514A Now, I said, after this you should compare our nature in respect of education or lack of education to a condition such as this. Behold men in a sort of underground cave-like dwelling, with a long entrance facing towards the light along the side of the entire cave. They have been in this from childhood, with bonds both on their legs and on their necks 514B so that they remain looking only at what is in front of them, being unable to turn their heads around because of the bond on the neck.
Light comes to them from a fire burning above and at a distance behind them, and higher up, between the fire and the prisoners, there is a path and you can see a low wall built along the path, just like the screens which puppet makers place in front of themselves, over which they display their puppets.
I see, he said.
Besides this you should also see men carrying a variety of objects 514C past the wall including statues of men and other 515A animals, made of wood, stone and all sorts of materials. Some of the object carriers are likely to be speaking, while others are silent.
You are describing a strange image, he said, and strange prisoners.
They are just like us, I said. For in the first place, do you think such people would ever have seen anything of themselves or one another, apart from the shadows cast by the fire onto the cave wall in front of them?
How could they, he replied, if they were compelled 515B to keep their heads motionless throughout life?
And what about the objects being carried, isn’t the situation the same?
Now if they could converse with one another, don’t you think they would call the very things they saw, things that are?
What if the prison had an echo coming from the opposite wall? Whenever one of the passers-by spoke, do you think the men would believe the speaker to be anything other than the passing shadow?
By Zeus, I do not, he said.
515C Then such people would believe, without reservation that truth is nothing but the shadows of the artificial objects.
They really must, he said.
Now, I said, consider what liberation from their bonds, and cure of their ignorance, would be like for them, if it happened naturally in the following way. Suppose one of them were released, and compelled suddenly to stand up, turn his neck, walk, and look up towards the light. Wouldn’t he be pained by all this and, on account of the brightness, 515D be unable to see the objects whose shadows he previously beheld. And if someone were to tell him that he beheld foolishness before, but now he sees more truly, as he is much closer to “what is”, and is turned towards things which partake of more being, what do you think he would say? Moreover, if they showed him each of the passing objects and forced him to answer the question “what is this?”, don’t you think he would be perplexed, and would believe that what he saw before was truer than what he is now being shown?
Very much so, he replied.
And if he were compelled to look towards the light itself, wouldn’t his eyes be pained? 515E Wouldn’t he turn about and flee to those things he really can see, and regard these as, in fact, clearer than what he is being shown?
Just so, he replied.
And if someone were to drag him forcibly, from there, along the rough upward path, and not let him go until he had been dragged out into the light of the sun, wouldn’t he be distressed and upset by the process? 516A And once he had come into the light, wouldn’t his eyes be flooded with its glare, and be unable to see even one of what are now called truths.
No, they would not, he said, not immediately anyway.
Yes, I think he would need to become accustomed to it, if he was ever to behold the objects of the upper realm. At first he would discern shadows very easily, after that, images of men and other objects in water, then the actual objects. From these he would proceed to view the heavenly bodies and the heaven itself by night, looking to the light of the stars 516B and the moon more easily than the sun and the light of the sun by day.
What else could he do?
Then I imagine he would finally be able to behold the sun, not its appearance in water or in an alien setting, but just by itself, in its own place, and he would see it as it is.
This must be so, he said.
And after this, he would then make deductions about it: that this is what provides the seasons and the years, presiding over everything in the visible realm 516C and, in a way, the cause of everything they have been seeing.
Obviously, he said, those are the steps he would take.
What then? Remembering his first dwelling place, and the wisdom there, and his former fellow prisoners, wouldn’t he believe that he himself was blessed by the transformation, but feel compassion for them?
Very much so.
And suppose they received certain honours and praises from one another, and there were privileges for whoever discerns the passing shadows most keenly, and is best at remembering which of them usually 516D comes first or last, which are simultaneous and, on that basis, is best able to predict what is going to happen next. Do you think he would have any desire for these prizes, or envy those who are honoured by the prisoners and hold power over them? Or would he much prefer the fate described by Homer and “work as a serf for a man with no land” and suffer anything at all, rather than hold their opinions, and live as they do?
516E I think it is just as you say; he would accept any fate rather than live as they do.
Yes, and think about this, I said, if such a person were to go back down and sit in the same seat, wouldn’t his eyes become filled with darkness after this sudden return from the sunlight?
Very much so, he said.
Now suppose that he had to compete once more with those perpetual prisoners, in recognising these shadows, while his eyesight was still poor, before 517A his eyes had settled down: since it would take some time to become accustomed to the dark, wouldn’t he become a figure of fun? Wouldn’t they say that he went up, but came back down with his eyes ruined, and that it is not worth even trying to go upwards? And if they could somehow catch and kill a person who was trying to free people and lead them upwards, wouldn’t they do just that?
Definitely, he said.
Then, dear Glaucon, I said, you should connect 517B this image, in its entirety, with what we were saying before. Compare the realm revealed by sight to the prison house, and the firelight within it to the power of our sun. And if you suggest that the upward journey, and seeing the objects of the upper world, is the ascent of the soul to the realm known by reason, you will not be misreading my intention since that is what you wanted to hear. God knows whether it happens to be true, but in any case, this is how it all seems to me: when it comes to knowledge, the form of the good is seen last and is seen only through effort. Once seen it is reckoned to be the actual cause of all 517C that is beautiful and right in everything, bringing to birth light, and the lord of light, in the visible realm, and providing truth and reason in the realm known by reason, where it is lord. Anyone who is to act intelligently either in private or in public must have had sight of this.
I also hold the same views that you hold, he said, after my own fashion, anyway.
Come on then, I said, and agree with me about something else; do not be surprised that those who have attained these heights have no desire for involvement in human affairs, their souls, 517D rather, are constantly hastening to commune with the upper realm. For I presume that’s what is likely to happen, if this really does accord with the image we described earlier.
Yes, quite likely, he said.
Yes, and do you think it would it be any surprise, I asked, if someone who has returned from divine contemplations, to human affairs, disgraces himself badly and appears utterly ridiculous, while his eyes are still dim and if, before he has become accustomed to the prevailing darkness, he is compelled to argue, in courtrooms or elsewhere, about the shadows of justice, or the artificial objects which cast those shadows, and dispute about these matters as understood by people who have never seen justice itself?
No, that would be no surprise at all, he replied.
