Meno

Meno

PERSONS OF THE DIALOGUE: Meno, Socrates, A Slave of Meno (Boy), Anytus.

MENO: Can you tell me, Socrates, whether virtue is acquired by teaching or by practice; or if neither by teaching nor by practice, then whether it comes to man by nature, or in what other way?

SOCRATES: O Meno, there was a time when the Thessalians were famous among the other Hellenes only for their riches and their riding; but now, if I am not mistaken, they are equally famous for their wisdom, especially at Larisa, which is the native city of your friend Aristippus. And this is Gorgias' doing; for when he came there, the flower of the Aleuadae, among them your admirer Aristippus, and the other chiefs of the Thessalians, fell in love with his wisdom. And he has taught you the habit of answering questions in a grand and bold style, which becomes those who know, and is the style in which he himself answers all comers; and any Hellene who likes may ask him anything. How different is our lot! my dear Meno. Here at Athens there is a dearth of the commodity, and all wisdom seems to have emigrated from us to you. I am certain that if you were to ask any Athenian whether virtue was natural or acquired, he would laugh in your face, and say: 'Stranger, you have far too good an opinion of me, if you think that I can answer your question. For I literally do not know what virtue is, and much less whether it is acquired by teaching or not.' And I myself, Meno, living as I do in this region of poverty, am as poor as the rest of the world; and I confess with shame that I know literally nothing about virtue; and when I do not know the 'quid' of anything how can I know the 'quale'? How, if I knew nothing at all of Meno, could I tell if he was fair, or the opposite of fair; rich and noble, or the reverse of rich and noble? Do you think that I could?

MENO: No, indeed. But are you in earnest, Socrates, in saying that you do not know what virtue is? And am I to carry back this report of you to Thessaly?

SOCRATES: Not only that, my dear boy, but you may say further that I have never known of any one else who did, in my judgment.

MENO: Then you have never met Gorgias when he was at Athens?

SOCRATES: Yes, I have.

MENO: And did you not think that he knew?

SOCRATES: I have not a good memory, Meno, and therefore I cannot now tell what I thought of him at the time. And I dare say that he did know, and that you know what he said: please, therefore, to remind me of what he said; or, if you would rather, tell me your own view; for I suspect that you and he think much alike.

MENO: Very true.

SOCRATES: Then as he is not here, never mind him, and do you tell me: By the gods, Meno, be generous, and tell me what you say that virtue is; for I shall be truly delighted to find that I have been mistaken, and that you and Gorgias do really have this knowledge; although I have been just saying that I have never found anybody who had.

MENO: There will be no difficulty, Socrates, in answering your question. Let us take first the virtue of a man--he should know how to administer the state, and in the administration of it to benefit his friends and harm his enemies; and he must also be careful not to suffer harm himself. A woman's virtue, if you wish to know about that, may also be easily described: her duty is to order her house, and keep what is indoors, and obey her husband. Every age, every condition of life, young or old, male or female, bond or free, has a different virtue: there are virtues numberless, and no lack of definitions of them; for virtue is relative to the actions and ages of each of us in all that we do. And the same may be said of vice, Socrates (Compare Arist. Pol.).

SOCRATES: How fortunate I am, Meno! When I ask you for one virtue, you present me with a swarm of them (Compare Theaet.), which are in your keeping. Suppose that I carry on the figure of the swarm, and ask of you, What is the nature of the bee? and you answer that there are many kinds of bees, and I reply: But do bees differ as bees, because there are many and different kinds of them; or are they not rather to be distinguished by some other quality, as for example beauty, size, or shape? How would you answer me?

MENO: I should answer that bees do not differ from one another, as bees.

SOCRATES: And if I went on to say: That is what I desire to know, Meno; tell me what is the quality in which they do not differ, but are all alike;--would you be able to answer?

MENO: I should.

SOCRATES: And so of the virtues, however many and different they may be, they have all a common nature which makes them virtues; and on this he who would answer the question, 'What is virtue?' would do well to have his eye fixed: Do you understand?

MENO: I am beginning to understand; but I do not as yet take hold of the question as I could wish.

SOCRATES: When you say, Meno, that there is one virtue of a man, another of a woman, another of a child, and so on, does this apply only to virtue, or would you say the same of health, and size, and strength? Or is the nature of health always the same, whether in man or woman?

MENO: I should say that health is the same, both in man and woman.

