Theaetetus

​SOCRATES: Consider this too. If someone should ask us about one of the common and obvious things, for example, what clay actually is, and we should answer him that clay is that of the potters, and clay that of the oven-makers, and clay that of the brick-makers, would we not be ridiculous? THEAETETUS: Perhaps. SOCRATES: First, I suppose, because we think the questioner understands something from our answer when we say “clay,” whether we add that of the doll-makers or of any other artisans whatsoever. Or do you think anyone understands the name of anything when he does not know what that thing is? THEAETETUS: By no means. SOCRATES: Then he does not understand the knowledge of shoes either, if he does not know what knowledge is. THEAETETUS: No, indeed. SOCRATES: Therefore, he who is ignorant of knowledge does not understand shoemaking, nor any other craft. THEAETETUS: That is so. SOCRATES: Therefore, the answer is ridiculous when one is asked what knowledge is, if he replies with the name of some craft; for he answers with a knowledge of something, when he was not asked that. THEAETETUS: So it seems. SOCRATES: Secondly, I suppose, when it is possible to answer easily and briefly, he goes in an endless circle. For instance, in the question about clay, it is simple and easy to say that earth mixed with moisture would be clay, and to let the question of whose clay it is go. THEAETETUS: That seems easy now, Socrates, in this way. But you seem to be asking the sort of thing that occurred to us just recently when we were conversing, myself and your namesake here, Socrates. SOCRATES: What sort of thing was that, Theaetetus? THEAETETUS: Theodorus here was drawing some figures for us about roots, showing that those of three feet and of five feet are not commensurate in length with the unit foot, and so selecting each one individually up to seventeen feet, at which point he somehow stopped. So a thought of this kind occurred to us, since the roots appeared to be infinite in number, to try to collect them into one, by which we could address all these roots. SOCRATES: And did you find any such thing? THEAETETUS: I think we did; but you must consider it too. SOCRATES: Speak. THEAETETUS: We divided all numbers into two classes. The number which can be formed by multiplying equal by equal, we likened to the square in shape and called it square and equilateral. SOCRATES: And very well too.

​THEAETETUS: The number, then, between this, of which three and five and every number that is unable to be formed by equal multiplied by equal, but is formed either of more times fewer or fewer times more, and is always enclosed by a larger and smaller side—this we likened to the oblong shape and called it an oblong number. SOCRATES: Excellent! But what after this? THEAETETUS: All the lines which square the equilateral and plane number, we defined as “length”; and those which square the oblong, we defined as “powers,” because, though not commensurate in length with the former, they are commensurate in the planes which they have the power to form. And a similar thing was done concerning solids. SOCRATES: Best of men, my boys! So it seems to me Theodorus will not be liable to the charge of bearing false witness. THEAETETUS: And yet, Socrates, I could not answer your question about knowledge as I did about length and power. Although you seem to me to be looking for something of that sort; so that Theodorus appears to be false after all. SOCRATES: What? If he had praised you for running, saying he had never met any of the youths who was such a runner, and then you were defeated in a race by the swiftest runner in his prime, do you think he would have praised you with any less truth? THEAETETUS: Not I. SOCRATES: But do you think that finding out what knowledge is, as I was saying just now, is a small thing and not one of the tasks of the very highest class? THEAETETUS: By Zeus, I think it is indeed of the very highest. SOCRATES: Be of good courage then about yourself, and believe that there is something in what Theodorus says, and be eager in every way to get a definition of other things and of knowledge, what it actually is. THEAETETUS: As far as eagerness is concerned, Socrates, it will be shown. SOCRATES: Come then—for you just now guided us beautifully—try, in imitation of your answer about the powers, just as you embraced them, many as they are, in one class, to address also the many knowledges in one definition. THEAETETUS: But you may be sure, Socrates, I have often tried to examine this, when I heard the questions that are reported from you. But indeed I can neither persuade myself that I say anything sufficient, nor hear anyone else speaking in the way you command, yet on the other hand, I cannot rid myself of the concern. SOCRATES: That is because you are in labor, my dear Theaetetus, because you are not empty, but pregnant. THEAETETUS: I do not know, Socrates; but I am telling you what I experience.