518A But if someone were endowed with reason, I said, he would recall that the confounding of the eyes is of two kinds, and has two sources: a change from light to darkness, or from darkness to light. And having realised that the same thing happens to the soul, he will not laugh boorishly whenever he sees a soul confused and unable to see clearly, instead he will enquire whether she has come from a brighter life and is darkened because she isn’t used to the gloom, or she is coming from the utter darkness of ignorance into a brighter 518B realm, and is dazzled by the greater brilliance. So on this basis, he would regard the condition and the life of one soul as blessed, while he would feel compassion for the other, and if he wished to laugh at her, his laughter would be less scornful than it would for a soul descended from the light above.
Yes, he said, what you are saying is very reasonable.
Then, I said, if this is all true, there is something we need to recognise: education is not the sort of thing which some people profess it to be. They somehow claim that although knowledge 518C is not present in the soul, they can put it there as if they were putting sight into blind eyes.
Yes, that is what they say.
Yes, but the argument is now indicating that this capacity, present in the soul of each person, the organ by which each learns, is like an eye which cannot turn to the light from the darkness unless the whole body turns. So this organ must be turned, along with the entire soul, away from becoming, until it becomes capable of enduring the contemplation 518D of what is, and the very brightest of what is, which we call the good. Is this so?
Then, I said, there would be a particular skill dealing with this turning of the soul, some manner in which it might be turned around most easily and effectively: a skill which does not produce sight in the soul, but assumes that although sight is already present, it is not directed properly, or looking where it should, and sets about correcting this.
Yes, so it seems.
Now the other excellences which are said to belong to the soul are really somewhat closer to physical excellence, for they are not actually present at first, but are generated later through habit and practice. However, 518E that excellence wherein we employ reason surely belongs, most of all, to something more divine, it seems, something whose power is never destroyed, but becomes either useful and beneficial, or useless and harmful, 519A depending upon how the soul is turned. Or have you never noticed those men who are said to be evil and yet wise? Have you noticed the keen vision of their tiny soul and how sharply it discerns whatever it happens to turn to? For there is no problem with its sight, but it is forced into the service of evil, and consequently, the more keenly it sees, the more evil it accomplishes.
Yes, certainly, he said.
However, I said, if this part of someone with such a nature is worked upon from earliest childhood, the relationships 519B with becoming are cut away as if they were leaden weights. These grow upon the soul through gluttony and similar pleasures and the refinements thereof, and turn the vision of the soul downwards. But once she is quit of them she turns around to the realm of truth, and the same part of the same people beholds that realm, just as clearly as it beholds whatever is in front of it now.
Quite likely, he said.
What about this? Isn’t it also likely, I said, and mustn’t it follow from what we said before, that neither the uneducated, with no experience of truth, nor those who are allowed519Cto spend all their time in education, would ever be adequate custodians of the city? The one, because they don’t have a single purpose in life which they should aim at in all the actions they perform in public or in private; the other, because they will not willingly engage in action, as they believe that whilst still alive, they are already dwelling on the far off islands of the blessed.
True, he said.
Now it is our task as founders to compel the best natures to attain the learning which we said, previously, was the most important; to see the good, and ascend 519D that upward path. And once they have ascended, and seen enough, we must not allow them to do what is permitted at present.
What is that?
They are allowed to remain there, with no desire to descend once more among those prisoners, or to partake of their endeavours and their honours, whether these are mundane or more serious.
In that case, he said, shall we be doing them an injustice? Shall we make them live an inferior life when a better one is available to them?
519E My friend, you have just forgotten that the law is not concerned with how one particular class in the city may fare better than the others. Instead, it tries to bring this about in the city as a whole, creating harmony among the citizens by persuasion and compulsion, and making them share, with one another, 520A any benefit that each of them is able to contribute to the community. And the law itself produces men like these in the city, not so that each may go in any direction he pleases, but to use them to bind the city together.
True, he said, I had forgotten this.
Then, I said, you must see, dear Glaucon, that we are not doing an injustice to the philosophers in our midst, but we shall be making just demands when we compel them to care for and protect 520B the other citizens. We shall say that “when people like you arise in the other cities, it is reasonable that they don’t share in the labours of those cities, and this is justified there, because such people develop of their own accord, through no intention on the part of that civic arrangement, and it is only fair that whatever develops of its own accord, owes its nurture to no one, and should feel no urge to pay for that nurture.”
“But you have been bred by us like kings and rulers of the hive, both for your own sakes and for the rest of the city. Having been better and more perfectly educated than them, you are more capable of participating in both realms. 520C Therefore, you must each play your part, and go down to where the others dwell together, and become accustomed with them to the dark shadows. For once you are used to the darkness, you will see a thousand times better than the people there, and you will know what each of the images is, and what it is an image of, because you have seen the truth about things beautiful, just and good. Accordingly, the city will be governed by us and by you in a wakeful state, and not in a dream, as most cities are governed today, by men who fight one another over shadows, and battle 520D for public office as if that was the greatest good. But surely the truth is that, that city in which those who are going to rule have the least desire to do so must be the best governed city and the one most free from strife, and if it gets the opposite sort of rulers, it must be ruled in the opposite manner.”
Yes, certainly, he said.
Now will our charges be unmoved when they hear this, and will they be reluctant to join in the work of the city when it is their turn, and then live together, most of the time, in the pure realm?
520E Impossible, he replied. We are laying just injunctions upon just men. However, each of them will approach public office very much as a necessity, in contrast to those who now rule every city.
So, on this basis, my friend, if you can find a better 521A life than ruling, for these who are going to rule, a well governed city becomes a possibility for you. For only there will the truly wealthy be the rulers, wealthy not in gold but in the wealth which a blessed man needs; a good and reasonable life. However, if beggars, starved of goods of their own, enter public affairs thinking that therein they may seize the good, then it is an impossibility. For, public office then becomes something to fight over, and a domestic and internal battle like this destroys the disputants, and the rest of the city.
Very true, he said.
521B Now other than the life of true philosophy, can you think of any life that despises political office?
By Zeus, I cannot, he said.
Well in that case, those who are not lovers of public office must take it on; otherwise the competing lovers will fight over it.
How could it be otherwise?
Now are there any others whom you would compel to act as guardians of the city, others who would manage it better than those who are wisest about these matters who have other honours, and a better life than politics?
There are no others, he replied.
521C Then would you like to go on to consider the manner in which people like this will arise in our city, and how we shall lead them to the light, just as certain people are said to have ascended from Hades to the gods?
How could I refuse, he said?
Well this, it seems, would not be the mere flipping over of an oyster shell, but a process of turning the soul around from a day which is more like night, to the true day, the ascent to what is, an ascent which we may truly call philosophy.