SOCRATES: And is not this true of size and strength? If a woman is strong, she will be strong by reason of the same form and of the same strength subsisting in her which there is in the man. I mean to say that strength, as strength, whether of man or woman, is the same. Is there any difference?

MENO: I think not.

SOCRATES: And will not virtue, as virtue, be the same, whether in a child or in a grown-up person, in a woman or in a man?

MENO: I cannot help feeling, Socrates, that this case is different from the others.

SOCRATES: But why? Were you not saying that the virtue of a man was to order a state, and the virtue of a woman was to order a house?

MENO: I did say so.

SOCRATES: And can either house or state or anything be well ordered without temperance and without justice?

MENO: Certainly not.

SOCRATES: Then they who order a state or a house temperately or justly order them with temperance and justice?

MENO: Certainly.

SOCRATES: Then both men and women, if they are to be good men and women, must have the same virtues of temperance and justice?

MENO: True.

SOCRATES: And can either a young man or an elder one be good, if they are intemperate and unjust?

MENO: They cannot.

SOCRATES: They must be temperate and just?

MENO: Yes.

SOCRATES: Then all men are good in the same way, and by participation in the same virtues?

MENO: Such is the inference.

SOCRATES: And they surely would not have been good in the same way, unless their virtue had been the same?

MENO: They would not.

SOCRATES: Then now that the sameness of all virtue has been proven, try and remember what you and Gorgias say that virtue is.

MENO: Will you have one definition of them all?

SOCRATES: That is what I am seeking.

MENO: If you want to have one definition of them all, I know not what to say, but that virtue is the power of governing mankind.

SOCRATES: And does this definition of virtue include all virtue? Is virtue the same in a child and in a slave, Meno? Can the child govern his father, or the slave his master; and would he who governed be any longer a slave?

MENO: I think not, Socrates.

SOCRATES: No, indeed; there would be small reason in that. Yet once more, fair friend; according to you, virtue is 'the power of governing;' but do you not add 'justly and not unjustly'?

MENO: Yes, Socrates; I agree there; for justice is virtue.

SOCRATES: Would you say 'virtue,' Meno, or 'a virtue'?

MENO: What do you mean?

SOCRATES: I mean as I might say about anything; that a round, for example, is 'a figure' and not simply 'figure,' and I should adopt this mode of speaking, because there are other figures.

MENO: Quite right; and that is just what I am saying about virtue--that there are other virtues as well as justice.

SOCRATES: What are they? tell me the names of them, as I would tell you the names of the other figures if you asked me.

MENO: Courage and temperance and wisdom and magnanimity are virtues; and there are many others.

SOCRATES: Yes, Meno; and again we are in the same case: in searching after one virtue we have found many, though not in the same way as before; but we have been unable to find the common virtue which runs through them all.

MENO: Why, Socrates, even now I am not able to follow you in the attempt to get at one common notion of virtue as of other things.

SOCRATES: No wonder; but I will try to get nearer if I can, for you know that all things have a common notion. Suppose now that some one asked you the question which I asked before: Meno, he would say, what is figure? And if you answered 'roundness,' he would reply to you, in my way of speaking, by asking whether you would say that roundness is 'figure' or 'a figure;' and you would answer 'a figure.'

MENO: Certainly.

SOCRATES: And for this reason--that there are other figures?

MENO: Yes.

SOCRATES: And if he proceeded to ask, What other figures are there? you would have told him.

MENO: I should.

SOCRATES: And if he similarly asked what colour is, and you answered whiteness, and the questioner rejoined, Would you say that whiteness is colour or a colour? you would reply, A colour, because there are other colours as well.

MENO: I should.

SOCRATES: And if he had said, Tell me what they are?--you would have told him of other colours which are colours just as much as whiteness.

MENO: Yes.

SOCRATES: And suppose that he were to pursue the matter in my way, he would say: Ever and anon we are landed in particulars, but this is not what I want; tell me then, since you call them by a common name, and say that they are all figures, even when opposed to one another, what is that common nature which you designate as figure--which contains straight as well as round, and is no more one than the other--that would be your mode of speaking?

MENO: Yes.

SOCRATES: And in speaking thus, you do not mean to say that the round is round any more than straight, or the straight any more straight than round?

MENO: Certainly not.

SOCRATES: You only assert that the round figure is not more a figure than the straight, or the straight than the round?

MENO: Very true.

