Complete Works

by Plato, Cooper, John M. , Hutchinson, D. S.

  I agree.

  Let that, then, be one of our subjects. Second, let’s consider whether the subject that comes next is also appropriate for our purposes.

  What subject is that? Do you mean geometry?

  That’s the very one I had in mind.

  Insofar as it pertains to war, it’s obviously appropriate, for when it [d] comes to setting up camp, occupying a region, concentrating troops, deploying them, or with regard to any of the other formations an army adopts in battle or on the march, it makes all the difference whether someone is a geometer or not.

  But, for things like that, even a little geometry—or calculation for that matter—would suffice. What we need to consider is whether the greater and more advanced part of it tends to make it easier to see the form of the good. And we say that anything has that tendency if it compels the [e] soul to turn itself around towards the region in which lies the happiest of the things that are, the one the soul must see at any cost.

  You’re right.

  Therefore, if geometry compels the soul to study being, it’s appropriate, but if it compels it to study becoming, it’s inappropriate.

  So we’ve said, at any rate.

  Now, no one with even a little experience of geometry will dispute that [527] this science is entirely the opposite of what is said about it in the accounts of its practitioners.

  How do you mean?

  They give ridiculous accounts of it, though they can’t help it, for they speak like practical men, and all their accounts refer to doing things. They talk of “squaring,” “applying,” “adding,” and the like, whereas the entire subject is pursued for the sake of knowledge. [b]

  Absolutely.

  And mustn’t we also agree on a further point?

  What is that?

  That their accounts are for the sake of knowing what always is, not what comes into being and passes away.

  That’s easy to agree to, for geometry is knowledge of what always is.

  Then it draws the soul towards truth and produces philosophic thought by directing upwards what we now wrongly direct downwards.

  As far as anything possibly can.

  [c] Then as far as we possibly can, we must require those in your fine city not to neglect geometry in any way, for even its by-products are not insignificant.

  What are they?

  The ones concerned with war that you mentioned. But we also surely know that, when it comes to better understanding any subject, there is a world of difference between someone who has grasped geometry and someone who hasn’t.

  Yes, by god, a world of difference.

  Then shall we set this down as a second subject for the young?

  Let’s do so, he said.

  And what about astronomy? Shall we make it the third? Or do you disagree? [d]

  That’s fine with me, for a better awareness of the seasons, months, and years is no less appropriate for a general than for a farmer or navigator.

  You amuse me: You’re like someone who’s afraid that the majority will think he is prescribing useless subjects. It’s no easy task—indeed it’s very difficult—to realize that in every soul there is an instrument that is purified and rekindled by such subjects when it has been blinded and destroyed [e] by other ways of life, an instrument that it is more important to preserve than ten thousand eyes, since only with it can the truth be seen. Those who share your belief that this is so will think you’re speaking incredibly well, while those who’ve never been aware of it will probably think you’re talking nonsense, since they see no benefit worth mentioning in these subjects. So decide right now which group you’re addressing. Or are your [528] arguments for neither of them but mostly for your own sake—though you won’t begrudge anyone else whatever benefit he’s able to get from them?

  The latter: I want to speak, question, and answer mostly for my own sake.

  Then let’s fall back to our earlier position, for we were wrong just now about the subject that comes after geometry.

  What was our error?

  After plane surfaces, we went on to revolving solids before dealing with solids by themselves. But the right thing to do is to take up the third [b] dimension right after the second. And this, I suppose, consists of cubes and of whatever shares in depth.

  You’re right, Socrates, but this subject hasn’t been developed yet.

  There are two reasons for that: First, because no city values it, this difficult subject is little researched. Second, the researchers need a director, for, without one, they won’t discover anything. To begin with, such a director is hard to find, and, then, even if he could be found, those who [c] currently do research in this field would be too arrogant to follow him. If an entire city helped him to supervise it, however, and took the lead in valuing it, then he would be followed. And, if the subject was consistently and vigorously pursued, it would soon be developed. Even now, when it isn’t valued and is held in contempt by the majority and is pursued by researchers who are unable to give an account of its usefulness, nevertheless, in spite of all these handicaps, the force of its charm has caused it to develop somewhat, so that it wouldn’t be surprising if it were further developed even as things stand.

  The subject has outstanding charm. But explain more clearly what you [d] were saying just now. The subject that deals with plane surfaces you took to be geometry.

  Yes.

  And at first you put astronomy after it, but later you went back on that.

  In my haste to go through them all, I’ve only progressed more slowly. The subject dealing with the dimension of depth was next. But because it is in a ridiculous state, I passed it by and spoke of astronomy (which deals with the motion of things having depth) after geometry. [e]

  That’s right.

  Let’s then put astronomy as the fourth subject, on the assumption that solid geometry will be available if a city takes it up.

  That seems reasonable. And since you reproached me before for praising astronomy in a vulgar manner, I’ll now praise it your way, for I think it’s clear to everyone that astronomy compels the soul to look upward and [529] leads it from things here to things there.

