Plato's Meno is concerned with defining 'virtue', though Socrates discusses some other topics along the way. I'm reading Grube's translation.

The Meno begins with Meno asking Socrates whether virtue can be taught, or otherwise how men come to possess it. Socrates replies that he does not know, nor even does he know what virtue is, and moreover he has never yet met anyone who did know. So begins the first part, in which Meno attempts to define, to Socrates's satisfaction, what is virtue.

At first, Meno says that "a man's virtue consists of being able to manage public affairs and in so doing to benefit his friends and harm his enemies and to be careful that no harm comes to himself." Of a woman, he says that "she must manage the home well, preserve its possessions, and be submissive to her husband." For the rest, he says that "the virtue of a child, whether male or female, is different again, and so is that of an elderly man, if you want that, or if you want that of a free man or a slave."

Socrates is unsatisfied with Meno's response, and says "I seem to be in great luck, Meno; while I am looking for one virtue, I have found you to have a whole swarm of them." Socrates insists that Meno should give him a definition of virtue, rather than naming some collection of virtues. As an example, at Meno's insistence, he gives definitions of shape and color, contrasting them with definitions of a shape or a color.

After a bit more discussion, Meno admits that he does not know what virtue is. He says that he has "made many speeches about virtue before large audiences on a thousand occasions, very good speeches as [he] thought, but now [he] cannot even say what it is."

Here begins the second part, in which Socrates and Meno discuss knowledge, and how one may come to know a thing. Meno asks Socrates how he will look for a definition of virtue, if, since he claims not to know what it is, he will not be able to recognize it if he should find it. This is Meno's paradox, but Socrates rejects it.

Socrates posits that "as the soul is immortal, has been born often and has seen all things here and in the underworld, there is nothing which it has not learned." Because of this, Socrates says, men do not ever learn anything, but only 'recollect' that knowledge which their souls already possess. Meno is skeptical, so Socrates offers to demonstrate his claim, and asks Meno to call one of his slaves, that Socrates may talk with him.

Now Socrates asks the boy a series of questions regarding geometry, of which Meno avers the boy has never been taught. By the end of Socrates's questioning, the boy has come to be able to tell how to construct a square with twice the area of a given square. Now Socrates asks Meno whether the boy has "in his answers, expressed any opinion that was not his own." When Meno agrees that he has not, Socrates presses the issue, asking "So these opinions were in him, were they not?" Upon Meno's further agreement, Socrates asks "then if the truth about reality is always in our soul, the soul would be immortal so that you should always confidently try to seek out and recollect what you do not know at present–that is, what you do not recollect?", and Meno again agrees that Socrates is right.

Finally Socrates states his rejection of Meno's paradox. He says: "I do not insist that my argument is right in all other respects, but I would contend at all costs both in word and deed a far as I could that we will be better men, braver and less idle, if we believe that one must search for the things one does not know, rather than if we believe that it is not possible to find out what we do not know and that we must not look for it."

Having established that it is worthwhile to seek knowledge, Socrates moves on to inquiring whether virtue can be taught, as Meno originally asked him. Socrates says, at length, that if virtue is knowledge, then it can be taught, but then questions whether virtue is knowledge–using Meno's question about the teachability of virtue as a cunning way to inquire into the nature of virtue, which he said he preferred to learn first, but which Meno wished to ignore.

Socrates says that if one wishes to learn a thing, he should go to one who knows it and charges a fee for teaching it, since it would be foolish to seek to learn from those who do not know a thing, and since no one would pay to be taught if the teachers could not improve their pupils. He goes on to say that if virtue were teachable, then virtuous men would certainly teach their sons to be virtuous. He then provides examples of virtuous men whose sons were not virtuous, taking this as proof that there were no teachers of virtue. And, he says, "if there are no teachers, neither are there pupils", and "a subject that has neither teachers nor pupils is not teachable", and so virtue cannot be taught.

After coming to this conclusion, Socrates distinguishes between knowledge and 'true opinion', saying that these two things, and these two alone, could give correct guidance. Since virtue cannot be taught, it is not knowledge, but must be true opinion. Socrates and Meno agree, then, that true opinion, like knowledge, does not come to men by nature but must be acquired. Since only knowledge can be taught, true opinions must be acquired in some other way. Therefore, Socrates claims, virtue "comes to those who possess it as a gift from the gods."

I have some disagreement with Socrates. In particular, his theory that the soul is immortal and that all knowledge is merely 'recollected', rather than learned, is poorly supported by his demonstration with the slave. Even if we accept that the slave truly does come to know how to construct the square with twice the area of a given square, and is not merely saying what he believes Socrates wants to hear, Socrates's argument is weak. Socrates argues as though his questions convey no information, but they are in fact highly leading. I contend that Socrates did not awaken knowledge in the slave by questioning him, but provided knowledge to the slave by his choice of questions. That is, the slave deduced the answers thus:

1. Socrates knows the answer to the problem he has set me.
2. Socrates's questioning is purposeful.
3. Since (1) and (2), when Socrates presents me with something and asks whether it is true, it is likely to be true.
4. Socrates has constructed a square and asked whether it answers the problem set me.
5. Since (3) and (4), this square likely answers the problem set me.

So, although Socrates does not explicitly state "this is the answer to the problem," by his questioning he reveals the answer to the problem. If we accept that it is possible to verify the truth of something without first knowing in advance of reaching the conclusion whether it is true, then we may even be able to eliminate 'likely' from this reasoning. Whether this is acceptable isn't totally clear. For example, I would say that I do not, at this moment know what 17 multiplied by 29 equals. But, merely by considering, I can come to the conclusion that it equals 493, and so I now do know the answer to that question, though the knowledge has not been conveyed to me by any outside agent. If we believe that men can only come to know a thing if the knowledge is conveyed to them, then, as Socrates says, we must accept that I always knew the answer to that question, but merely did not then recall it. I am not satisfied with this characterization of knowledge.

Further, I take issue with Socrates's claim that a man who knows a thing must be capable of teaching it, and that no one who does not know a thing could teach it. I think it is easy enough to accept that it is possible that merely knowing a thing does not necessarily imply the ability to teach that thing, so I will not defend my claim of that here. Rather, let's consider whether it is possible to teach a thing without knowing it.

A man is hired to investigate the contents of a chemical sample. He has, himself, no expertise with chemistry–he is merely given the tools to identify the contents of the sample, and asked to record his findings. When he has done this, he reports what he has found to others who do know about chemistry, but do not know the contents of the sample. When he has given his report, the chemists now know, from his report, that the sample is a compound of two other chemicals. They did not know this before, and the man who taught them still does not know it.

In some ways, this requires a somewhat uncomfortable definition of teaching. But if we do not accept, in the second case, that the man taught the chemists, then we must instead say that the knowledge was generated spontaneously–or how else would you describe someone teaching themselves? Even if, as Socrates says, my argument is not correct in every particular, I still contend that Socrates's characterization of knowledge is not supported by his arguments.