521D Then is it necessary to consider which branch of learning possesses a power like this?
Now Glaucon, what subject would draw the soul from becoming towards what is? And something else occurs to me as I say this: didn’t we state that these guardians must be practised in war, when they are young?
Yes, we said that.
So the subject we are looking for must also have this characteristic as well as the other.
It must not be useless to military men.
It certainly must not, if that is actually possible.
In the earlier account they were educated by us in gymnastic and in music.
They were, he said.
521E Gymnastic is presumably concerned with what comes into being and passes away, for it presides over the development and the decline of the body.
So it appears.
Then this would not be the subject we are looking for.
It would not. 522A
So in that case, is it music in the sense we described it earlier?
But that was the counterpart of gymnastic, he said, and if you recall, it educated the guardians through habit, imparting gracefulness through its harmony, and orderliness through its rhythm, without imparting knowledge. And it also contained habits akin to these in its words, both in the mythical stories and in the truer versions. However music does not include a branch of learning that leads towards the sort of thing you are looking for now.
522B Your reminder is very precise, I said, music actually contains nothing of that sort. But what kind of subject would this be? Indeed all of the skills seemed somehow to be mechanical.
Yes, they must be. And yet what other subject is left apart from music, gymnastic and the various skills?
Come on, if we can’t come up with anything besides these, let’s select something applicable to them all.
522C Like this, what they have in common, that which all skills, concepts, and knowledge refer to, and which is also the first thing everyone learns.
What is it, he asked?
The ordinary process, I said, of distinguishing one, two and three, in short, arithmetic and calculation. Isn’t it the case that all skill and knowledge must involve recourse to these?
Very much so, he replied.
Military skill too, I asked?
It certainly must, he replied.
522D In that case, Palamedes in the tragedies repeatedly shows up Agamemnon as an utterly ridiculous general. Or have you not noticed that he claims to have discovered number and arranged the ranks of the army at Troy and counted the ships and everything else, as though they hadn’t been counted before? And apparently Agamemnon didn’t know how many feet he had since he did not know how to count. So what sort of general do you think he was?
A strange one, he replied, if this is true.
522E So, should we propose that the ability to calculate and count is a necessary branch of learning for a military man?
It is the most necessary of all, if he is going to have any understanding whatsoever of arranging armies, and more importantly, if he is even to be human.
Now do you notice what I notice about this subject?
523A It is quite likely to be one of the subjects we are seeking which, by nature, leads us towards reason. However, no one uses it correctly as a subject which can draw one comprehensively towards being.
How so, he said?
Well, I shall try to set out my opinion, I said. Look at this with me and agree or disagree so that we may see more clearly if my suspicion is correct. For I am distinguishing for myself between what leads, and what does not lead, in the direction we spoke of.
Give an example, he said.
Take this example, I said, observe, if you can, that in the case of sense perceptions there are some which do not call upon 523B reason to investigate them, as they are adequately judged by the senses. Others, however, completely depend upon reason to investigate them, as the senses produce nothing trustworthy.
You are obviously referring to distant phenomena and shadow drawing, he said.
You haven’t really got my meaning, I said.
Then what do you mean, he said?
Those which do not call upon reason are those which do not extend into the opposite 523C sensation at the same time. However, in the case of those which do extend, I suggest that they call upon reason whenever the sense impression reveals something, no more than its opposite, regardless of whether it impinges upon us from near or far. My meaning will be clearer from this example: we would say that these are three fingers; the smallest, the second and the middle.
Certainly, he said.
Assume that I am describing them as seen from close up. Now there is a question you must consider in relation to them.
What is it?
Well each of them, in the same way, appears to be a finger and in this respect, there is no 523D difference whether it is seen in the middle or at either extreme, whether it is white or black, or whether it is fat or thin or anything of that sort. For in all these cases, the soul of most people is not compelled to put a question to reason as to what precisely a finger is. For at no stage does sight indicate to her that the finger is the opposite of a finger at the same time.
No, it does not, he said.
Therefore, I said, a case such as this would be unlikely to call upon or awaken reason.
523E What about this? Does sight see their largeness or smallness adequately, and does it make no difference to sight whether one of them lies in the middle or on either side? Does the same apply to thickness and thinness, and hardness and softness in the case of touch? And do the other senses reveal things like this without any deficiency? Or does each of them 524A behave in the following manner: the sense which extends to hard must also extend to soft, and it proclaims to the soul that the same thing is being perceived as both hard and soft?
Just so, he replied.
Mustn’t the soul, for its part, be perplexed in such circumstances as to what precisely the hard that the particular sense is indicating, actually is, since it also says that the same thing is soft. And if the sense of light and heavy indicates that heavy is light and light is heavy, mustn’t the soul be perplexed as to what is heavy and what is light?
524B Yes, indeed, he replied. These messages to the soul are strange and require further investigation.
So, I said, it is likely that in these situations the soul first calls upon calculation and reason and tries to investigate whether each of the proclamations is two or one.
Yes, what else could it do?
If it turns out that it is two, wouldn’t each of the two appear to be both different and one?
So if each is one and both are two, soul will recognise the two as separate, 524C for if they were not separate it would not have recognised two but only one.
And we say sight too has seen large and small, not separately, however, but in combination, is this so?
But for the sake of clarity in this, reason, in contrast to sight, is compelled to view large and small, not mixed together but separately.
Hence, the first thing that occurs to us is to ask what precisely “large” and “small” actually are, isn’t this so?
And on this basis, of course, we said there was a realm known by reason and also a realm known by sight.
You are perfectly right.
524D Well this is what I was trying to explain earlier: that there are some things which call upon thought and others which do not. Now I define those which impinge upon the sense at the same time as their own opposites, as provoking reason, while those which don’t do this don’t awaken it.
Very well I understand now, he said, and I think this is right.
Well then, to which realm do you think number and the one belong?
I can’t decide, he replied.
But you can work it out from what was said before. If the one were seen adequately just by itself, or apprehended by 524E some other sense, it would be like the finger we referred to and would not draw people towards being. However, if the one is always seen along with something which is opposite to it, so that what is presented is no more one than its opposite, discrimination would then be required, and in that situation the soul, activating the intelligence within herself, would have to be perplexed, and search, and ask 525A “what, precisely, is the one itself”? And accordingly, getting knowledge of the one would be among the branches of knowledge that lead the soul and turn her around towards the contemplation of what is.
And indeed, he said, this applies in no less measure, to seeing it, for we see the same thing both as one, and as an unlimited multiplicity at the same time.