SOCRATES: To what then do we give the name of figure? Try and answer. Suppose that when a person asked you this question either about figure or colour, you were to reply, Man, I do not understand what you want, or know what you are saying; he would look rather astonished and say: Do you not understand that I am looking for the 'simile in multis'? And then he might put the question in another form: Meno, he might say, what is that 'simile in multis' which you call figure, and which includes not only round and straight figures, but all? Could you not answer that question, Meno? I wish that you would try; the attempt will be good practice with a view to the answer about virtue.

MENO: I would rather that you should answer, Socrates.

SOCRATES: Shall I indulge you?

MENO: By all means.

SOCRATES: And then you will tell me about virtue?

MENO: I will.

SOCRATES: Then I must do my best, for there is a prize to be won.

MENO: Certainly.

SOCRATES: Well, I will try and explain to you what figure is. What do you say to this answer?--Figure is the only thing which always follows colour. Will you be satisfied with it, as I am sure that I should be, if you would let me have a similar definition of virtue?

MENO: But, Socrates, it is such a simple answer.

SOCRATES: Why simple?

MENO: Because, according to you, figure is that which always follows colour.

(SOCRATES: Granted.)

MENO: But if a person were to say that he does not know what colour is, any more than what figure is--what sort of answer would you have given him?

SOCRATES: I should have told him the truth. And if he were a philosopher of the eristic and antagonistic sort, I should say to him: You have my answer, and if I am wrong, your business is to take up the argument and refute me. But if we were friends, and were talking as you and I are now, I should reply in a milder strain and more in the dialectician's vein; that is to say, I should not only speak the truth, but I should make use of premisses which the person interrogated would be willing to admit. And this is the way in which I shall endeavour to approach you. You will acknowledge, will you not, that there is such a thing as an end, or termination, or extremity?--all which words I use in the same sense, although I am aware that Prodicus might draw distinctions about them: but still you, I am sure, would speak of a thing as ended or terminated--that is all which I am saying--not anything very difficult.

MENO: Yes, I should; and I believe that I understand your meaning.

SOCRATES: And you would speak of a surface and also of a solid, as for example in geometry.

MENO: Yes.

SOCRATES: Well then, you are now in a condition to understand my definition of figure. I define figure to be that in which the solid ends; or, more concisely, the limit of solid.

MENO: And now, Socrates, what is colour?

SOCRATES: You are outrageous, Meno, in thus plaguing a poor old man to give you an answer, when you will not take the trouble of remembering what is Gorgias' definition of virtue.

MENO: When you have told me what I ask, I will tell you, Socrates.

SOCRATES: A man who was blindfolded has only to hear you talking, and he would know that you are a fair creature and have still many lovers.

MENO: Why do you think so?

SOCRATES: Why, because you always speak in imperatives: like all beauties when they are in their prime, you are tyrannical; and also, as I suspect, you have found out that I have weakness for the fair, and therefore to humour you I must answer.

MENO: Please do.

SOCRATES: Would you like me to answer you after the manner of Gorgias, which is familiar to you?

MENO: I should like nothing better.

SOCRATES: Do not he and you and Empedocles say that there are certain effluences of existence?

MENO: Certainly.

SOCRATES: And passages into which and through which the effluences pass?

MENO: Exactly.

SOCRATES: And some of the effluences fit into the passages, and some of them are too small or too large?

MENO: True.

SOCRATES: And there is such a thing as sight?

MENO: Yes.

SOCRATES: And now, as Pindar says, 'read my meaning:'--colour is an effluence of form, commensurate with sight, and palpable to sense.

MENO: That, Socrates, appears to me to be an admirable answer.

SOCRATES: Why, yes, because it happens to be one which you have been in the habit of hearing: and your wit will have discovered, I suspect, that you may explain in the same way the nature of sound and smell, and of many other similar phenomena.

MENO: Quite true.

SOCRATES: The answer, Meno, was in the orthodox solemn vein, and therefore was more acceptable to you than the other answer about figure.

MENO: Yes.

SOCRATES: And yet, O son of Alexidemus, I cannot help thinking that the other was the better; and I am sure that you would be of the same opinion, if you would only stay and be initiated, and were not compelled, as you said yesterday, to go away before the mysteries.

MENO: But I will stay, Socrates, if you will give me many such answers.

SOCRATES: Well then, for my own sake as well as for yours, I will do my very best; but I am afraid that I shall not be able to give you very many as good: and now, in your turn, you are to fulfil your promise, and tell me what virtue is in the universal; and do not make a singular into a plural, as the facetious say of those who break a thing, but deliver virtue to me whole and sound, and not broken into a number of pieces: I have given you the pattern.

