Greek Texts & Translations

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. 820e

Yes, obviously.

Shall we not, then, lay these down as necessary subjects of instruction, so that there may be no gap in our code of laws? Yet we ought to lay them down provisionally—like pledges capable of redemption—apart from the rest of our constitution, in case they fail to satisfy either us who enact them or you for whom they are enacted.

Yes, that is the right way to lay them down.

Consider next whether or not we approve of the children learning astronomy.

Just tell us your opinion.

About this there is a very strange fact—indeed, quite intolerable. 821a

What is that?

We commonly assert that men ought not to enquire concerning the greatest god and about the universe, nor busy themselves in searching out their causes, since it is actually impious to do so; whereas the right course, in all probability, is exactly the opposite.

Explain yourself.

My statement sounds paradoxical, and it might be thought to be unbecoming in an old man; but the fact is that, when a man believes that a science is fair and true and beneficial to the State and altogether well-pleasing to God, 821bhe cannot possibly refrain any longer from declaring it. ^note

That is reasonable; but what science of this kind shall we find on the subject of stars?

At present, my good sirs, nearly all we Greeks say what is false about those mighty deities, the Sun and Moon.

What is the falsehood?

We assert that they, and some other stars along with them, never travel along the same path; and we call them “planets.” ^note 821c

Yes, by Zeus, Stranger, that is true; for I, during my life, have often noticed how Phosphorus and Hesperus and other stars never travel on the same course, but “wander” all ways; but as to the Sun and Moon, we all know that they are constantly doing this.

It is precisely for this reason, Megillus and Clinias, that I now assert that our citizens and our children ought to learn so much concerning all these facts about the gods of Heaven