Since this is what happens in the case of the one, said I, won’t the same thing happen with all number?
And indeed calculation and arithmetic are entirely concerned with number.
Very much so.
Yes, and these appear to lead towards truth.
Yes, to an enormous extent.
525B So apparently, these would be among the subjects we are seeking. For a military man must learn them in order to arrange an army in ranks, and a philosopher has to learn them too, because he must lay hold of being, and rise out of becoming, otherwise he will never be able to calculate.
This is the case, he replied.
Now our guardian happens to be both a military man and a philosopher.
In that case, Glaucon, it would be appropriate to establish this subject by law, and persuade those who are going to participate 525C in the most important affairs of the city to have recourse to calculation and take it up, not as a personal matter, but until they attain the contemplation of the nature of the numbers by means of reason itself. They should not practise it for the sake of buying and selling like merchants or retailers, but for the sake of war, and the ready turning of the soul herself, away from becoming, towards truth and being.
That is beautifully expressed, he said.
And indeed in the light of what is being said about the subject of calculation, 525D I realise that it is nicely and entirely suited to our purpose, provided it is pursued for the sake of knowledge and not for shop-keeping.
In what way then, he asked?
In the way we already described. It leads the soul powerfully upwards to some place, and compels her to engage in dialectic in relation to the numbers themselves. It won’t accept it at all if someone presents the soul with numbers associated with visible or tangible objects and discusses them. For I presume you know that its skilled exponents are amused if anyone, in discussion, 525E attempts to divide the one itself, and they will not accept this. If you divide it, they will multiply, being careful lest the one ever proves to be not one, but a multiplicity of parts.
What you are saying is very true, he said.
526A Glaucon, if someone were to ask them: “wonderful men, what sort of numbers are you talking about in which the one is as you are proposing; each, in every case, equal to each, not the slightest bit different, and having no parts within itself?” What do you think their reply would be?
I think they would say that they are referring to those numbers which it is possible to grasp only by thought, and which are not capable of being dealt with in any other way at all.
Now my friend, I said, do you see that in truth, this is likely 526B to be the subject we require, since it evidently compels the soul to resort to reason itself for the sake of truth itself.
Yes, indeed, he said, it certainly does that.
Well then have you ever considered the fact that those who take naturally to calculation are said to be bright in all subjects? While those who are dull, if they are educated and exercised in this subject, all improve and become brighter than they were before, even if they derive no other benefit.
That’s the way it is, he replied.
526C And indeed in my view, you would not easily find many subjects which involve greater toil in learning or in practising than this one.
So for all these reasons, the subject must not be dismissed, and the best natures must be educated in it.
I agree, he said.
Then let’s leave it at that and consider whether the second subject, the one that follows it, is appropriate to our purpose.
What sort of subject? He asked. Do you mean geometry?
The very one, I replied.
Insofar as it is applicable to military affairs, it will obviously be appropriate, 526D he said. Indeed, the man who knows geometry would be superior to one who does not, in setting up camp, capturing territory, drawing the army into close formation, or dispersing it, and in any other arrangements of the army in the battle itself, or on a march.
But of course, said I, even a little geometry and calculation would be sufficient for these purposes, but we need to consider whether most of it, 526E and the more advanced part thereof, is inclined to make the form of the good easier to discern; that is the objective. And according to us, any subject inclines to this provided it compels the soul to turn around to that place where the most blessed part of what is resides, a part that the soul must behold in every way.
Correct, said he.
And in that case, if it compels the soul to behold being, it is an appropriate subject, but if it compels her to behold becoming, it is not appropriate.
Yes, so we say.
527A Well, said I, no one with even the slightest experience of geometry will argue with us over this proposition; that this knowledge, itself, stands in total contrast to what’s said about it, in discussion, by those who practise it.
How so? said he.
Well they somehow speak quite comically, and they are actually compelled to do so. In fact, by using terms like “squaring” and “applying” and “extending” and so on, they speak as though they are engaging in activity, and as if they are constructing arguments for some practical purpose, even though, I presume, the entire subject is pursued for the sake of knowledge.
527B Yes, entirely so, he said.
Can we agree on a further point?
What is it?
They pursue it for the sake of knowledge of what always is, and not of what becomes something, sometime, and is then destroyed.
That’s easy to accept, said he; geometrical knowledge is knowledge of what always is.
So, my noble friend, it would be a subject that draws the soul towards truth, and produces a philosophic mind, directing upwards whatever we now, incorrectly, direct downwards.
Yes, as best it can, said he.
527C So, said I, you must arrange, as best you can, that the people in “Noble-City” don’t refrain from geometry in any way, for even its incidental benefits are significant.
What are they? he asked.
Those you mentioned, said I; those concerned with warfare, and of course we know, I presume, that for any subject to be better assimilated, it generally makes all the difference whether the student has already taken to geometry or not.
All the difference indeed, by Zeus, said he.
So should we propose this as the second subject for our young folk?
527D Should we propose astronomy as a third subject? Do you think so?
I do indeed, said he. For being better able to discern the seasons, the months, and the years, is appropriate not only for agriculture and navigation, but also for generalship, no less.
You amuse me, said I; you seem to be afraid of what most people may think of you if you prescribe impractical subjects. It is no ordinary matter, in fact it is quite difficult to be convinced that some organ of the soul, an organ that everyone has, is purified and rekindled 527E by these studies, having been corrupted and blinded by our other pursuits, and that it is more important to preserve this organ than it is to preserve ten thousand eyes, for truth is seen only by this. Now those who hold these opinions already will think that what you are saying is really sound, while those with no awareness of this at all, are likely to think you are talking nonsense, for they will see no other benefit worth mentioning from these. So decide 528A here and now which group you are conversing with, if any. Or perhaps you are formulating the arguments mainly for your own sake, although you would not, of course, begrudge anyone else who might derive some benefit from them.
That’s my choice, said he; I am speaking, asking questions and answering them, mostly for my own sake.
Let’s fall back then, said I, since we didn’t pick the subject that comes next, after geometry, correctly just now.
How did we go wrong? He asked.
After flat surfaces, we took solids, already in rotation, before taking solids just by themselves. The correct sequence is to take the third dimension after 528B the second, and this is presumably the dimension associated with cubes and whatever has depth.
Quite so, Socrates, he said, but these don’t seem to have been found yet.