MENO: Well then, Socrates, virtue, as I take it, is when he, who desires the honourable, is able to provide it for himself; so the poet says, and I say too--

'Virtue is the desire of things honourable and the power of attaining them.'

SOCRATES: And does he who desires the honourable also desire the good?

MENO: Certainly.

SOCRATES: Then are there some who desire the evil and others who desire the good? Do not all men, my dear sir, desire good?

MENO: I think not.

SOCRATES: There are some who desire evil?

MENO: Yes.

SOCRATES: Do you mean that they think the evils which they desire, to be good; or do they know that they are evil and yet desire them?

MENO: Both, I think.

SOCRATES: And do you really imagine, Meno, that a man knows evils to be evils and desires them notwithstanding?

MENO: Certainly I do.

SOCRATES: And desire is of possession?

MENO: Yes, of possession.

SOCRATES: And does he think that the evils will do good to him who possesses them, or does he know that they will do him harm?

MENO: There are some who think that the evils will do them good, and others who know that they will do them harm.

SOCRATES: And, in your opinion, do those who think that they will do them good know that they are evils?

MENO: Certainly not.

SOCRATES: Is it not obvious that those who are ignorant of their nature do not desire them; but they desire what they suppose to be goods although they are really evils; and if they are mistaken and suppose the evils to be goods they really desire goods?

MENO: Yes, in that case.

SOCRATES: Well, and do those who, as you say, desire evils, and think that evils are hurtful to the possessor of them, know that they will be hurt by them?

MENO: They must know it.

SOCRATES: And must they not suppose that those who are hurt are miserable in proportion to the hurt which is inflicted upon them?

MENO: How can it be otherwise?

SOCRATES: But are not the miserable ill-fated?

MENO: Yes, indeed.

SOCRATES: And does any one desire to be miserable and ill-fated?

MENO: I should say not, Socrates.

SOCRATES: But if there is no one who desires to be miserable, there is no one, Meno, who desires evil; for what is misery but the desire and possession of evil?

MENO: That appears to be the truth, Socrates, and I admit that nobody desires evil.

SOCRATES: And yet, were you not saying just now that virtue is the desire and power of attaining good?

MENO: Yes, I did say so.

SOCRATES: But if this be affirmed, then the desire of good is common to all, and one man is no better than another in that respect?

MENO: True.

SOCRATES: And if one man is not better than another in desiring good, he must be better in the power of attaining it?

MENO: Exactly.

SOCRATES: Then, according to your definition, virtue would appear to be the power of attaining good?

MENO: I entirely approve, Socrates, of the manner in which you now view this matter.

SOCRATES: Then let us see whether what you say is true from another point of view; for very likely you may be right:--You affirm virtue to be the power of attaining goods?

MENO: Yes.

SOCRATES: And the goods which you mean are such as health and wealth and the possession of gold and silver, and having office and honour in the state--those are what you would call goods?

MENO: Yes, I should include all those.

SOCRATES: Then, according to Meno, who is the hereditary friend of the great king, virtue is the power of getting silver and gold; and would you add that they must be gained piously, justly, or do you deem this to be of no consequence? And is any mode of acquisition, even if unjust and dishonest, equally to be deemed virtue?

MENO: Not virtue, Socrates, but vice.

SOCRATES: Then justice or temperance or holiness, or some other part of virtue, as would appear, must accompany the acquisition, and without them the mere acquisition of good will not be virtue.

MENO: Why, how can there be virtue without these?

SOCRATES: And the non-acquisition of gold and silver in a dishonest manner for oneself or another, or in other words the want of them, may be equally virtue?

MENO: True.

SOCRATES: Then the acquisition of such goods is no more virtue than the non-acquisition and want of them, but whatever is accompanied by justice or honesty is virtue, and whatever is devoid of justice is vice.

MENO: It cannot be otherwise, in my judgment.

SOCRATES: And were we not saying just now that justice, temperance, and the like, were each of them a part of virtue?

MENO: Yes.

SOCRATES: And so, Meno, this is the way in which you mock me.

MENO: Why do you say that, Socrates?

SOCRATES: Why, because I asked you to deliver virtue into my hands whole and unbroken, and I gave you a pattern according to which you were to frame your answer; and you have forgotten already, and tell me that virtue is the power of attaining good justly, or with justice; and justice you acknowledge to be a part of virtue.

