Meno

Soc.

I remarked just now, Meno, that you are a rogue and so here you are asking if I can instruct you, when I say there is no teaching but only recollection: you hope that I may be caught contradicting myself forthwith.

Men.

I assure you, Socrates; that was not my intention I only spoke from habit. But if you can somehow prove to me that it is as you say, pray do so.

Soc.

It is no easy matter, but still I am willing to try my best for your sake. Just call one of your own troop of attendants there, whichever one you please, that he may serve for my demonstration.

Men.

Certainly. You, I say, come here.

Soc.

He is a Greek, I suppose, and speaks Greek?

Men.

Oh yes, to be sure—born in the house.

Soc.

Now observe closely whether he strikes you as recollecting or as learning from me.

Men.

I will.

Soc.

Tell me, boy, do you know that a square figure is like this?[*](Socrates draws in the sand.)

Boy.

I do.

Soc.

Now, a square figure has these lines, four in number, all equal?

Boy.

Certainly.

Soc.

And these, drawn through the middle,[*](i.e., the middle of each side of the square.) are equal too, are they not?

Boy.

Yes.

Soc.

And a figure of this sort may be larger or smaller?

Boy.

To be sure.

Soc.

Now if this side were two feet and that also two, how many feet would the whole be? Or let me put it thus: if one way it were two feet, and only one foot the other, of course the space would be two feet taken once ?

Boy.

Yes.

Soc.

But as it is two feet also on that side, it must be twice two feet?

Boy.

It is.

Soc.

Then the space is twice two feet?

Boy.

Yes.

Soc.

Well, how many are twice two feet? Count and tell me.

Boy.

Four, Socrates.

Soc.

And might there not be another figure twice the size of this, but of the same sort, with all its sides equal like this one?

Boy.

Yes.

Soc.

Then how many feet will it be?

Boy.

Eight.

Soc.

Come now, try and tell me how long will each side of that figure be. This one is two feet long: what will be the side of the other, which is double in size?

Boy.

Clearly, Socrates, double.

Soc.

Do you observe, Meno, that I am not teaching the boy anything, but merely asking him each time? And now he supposes that he knows about the line required to make a figure of eight square feet; or do you not think he does?

Men.

I do.

Soc.

Well, does he know?

Men.

Certainly not.

Soc.

He just supposes it, from the double size required?

Men.

Yes.

Soc.

Now watch his progress in recollecting, by the proper use of memory. Tell me, boy, do you say we get the double space from the double line? The space I speak of is not long one way and short the other, but must be equal each way like this one, while being double its size—eight square feet. Now see if you still think we get this from a double length of line.

Boy.

I do.

Soc.

Well, this line is doubled, if we add here another of the same length?

Boy.

Certainly.

Soc.

And you say we shall get our eight-foot space from four lines of this length?

Boy.

Yes.

Soc.

Then let us describe the square, drawing four equal lines of that length. This will be what you say is the eight-foot figure, will it not?

Boy.

Certainly.

Soc.

And here, contained in it, have we not four squares, each of which is equal to this space of four feet?

Boy.

Yes.

Soc.

Then how large is the whole? Four times that space, is it not?

Boy.

It must be.

Soc.

And is four times equal to double?

Boy.

No, to be sure.

Soc.

But how much is it?

Boy.

Fourfold.

Soc.

Thus, from the double-sized line, boy, we get a space, not of double, but of fourfold size.

Boy.

That is true.

Soc.

And if it is four times four it is sixteen, is it not?

Boy.

Yes.

Soc.

What line will give us a space of eight feet? This one gives us a fourfold space, does it not?

Boy.

It does.

Soc.

And a space of four feet is made from this line of half the length?

Boy.

Yes.

Soc.

Very well; and is not a space of eight feet double the size of this one, and half the size of this other?

Boy.

Yes.

Soc.

Will it not be made from a line longer than the one of these, and shorter than the other?

Boy.

I think so.

Soc.

Excellent: always answer just what you think. Now tell me, did we not draw this line two feet, and that four?

Boy.

Yes.

Soc.

Then the line on the side of the eight-foot figure should be more than this of two feet, and less than the other of four?

Boy.

It should.

Soc.

Try and tell me how much you would say it is.

Boy.

Three feet.

Soc.

Then if it is to be three feet, we shall add on a half to this one, and so make it three feet? For here we have two, and here one more, and so again on that side there are two, and another one; and that makes the figure of which you speak.

Boy.

Yes.

Soc.

Now if it be three this way and three that way, the whole space will be thrice three feet, will it not?

Boy.

So it seems.

Soc.

And thrice three feet are how many?

Boy.

Nine.

Soc.

And how many feet was that double one to be?

Boy.

Eight.

Soc.

So we fail to get our eight-foot figure from this three-foot line.

Boy.

Yes, indeed.

Soc.

But from what line shall we get it? Try and tell us exactly; and if you would rather not reckon it out, just show what line it is.

Boy.

Well, on my word, Socrates, I for one do not know.

Soc.

There now, Meno, do you observe who progress he has already made in his recollection? At first he did not know what is the line that forms the figure of eight feet, and he does not know even now: but at any rate he thought he knew then, and confidently answered as though he knew, and was aware of no difficulty; whereas now he feels the difficulty he is in, and besides not knowing does not think he knows.

Men.

That is true.

Soc.

And is he not better off in respect of the matter which he did not know?

Men.

I think that too is so.

Soc.

Now, by causing him to doubt and giving him the torpedo’s shock, have we done him any harm?

Men.

I think not.

Soc.

And we have certainly given him some assistance, it would seem, towards finding out the truth of the matter: for now he will push on in the search gladly, as lacking knowledge; whereas then he would have been only too ready to suppose he was right in saying, before any number of people any number of times, that the double space must have a line of double the length for its side.

Men.

It seems so.

Soc.

Now do you imagine he would have attempted to inquire or learn what he thought he knew, when he did not know it, until he had been reduced to the perplexity of realizing that he did not know, and had felt a craving to know?

Men.

I think not, Socrates.

Soc.

Then the torpedo’s shock was of advantage to him?

Men.

I think so.

Soc.

Now you should note how, as a result of this perplexity, he will go on and discover something by joint inquiry with me, while I merely ask questions and do not teach him; and be on the watch to see if at any point you find me teaching him or expounding to him, instead of questioning him on his opinions. Tell me, boy: here we have a square of four feet,[*](ABCD.) have we not? You understand?

Boy.

Yes.

Soc.

And here we add another square[*](DCFE.) equal to it?

Boy.

Yes.

Soc.

And here a third,[*](CHGF.) equal to either of them?

Boy.

Yes.

Soc.

Now shall we fill up this vacant space[*](BIHC.) in the corner?

Boy.

By all means.

Soc.

So here we must have four equal spaces? BOY. Yes.

Soc.

Well now, how many times larger is this whole space than this other?

Boy.

Four times.

Soc.

But it was to have been only twice, you remember?

Boy.

To be sure.