Yes, said I, for two reasons: firstly, no city has proper respect for them, and they are not thoroughly investigated because they are so difficult. Secondly, investigators in this area need a guide, without whom they won’t discover anything, but a guide is hard to find in the first place, and when found, as matters now stand, the arrogant fellows who would be able to investigate this would 528C pay no heed to him. But if an entire city were to co-operate with the guide by treating these matters with respect, these people would heed him, and under close and intensive investigation, the true state of affairs would become evident. Since, even now, although they are disrespected and criticised by most people, and by those who investigate them without being able to explain their usefulness, nevertheless, in the face of all this they develop by force, due to their inherent charm, and it would be no surprise if they were to come to light.
528D Yes indeed, said he, they do possess exceptional charm, but explain what you are saying more clearly. For I presume you designated the study of flat surfaces as geometry.
Yes, said I.
Then, said he, initially you put astronomy after that, but later on you changed your mind.
Yes, said I, in my haste to recount everything quickly I am making slower progress. For, although the study of the dimension of depth is next in sequence, I passed over this because of the comical state of the investigation, and after geometry I spoke of astronomy which is the motion of objects with depth.
Right, said he.
528E Then, provided the city pursues it, let’s propose astronomy as the fourth subject, on the assumption that the third, the one we are now passing over, exists.
Quite likely, said he, and I will now praise astronomy in the way you set about it, and avoid the commonplace manner of praise for which you rebuked me. Indeed it is obvious to everyone, that this study compels 529A the soul to look upwards and leads it away from what is here, to what is there, above.
This is probably obvious to everyone except me, said I, since that’s not how it seems to me.
How does it seem to you? He asked.
Handled as it is nowadays by those who are elevating us towards philosophy, it really makes the soul look downwards.
How do you mean? he asked.
I think you have a very liberal understanding of the subject concerned with the upper realm. Indeed if someone were to throw his head back and contemplate adornments on the ceiling 529B and arrive at some understanding, you would probably think he was contemplating them with his intellect rather than his eyes. Now perhaps your thinking is sound and I am being simpleminded, for I cannot think of anything that makes the soul look to the upper realm except the subject that is concerned with what is, and the unseen. Whether someone attempts to understand sense objects by gaping upwards or squinting downwards, I would never maintain that he has ever understood anything, for things of this sort529Cdo not admit of knowledge, and his soul is not gazing upwards but downwards even if he tries to understand while floating on his back, on land or in the sea.
I am getting my just deserts, said he, and you are right to rebuke me. But in what way are you saying astronomy should be studied, contrary to the way they study it nowadays, if its study is to confer the benefits we are speaking of?
As follows, said I; these adornments that are in the heavens adorn in the visible realm, and although they should be regarded as the most beautiful and perfect 529D of visible objects they do fall far short of the true adornments, the motions with which speed itself and slowness itself are moved with respect to one another, in the true number, and in all the true shapes, carrying whatever they contain; these can be apprehended by reason and by thought but not by sight. Or do you think otherwise?
Not at all, he replied.
Therefore, said I, we should use the heavenly adornments as patterns in order to understand what is unseen, just as if we had come across diagrams, exceptionally well drawn and executed by Daedalus or some other craftsman or draughtsman. 529E For anyone experienced in geometry, on seeing this sort of thing, would surely think that although the workmanship is very beautiful, it would be quite ridiculous to scrutinise them seriously with a view to finding 530A the truth about equals, or doubles, or any other proportion, in these.
Yes, it must be ridiculous, said he.
Don’t you think then, I asked, that the genuine astronomer will come to the same conclusion when he looks upon the motions of the stars? Won’t he be of the opinion that these and whatever they contain have been fashioned in the most beautiful manner possible for objects of this sort, by the craftsman of the heaven? But what about the proportion of night to day, of these to the month, of the month to the year and of the other stars to these, 530B and to one another? Well don’t you think the true astronomer will think it strange, if anyone regards these as unchanging and as undergoing no alteration whatsoever, even though they are physical objects and are visible, and if he seeks in various ways to grasp the truth about these,
Well I think so now, at any rate, said he, now that I hear you saying so.
So said I, we should engage in astronomy by making use of problems, just as we do in geometry, and bid farewell to the heavenly bodies, if we are actually going to 530C engage in astronomy so as to make the intelligence that is naturally present in the soul, useful rather than useless.
You are prescribing a task said he, that is very much larger than what astronomy deals with nowadays.
I think, said I, that our other prescriptions will be of the same sort if we are to be of any use as lawgivers. But anyway, do you have any other appropriate subject to suggest?
I don’t have any, said he, not immediately at any rate.
Well, said I, motion, in my opinion, 530D doesn’t consist of one form only, but of many. Now a wise man could perhaps list them all, but two are evident even to us.
What are they?
Besides this one, astronomy, there is the counterpart of this.
It’s quite likely, said I, that just as the eyes have been framed for astronomy, so too were the ears framed for harmonic motion, and that these two branches of knowledge are kindred to one another, as the Pythagoreans maintain, and we are agreeing with them, Glaucon. Is that what we are doing?
Just so, he replied.
530E Therefore, said I, since this is a considerable task, we shall find out from them what they have to say on these matters and whether there is anything else besides these. But throughout the entire process, we shall guard our own concern.
That our charges should never attempt to learn anything incomplete, anything that does not consistently reach the point which everything needs to reach; a failing we ascribed earlier to astronomy. Or don’t you know that in the case of harmony too, the practitioners do something similar? 531A Indeed they, for their part, measure the concords and sounds that are heard, against one another; engaging in useless labour, just like the astronomers.
Yes, by the gods, said he, and they call some intervals “dense”, bending their ears towards them, as if they were eavesdropping on their neighbours, some declaring that they still hear a note in between, and that this is the smallest interval we should measure by, while others dispute this and say it’s the same as the note already sounding; both parties granting their ears 531B priority over their intelligence.
You are referring, said I, to the good fellows who inflict trouble upon the strings, and torture them by tightening them upon the pegs. But in case this image gets out of hand, I’ll put a stop to it now before it refers to the strings being beaten with the plectrum, the various accusations against them, and their reluctance or readiness to answer. These are not the people I am referring to, but the others, those we said we would ask about harmony just now. Indeed these fellows do the same thing as those who are involved in astronomy, 531C since they are looking for numbers in the concords that they can hear, and they do not ascend to the level of problems, and investigate which numbers are concordant and which are not, and the reason why this is so.
The task you are describing, said he, is not of this world.
Well, said I, it is useful if it is done in search of the beautiful and the good, otherwise it is useless.
Quite likely, said he.
