Part 5
_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 the other direction of one foot, the whole would be of two feet taken once?
_Boy._ Yes.
[Sidenote: _Socrates and the boy._]
_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.
[Sidenote: He is partly guessing.]
_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 83 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.
_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.
[Sidenote: _Socrates and the boy._]
_Soc._ Let us describe such a figure: Would you not say that this is the figure of eight feet?
[Illustration]
_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.
[Sidenote: He has now learned to realize his own ignorance, and therefore will endeavour to remedy it.]
_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.
[Sidenote: _The progress of the boy’s education._]
_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 line of three?
_Boy._ No.
_Soc._ But from what line?—tell me exactly; and if you 84 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.
[Sidenote: _Construction of the figure of eight feet square._]
[Sidenote: The boy arrives at another true conclusion: which is, that the square of the diagonal is double the square of the side.]
_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? 85
_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 such spaces are there in this section?
_Boy._ Four.
_Soc._ And how many in this?
_Boy._ Two.
[Sidenote: _The doctrine of reminiscence._]
_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?
_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.
[Sidenote: At present he is in a dream; he will soon grow clearer.]
_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.
[Sidenote: _Socrates is more confident of some things than of others._]
[Sidenote: Either this knowledge was acquired by him in a former state of existence, or was always known to him.]
_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? 86
_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.
[Sidenote: Better to enquire than to fancy that there is no such thing as enquiry and no use in it.]
_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.
_Men._ There again, Socrates, your words seem to me excellent.
_Soc._ 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?
[Sidenote: _The nature of hypothesis._]
_Men._ 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?
[Sidenote: Socrates cannot enquire whether virtue can be taught until he knows what virtue is, except upon an hypothesis, such as geometricians sometimes employ: e. g. can a triangle of given area be inscribed in a given circle, if when the side of it is produced this or that consequence follows? [The hypothesis appears to be rather trivial and to have no mathematical value.]]
[Sidenote: Upon the hypothesis ‘that virtue is knowledge,’ can it be taught?]
_Soc._ 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 [7]whether 87 a certain triangle is capable of being inscribed in a certain circle[7], 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 [8]when you have produced a given side of it[8], the given area of the triangle falls short by an area [9]corresponding to the part produced[9], 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 is not knowledge,—in that case will it be taught or not? or, as we were just now saying, ‘remembered’? For there is no use in disputing about the name. But is virtue taught or not? or rather, does not every one see that knowledge alone is taught?
_Men._ I agree.
_Soc._ Then if virtue is knowledge, virtue will be taught?
_Men._ Certainly.
[Sidenote: _Virtue and knowledge._]
_Soc._ Then now we have made a quick end of this question: if virtue is of such a nature, it will be taught; and if not, not?
_Men._ Certainly.
[Sidenote: ‘Of course.’]
_Soc._ The next question is, whether virtue is knowledge or of another species?
_Men._ Yes, that appears to be the question which comes next in order.
[Sidenote: But is virtue knowledge?]
_Soc._ Do we not say that virtue is a good?—This is a hypothesis which is not set aside.
_Men._ Certainly.
[Sidenote: Virtue is a good, and profitable: and all profitable things are either profitable or the reverse according as they are or are not under the guidance of knowledge.]
_Soc._ Now, if there be any sort of good which is distinct from knowledge, virtue may be that good; but if knowledge embraces all good, then we shall be right in thinking that virtue is knowledge?
_Men._ True.
_Soc._ And virtue makes us good?
_Men._ Yes.
_Soc._ And if we are good, then we are profitable; for all good things are profitable?
_Men._ Yes.
_Soc._ Then virtue is profitable?
_Men._ That is the only inference.
_Soc._ Then now let us see what are the things which severally profit us. Health and strength, and beauty and wealth—these, and the like of these, we call profitable?
_Men._ True.
_Soc._ And yet these things may also sometimes do us 88 harm: would you not think so?
_Men._ Yes.
_Soc._ And what is the guiding principle which makes them profitable or the reverse? Are they not profitable when they are rightly used, and hurtful when they are not rightly used?
_Men._ Certainly.
_Soc._ Next, let us consider the goods of the soul: they are temperance, justice, courage, quickness of apprehension, memory, magnanimity, and the like?
_Men._ Surely.
_Soc._ And such of these as are not knowledge, but of another sort, are sometimes profitable and sometimes hurtful; as, for example, courage wanting prudence, which is only a sort of confidence? When a man has no sense he is harmed by courage, but when he has sense he is profited?
[Sidenote: _Virtue is knowledge._]
_Men._ True.
_Soc._ And the same may be said of temperance and quickness of apprehension; whatever things are learned or done with sense are profitable, but when done without sense they are hurtful?
_Men._ Very true.
_Soc._ And in general, all that the soul attempts or endures, when under the guidance of wisdom, ends in happiness; but when she is under the guidance of folly, in the opposite?
_Men._ That appears to be true.
[Sidenote: And so all virtue must be a sort of wisdom or knowledge.]
