Western Philosophy. Группа авторов
Читать онлайн книгу.
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 [figure 1]?
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 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 a double line?
BOY: Yes.
SOCRATES: But does not this line become doubled if we add another such line here [Figure 2]?
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 now 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 [Figure 3]?
Figure 3
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