When the higher natures are corrupted by politics, the lower take possession of the vacant place of philosophy. This is described in one of those continuous images in which the argument, to use a Platonic expression, 'veils herself,' and which is dropped and reappears at intervals. The question is asked, – Why are the citizens of states so hostile to philosophy? The answer is, that they do not know her. And yet there is also a better mind of the many; they would believe if they were taught. But hitherto they have only known a conventional imitation of philosophy, words without thoughts, systems which have no life in them; a (divine) person uttering the words of beauty and freedom, the friend of man holding communion with the Eternal, and seeking to frame the state in that image, they have never known. The same double feeling respecting the mass of mankind has always existed among men. The first thought is that the people are the enemies of truth and right; the second, that this only arises out of an accidental error and confusion, and that they do not really hate those who love them, if they could be educated to know them.

In the latter part of the sixth book, three questions have to be considered: 1st, the nature of the longer and more circuitous way, which is contrasted with the shorter and more imperfect method of Book IV; 2nd, the heavenly pattern or idea of the state; 3rd, the relation of the divisions of knowledge to one another and to the corresponding faculties of the soul:

1. Of the higher method of knowledge in Plato we have only a glimpse. Neither here nor in the Phaedrus or Symposium, nor yet in the Philebus or Sophist, does he give any clear explanation of his meaning. He would probably have described his method as proceeding by regular steps to a system of universal knowledge, which inferred the parts from the whole rather than the whole from the parts. This ideal logic is not practised by him in the search after justice, or in the analysis of the parts of the soul; there, like Aristotle in the Nicomachean Ethics, he argues from experience and the common use of language. But at the end of the sixth book he conceives another and more perfect method, in which all ideas are only steps or grades or moments of thought, forming a connected whole which is self-supporting, and in which consistency is the test of truth. He does not explain to us in detail the nature of the process. Like many other thinkers both in ancient and modern times his mind seems to be filled with a vacant form which he is unable to realize. He supposes the sciences to have a natural order and connexion in an age when they can hardly be said to exist. He is hastening on to the 'end of the intellectual world' without even making a beginning of them.

In modern times we hardly need to be reminded that the process of acquiring knowledge is here confused with the contemplation of absolute knowledge. In all science a priori and a posteriori truths mingle in various proportions. The a priori part is that which is derived from the most universal experience of men, or is universally accepted by them; the a posteriori is that which grows up around the more general principles and becomes imperceptibly one with them. But Plato erroneously imagines that the synthesis is separable from the analysis, and that the method of science can anticipate science. In entertaining such a vision of a priori knowledge he is sufficiently justified, or at least his meaning may be sufficiently explained by the similar attempts of Descartes, Kant, Hegel, and even of Bacon himself, in modern philosophy. Anticipations or divinations, or prophetic glimpses of truths whether concerning man or nature, seem to stand in the same relation to ancient philosophy which hypotheses bear to modern inductive science. These 'guesses at truth' were not made at random; they arose from a superficial impression of uniformities and first principles in nature which the genius of the Greek, contemplating the expanse of heaven and earth, seemed to recognize in the distance. Nor can we deny that in ancient times knowledge must have stood still, and the human mind been deprived of the very instruments of thought, if philosophy had been strictly confined to the results of experience.

2. Plato supposes that when the tablet has been made blank the artist will fill in the lineaments of the ideal state. Is this a pattern laid up in heaven, or mere vacancy on which he is supposed to gaze with wondering eye? The answer is, that such ideals are framed partly by the omission of particulars, partly by imagination perfecting the form which experience supplies (Phaedo). Plato represents these ideals in a figure as belonging to another world; and in modern times the idea will sometimes seem to precede, at other times to co-operate with the hand of the artist. As in science, so also in creative art, there is a synthetical as well as an analytical method. One man will have the whole in his mind before he begins; to another the processes of mind and hand will be simultaneous.

