Complete Works

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

  [c] SOCRATES: Then, Theaetetus, according to our present argument, a syllable is an absolutely single form, indivisible into parts.

  THEAETETUS: It looks like it.

  SOCRATES: Now, my friend, a little while ago, if you remember, we were inclined to accept a certain proposition which we thought put the matter very well—I mean the statement that no account can be given of the primaries of which other things are constituted, because each of them is in itself incomposite; and that it would be incorrect to apply even the term ‘being’ to it when we spoke of it or the term ‘this’, because these terms signify different and alien things; and that is the reason why a primary is an unaccountable and unknowable thing. Do you remember?

  THEAETETUS: I remember.

  [d] SOCRATES: And is that the reason also why it is single in form and indivisible into parts or is there some other reason for that?45 I can see no other myself.

  THEAETETUS: No, there really doesn’t seem to be any other.

  SOCRATES: And hasn’t the complex now fallen into the same class as the primary, seeing it has no parts and is a single form?

  THEAETETUS: Yes, it certainly has.

  SOCRATES: Well now, if the complex is both many elements and a whole, with them as its parts, then both complexes and elements are equally capable of being known and expressed, since all the parts turned out to be the same thing as the whole.

  [e] THEAETETUS: Yes, surely.

  SOCRATES: But if, on the other hand, the complex is single and without parts, then complexes and elements are equally unaccountable and unknowable—both of them for the same reason.

  THEAETETUS: I can’t dispute that.

  SOCRATES: Then if anyone tries to tell us that the complex can be known and expressed, while the contrary is true of the element, we had better not listen to him.

  THEAETETUS: No, we’d better not, if we go along with the argument.

  [206] SOCRATES: And, more than this, wouldn’t you more easily believe somebody who made the contrary statement, because of what you know of your own experience in learning to read and write?

  THEAETETUS: What kind of thing do you mean?

  SOCRATES: I mean that when you were learning you spent your time just precisely in trying to distinguish, by both eye and ear, each individual letter in itself so that you might not be bewildered by their different positions in written and spoken words.

  THEAETETUS: That’s perfectly true.

  SOCRATES: And at the music-teacher’s, wasn’t the finished pupil the one who would follow each note and tell to which string it belonged—the [b] notes being generally admitted to be the elements in music?

  THEAETETUS: Yes, that’s just what it amounted to.

  SOCRATES: Then if the proper procedure is to take such elements and complexes as we ourselves have experience of, and make an inference from them to the rest, we shall say that the elements are much more clearly known, and the knowledge of them is more decisive for the mastery of any branch of study than knowledge of the complex. And if anyone maintains that the complex is by nature knowable, and the element unknowable, we shall regard this as tomfoolery, whether it is intended to be or not.

  THEAETETUS: Oh, quite.

  SOCRATES: I think that might be proved in other ways too. But we mustn’t [c] let them distract us from the problem before us. We wanted to see what can be meant by the proposition that it is in the addition of an account to a true judgment that knowledge is perfected.

  THEAETETUS: Well yes, we must try to see that.

  SOCRATES: Come then, what are we intended to understand by an ‘account’? I think it must be one of three meanings.

  THEAETETUS: What are they?

  SOCRATES: The first would be, making one’s thought apparent vocally [d] by means of words and verbal expressions—when a man impresses an image of his judgment upon the stream of speech, like reflections upon water or in a mirror. Don’t you think this kind of thing is an account?

  THEAETETUS: Yes, I do. At least, a man who does this is said to be giving an account.46

  SOCRATES: But isn’t that a thing that everyone is able to do more or less readily—I mean, indicate what he thinks about a thing, if he is not deaf or dumb to begin with? And that being so, anyone at all who makes a correct judgment will turn out to have it ‘together with an account’; correct [e] judgment without knowledge will no longer be found anywhere.

  THEAETETUS: True.

  SOCRATES: Well then, we mustn’t be too ready to condemn the author of the definition of knowledge now before us for talking nonsense. Perhaps he didn’t mean this; perhaps he meant being able, when questioned about [207] what a thing is, to give an answer by reference to its elements.

