Dialogues

involve me in a contradiction. Meno Indeed, Socrates, I protest that I had no such intention. I only asked the question from habit; but if you can prove to me that what you say is true, I wish that you would. Socrates It will be no easy matter, but I will try to please you to the utmost of my power. Suppose that you call one of your numerous attendants, that I may demonstrate on him. Meno Certainly. Come hither, boy. Socrates He is Greek, and speaks Greek, does he not? Meno Yes, indeed; he was born in the house. Socrates Attend now to the questions which I ask him, and observe whether he learns of me or only remembers. Meno I will. Socrates Tell me, boy, do you know that a figure like this is a square? Boy I do. Socrates And you know that a square figure has these four lines equal? Boy Certainly. Socrates And these lines which I have drawn through the middle of the square are also equal? Boy Yes. Socrates A square may be of any size? Boy Certainly. Socrates And if one side of the figure be of two feet, and the other side be of two feet, how much will the whole be? Let me explain: if in one direction the space was of two feet, and in the other direction of one foot, the whole would be of two feet taken once? Boy Yes. Socrates But since this side is also of two feet, there are twice two feet? Boy There are. Socrates Then the square is of twice two feet? Boy Yes. Socrates And how many are twice two feet? count and tell me. Boy Four, Socrates. Socrates And might there not be another square twice as large as this, and having like this the lines equal? Boy Yes. Socrates And of how many feet will that be? Boy Of eight feet. Socrates And now try and tell me the length of the line which forms the side of that double square: this is two feet⁠—what will that be? Boy Clearly, Socrates, it will be double. Socrates Do you observe, Meno, that I am not teaching the boy anything, but only asking him questions; and now he fancies that he knows how long a line is necessary in order to produce a figure of eight square feet; does he not? Meno Yes. Socrates And does he really know? Meno Certainly not. Socrates He only guesses that because the square is double, the line is double. Meno True. Socrates Observe him while he recalls the steps in regular order. (To the Boy:) Tell me, boy, do you assert that a double space comes from a double line? Remember that I am not speaking of an oblong, but of a figure equal every way, and twice the size of this⁠—that is to say of eight feet; and I want to know whether you still say that a double square comes from double line? Boy Yes. Socrates But does not this line become doubled if we add another such line here? Boy Certainly. Socrates And four such lines will make a space containing eight feet? Boy Yes. Socrates Let us describe such a figure: Would you not say that this is the figure of eight feet? Boy Yes. Socrates And are there not these four divisions in the figure, each of which is equal to the figure of four feet? Boy True. Socrates And is not that four times four? Boy Certainly. Socrates And four times is not double? Boy No, indeed. Socrates But how much? Boy Four times as much. Socrates Therefore the double line, boy, has given a space, not twice, but four times as much. Boy True. Socrates Four times four are sixteen⁠—are they not? Boy Yes. Socrates What line would give you a space of eight feet, as this gives one of sixteen feet;⁠—do you see? Boy Yes. Socrates And the space of four feet is made from this half line? Boy Yes. Socrates Good; and is not a space of eight feet twice the size of this, and half the size of the other? Boy Certainly. Socrates Such a space, then, will be made out of a line greater than this one, and less than that one? Boy Yes; I think so. Socrates Very good; I like to hear you say what you think. And now tell me, is not this a line of two feet and that of four? Boy Yes. Socrates Then the line which forms the side of eight feet ought to be more than this line of two feet, and less than the other of four feet? Boy It ought. Socrates Try and see if you can tell me how much it will be. Boy Three feet. Socrates Then if we add a half to this line of two, that will be the line of three. Here are two and there is one; and on the other side, here are two also and there is one: and that makes the figure of which you speak? Boy Yes. Socrates But if there are three feet this way and three feet that way, the whole space will be three times three feet? Boy That is evident. Socrates And how much are three times three feet? Boy Nine. Socrates And how much is the double of four? Boy Eight. Socrates Then the figure of eight is not made out of a line of three? Boy No. Socrates But from what line?⁠—tell me exactly; and if you would rather not reckon, try and show me the line. Boy Indeed, Socrates, I do not know. Socrates Do you see, Meno, what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a figure of eight feet: but then he thought that he knew, and answered confidently as if he knew, and had no difficulty; now he has a difficulty, and neither knows nor fancies that he knows. Meno True. Socrates Is he not better off in knowing his ignorance? Meno I think that he is. Socrates If we have made him doubt, and given him the “torpedo’s shock,” have we done him any harm? Meno I think not. Socrates We have certainly, as would seem, assisted him in some degree to the discovery of the truth; and now he will wish to remedy his ignorance, but then