_Soc._ If then virtue is a quality of the soul, and is admitted to be profitable, it must be wisdom or prudence, since none of the things of the soul are either profitable or hurtful in themselves, but they are all made profitable or hurtful by the addition of wisdom or of folly; and therefore if virtue is profitable, virtue must be a sort of wisdom or prudence?
_Men._ I quite agree.
_Soc._ And the other goods, such as wealth and the like, of which we were just now saying that they are sometimes good and sometimes evil, do not they also become profitable or hurtful, accordingly as the soul guides and uses them rightly or wrongly; just as the things of the soul herself are benefited when under the guidance of wisdom and harmed by folly?
_Men._ True.
_Soc._ And the wise soul guides them rightly, and the foolish soul wrongly?
_Men._ Yes.
_Soc._ And is not this universally true of human nature? All other things hang upon the soul, and the things of the soul herself hang upon wisdom, if they are to be good; and 89 so wisdom is inferred to be that which profits—and virtue, as we say, is profitable?
_Men._ Certainly.
[Sidenote: Virtue is either wholly or partly wisdom.]
_Soc._ And thus we arrive at the conclusion that virtue is either wholly or partly wisdom?
_Men._ I think that what you are saying, Socrates, is very true.
[Sidenote: _Can virtue be taught?_]
_Soc._ But if this is true, then the good are not by nature good?
_Men._ I think not.
[Sidenote: If this is true, virtue must be taught; but then where are the teachers?]
_Soc._ If they had been, there would assuredly have been discerners of characters among us who would have known our future great men; and on their showing we should have adopted them, and when we had got them, we should have kept them in the citadel out of the way of harm, and set a stamp upon them far rather than upon a piece of gold, in order that no one might tamper with them; and when they grew up they would have been useful to the state?
_Men._ Yes, Socrates, that would have been the right way.
_Soc._ But if the good are not by nature good, are they made good by instruction?
_Men._ There appears to be no other alternative, Socrates. On the supposition that virtue is knowledge, there can be no doubt that virtue is taught.
_Soc._ Yes, indeed; but what if the supposition is erroneous?
_Men._ I certainly thought just now that we were right.
_Soc._ Yes, Meno; but a principle which has any soundness should stand firm not only just now, but always.
_Men._ Well; and why are you so slow of heart to believe that knowledge is virtue?
_Soc._ I will try and tell you why, Meno. I do not retract the assertion that if virtue is knowledge it may be taught; but I fear that I have some reason in doubting whether virtue is knowledge: for consider now and say whether virtue, and not only virtue but anything that is taught, must not have teachers and disciples?
_Men._ Surely.
_Soc._ And conversely, may not the art of which neither teachers nor disciples exist be assumed to be incapable of being taught?
_Men._ True; but do you think that there are no teachers of virtue?
[Sidenote: _The appeal to Anytus._]
[Sidenote: Can Anytus tell us who they are?]
_Soc._ I have certainly often enquired whether there were any, and taken great pains to find them, and have never succeeded; and many have assisted me in the search, and they were the persons whom I thought the most likely to know. Here at the moment when he is wanted we fortunately 90 have sitting by us Anytus, the very person of whom we should make enquiry; to him then let us repair. In the first place, he is the son of a wealthy and wise father, Anthemion, who acquired his wealth, not by accident or gift, like Ismenias the Theban (who has recently made himself as rich as Polycrates), but by his own skill and industry, and who is a well-conditioned, modest man, not insolent, or overbearing, or annoying; moreover, this son of his has received a good education, as the Athenian people certainly appear to think, for they choose him to fill the highest offices. And these are the sort of men from whom you are likely to learn whether there are any teachers of virtue, and who they are. Please, Anytus, to help me and your friend Meno in answering our question, Who are the teachers? Consider the matter thus: If we wanted Meno to be a good physician, to whom should we send him? Should we not send him to the physicians?
_Any._ Certainly.
_Soc._ Or if we wanted him to be a good cobbler, should we not send him to the cobblers?
_Any._ Yes.
_Soc._ And so forth?
_Any._ Yes.
[Sidenote: The arts are taught by the professors of them. And have we not heard of those who profess to teach virtue at a fixed price?]
_Soc._ Let me trouble you with one more question. When we say that we should be right in sending him to the physicians if we wanted him to be a physician, do we mean that we should be right in sending him to those who profess the art, rather than to those who do not, and to those who demand payment for teaching the art, and profess to teach it to any one who will come and learn? And if these were our reasons, should we not be right in sending him?
_Any._ Yes.
_Soc._ And might not the same be said of flute-playing, and of the other arts? Would a man who wanted to make another a flute-player refuse to send him to those who profess to teach the art for money, and be plaguing other persons to give him instruction, who are not professed teachers and who never had a single disciple in that branch of knowledge which he wishes him to acquire—would not such conduct be the height of folly?
[Sidenote: _Anytus attacks, Socrates defends, the Sophists._]
_Any._ Yes, by Zeus, and of ignorance too.