Theaetetus

EU. Just in from the country, Terpsion, or did you come some time ago?

TERP. Quite a while ago; and I was looking for you in the market-place and wondering that I could not find you.

EU. Well, you see, I was not in the city.

TERP. Where then?

EU. As I was going down to the harbor I met Theaetetus being carried to Athens from the camp at Corinth.

TERP. Alive or dead?

EU. Just barely alive; for he is suffering severely from wounds, and, worse than that, he has been taken with the sickness that has broken out in the army.

TERP. You mean the dysentery?

EU. Yes.

TERP. What a man he is who you say is in danger!

EU. A noble man, Terpsion, and indeed just now I heard some people praising him highly for his conduct in the battle.

TERP. That is not at all strange; it would have been much more remarkable if he had not so conducted himself. But why did he not stop here in Megara?

EU. He was in a hurry to get home; for I begged and advised him to stop, but he would not. So I went along with him, and as I was coming back I thought of Socrates and wondered at his prophetic gift, especially in what he said about him. For I think he met him a little before his own death, when Theaetetus was a mere boy, and as a result of acquaintance and conversation with him, he greatly admired his qualities. When I went to Athens he related to me the conversation he had with him, which was well worth hearing, and he said he would surely become a notable man if he lived.

TERP. And he was right, apparently. But what was the talk? Could you relate it?

EU. No, by Zeus, at least not offhand. But I made notes at the time as soon as I reached home, then afterwards at my leisure, as I recalled things, I wrote them down, and whenever I went to Athens I used to ask Socrates about what I could not remember, and then I came here and made corrections; so that I have pretty much the whole talk written down.

TERP. That is true. I heard you say so before; and really I have been waiting about here all along intending to ask you to show it to me. What hinders us from reading it now? Certainly I need to rest, since I have come from the country.

EU. And I myself went with Theaetetus as far as Erineum, [*](Erineum was between Eleusis and Athens, near the Cephissus. Apparently Eucleides had walked some thirty miles.) so I also should not be sorry to take a rest. Come, let us go, and while we are resting, the boy shall read to us.

TERP. Very well.

EU. Here is the book, Terpsion. Now this is the way I wrote the conversation: I did not represent Socrates relating it to me, as he did, but conversing with those with whom he told me he conversed. And he told me they were the geometrician Theodorus and Theaetetus. Now in order that the explanatory words between the speeches might not be annoying in the written account, such as and I said or and I remarked, whenever Socrates spoke, or he agreed or he did not agree, in the case of the interlocutor, I omitted all that sort of thing and represented Socrates himself as talking with them.

TERP. That is quite fitting, Eucleides.

EU. Come, boy, take the book and read.

SOC. If I cared more for Cyrene and its affairs, Theodorus, I should ask you about things there and about the people, whether any of the young men there are devoting themselves to geometry or any other form of philosophy; but as it is, since I care less for those people than for the people here, I am more eager to know which of our own young men are likely to gain reputation. These are the things I myself investigate, so far as I can, and about which I question those others with whom I see that the young men like to associate. Now a great many of them come to you, and rightly, for you deserve it on account of your geometry, not to speak of other reasons. So if you have met with any young man who is worth mentioning, I should like to hear about him.

THEO. Truly, Socrates, it is well worth while for me to talk and for you to hear about a splendid young fellow, one of your fellow-citizens, whom I have met. Now if he were handsome, I should be very much afraid to speak, lest someone should think I was in love with him. But the fact is—now don’t be angry with me—he is not handsome, but is like you in his snub nose and protruding eyes, only those features are less marked in him than in you. You see I speak fearlessly. But I assure you that among all the young men I have ever met—and I have had to do with a great many—I never yet found one of such marvelously fine qualities. He is quick to learn, beyond almost anyone else, yet exceptionally gentle, and moreover brave beyond any other; I should not have supposed such a combination existed, and I do not see it elsewhere. On the contrary, those who, like him, have quick, sharp minds and good memories, have usually also quick tempers; they dart off and are swept away, like ships without ballast; they are excitable rather than courageous; those, on the other hand, who are steadier are somewhat dull when brought face to face with learning, and are very forgetful. But this boy advances toward learning and investigation smoothly and surely and successfully, with perfect gentleness, like a stream of oil that flows without a sound, so that one marvels how he accomplishes all this at his age.

