Greek Texts & Translations

Yes, Stranger, this account of yours does seem to be in accord with nature, and true.

That is indeed the truth of the matter, Clinias; but to give legal enactment to this program of ours is difficult. We will, if you agree, enact this more precisely on a later occasion.

You appear to us, Stranger, to be scared by the neglect of such studies which is the habit in our countries; but you are wrong to be scared. Do not be deterred on that account, but try to proceed with your statement. 819a

I am indeed scared about the habit you mention, but I am still more alarmed about the people who take up these very sciences for study, and do so badly. ^note Complete and absolute ignorance of them is never alarming, nor is it a very great evil; much more mischievous is a wide variety of knowledge and learning combined with bad training.

That is true.

One ought to declare, then, that the freeborn children should learn as much of these subjects as the innumerable crowd of children in Egypt ^note learn along with their letters. 819bFirst, as regards counting, lessons have been invented for the merest infants to learn, by way of play and fun,—modes of dividing up apples and chaplets, so that the same totals are adjusted to larger and smaller groups, and modes of sorting out boxers and wrestlers, in byes and pairs, taking them alternately or consecutively, in their natural order. Moreover, by way of play, the teachers mix together bowls made of gold, bronze, 819csilver and the like, and others distribute them, as I said, by groups of a single kind, adapting the rules of elementary arithmetic to play; and thus they are of service to the pupils for their future tasks of drilling, leading and marching armies, or of household management, and they render them both more helpful in every way to themselves and more alert. 819dThe next step of the teachers is to clear away, by lessons in weights and measures, a certain kind of ignorance, both absurd and disgraceful, which is naturally inherent in all men touching lines, surfaces and solids.

What ignorance do you mean, and of what kind is it?

My dear Clinias, when I was told quite lately of our condition in regard to this matter, I was utterly astounded myself: it seemed to me to be the condition of guzzling swine rather than of human beings, and I was ashamed, not only of myself, but of all the Greek world. ^note 819e

Why? Tell us what you mean, Stranger.

I am doing so. But I can explain it better by putting a question. Answer me briefly: you know what a line is?

Yes.

And surface?

Certainly.

And do you know that these are two things, and that the third thing, next to these, is the solid?

I do.

Do you not, then, believe that all these are commensurable one with another?

Yes.

And you believe, I suppose, that line is really commensurable with line, surface with surface, 820aand solid with solid?

Absolutely.

But supposing that some of them are neither absolutely nor moderately commensurable, some being commensurable and some not, whereas you regard them all as commensurable,—what do you think of your mental state with respect to them?

Evidently it is a sorry state.

Again, as regards the relation of line and surface to solid, or of surface and line to each other—do not all we Greeks imagine that these are somehow commensurable with one another? 820b

Most certainly.

But if they cannot be thus measured by any way or means, while, as I said, all we Greeks imagine that they can, are we not right in being ashamed for them all, and saying to them, “O most noble Greeks, this is one of those ‘necessary’ things which we said ^note it is disgraceful not to know, although there is nothing very grand in knowing such things.”

Of course.

In addition to these there are other matters, closely related to them, 820cin which we find many errors arising that are nearly akin to the errors mentioned.

What are they?

Problems concerning the essential nature of the commensurable and the incommensurable. For students who are not to be absolutely worthless it is necessary to examine these and to distinguish the two kinds, and, by proposing such problems one to another, to compete in a game that is worthy of them,—for this is a much more refined pastime than draughts for old men. 820d

No doubt. And, after all, draughts and these studies do not seem to be so very far apart.

I assert, then, Clinias, that these subjects must be learnt by the young; for they are, in truth, neither harmful nor hard, and when learnt by way of play they will do no damage at all to our State, but will do it good. Should anyone disagree, however, we must listen to him.

Of course.

Well then, if this is clearly the case, obviously we shall adopt these subjects; but if it seems clearly to be otherwise, we shall rule them out.