The Demonstration of Learning as Recollection
from Meno
Meno, one of Plato's most famous dialogs, concerns the meaning of
virtue, but takes an interesting side track into the true nature of
learning, which in turn "proves" that the soul is immortal and we have
had an infinite number of lives prior to this one. Socrates
offers to show Meno that a certain slave boy,
ignorant of geometry, actually already knows Pythagorus' Theorum.
Although he certainly cannot remember the theorum all by himself, with
a
little "midwifery" (the Socratic method of question and answer), the
slave boy apparently gives answers that suggest he understands the
theorum even though he never encountered it in this life. In
exactly the same way, Meno "recollects" that learning is really a kind
of remembering of what we already know and, oh yes, that the soul is
immortal!
Men. ... [W]hat do you mean by saying that we do not learn, and
that
what we call learning is only a process of recollection? Can you teach
me how this is?
Soc. I told you, Meno, just now that
you were a rogue, and now you ask whether I can teach you, when I am
saying that there is no teaching, but only recollection; and thus you
imagine that you will involve me in a contradiction.
Men.
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.
Soc. 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.
Men. Certainly. Come hither, boy.
Soc. He is Greek, and speaks Greek, does he not?
Men. Yes, indeed; he was born in the house.
Soc. Attend now to the questions which I ask him, and observe
whether he learns of me or only remembers.
Men. I will.
Soc. Tell me, boy, do you know that a figure like this is a
square?
Boy. I do.
Soc. And you know that a square figure has these four lines
equal?
Boy. Certainly.
Soc. And these lines which I have drawn through the middle of
the square are also equal?
Boy. Yes.
Soc. A square may be of any size?
Boy. Certainly.
Soc.
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 other direction of one
foot, the whole would be of two feet taken once?
Boy. Yes.
Soc. But since this side is also of two feet, there are twice
two feet?
Boy. There are.
Soc. Then the square is of twice two feet?
Boy. Yes.
Soc. And how many are twice two feet? count and tell me.
Boy. Four, Socrates.
Soc. And might there not be another square twice as large as
this, and having like this the lines equal?
Boy. Yes.
Soc. And of how many feet will that be?
Boy. Of eight feet.
Soc.
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.
Soc.
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?
Men. Yes.
Soc. And does he really know?
Men. Certainly not.
Soc. He only guesses that because the square is double, the line
is double.
Men. True.
Soc.
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.
Soc. But does not this line become doubled if we add another
such line here?
Boy. Certainly.
Soc. And four such lines will make a space containing eight
feet?
Boy. Yes.
Soc. Let us describe such a figure: Would you not say that this
is the figure of eight feet?
Boy. Yes.
Soc. And are there not these four divisions in the figure, each
of which is equal to the figure of four feet?
Boy. True.
Soc. And is not that four times four?
Boy. Certainly.
Soc. And four times is not double?
Boy. No, indeed.
Soc. But how much?
Boy. Four times as much.
Soc. Therefore the double line, boy, has given a space, not
twice, but four times as much.
Boy. True.
Soc. Four times four are sixteen -- are they not?
Boy. Yes.
Soc. What line would give you a space of eight feet, as this
gives one of sixteen feet -- do you see?
Boy. Yes.
Soc. And the space of four feet is made from this half line?
Boy. Yes.
Soc. Good; and is not a space of eight feet twice the size of
this, and half the size of the other?
Boy. Certainly.
Soc. 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.
Soc. 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.
Soc.
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.
Soc. Try and see if you can tell me how much it will be.
Boy. Three feet.
Soc.
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.
Soc. 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.
Soc. And how much are three times three feet?
Boy. Nine.
Soc. And how much is the double of four?
Boy. Eight.
Soc. Then the figure of eight is not made out of a square of
three?
Boy. No.
Soc. 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.
Soc.
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.
Men. True.
Soc. Is he not better off in knowing his ignorance?
Men. I think that he is.
Soc. If we have made him doubt, and given him the "torpedo's
shock," have we done him any harm?
Men. I think not.
Soc. 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.
Men. True.
Soc.
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?
Men. I think not, Socrates.
Soc. Then he was the better for the torpedo's touch?
Men. I think so.
Soc.
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.
Soc. And now I add another square equal to the former one?
Boy. Yes.
Soc. And a third, which is equal to either of them?
Boy. Yes.
Soc. Suppose that we fill up the vacant corner?
Boy. Very good.
Soc. Here, then, there are four equal spaces?
Boy. Yes.
Soc. And how many times larger is this space than this other?
Boy.
Four times.
Soc. But it ought to have been twice only, as you will remember.
Boy. True.
Soc. And does not this line, reaching from corner to corner,
bisect each of these spaces?
Boy. Yes.
Soc. And are there not here four equal lines which contain this
space?
Boy. There are.
Soc. Look and see how much this space is.
Boy. I do not understand.
Soc. Has not each interior line cut off half of the four spaces?
Boy. Yes.
Soc. And how many spaces are there in this section?
Boy. Four.
Soc. And how many in this?
Boy. Two.
Soc. And four is how many times two?
Boy. Twice.
Soc. And this space is of how many feet?
Boy. Of eight feet.
Soc. And from what line do you get this figure?
Boy. From this.
Soc. That is, from the line which extends from corner to corner
of the figure of four feet?
Boy. Yes.
Soc.
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?
[that is, 2a2 = d2, a partial form of Pythagorus'
Theorum, h2 = a2 + b2]
Boy. Certainly, Socrates.
Soc. What do you say of him, Meno? Were not all these answers
given out of his own head?
Men. Yes, they were all his own.
Soc. And yet, as we were just now saying, he did not know?
Men. True.
Soc. But still he had in him those notions of his -- had he not?
Men. Yes.
Soc. Then he who does not know may still have true notions of
that which he does not know?
Men. He has.
Soc.
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?
Men. I dare say.
Soc. Without any one teaching him he will recover his knowledge
for himself, if he is only asked questions?
Men. Yes.
Soc. And this spontaneous recovery of knowledge in him is
recollection?
Men. True.
Soc. And this knowledge which he now has must he not either have
acquired or always possessed?
Men. Yes.
Soc.
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.
Men. And I am certain that no one ever did teach him.
Soc. And yet he has the knowledge?
Men. The fact, Socrates, is undeniable.
Soc. But if he did not acquire the knowledge in this life, then
he must have had and learned it at some other time?
Men. Clearly he must.
Soc. Which must have been the time when he was not a man?
Men. Yes.
Soc.
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?
Men. Obviously.
Soc.
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.
Men. I feel, somehow, that I like what you are saying.
Soc.
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.