  THEAETETUS: As for example, Socrates?

  SOCRATES: As for example, what Hesiod is doing when he says, ‘One hundred are the timbers of a wagon.’47 Now I couldn’t say what they are; and I don’t suppose you could either. If you and I were asked what a wagon is, we should be satisfied if we could answer, ‘Wheels, axle, body, rails, yoke.’

  THEAETETUS: Yes, surely.

  SOCRATES: But he might think us ridiculous, just as he would if we were asked what your name is, and replied by giving the syllables. In that case, [b] he would think us ridiculous because although we might be correct in our judgment and our expression of it, we should be fancying ourselves as scholars, thinking we knew and were expressing a scholar’s account of Theaetetus’ name. Whereas in fact no one gives an account of a thing with knowledge till, in addition to his true judgment, he goes right through the thing element by element—as I think we said before.

  THEAETETUS: We did, yes.

  SOCRATES: In the same way, in the example of the wagon, he would say [c] that we have indeed correct judgment; but it is the man who can explore its being by going through those hundred items who has made the addition which adds an account to his true judgment. It is this man who has passed from mere judgment to expert knowledge of the being of a wagon; and he has done so in virtue of having gone over the whole by means of the elements.

  THEAETETUS: And doesn’t that seem sound to you, Socrates?

  SOCRATES: Well, tell me if it seems sound to you, my friend. Tell me if you are prepared to accept the view that an account is a matter of going through a thing element by element, while going through it by ‘syllables’ [d] or larger divisions falls short of being an account. Then we shall be able to discuss it.

  THEAETETUS: I’m certainly prepared to accept that.

  SOCRATES: And do you at the same time think that a man has knowledge of anything when he believes the same thing now to be part of one thing and now part of something else? Or when he judges that now one thing and now something different belongs to one and the same object?

  THEAETETUS: No, indeed I don’t.

  SOCRATES: Then have you forgotten that at first when you were learning to read and write that is just what you and the other boys used to do?

  THEAETETUS: You mean we used to think that sometimes one letter [e] and sometimes another belonged to the same syllable, and used to put the same letter sometimes into its proper syllable and sometimes into another?

  SOCRATES: Yes, that is what I mean.

  THEAETETUS: Well, I certainly haven’t forgotten; and I don’t think people at that stage can be said to have knowledge yet.

  SOCRATES: Well, suppose now that someone who is at this sort of stage is writing the name ‘Theaetetus’; he thinks he ought to write THE and [208] does so. Then suppose another time he is trying to write ‘Theodorus’, and this time he thinks he should write TE and proceeds to do so. Are we going to say that he knows the first syllable of your names?

  THEAETETUS: No. We’ve admitted that anyone who is at that stage has not yet knowledge.

  SOCRATES: And is there anything to prevent the same person being in that situation as regards the second and third and fourth syllables?

  THEAETETUS: No, nothing.

  SOCRATES: Now at the time when he does this, he will be wri
ting ‘Theaetetus’ not only with correct judgment, but with command of the way through its letters; that must be so whenever he writes them out one after another in their order.

  THEAETETUS: Yes, clearly.

  SOCRATES: And still without knowledge though with correct judgment—isn’t [b] that our view?

  THEAETETUS: Yes.

  SOCRATES: Yet possessing an account of it along with his correct judgment. He was writing it, you see, with command of the way through its letters; and we agreed that that is an account.

  THEAETETUS: True.

  SOCRATES: So here, my friend, we have correct judgment together with an account, which we are not yet entitled to call knowledge.

  THEAETETUS: Yes, I’m afraid that’s so.

  SOCRATES: So it was only the poor man’s dream of gold that we had when we thought we had got the truest account of knowledge. Or is it early days to be harsh? Perhaps this is not the way in which one is to [c] define ‘account’. We said that the man who defines knowledge as correct judgment together with an account would choose one of three meanings for ‘account’. Perhaps the last is the one to define it by.