3. There is no difficulty in seeing that Plato's divisions of knowledge are based, first, on the fundamental antithesis of sensible and intellectual which pervades the whole pre-Socratic philosophy; in which is implied also the opposition of the permanent and transient, of the universal and particular. But the age of philosophy in which he lived seemed to require a further distinction; – numbers and figures were beginning to separate from ideas. The world could no longer regard justice as a cube, and was learning to see, though imperfectly, that the abstractions of sense were distinct from the abstractions of mind. Between the Eleatic being or essence and the shadows of phenomena, the Pythagorean principle of number found a place, and was, as Aristotle remarks, a conducting medium from one to the other. Hence Plato is led to introduce a third term which had not hitherto entered into the scheme of his philosophy. He had observed the use of mathematics in education; they were the best preparation for higher studies. The subjective relation between them further suggested an objective one; although the passage from one to the other is really imaginary (Metaph.). For metaphysical and moral philosophy has no connexion with mathematics; number and figure are the abstractions of time and space, not the expressions of purely intellectual conceptions. When divested of metaphor, a straight line or a square has no more to do with right and justice than a crooked line with vice. The figurative association was mistaken for a real one; and thus the three latter divisions of the Platonic proportion were constructed.

There is more difficulty in comprehending how he arrived at the first term of the series, which is nowhere else mentioned, and has no reference to any other part of his system. Nor indeed does the relation of shadows to objects correspond to the relation of numbers to ideas. Probably Plato has been led by the love of analogy (Timaeus) to make four terms instead of three, although the objects perceived in both divisions of the lower sphere are equally objects of sense. He is also preparing the way, as his manner is, for the shadows of images at the beginning of the seventh book, and the imitation of an imitation in the tenth. The line may be regarded as reaching from unity to infinity, and is divided into two unequal parts, and subdivided into two more; each lower sphere is the multiplication of the preceding. Of the four faculties, faith in the lower division has an intermediate position (cp. for the use of the word faith or belief, (Greek), Timaeus), contrasting equally with the vagueness of the perception of shadows (Greek) and the higher certainty of understanding (Greek) and reason (Greek).

The difference between understanding and mind or reason (Greek) is analogous to the difference between acquiring knowledge in the parts and the contemplation of the whole. True knowledge is a whole, and is at rest; consistency and universality are the tests of truth. To this self-evidencing knowledge of the whole the faculty of mind is supposed to correspond. But there is a knowledge of the understanding which is incomplete and in motion always, because unable to rest in the subordinate ideas. Those ideas are called both images and hypotheses – images because they are clothed in sense, hypotheses because they are assumptions only, until they are brought into connexion with the idea of good.

The general meaning of the passage, 'Noble, then, is the bond which links together sight…And of this kind I spoke as the intelligible…' so far as the thought contained in it admits of being translated into the terms of modern philosophy, may be described or explained as follows: – There is a truth, one and self-existent, to which by the help of a ladder let down from above, the human intelligence may ascend. This unity is like the sun in the heavens, the light by which all things are seen, the being by which they are created and sustained. It is the IDEA of good. And the steps of the ladder leading up to this highest or universal existence are the mathematical sciences, which also contain in themselves an element of the universal. These, too, we see in a new manner when we connect them with the idea of good. They then cease to be hypotheses or pictures, and become essential parts of a higher truth which is at once their first principle and their final cause.

We cannot give any more precise meaning to this remarkable passage, but we may trace in it several rudiments or vestiges of thought which are common to us and to Plato: such as (1) the unity and correlation of the sciences, or rather of science, for in Plato's time they were not yet parted off or distinguished; (2) the existence of a Divine Power, or life or idea or cause or reason, not yet conceived or no longer conceived as in the Timaeus and elsewhere under the form of a person; (3) the recognition of the hypothetical and conditional character of the mathematical sciences, and in a measure of every science when isolated from the rest; (4) the conviction of a truth which is invisible, and of a law, though hardly a law of nature, which permeates the intellectual rather than the visible world.