SOC. That is good news; but which of our citizens is his father?

THEO. I have heard the name, but do not remember it. However, it does not matter, for the youth is the middle one of those who are now coming toward us. He and those friends of his were anointing themselves in the outer course, [*](The scene is evidently laid in a gymnasium; the young men have been exercising.) and now they seem to have finished and to be coming here. See if you recognize him.

SOC. Yes, I do. He is the son of Euphronius of Sunium, who is a man of just the sort you describe, and of good repute in other respects; moreover he left a very large property. But the youth’s name I do not know.

THEO. Theaetetus is his name, Socrates; but I believe the property was squandered by trustees. Nevertheless, Socrates, he is remarkably liberal with his money, too.

SOC. It is a noble man that you describe. Now please tell him to come here and sit by us.

THEO. I will. Theaetetus, come here to Socrates.

SOC. Yes, do so, Theaetetus, that I may look at myself and see what sort of a face I have; for Theodorus says it is like yours. Now if we each had a lyre, and he said we had tuned them to the same key, should we take his word for it without more ado, or should we inquire first whether he who said it was a musician?

THEAET. We should inquire.

SOC. Then if we found that he was a musician, we should believe him, but if not, we should refuse to take his word?

THEAET. Yes.

SOC. But now, if we are concerned about the likeness of our faces, we must consider whether he who speaks is a painter, or not.

THEAET. I think we must.

SOC. Well, is Theodorus a painter?

THEAET. Not so far as I know.

SOC. Nor a geometrician, either?

THEAET. Oh yes, decidedly, Socrates.

SOC. And an astronomer, and an arithmetician, and a musician, and in general an educated man?

THEAET. I think so.

SOC. Well then, if he says, either in praise or blame, that we have some physical resemblance, it is not especially worth while to pay attention to him.

THEAET. Perhaps not.

SOC. But what if he should praise the soul of one of us for virtue and wisdom? Is it not worth while for the one who hears to examine eagerly the one who is praised, and for that one to exhibit his qualities with eagerness?

THEAET. Certainly, Socrates.

SOC. Then, my dear Theaetetus, this is just the time for you to exhibit your qualities and for me to examine them; for I assure you that Theodorus, though he has praised many foreigners and citizens to me, never praised anyone as he praised you just now.

THEAET. A good idea, Socrates; but make sure that he was not speaking in jest.

SOC. That is not Theodorus’s way. But do not seek to draw back from your agreement on the pretext that he is jesting, or he will be forced to testify under oath; for certainly no one will accuse him of perjury. Come, be courageous and hold to the agreement.

THEAET. I suppose I must, if you say so.

SOC. Now tell me; I suppose you learn some geometry from Theodorus?

THEAET. Yes.

SOC. And astronomy and harmony and arithmetic?

THEAET. I try hard to do so.

SOC. And so do I, my boy, from him and from any others who I think know anything about these things. But nevertheless, although in other respects I get on fairly well in them, yet I am in doubt about one little matter, which should be investigated with your help and that of these others. Tell me, is not learning growing wiser about that which one learns?

THEAET. Of course.

SOC. And the wise, I suppose, are wise by wisdom.

THEAET. Yes.

SOC. And does this differ at all from knowledge?

THEAET. Does what differ?

SOC. Wisdom. Or are not people wise in that of which they have knowledge?

THEAET. Of course.

SOC. Then knowledge and wisdom are the same thing?

THEAET. Yes.

SOC. Well, it is just this that I am in doubt about and cannot fully grasp by my own efforts—what knowledge really is. Can we tell that? What do you say? Who of us will speak first? And he who fails, and whoever fails in turn, shall go and sit down and be donkey, as the children say when they play ball; and whoever gets through without failing shall be our king and shall order us to answer any questions he pleases. Why are you silent? I hope, Theodorus, I am not rude, through my love of discussion and my eagerness to make us converse and show ourselves friends and ready to talk to one another.

THEO. That sort of thing would not be at all rude, Socrates; but tell one of the youths to answer your questions; for I am unused to such conversation and, moreover, I am not of an age to accustom myself to it. But that would be fitting for these young men, and they would improve much more than I; for the fact is, youth admits of improvement in every way. Come, question Theaetetus as you began to do, and do not let him off.