And I also think, said I, that if the method we have described for all these subjects, gets to 531D their kinship and what they have in common, and works out their mutual affinities, then their pursuit does contribute something to our desired ends, and is not unprofitable, otherwise it is pointless.
And I feel the same way, Socrates said he, but you are describing an enormous undertaking.
Are you speaking of the prelude said I, or what? Or don’t we know that these are all a prelude to the main theme, the one that we must learn? For you surely don’t think that those who are clever in these subjects are skilled in dialectic?
531E By Zeus, I do not, said he, apart from a few exceptions I have come across.
Well then, said I, do you think those who are unable to present an argument and respond to one, will ever know anything of what we say they must know?
In that case too, said he, the answer is no.
532A Glaucon, said I, isn’t this, at last, the main theme, the very one that dialectic performs? And although it is intellectual, it would imitate the power of sight that we described in our earlier image, which, at a certain stage, tries to look at the actual living creatures, then at the stars themselves, and finally at the sun itself. And whenever someone attempts, in this way, by dialectic, without any of the senses, to get to what each thing itself is, through reason, and does not give up until 532B he apprehends, what the good itself is, by intellect itself, he then arrives at the end of the intellectual realm, just as the other man, in our allegory, came to the end of the visible realm.
Entirely so, said he.
Yes, and don’t you refer to this process as dialectical?
And what about the release of the prisoner from his bonds, his turning from the shadows to the images that cast them, and to the light, the ascent from underground into the sunlight, and his inability, when he gets there, to look yet at the actual animals 532C and plants and the light of the sun, and his looking instead at divine appearances in water, or at shadows of things that are, rather than the shadows of images, cast by another such light which, when compared to the sun, is like another shadow? All this practice of the subjects we have described has this power, and leads what’s best in the soul upwards to the sight of what is most excellent among things that are, just as, in our allegory, what’s brightest in the body was led upwards towards the sight 532D of what is most resplendent in the realm of the physical and visible.
I accept, said he, that this is so, and yet, although I find it extremely difficult to accept, in another way it is difficult not to. Nevertheless this needs to be heard, not only today, but in future, often. So we should return to this, but let’s assume, for now, that what has been proposed is indeed so, and then proceed to the main theme itself and go through it in detail, just as we did with the prelude. So tell me, what is the manner of this power of dialectic, what sort of forms 532E is it divided into, and what paths does it follow? For, these would be the ones that lead, at last, to where there is, for whoever gets there, a sort of rest from the journey and an end to the process.
533A Dear Glaucon, said I, you will not be able to follow me any longer, even though there won’t be any lack of eagerness on my part, nor would you still be seeing an image of what we are speaking of, but the truth itself, as it appears to me, anyway. At the moment it is not right to insist that this is actually so, or that it isn’t, but we should insist that there is something of this sort to be seen. Is this so?
And shouldn’t we also insist that the power of dialectic, alone, would reveal this to someone with experience in what we have been describing just now, and that this is not possible in any other way?
It’s only right, said he, that we insist upon this too.
Well, said I, no one will argue against us when we say that 533B some other method, apart from the five subjects, attempts to grasp systematically, in each and every case, what each itself is. But all the other skills are concerned with people’s opinions and desires, or with producing things or assembling them, or with looking after them once they have been produced or assembled. As for the rest, geometry and so on, 533C we maintained that these apprehended something of what is, but we see that although they dream about what is, they are unable to see it, wide awake, as long as they make use of hypotheses that are left unchallenged because they are unable to give an account of them. For when the first principle is something that is not known, and the conclusion, and everything in between is woven from what is not known, is there any way that a combination like this could ever constitute knowledge?
None at all, said he.
Doesn’t the dialectical method alone, said I, proceed in this way to the first principle itself, by doing away with hypotheses in order to be sure of its ground? 533D It draws the eye of the soul, which is actually buried in some outlandish mire, and leads her upwards, using the very subjects we have described as helpmates and assistants in the conversion. We have often referred to these subjects as branches of knowledge, out of habit, but they need another name to indicate greater clarity than opinion, and more vagueness than knowledge. I think we used “understanding” to make the distinction earlier but, in my opinion, there is no point in arguing over a name when an enquiry into such important matters lies before us.
533E No indeed, he replied.
So said I, are you content to do what we did before and call the first part knowledge, the second understanding, the third 534A belief, and the fourth imagination; the last two, both together, constitute opinion; the first two, intelligence. Opinion is concerned with becoming, while intelligence is concerned with being, and as being is to becoming so is intelligence to opinion, and as intelligence is to opinion so is knowledge to belief, and understanding to imagination.
But the proportion between what these two are directed towards, and the twofold division of each of these, what’s grasped by opinion and what’s grasped by intelligence, this we should leave aside in case we get involved in many times more arguments than we have already been through.
534B Well, said he, insofar as I am able to follow, I agree with you about the others.
And do you describe someone who acquires an account of the being of each thing, as dialectical? And wouldn’t you say that someone who cannot do so, insofar as he is unable to give an account either to himself or to anyone else, lacks intelligence about the thing to that extent?
How could I say otherwise? he replied.
Doesn’t the same also apply to the good? If someone is not able to separate the form of the good, 534C by argument, setting it apart from everything else, going through all the refutations like a warrior, eager to practice refutation based upon being, rather than opinion, and coming through all this with his argument still standing, you’ll say, won’t you, that someone who can’t do this, does not know the good itself, nor any other good either, and if he does, somehow, get hold of some image of the good he does so by opinion and not by knowledge? He is dreaming and sleeping this life away and before he ever wakes up here, he 534D arrives finally in Hades and sleeps on forever; isn’t this what you would say?
Yes, by Zeus, said he, I’d say all that; very much so.
But of course in the case of your own children whom you are bringing up and educating in the discussion, verbally, if you were actually bringing them up, I presume you wouldn’t allow them to be irrational, like lines in geometry, when ruling the city and presiding over matters of the utmost importance?
Indeed not, said he.
Then will you pass a law whereby they receive an education that enables them, above all, to ask and answer questions in the most knowledgeable manner possible?
534E I shall indeed, said he, with your help.
In that case, said I, do you think we now have dialectic positioned above the other subjects, like a coping stone, that no other subject may rightly be placed higher, and that our 535A discussion of the various subjects is now complete?
I do indeed, said he.
Well, said I, your remaining task is their distribution, and deciding to whom we shall allocate these subjects and in what way.
Of course, said he.
Do you remember the kind of people we chose when we selected our rulers earlier?
How could I forget? said he.