The method of Socrates is hesitating and tentative, awaiting the fuller explanation of the idea of good, and of the nature of dialectic in the seventh book. The imperfect intelligence of Glaucon, and the reluctance of Socrates to make a beginning, mark the difficulty of the subject. The allusion to Theages' bridle, and to the internal oracle, or demonic sign, of Socrates, which here, as always in Plato, is only prohibitory; the remark that the salvation of any remnant of good in the present evil state of the world is due to God only; the reference to a future state of existence, which is unknown to Glaucon in the tenth book, and in which the discussions of Socrates and his disciples would be resumed; the surprise in the answers; the fanciful irony of Socrates, where he pretends that he can only describe the strange position of the philosopher in a figure of speech; the original observation that the Sophists, after all, are only the representatives and not the leaders of public opinion; the picture of the philosopher standing aside in the shower of sleet under a wall; the figure of 'the great beast' followed by the expression of good-will towards the common people who would not have rejected the philosopher if they had known him; the 'right noble thought' that the highest truths demand the greatest exactness; the hesitation of Socrates in returning once more to his well-worn theme of the idea of good; the ludicrous earnestness of Glaucon; the comparison of philosophy to a deserted maiden who marries beneath her – are some of the most interesting characteristics of the sixth book.

Yet a few more words may be added, on the old theme, which was so oft discussed in the Socratic circle, of which we, like Glaucon and Adeimantus, would fain, if possible, have a clearer notion. Like them, we are dissatisfied when we are told that the idea of good can only be revealed to a student of the mathematical sciences, and we are inclined to think that neither we nor they could have been led along that path to any satisfactory goal. For we have learned that differences of quantity cannot pass into differences of quality, and that the mathematical sciences can never rise above themselves into the sphere of our higher thoughts, although they may sometimes furnish symbols and expressions of them, and may train the mind in habits of abstraction and self-concentration. The illusion which was natural to an ancient philosopher has ceased to be an illusion to us. But if the process by which we are supposed to arrive at the idea of good be really imaginary, may not the idea itself be also a mere abstraction? We remark, first, that in all ages, and especially in primitive philosophy, words such as being, essence, unity, good, have exerted an extraordinary influence over the minds of men. The meagreness or negativeness of their content has been in an inverse ratio to their power. They have become the forms under which all things were comprehended. There was a need or instinct in the human soul which they satisfied; they were not ideas, but gods, and to this new mythology the men of a later generation began to attach the powers and associations of the elder deities.

The idea of good is one of those sacred words or forms of thought, which were beginning to take the place of the old mythology. It meant unity, in which all time and all existence were gathered up. It was the truth of all things, and also the light in which they shone forth, and became evident to intelligences human and divine. It was the cause of all things, the power by which they were brought into being. It was the universal reason divested of a human personality. It was the life as well as the light of the world, all knowledge and all power were comprehended in it. The way to it was through the mathematical sciences, and these too were dependent on it. To ask whether God was the maker of it, or made by it, would be like asking whether God could be conceived apart from goodness, or goodness apart from God. The God of the Timaeus is not really at variance with the idea of good; they are aspects of the same, differing only as the personal from the impersonal, or the masculine from the neuter, the one being the expression or language of mythology, the other of philosophy.

This, or something like this, is the meaning of the idea of good as conceived by Plato. Ideas of number, order, harmony, development may also be said to enter into it. The paraphrase which has just been given of it goes beyond the actual words of Plato. We have perhaps arrived at the stage of philosophy which enables us to understand what he is aiming at, better than he did himself. We are beginning to realize what he saw darkly and at a distance. But if he could have been told that this, or some conception of the same kind, but higher than this, was the truth at which he was aiming, and the need which he sought to supply, he would gladly have recognized that more was contained in his own thoughts than he himself knew. As his words are few and his manner reticent and tentative, so must the style of his interpreter be. We should not approach his meaning more nearly by attempting to define it further. In translating him into the language of modern thought, we might insensibly lose the spirit of ancient philosophy. It is remarkable that although Plato speaks of the idea of good as the first principle of truth and being, it is nowhere mentioned in his writings except in this passage. Nor did it retain any hold upon the minds of his disciples in a later generation; it was probably unintelligible to them. Nor does the mention of it in Aristotle appear to have any reference to this or any other passage in his extant writings.

BOOK VII. 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.