Plato presents Socrates views on the question whether virtue can be taught in several dialogues, most notably in Protagoras and Meno. In Meno Menon puts the question to Socrates this way: "Can you tell me, Socrates--can virtue be taught? Or if not, does it come by practice? Or does it come neither by practice nor by teaching, but do people get it by nature, or in some other way?" . Socrates claims to not "know the least little thing about virtue" and unable to speak as to its qualities.
Moreover, he claims to know no one that does. . There follows a discussion as to whether Gorgias, the Sophist, might not be such a person. Both Socrates and Menon know Gorgias' teaching. Menon obviously has a higher opinion of Gorgias' teaching than does Socrates. It is agreed, upon Socrates suggestion, that the conversation should proceed to explore what Menon, not Gorgias, knows about virtue. And so Socrates, puts the question to Menon: "[W]hat do you say virtue is?" 
Menon finds "nothing difficult" in the question and attempts, forthwith, to answer it. But there are complications with the answer, for Menon has suggested that men, slaves, children, women all demonstrate a different kind of virtue, and concludes that there is a virtue "for doing each sort of work" associated with being a slave, a child, a woman, a free man. Menon's idea of virtue is what we would call role specific.
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Virtue in Several Dialogues
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Socrates attempts to show that Menon's initial answer misses the point because it does not show what is common to the virtues of these various actors. If the virtue of men and women, free men and slaves, does not share something in common then it cannot be said to be the same thing and one would necessarily call the one virtue, and the other something else. As Socrates puts it, "Even if there are many different kinds of them [virtues], they all have one something, the same in all, which makes them virtues." . Menon accepts Socrates criticism and argues that it is indeed one thing of which he speaks.
In order to determine what the common quality of virtue is, Socrates observes that Menon has associated virtue with the ability to manage public affairs well. Socrates now sets out to question Menon on whether virtue would be present in the management of public affairs in the absence of temperance and justice and Menon readily agrees that it would not.
Socrates has already disclaimed any personal knowledge of virtue and he has steered Menon away from a discussion of Gorgias' view of virtue. But when Menon fails to provide a persuasive account of his conception of virtue, Socrates poses a question with substantive content. Socrates may know nothing about virtue, but he knows enough to ask whether virtue can be present without temperance and justice. The question suggest that it is Socrates rather than Menon who knows enough about virtue to keep the conversation going.
Socrates interrupts the dialogue to make a brief statement about the conversation he has been having with Menon. He distinguishes the conversation he is having with Menon from those where the questioner is "one of those clever fellow, who just chop logic and argue to win." Questions such as the one that Socrates and Menon are discussing -- whether virtue can be taught? -- are best left, says Socrates, to "friends" who wish to talk together. In such a relationship argues Socrates, "I must answer more gently and more like friends talking together; and perhaps it is more like friends talking together, not only to answer with truth, but to use only what the one who is questioned admits that he knows." 
Socrates, in rapport with Menon, tries to clear up a possible confusion as to whether it is possible to seek that which is bad. Socrates suggests, as he does in other dialogues, that we "all desire good things." Menon has responded to Socrates question by saying that one can desire bad things. Socrates tries to clarify this point by asking whether one desires that which is bad because of a mistake, that it is assumed to be bad.
But Menon does not pick up on the point and contends that one desires the bad both as a result of a misplaced assumption as to its value and we can also desire the bad even when it is known to be bad. But upon further questions, Menon agrees with Socrates that no one seeks to inflict injury and misery upon himself, and it is injury and misery that are the results of that which is bad. Socrates summary of their agreement goes like this: "Then it is plain that those who desire bad things are those who don't know what they are, but they desire what they thought were good whereas they really are bad. . . ." 
Menon has mentioned in passing that virtue consists of the desire of good things and to provide the good. Menon admits that one good thing it is possible to desire is "to possess gold and silver and public honour and appointments." . Socrates inquires now whether the virtue of possession of gold and silver must be qualified so that its possession is fair and just. Menon agrees that it is not a virtue to have such possessions if they have been unjustly acquired. On the contrary it would be a vice. "It is necessary," Socrates says, "to add to this getting, justice or temperance or piety or some other bit of virtue, or else it will not be virtue, although it provides good things." 
Socrates rebuffs Menon for trying to talk about virtue by looking at it piece by piece and drawing into the discussion a sense of virtue that he has not yet presented. Menon agrees that it is a problem and comments on his reaction to what has gone on:
Well now, my dear Socrates, you are just like what I always heard before I met you: always puzzled yourself and puzzling everybody else. And now you seem to me to be a regular wizard, you dose me with drugs and bewitch me with charms and spells, and drown me in puzzledom. I'll tell you just what you are like, if you will forgive a little jest: your looks and the rest of you are exactly like a flatfish and you sting like this stingray--only go near and touch one of those fish and you go numb, and that is the sort of thing you seem to have done to me. 
Socrates response to Menon's description of his puzzlement is that he himself is "not clear-headed" when he puzzles others, and that he is "as puzzled as puzzled can be, and thus I make others puzzled too." . And where can the conversation go from here? Socrates says, that he wishes to investigate virtue with Menon's help so "that we may both try to find out what it is." 
Socrates argues that there is no such thing as teaching, only remembering. This notion of teaching comes out of Socrates belief in the immortality of the soul. The soul dies but is reborn and thus never destroyed. (This is given by Socrates as a reason for why "we must live our lives as much as we can in holiness. . . .") "Then, since the soul is immortal and often born, having seen what is on earth and what is in the house of Hades, and everything, there is nothing it has not learnt; so there is no wonder it can remember about virtue and other things, because it knew about these before. For since all nature is akin, and the soul has learnt everything, there is nothing to hinder a man, remembering one thing only--which men call learning--from himself finding out all else, if he is brave and does not weary in seeking; for seeking and learning is all remembrance." 
After questioning the slave boy about geometry Socrates seeks Menon's concurrence in the proposition that the boy, shown to have been in error about geometry, is better off now, that he too is numbed but has knowledge about the limits of what he knows. By being numbed by the sting of Socrates' conversation the slave has come a step "onwards, as it seems, to find out how he stands." . Menon answers yes, when Socrates asked: "Then do you think he would have tried to find out or to learn what he thought he knew, not knowing, until he tumbled into difficulty by thinking he did not know, and longed to know?" Menon agrees, that he does not think he would and thus gains from being numbed.
Menon takes up again his original question, whether virtue can be taught, or one gets it by nature or in some other way. Socrates agrees to proceed but contends that they need a common ground as neither of them can say at this point what virtue is. Socrates has Menon agree that if virtue is knowledge then it can be taught, and if not a knowledge then it cannot be taught. (Conclusion: All that is taught call be called knowledge.)
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