Well, in general, said I, those very natures are the ones that must be selected; the most steadfast and the bravest should be chosen and, as far as possible, the most comely. 535B As well as this, we must look, not only for those who are noble and virile in character, but they should also have the natural qualities suited to this particular education.
They need to be keen, my friend, on the subjects they learn, and have no difficulty in understanding them. Indeed men’s souls are much more inclined to turn coward in the face of demanding studies, than in the gymnasium, since the exertion is more personal to themselves because it is private and not shared with the body.
True, said he.
535C Well we should look for good memory, robustness, and a total love of hard work, or how else do you think anyone would be prepared to undertake the physical labour, and also complete so much study and practice?
No one would, said he, not unless he was extraordinarily gifted by nature.
Our current problem, said I, and the associated disrespect for philosophy, has come about because, as I said before, those who take to philosophy are unworthy of her; what she needs are genuine adherents, not fakes.
In what way, he asked?
535D Firstly, said I, someone who takes to philosophy shouldn’t be handicapped in his love of hard work, so that he loves half the work and doesn’t bother with the other half. This happens when someone loves exercise and loves hunting and loves all physical labour, but is not a lover of learning, doesn’t like to listen, has no spirit of enquiry, and hates any work that involves any of these. And when the situation is reversed, the man’s love of labour is handicapped in the opposite way.
Very true, said he.
And won’t we suggest that a soul is maimed in relation to truth in the same way, if it hates the deliberate lie, finds it unbearable in itself, and gets extremely angry when lied to by others, and yet, calmly accepts the unintentional lie, is untroubled by the lack of understanding when caught out somehow, and has no qualms about being debased in ignorance like some swinish beast?
536A Yes, entirely so, said he.
And when it comes to sound-mindedness, courage, magnanimity and all the other parts of excellence, mustn’t we be on our guard, just as much, to distinguish between the genuine and the fake. For whenever a city or an individual does not know how to look at things like this, comprehensively, they unwittingly rely on fakes, or those whose work is handicapped, as their allies or rulers, as the case may be.
That’s what happens, said he, very much so.
536B Then we should be extremely careful about everything of this sort because, if we introduce sensible people, sound of body, to such extensive study and exercise, and educate them, justice herself will find no fault with us, and we shall save our city and its form of government. But if we introduce people of the wrong sort to these studies, we shall achieve the complete opposite and deluge philosophy with even more ridicule.
That, said he, indeed would be shameful.
It certainly would, said I, but at the moment, I too seem to be inviting ridicule?
How so? said he.
536C I forgot, said I, that we were just playing, and I spoke with too much intensity. For as I was speaking, I turned my gaze towards philosophy, and seeing her being trampled, undeservedly, in the mire, I think I went into a rage, and said what I said, too seriously, as though I was angry with those responsible.
By Zeus, no, said he, that’s not how it sounded to me, as I listened.
Well, said I, that is how it sounded to me as I said it. But we must not forget that in the previous selection process, we picked old men, but in this case that is not allowed. Indeed we should not believe Solon, that a person is able to learn a lot in old 536D age; he can no more learn than run a race! No, all great labours, and there are many, belong to the young.
They must, said he.
Now calculation, geometry, and all the preliminary instruction that should precede education in dialectic, needs to be set before them when they are still children, without presenting it in the form of compulsory instruction that they must learn.
Because, said I, a free man should 536E never learn any subject under conditions of slavery. Indeed physical labours performed under compulsion don’t make the body any worse, but no instruction, forcibly imparted, is retained by the soul.
True, said he.
So, my friend, as you bring up the children in these various subjects 537A don’t do it forcibly but playfully, so that you will be better able to discern what each of them is naturally adapted to.
That sounds reasonable, said he.
Don’t you remember, said I, that assuming it was safe to do so, we also maintained that the children should be brought to the battlefield, on horseback, as spectators, and brought close to the fray, to get a taste of blood like young hunting dogs?
I remember, said he.
And in all these exertions, studies, and dangers, said I, whoever should prove, consistently, to be most adept, is to be admitted to a select number.
At what age? He asked.
537B At the time, said I, when their compulsory gymnastics comes to an end, for during that period of about two or three years, it is impossible to undertake anything else, since tiredness and sleep are inimical to study. And at the same time, their prowess in gymnastics is, in itself, one of their most important tests.
Yes, said he, it would have to be.
And when this period is over, said I, those twenty-year-olds who have been selected will have to bring the subjects that were presented unsystematically 537C during their childhood education, into a combined view of the interrelatedness of the subjects with one another, and with the nature of what is.
Yes, said he, only this sort of learning becomes steadfast in those who receive it.
And this is the greatest test for the dialectical nature; someone who can take a combined view is dialectical, while someone who cannot do so, is not.
I concur, said he.
Well, said I, you will need to consider all this. Those among our young folk who are most 537D like these people, and are also reliable in their studies, in war, and in their other appointed duties, these again, once they reach thirty, should be selected from among the previous selection and awarded even greater honour. You should then see, testing them by the power of dialectic, who is able to let go the eyes and the other senses, and proceed, in the company of truth, to what just is. And here, my friend, the task requires the utmost care.
Why exactly? Said he.
537E Aren’t you aware, said I, of how much harm is done by the practice of dialectic nowadays?
What sort of harm? He asked.
Its practitioners, said I, are filled with lawlessness.
Very much so, said he.
Now, said I, do you think it is any surprise that this happens to them, and don’t you sympathise with them?
In what way, exactly? He asked.
Suppose, said I, that a changeling child was brought up amidst great wealth, 538A in a large and extensive family, surrounded by lots of flatterers. What if he became aware, as a grown man, that he was not related to these so-called parents and was unable to find his real parents. Can you guess what his attitude would be towards those flatterers and the substitute parents, either during the time when he did not know about the switch, or later when he did know? Or would you like to hear my guess?
I’d like that, said he.
Well, said I, my guess is that during the time when he did not know the truth, he would honour his father 538B and mother, and his other supposed family members, more than those who flatter him. He would be less inclined to allow them to want for anything, or to do or say anything unlawful to them, and more inclined to be persuaded by them, rather than by the flatterers, on important matters.
Quite likely, said he.
But once he had become aware of the actual situation, my guess is that, in contrast, he would lose his honour and respect for them, intensify his respect for the flatterers, and be persuaded by them to a greater extent than before. He would then live 538C as they do, associate openly with them, and pay no heed to that pretended father and the rest of his pretended relatives, unless he was extremely reasonable, by nature.
Everything you are describing, said he, is the sort of thing that would actually happen, but what relevance does this image have for those who are encountering dialectic?