  THEAETETUS: Yes, you’re right to remind me; there is one possibility still left. The first was, a kind of vocal image of thought; the one we have just discussed was the way to the whole through the elements. Now what’s your third suggestion?

  SOCRATES: What the majority of people would say—namely, being able to tell some mark by which the object you are asked about differs from all other things.

  THEAETETUS: Can you give me an example of such an ‘account’ of something?

  SOCRATES: Well, take the sun, if you like. You would be satisfied, I [d] imagine, with the answer that it is the brightest of the bodies that move round the earth in the heavens.

  THEAETETUS: Oh yes, quite.

  SOCRATES: Now I want you to get hold of the principle that this illustrates. It is what we were just saying—that if you get hold of the difference that distinguishes a thing from everything else, then, so some people say, you will have got an account of it. On the other hand, so long as it is some common feature that you grasp, your account will be about all those things which have this in common.

  [e] THEAETETUS: I see; I think it’s very good to call this kind of thing an account.

  SOCRATES: Then if a man with correct judgment about any one of the things that are grasps in addition its difference from the rest, he has become a knower of the thing he was a judger of before.

  THEAETETUS: That’s our present position, anyway.

  SOCRATES: Well, at this point, Theaetetus, as regards what we are saying, I’m for all the world like a man looking at a shadow-painting;48 when I’m close up to it I can’t take it in in the least, though when I stood well back from it, it appeared to me to have some meaning.

  THEAETETUS: How’s that?

  [209] SOCRATES: I’ll see if I can explain. Suppose I have formed a correct judgment about you; if I can grasp your account in addition, I know you, but if not, I am merely judging you.

  THEAETETUS: Yes.

  SOCRATES: And an account was to be a matter of expounding your differentness?

  THEAETETUS: That is so.

  SOCRATES: Then when I was merely judging, my thought failed to grasp any point of difference between you and the rest of mankind?

  THEAETETUS: Apparently.

  SOCRATES: What I had in mind, it seems, was some common characteristic—something that belongs no more to you than to anybody else.

  [b] THEAETETUS: Yes, that must be so.

  SOCRATES: Then tell me, in Heaven’s name how, if that was so, did it come about that you were the object of my judgment and nobody else? Suppose my thought is that ‘This is Theaetetus—one who is a human being, and has a nose and eyes and mouth’, and so on through the whole list of limbs. Will this thought cause me to be thinking of Theaetetus rather than of Theodorus, or of the proverbial ‘remotest Mysian’?

  THEAETETUS: No, how could it?

  SOCRATES: But suppose I think not merely of ‘the one with nose and [c] eyes’, but of ‘the one with a snub nose and prominent eyes’. Shall I even then be judging you any more than myself or anyone who is like that?

  THEAETETUS: Not at all.

  SOCRATES: It will not, I take it, be Theaetetus who is judged in my mind until this snub-nosedness of yours has left imprinted and established in me a record that is different in some way from the other snub-nosednesses I have seen; and so with the other details of your makeup. And this will remind me, if I meet you tomorrow, and make me judge correctly about you.

  THEAETETUS: That’s perfectly true.

  SOCRATES: Then correct judgment also must be concerned with the differentness [d] of what it is about?

  THEAETETUS: So it seems, anyway.

  SOCRATES: Then what more might this ‘adding an account to correct judgment’ be? If, on the one hand, it means that we must make another judgment about the way in which a thing differs from the rest of things, we are being required to do something very absurd.

  THEAETETUS: How’s that?

  SOCRATES: Because we already have a correct judgment about the way a thing differs from other things; and we are then directed to add a correct judgment about the way it differs from other things. At that rate, the way a roller goes round or a pestle or anything else proverbial would be nothing [e] compared with such directions; they might be more justly called a matter of ‘the blind leading the blind’. To tell us to add what we already have, in order to come to know what we are judging about, bears a generous resemblance to the behavior of a man benighted.

  THEAETETUS: Whereas if, on the other hand, … ?49 What else were you going to suggest when you started this inquiry just now?