  It may be obvious to everyone except me, but that’s not my view about it.

  Then what is your view?

  As it’s practiced today by those who teach philosophy, it makes the soul look very much downward.

  How do you mean?

  In my opinion, your conception of “higher studies” is a good deal too generous, for if someone were to study something by leaning his head back and studying ornaments on a ceiling, it looks as though you’d say he’s studying not with his eyes but with his understanding. Perhaps you’re [b] right, and I’m foolish, but I can’t conceive of any subject making the soul look upward except one concerned with that which is, and that which is is invisible. If anyone attempts to learn something about sensible things, whether by gaping upward or squinting downward, I’d claim—since there’s no knowledge of such things—that he never learns anything and that, even if he studies lying on his back on the ground or floating on it [c] in the sea, his soul is looking not up but down.

  You’re right to reproach me, and I’ve been justly punished, but what did you mean when you said that astronomy must be learned in a different way from the way in which it is learned at present if it is to be a useful subject for our purposes?

  It’s like this: We should consider the decorations in the sky to be the most beautiful and most exact of visible things, seeing that they’re embroidered on a visible surface. But we should consider their motions to fall far short of the true ones—motions that are really fast or slow as measured [d] in true numbers, that trace out true geometrical figures, that are all in relation to one another, and that are the true motions of the things carried along in them. And these, of course, must be grasped by reason and thought, not by sight. Or do you think otherwise?

  Not at all.

  Therefore, we should use the embroidery in the sky as a model in the st
udy of these other things. If someone experienced in geometry were to come upon plans very carefully drawn and worked out by Daedalus or [e] some other craftsman or artist, he’d consider them to be very finely executed, but he’d think it ridiculous to examine them seriously in order to [530] find the truth in them about the equal, the double, or any other ratio.

  How could it be anything other than ridiculous?

  Then don’t you think that a real astronomer will feel the same when he looks at the motions of the stars? He’ll believe that the craftsman of the heavens arranged them and all that’s in them in the finest way possible for such things. But as for the ratio of night to day, of days to a month, of a month to a year, or of the motions of the stars to any of them or to each other, don’t you think he’ll consider it strange to believe that they’re [b] always the same and never deviate anywhere at all or to try in any sort of way to grasp the truth about them, since they’re connected to body and visible?

  That’s my opinion anyway, now that I hear it from you.

  Then if, by really taking part in astronomy, we’re to make the naturally intelligent part of the soul useful instead of useless, let’s study astronomy by means of problems, as we do geometry, and leave the things in the [c] sky alone.

  The task you’re prescribing is a lot harder than anything now attempted in astronomy.

  And I suppose that, if we are to be of any benefit as lawgivers, our prescriptions for the other subjects will be of the same kind. But have you any other appropriate subject to suggest?

  Not offhand.

  Well, there isn’t just one form of motion but several. Perhaps a wise [d] person could list them all, but there are two that are evident even to us.

  What are they?

  Besides the one we’ve discussed, there is also its counterpart.

  What’s that?

  It’s likely that, as the eyes fasten on astronomical motions, so the ears fasten on harmonic ones, and that the sciences of astronomy and harmonics are closely akin. This is what the Pythagoreans say, Glaucon, and we agree, don’t we?

  We do.

  [e] Therefore, since the subject is so huge, shouldn’t we ask them what they have to say about harmonic motions and whether there is anything else besides them, all the while keeping our own goal squarely in view?

  What’s that?

  That those whom we are rearing should never try to learn anything incomplete, anything that doesn’t reach the end that everything should reach—the end we mentioned just now in the case of astronomy. Or don’t you know that people do something similar in harmonics? Measuring [531] audible consonances and sounds against one another, they labor in vain, just like present-day astronomers.

  Yes, by the gods, and pretty ridiculous they are too. They talk about something they call a “dense interval” or quartertone—putting their ears to their instruments like someone trying to overhear what the neighbors are saying. And some say that they hear a tone in between and that it is the shortest interval by which they must measure, while others argue that this tone sounds the same as a quarter tone. Both put ears before [b] understanding.

  You mean those excellent fellows who torment their strings, torturing them, and stretching them on pegs. I won’t draw out the analogy by speaking of blows with the plectrum or the accusations or denials and boastings on the part of the strings; instead I’ll cut it short by saying that these aren’t the people I’m talking about. The ones I mean are the ones we just said we were going to question about harmonics, for they do the same as the astronomers. They seek out the numbers that are to be found [c] in these audible consonances, but they do not make the ascent to problems. They don’t investigate, for example, which numbers are consonant and which aren’t or what the explanation is of each.

  But that would be a superhuman task.

  Yet it’s useful in the search for the beautiful and the good. But pursued for any other purpose, it’s useless.

  Probably so.

  Moreover, I take it that, if inquiry into all the subjects we’ve mentioned brings out their association and relationship with one another and draws conclusions about their kinship, it does contribute something to our goal [d] and isn’t labor in vain, but that otherwise it is in vain.