As follows: there are, I presume, certain doctrines about what’s just and beautiful, that we have from childhood, doctrines we have been brought up on, so that we grant them authority, and honour them like parents.
There are indeed.
538D And there are pursuits, opposed to these doctrines, pursuits that involve pleasure, which flatter this soul of ours and drag her in their direction. However these do not sway people who have some element of measure, who continue to honour the traditional doctrines and grant them authority.
Well now, said I, suppose there comes a time when someone in such a situation is faced with a question and asked, “what is the beautiful?”, and he gives the answer he heard from the conventional source, but the argument refutes this. Suppose it refutes him many times in lots of different ways and reduces him to the opinion 538E that this is no more beautiful than it is ugly, and the same thing happens with the just, the good and whatever is held in the highest esteem. How do you think he will behave, after this, towards those doctrines, in terms of honour and granting them authority?
Inevitably, said he, he will no longer honour them in the same way or be persuaded by them either.
Now, said I, when he regards these doctrines as no longer worthy of the honour he gave them before, and has no affinity with them, but cannot discover the true ones, is he likely to have recourse to any other life 539A besides the flatterer’s life?
He is not, said he.
In that case, I think, he will seem to have become lawless, having previously been law abiding.
Isn’t this, said I, the likely predicament of those who encounter dialectic in this way, and who, as I said earlier, deserve a lot of sympathy?
Yes, said he, and pity too.
Well, shouldn’t you be careful with every detail of their encounter with dialectic, so that there is no need to pity your thirty year old students?
Very much so, said he.
So there is one thing to be extremely careful about, isn’t there; that they do not get a taste of this when they are still young? 539B For I presume you have noticed that youngsters, when they first get a taste of dialectic, misuse it as if it was their plaything, by using it, always, to come up with counterarguments. They themselves imitate those who engage in refutation, by refuting other people, taking delight, like puppies, in verbally tugging at, and pulling apart anyone who ever comes near them.
Exceedingly so, said he.
And so, when they themselves have refuted many, and have been refuted 539C by many, they descend rapidly and inexorably to a state where they believe nothing they believed before, and as a consequence, they themselves, and philosophy in general, are held in low regard by everyone else.
Very true, he said.
But someone older, said I, wouldn’t want to be involved in such madness. He will imitate the one who is willing to engage in dialectic and consider the truth, rather than the one who plays with it for fun and just argues against people. And he himself will be more measured and 539D will bring honour to this activity rather than dishonour.
That’s right, said he.
Now, wasn’t everything that was said previous to this, said as a caution; that dialectic is to be imparted to the orderly and stable natures, and not, as is done nowadays, to anyone at all, even if they are unsuited.
Yes, certainly, said he.
Is it enough then to persist with the practice of dialectic, continuously and intensively, without any involvement in anything else, as a mental counterpart of the bodily exercises 539E they practised, for twice as many years as that?
Do you mean six years or four? He asked.
It doesn’t matter, said I, let’s suggest five. For after this, they will be brought down again into that cave for you, and compelled to rule over military matters, and take up other positions of authority suited to the young, so that they don’t lag behind the others in experience. And in these situations too they will still be tested 540A to see if they hold firm, or shift their ground, when they are being dragged in all directions.
How much time, he asked, are you proposing for this?
Fifteen years, said I. And when they have turned fifty, those who have come through safely, and have excelled in every way at everything, in action and in knowledge, should be led, at that stage, to the final destination. They should be compelled to lift the ray of the soul upwards to behold that which provides light to everything, and seeing the good itself, and using that as their pattern, bring order to the city, its citizens and themselves, 540B for the rest of their lives. Each in turn should spend most of their time in philosophy, but when their turn comes they should get involved in the drudgery of civic affairs, each exercising authority for the sake of the city, doing so, not as some fine activity but as a necessity. And having continually educated others in this way, others who are like themselves, and having left these behind as guardians of the city, they themselves depart to the Blessed Isles to dwell there. And the city should have memorials to them, and offer sacrifices, publicly, 540C as if to demigods, if the Pythia consents, and if not, as to blessed or divine personages.
You’re like a sculptor, Socrates, said he, fashioning rulers who are absolutely beautiful.
Female rulers too, said I. Do not presume that what I have said applies any more to men than it does to those women among their number who are naturally equipped for the role.
You’re right, said he, if they really are to share everything equally with the men, as we have explained.
540D Well then, said I, do you agree that what we have said about the city and its system of government has not been a mere aspiration, rather, although it is difficult, it is still possible, but only in the way we have described: whenever true philosophers, many or just one, come to power in the city, despise the honours of the age, which they regard as unworthy of free men, and attach most importance to what is right, and to the honours that come from that, and treat justice as supreme, and absolutely necessary, 540E then by serving this and strengthening this, they will set their own city in order.
How, said he.
They will send anyone in the city 541A who happens to be more than ten years old, out into the countryside. They will then isolate the children from their present habits, the habits of their parents, and bring them up in their own manners and regulations, the sort we just described. And once the city and form of government we were speaking of has been established, very quickly and easily in this way, don’t you agree that it will be a happy city, and that the people among whom it arises will benefit enormously?
Very much so, he said, and I think, 541B Socrates, that you have described nicely how it might come into existence, if it were ever to do so.
At this stage, said I, haven’t we had our fill of arguments about this city, and the sort of person who resembles it? For surely it is also obvious what sort of person we shall say he must be.
It is obvious, said he, and as for your question, I think that is the end of the matter.
End Book 7
 The man of reason has compassion for the ever darkened soul although he may find some amusement in her predicament. The descended soul is blessed but may still be a figure of fun.
 This provoking and awakening of reason is previously referred to at 523d.
 See next footnote.
 For other references to the one itself not having parts, see Parmenides 137d3 and 159c5 and Sophist 245a-b.
 See the abstraction step taken τῇ διανοίᾳ at Parmenides 143a7 for a similar reference to consideration of the one itself through thought alone.
 This section of Book VII concludes the description of arithmetic, the first of five subjects which precede the discussion of dialectic. Of the nine Stephanus pages devoted to these five subjects, four pages are occupied by arithmetic, i.e. almost half of the entire treatment of this important aspect of the guardians’ education is given over to arithmetic (about one page of the nine is simply connective or discursive).
 “Noble-City” is an attempt to render in English the Greek word καλλίπολις. Plato, here, gives that name to the city he is founding; there were cities if that name in the Greek world at that time.
 Following Shorey & Rowe in omitting what follows in the Greek text.