Meno
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 he would have been ready to tell all the world again
and again that the double space should have a double side.
MENO: True.
SOCRATES: But do you suppose that he would ever have enquired into or
learned what he fancied that he knew, though he was really ignorant of
it, until he had fallen into perplexity under the idea that he did not
know, and had desired to know?
MENO: I think not, Socrates.
SOCRATES: Then he was the better for the torpedo's touch?
MENO: I think so.
SOCRATES: Mark now the farther development. I shall only ask him, and
not teach him, and he shall share the enquiry with me: and do you watch
and see if you find me telling or explaining anything to him, instead of
eliciting his opinion. Tell me, boy, is not this a square of four feet
which I have drawn?
BOY: Yes.
SOCRATES: And now I add another square equal to the former one?
BOY: Yes.
SOCRATES: And a third, which is equal to either of them?
BOY: Yes.
SOCRATES: Suppose that we fill up the vacant corner?
BOY: Very good.
SOCRATES: Here, then, there are four equal spaces?
BOY: Yes.
SOCRATES: And how many times larger is this space than this other?
BOY: Four times.
SOCRATES: But it ought to have been twice only, as you will remember.
BOY: True.
SOCRATES: And does not this line, reaching from corner to corner, bisect
each of these spaces?
BOY: Yes.
SOCRATES: And are there not here four equal lines which contain this
space?
BOY: There are.
SOCRATES: Look and see how much this space is.
BOY: I do not understand.
SOCRATES: Has not each interior line cut off half of the four spaces?
BOY: Yes.
SOCRATES: And how many spaces are there in this section?
BOY: Four.
SOCRATES: And how many in this?
BOY: Two.
SOCRATES: And four is how many times two?
BOY: Twice.
SOCRATES: And this space is of how many feet?
BOY: Of eight feet.
SOCRATES: And from what line do you get this figure?
BOY: From this.
SOCRATES: That is, from the line which extends from corner to corner of
the figure of four feet?
BOY: Yes.
SOCRATES: And that is the line which the learned call the diagonal.
And if this is the proper name, then you, Meno's slave, are prepared to
affirm that the double space is the square of the diagonal?
BOY: Certainly, Socrates.
SOCRATES: What do you say of him, Meno? Were not all these answers given
out of his own head?
MENO: Yes, they were all his own.
SOCRATES: And yet, as we were just now saying, he did not know?
MENO: True.
SOCRATES: But still he had in him those notions of his--had he not?
MENO: Yes.
SOCRATES: Then he who does not know may still have true notions of that
which he does not know?
MENO: He has.
SOCRATES: And at present these notions have just been stirred up in him,
as in a dream; but if he were frequently asked the same questions, in
different forms, he would know as well as any one at last?
MENO: I dare say.
SOCRATES: Without any one teaching him he will recover his knowledge for
himself, if he is only asked questions?
MENO: Yes.
SOCRATES: And this spontaneous recovery of knowledge in him is
recollection?
MENO: True.
SOCRATES: And this knowledge which he now has must he not either have
acquired or always possessed?
MENO: Yes.
SOCRATES: But if he always possessed this knowledge he would always have
known; or if he has acquired the knowledge he could not have acquired it
in this life, unless he has been taught geometry; for he may be made to
do the same with all geometry and every other branch of knowledge. Now,
has any one ever taught him all this? You must know about him, if, as
you say, he was born and bred in your house.
MENO: And I am certain that no one ever did teach him.
SOCRATES: And yet he has the knowledge?
MENO: The fact, Socrates, is undeniable.
SOCRATES: But if he did not acquire the knowledge in this life, then he
must have had and learned it at some other time?
MENO: Clearly he must.
SOCRATES: Which must have been the time when he was not a man?
MENO: Yes.
SOCRATES: And if there have been always true thoughts in him, both at
the time when he was and was not a man, which only need to be awakened
into knowledge by putting questions to him, his soul must have always
possessed this knowledge, for he always either was or was not a man?
MENO: Obviously.
SOCRATES: And if the truth of all things always existed in the soul,
then the soul is immortal. Wherefore be of good cheer, and try to
recollect what you do not know, or rather what you do not remember.
MENO: I feel, somehow, that I like what you are saying.
SOCRATES: And I, Meno, like what I am saying. Some things I have said
of which I am not altogether confident. But that we shall be better and
braver and less helpless if we think that we ought to enquire, than
we should have been if we indulged in the idle fancy that there was no
knowing and no use in seeking to know what we do not know;--that is a
theme upon which I am ready to fight, in word and deed, to the utmost of
my power.
MENO: There again, Socrates, your words seem to me excellent.
SOCRATES: Then, as we are agreed that a man should enquire about that
which he does not know, shall you and I make an effort to enquire
together into the nature of virtue?
MENO: By all means, Socrates. And yet I would much rather return to my
original question, Whether in seeking to acquire virtue we should regard
it as a thing to be taught, or as a gift of nature, or as coming to men
in some other way?
SOCRATES: Had I the command of you as well as of myself, Meno, I would
not have enquired whether virtue is given by instruction or not,
until we had first ascertained 'what it is.' But as you think only
of controlling me who am your slave, and never of controlling
yourself,--such being your notion of freedom, I must yield to you,
for you are irresistible. And therefore I have now to enquire into the
qualities of a thing of which I do not as yet know the nature. At any
rate, will you condescend a little, and allow the question 'Whether
virtue is given by instruction, or in any other way,' to be argued upon
hypothesis? As the geometrician, when he is asked whether a certain
triangle is capable being inscribed in a certain circle (Or, whether a
certain area is capable of being inscribed as a triangle in a certain
circle.), will reply: 'I cannot tell you as yet; but I will offer a
hypothesis which may assist us in forming a conclusion: If the figure be
such that when you have produced a given side of it (Or, when you apply
it to the given line, i.e. the diameter of the circle (autou).), the
given area of the triangle falls short by an area corresponding to
the part produced (Or, similar to the area so applied.), then one
consequence follows, and if this is impossible then some other; and
therefore I wish to assume a hypothesis before I tell you whether
this triangle is capable of being inscribed in the circle':--that is
a geometrical hypothesis. And we too, as we know not the nature and
qualities of virtue, must ask, whether virtue is or is not taught, under
a hypothesis: as thus, if virtue is of such a class of mental goods,
will it be taught or not? Let the first hypothesis be that virtue is or