SOC. Well, Theaetetus, you hear what Theodorus says, and I think you will not wish to disobey him, nor is it right for a young person to disobey a wise man when he gives instructions about such matters. Come, speak up well and nobly. What do you think knowledge is?

THEAET. Well, Socrates, I must, since you bid me. For, if I make a mistake, you are sure to set me right.

SOC. Certainly, if we can.

THEAET. Well then, I think the things one might learn from Theodorus are knowledge—geometry and all the things you spoke of just now—and also cobblery and the other craftsmen’s arts; each and all of these are nothing else but knowledge.

SOC. You are noble and generous, my friend, for when you are asked for one thing you give many, and a variety of things instead of a simple answer.

THEAET. What do you mean by that, Socrates?

SOC. Nothing, perhaps; but I will tell you what I think I mean. When you say cobblery you speak of nothing else than the art of making shoes, do you?

THEAET. Nothing else.

SOC. And when you say carpentry? Do you mean anything else than the art of making wooden furnishings?

THEAET. Nothing else by that, either.

SOC. Then in both cases you define that to which each form of knowledge belongs?

THEAET. Yes.

SOC. But the question, Theaetetus, was not to what knowledge belongs, nor how many the forms of knowledge are; for we did not wish to number them, but to find out what knowledge itself really is. Or is there nothing in what I say?

THEAET. Nay, you are quite right.

SOC. Take this example. If anyone should ask us about some common everyday thing, for instance, what clay is, and we should reply that it is the potters’ clay and the oven makers’ clay and the brickmakers’ clay, should we not be ridiculous?

THEAET. Perhaps.

SOC. Yes in the first place for assuming that the questioner can understand from our answer what clay is, when we say clay, no matter whether we add the image-makers’ or any other craftsmen’s. Or does anyone, do you think, understand the name of anything when he does not know what the thing is?

THEAET. By no means.

SOC. Then he does not understand knowledge of shoes if he does not know knowledge.

THEAET. No.

SOC. Then he who is ignorant of knowledge does not understand cobblery or any other art.

THEAET. That is true.

SOC. Then it is a ridiculous answer to the question what is knowledge? when we give the name of some art; for we give in our answer something that knowledge belongs to, when that was not what we were asked.

THEAET. So it seems.

SOC. Secondly, when we might have given a short, everyday answer, we go an interminable distance round; for instance, in the question about clay, the everyday, simple thing would be to say clay is earth mixed with moisture without regard to whose clay it is.

THEAET. It seems easy just now, Socrates, as you put it; but you are probably asking the kind of thing that came up among us lately when your namesake, Socrates here, and I were talking together.

SOC. What kind of thing was that, Theaetetus?

THEAET. Theodorus here was drawing some figures for us in illustration of roots, showing that squares containing three square feet and five square feet are not commensurable in length with the unit of the foot, and so, selecting each one in its turn up to the square containing seventeen square feet and at that he stopped. Now it occurred to us, since the number of roots appeared to be infinite, to try to collect them under one name, by which we could henceforth call all the roots. [*](A simple form of the first statement would be: the square roots of 3, 5, etc., are irrational numbers or surds. The word δύναμις has not the meaning which we give in English to power, namely the result of multiplication of a number by itself, but that which we give to root, i.e. the number which, when multiplied by itself, produces a given result. Here Theaetetus is speaking of square roots only; and when he speaks of numbers and of equal factors he evidently thinks of rational whole numbers only, not of irrational numbers or fractions. He is not giving an exhaustive presentation of his investigation, but merely a brief sketch of it to illustrate his understanding of the purpose of Socrates. Toward the end of this sketch the word δύναμις is limited to the square roots of oblong numbers, i.e. to surds. The modern reader may be somewhat confused because Theaetetus seems to speak of arithmetical facts in geometrical terms. (Cf. Gow, Short History of Greek Mathematics, p. 85.))

SOC. And did you find such a name?

THEAET. I think we did. But see if you agree.

SOC. Speak on.

THEAET. We divided all number into two classes. The one, the numbers which can be formed by multiplying equal factors, we represented by the shape of the square and called square or equilateral numbers.

SOC. Well done!