  I, too, divine that this is true. But you’re still talking about a very big task, Socrates.

  Do you mean the prelude, or what? Or don’t you know that all these subjects are merely preludes to the song itself that must also be learned? Surely you don’t think that people who are clever in these matters are dialecticians. [e]

  No, by god, I don’t. Although I have met a few exceptions.

  But did it ever seem to you that those who can neither give nor follow an account know anything at all of the things we say they must know?

  My answer to that is also no.

  Then isn’t this at last, Glaucon, the song that dialectic sings? It is intelligible, [532] but it is imitated by the power of sight. We said that sight tries at last to look at the animals themselves, the stars themselves, and, in the end, at the sun itself. In the same way, whenever someone tries through argument and apart from all sense perceptions to find the being itself of each thing and doesn’t give up until he grasps the good itself with [b] understanding itself, he reaches the end of the intelligible, just as the other reached the end of the visible.

  Absolutely.

  And what about this journey? Don’t you call it dialectic?

  I do.

  Then the release from bonds and the turning around from shadows to statues and the light of the fire and, then, the way up out of the cave to the sunlight and, there, the continuing inability to look at the animals, the plants, and the light of the sun, but the newly acquired ability to look at [c] divine images in water and shadows of the things that are, rather than, as before, merely at shadows of statues thrown by another source of light that is itself a shadow in relation to the sun—all this business of the crafts we’ve mentioned has the power to awaken the best part of the soul and lead it upward to the study of the best among the things that are, just as, before, the clearest thing in the body was led to the brightest thing in the [d] bodily and visible realm.

  I accept that this is so, even though it seems very hard to accept in one way and hard not to accept in another. All the same, since we’ll have to return to these things often in the future, rather than having to hear them just once now, let’s assume that what you’ve said is so and turn to the song itself, discussing it in the same way as we did the prelude. So tell us: what is the sort of power dialectic has, what forms is it divided into, and what paths does it follow? For these lead at last, it seems, towards [e] that place which is a rest from the road, so to speak, and an end of journeying for the one who reaches it.

  [533] You won’t be able to follow me any longer, Glaucon, even though there is no lack of eagerness on my part to lead you, for you would no longer be seeing an image of what we’re describing, but the truth itself. At any rate, that’s how it seems to me. That it is really so is not worth insisting on any further. But that there is some such thing to be seen, that is something we must insist on. Isn’t that so?

  Of course.

  And mustn’t we also insist that the power of dialectic could reveal it only to someone experienced in the subjects we’ve described and that it cannot reveal it in any other way?

  That too is worth insisting on.

  [b] At any rate, no one will dispute it when we say that there is no other inquiry that systematically attempts to grasp with respect to each thing itself what the being of it is, for all the other crafts are concerned with human opinions and desires, with growing or construction, or with the care of growing or constructed things. And as for the rest, I mean geometry and the subjects that follow it, we described them as to some extent grasping what is, for we saw that, while they do dream about what is, they are unable to command a waking view of it as long as they make use of hypotheses that they leave untouched and that they cannot give any ac
count [c] of. What mechanism could possibly turn any agreement into knowledge when it begins with something unknown and puts together the conclusion and the steps in between from what is unknown?

  None.

  Therefore, dialectic is the only inquiry that travels this road, doing away with hypotheses and proceeding to the first principle itself, so as to be [d] secure. And when the eye of the soul is really buried in a sort of barbaric bog, dialectic gently pulls it out and leads it upwards, using the crafts we described to help it and cooperate with it in turning the soul around. From force of habit, we’ve often called these crafts sciences or kinds of knowledge, but they need another name, clearer than opinion, darker than knowledge. We called them thought somewhere before.5 But I presume that we won’t dispute about a name when we have so many more important matters to investigate. [e]

  Of course not.

  It will therefore be enough to call the first section knowledge, the second thought, the third belief, and the fourth imaging, just as we did before. The last two together we call opinion, the other two, intellect. Opinion is [534] concerned with becoming, intellect with being. And as being is to becoming, so intellect is to opinion, and as intellect is to opinion, so knowledge is to belief and thought to imaging. But as for the ratios between the things these are set over and the division of either the opinable or the intelligible section into two, let’s pass them by, Glaucon, lest they involve us in arguments many times longer than the ones we’ve already gone through.

  I agree with you about the others in any case, insofar as I’m able to follow. [b]

  Then, do you call someone who is able to give an account of the being of each thing dialectical? But insofar as he’s unable to give an account of something, either to himself or to another, do you deny that he has any understanding of it?

  How could I do anything else?

  Then the same applies to the good. Unless someone can distinguish in an account the form of the good from everything else, can survive all refutation, as if in a battle, striving to judge things not in accordance with [c] opinion but in accordance with being, and can come through all this with his account still intact, you’ll say that he doesn’t know the good itself or any other good. And if he gets hold of some image of it, you’ll say that it’s through opinion, not knowledge, for he is dreaming and asleep throughout his present life, and, before he wakes up here, he will arrive in Hades and go to sleep forever. [d]