  SOCRATES: Well, if ‘adding an account’ means that we are required to get to know the differentness, not merely judge it, this most splendid of our accounts of knowledge turns out to be a very amusing affair. For [210] getting to know of course is acquiring knowledge, isn’t it?

  THEAETETUS: Yes.

  SOCRATES: So, it seems, the answer to the question ‘What is knowledge?’ will be ‘Correct judgment accompanied by knowledge of the differentness’—for this is what we are asked to understand by the ‘addition of an account.’

  THEAETETUS: Apparently so.

  SOCRATES: And it is surely just silly to tell us, when we are trying to discover what knowledge is, that it is correct judgment accompanied by knowledge, whether of differentness or of anything else? And so, Theaetetus, knowledge is neither perception nor true judgment, nor an account added [b] to true judgment.

  THEAETETUS: It seems not.

  SOCRATES: Well now, dear lad, are we still pregnant, still in labor with any thoughts about knowledge? Or have we been delivered of them all?

  THEAETETUS: As far as I’m concerned, Socrates, you’ve made me say far more than ever was in me, Heaven knows.

  SOCRATES: Well then, our art of midwifery tells us that all of these offspring are wind-eggs and not worth bringing up?

  THEAETETUS: Undoubtedly.

  SOCRATES: And so, Theaetetus, if ever in the future you should attempt to conceive or should succeed in conceiving other theories, they will be [c] better ones as the result of this inquiry. And if you remain barren, your companions will find you gentler and less tiresome; you will be modest and not think you know what you don’t know. This is all my art can achieve—nothing more. I do not know any of the things that other men know—the great and inspired men of today and yesterday. But this art of midwifery my mother and I had allotted to us by God; she to deliver [210d] women, I to deliver men that are young and generous of spirit, all that have any beauty. And now I must go to the King’s Porch to meet the indictment that Meletus has brought against me; but let us meet here again in the morning, Theodorus.

  1. The words ‘wise’ and ‘wisdom’ in the argument which begins here represent the Greek sophos and sophia. The point of the argument will come across more naturally in English if readers su
bstitute in their mind the words ‘expert’ and ‘expertise’.

  2. ‘Powers’ is a mathematical term for squares. By contrast, at 148a–b ‘power’ is given a new, specially defined use to denominate a species of line, viz. the incommensurable lines for which the boys wanted a general account. It may be useful to give a brief explanation of the mathematics of the passage.

  Two lines are incommensurable if and only if they have no common measure; that is, no unit of length will measure both without remainder. Two squares are incommensurable in length if and only if their sides are incommensurable lines; the areas themselves may still be commensurable, i.e., both measurable by some unit of area, as is mentioned at 148b. When Theodorus showed for a series of powers (squares) that each is incommensurable in length with the one foot (unit) square, we can think of him as proving case by case the irrationality of , , … . But this was not how he thought of it himself. Greek mathematicians did not recognize irrational numbers but treated of irrational quantities as geometrical entities: in this instance, lines identified by the areas of the squares that can be constructed on them. Similarly, we can think of the boys’ formula for powers or square lines at 148a–b as making the point that, for any positive integer n, is irrational if and only if there is no positive integer m such that n = m × m. But, once again, a Greek mathematician would think of this generalization in the geometrical terms in which Theaetetus expounds it.

  3. The name means ‘She who brings virtue to light’.

  4. Aristides is one of the two young men whose education Socrates discusses in Laches (see 178a–179b).

  5. A famous Sophist. See Protagoras 315d, 337a–c, 340e–341c, 358a–b.

  6. Protagoras of Abdera was a fifth century B.C. philosopher and sophist; this appears to have been the title of his book.

  7. Heraclitus was famous for holding that ‘everything flows’ (cf. 179d ff.). Empedocles described a cosmic cycle in which things are constituted and dissolved by the coming together and separating of the four elements earth, air, fire, and water. Epicharmus made humorous use of the idea that everything is always changing by having a debtor claim he is not the same person as incurred the debt. Parmenides remains outside the chorus of agreement because he held that the only reality is one single, completely changeless thing (cf. 183e).