MENO: Yes.

SOCRATES: Then it follows from your own admissions, that virtue is doing what you do with a part of virtue; for justice and the like are said by you to be parts of virtue.

MENO: What of that?

SOCRATES: What of that! Why, did not I ask you to tell me the nature of virtue as a whole? And you are very far from telling me this; but declare every action to be virtue which is done with a part of virtue; as though you had told me and I must already know the whole of virtue, and this too when frittered away into little pieces. And, therefore, my dear Meno, I fear that I must begin again and repeat the same question: What is virtue? for otherwise, I can only say, that every action done with a part of virtue is virtue; what else is the meaning of saying that every action done with justice is virtue? Ought I not to ask the question over again; for can any one who does not know virtue know a part of virtue?

MENO: No; I do not say that he can.

SOCRATES: Do you remember how, in the example of figure, we rejected any answer given in terms which were as yet unexplained or unadmitted?

MENO: Yes, Socrates; and we were quite right in doing so.

SOCRATES: But then, my friend, do not suppose that we can explain to any one the nature of virtue as a whole through some unexplained portion of virtue, or anything at all in that fashion; we should only have to ask over again the old question, What is virtue? Am I not right?

MENO: I believe that you are.

SOCRATES: Then begin again, and answer me, What, according to you and your friend Gorgias, is the definition of virtue?

MENO: O Socrates, I used to be told, before I knew you, that you were always doubting yourself and making others doubt; and now you are casting your spells over me, and I am simply getting bewitched and enchanted, and am at my wits' end. And if I may venture to make a jest upon you, you seem to me both in your appearance and in your power over others to be very like the flat torpedo fish, who torpifies those who come near him and touch him, as you have now torpified me, I think. For my soul and my tongue are really torpid, and I do not know how to answer you; and though I have been delivered of an infinite variety of speeches about virtue before now, and to many persons--and very good ones they were, as I thought--at this moment I cannot even say what virtue is. And I think that you are very wise in not voyaging and going away from home, for if you did in other places as you do in Athens, you would be cast into prison as a magician.

SOCRATES: You are a rogue, Meno, and had all but caught me.

MENO: What do you mean, Socrates?

SOCRATES: I can tell why you made a simile about me.

MENO: Why?

SOCRATES: In order that I might make another simile about you. For I know that all pretty young gentlemen like to have pretty similes made about them--as well they may--but I shall not return the compliment. As to my being a torpedo, if the torpedo is torpid as well as the cause of torpidity in others, then indeed I am a torpedo, but not otherwise; for I perplex others, not because I am clear, but because I am utterly perplexed myself. And now I know not what virtue is, and you seem to be in the same case, although you did once perhaps know before you touched me. However, I have no objection to join with you in the enquiry.

MENO: And how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know?

SOCRATES: I know, Meno, what you mean; but just see what a tiresome dispute you are introducing. You argue that a man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire (Compare Aristot. Post. Anal.).

MENO: Well, Socrates, and is not the argument sound?

SOCRATES: I think not.

MENO: Why not?

SOCRATES: I will tell you why: I have heard from certain wise men and women who spoke of things divine that--

MENO: What did they say?

SOCRATES: They spoke of a glorious truth, as I conceive.

MENO: What was it? and who were they?

SOCRATES: Some of them were priests and priestesses, who had studied how they might be able to give a reason of their profession: there have been poets also, who spoke of these things by inspiration, like Pindar, and many others who were inspired. And they say--mark, now, and see whether their words are true--they say that the soul of man is immortal, and at one time has an end, which is termed dying, and at another time is born again, but is never destroyed. And the moral is, that a man ought to live always in perfect holiness. 'For in the ninth year Persephone sends the souls of those from whom she has received the penalty of ancient crime back again from beneath into the light of the sun above, and these are they who become noble kings and mighty men and great in wisdom and are called saintly heroes in after ages.' The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything; for as all nature is akin, and the soul has learned all things; there is no difficulty in her eliciting or as men say learning, out of a single recollection all the rest, if a man is strenuous and does not faint; for all enquiry and all learning is but recollection. And therefore we ought not to listen to this sophistical argument about the impossibility of enquiry: for it will make us idle; and is sweet only to the sluggard; but the other saying will make us active and inquisitive. In that confiding, I will gladly enquire with you into the nature of virtue.

MENO: Yes, Socrates; but what 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?

SOCRATES: 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.

MENO: 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.

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?

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 of 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 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?