they are often termed, although they require some other name, implying greater clearness than opinion and less clearness than science, and this in our previous sketch was understanding. And so we get four names — two for intellect, and two for opinion — reason or mind, understanding, faith, perception of shadows — which make a proportion — being:becoming::intellect:opinion — and science:belief::understanding: perception of shadows. Dialectic may be further described as that science which defines and explains the essence or being of each nature, which distinguishes and abstracts the good, and is ready to do battle against all opponents in the cause of good. To him who is not a dialectician life is but a sleepy dream; and many a man is in his grave before his is well waked up. And would you have the future rulers of your ideal State intelligent beings, or stupid as posts? ‘Certainly not the latter.’ Then you must train them in dialectic, which will teach them to ask and answer questions, and is the coping-stone of the sciences.

I dare say that you have not forgotten how our rulers were chosen; and the process of selection may be carried a step further:— As before, they must be constant and valiant, good-looking, and of noble manners, but now they must also have natural ability which education will improve; that is to say, they must be quick at learning, capable of mental toil, retentive, solid, diligent natures, who combine intellectual with moral virtues; not lame and one-sided, diligent in bodily exercise and indolent in mind, or conversely; not a maimed soul, which hates falsehood and yet unintentionally is always wallowing in the mire of ignorance; not a bastard or feeble person, but sound in wind and limb, and in perfect condition for the great gymnastic trial of the mind. Justice herself can find no fault with natures such as these; and they will be the saviours of our State; disciples of another sort would only make philosophy more ridiculous than she is at present. Forgive my enthusiasm; I am becoming excited; but when I see her trampled underfoot, I am angry at the authors of her disgrace. ‘I did not notice that you were more excited than you ought to have been.’ But I felt that I was. Now do not let us forget another point in the selection of our disciples — that they must be young and not old. For Solon is mistaken in saying that an old man can be always learning; youth is the time of study, and here we must remember that the mind is free and dainty, and, unlike the body, must not be made to work against the grain. Learning should be at first a sort of play, in which the natural bent is detected. As in training them for war, the young dogs should at first only taste blood; but when the necessary gymnastics are over which during two or three years divide life between sleep and bodily exercise, then the education of the soul will become a more serious matter. At twenty years of age, a selection must be made of the more promising disciples, with whom a new epoch of education will begin. The sciences which they have hitherto learned in fragments will now be brought into relation with............