The question that begins this dialogue is whether virtue can be taught. This quickly becomes a discussion about knowledge, as Socrates assumes that virtue can be taught only if it is a kind of knowledge.
Oddly enough, I want to spend most of our time talking about math and not really about virtue. Plato took mathematical knowledge as his model for knowledge in general. So I want to concentrate on 82a-86c.
This is a very shallow outline; it just divides the reading into four parts.
Meno asks Socrates if he thinks that virtue can be taught. Socrates says that he does not know what virtue is and so he cannot say whether it can be taught. Meno, as the other guy in these dialogues always does, says “that’s easy, I can tell you what virtue is!” Then Socrates ties him up in knots. This leads him to conclude that he does not know what virtue is. And to worry that if Socrates were to keep going, he might be convinced that he does not know his own name either. (I’m kidding about the last part.) (70a-80a)
This leads them to the question of how you go about looking for something if you do not know what it is. In this case, they were looking for virtue to see if it can be taught and are puzzled about how to move forward if they cannot say, even to their own satisfaction, what they think virtue is. Here, Socrates propose a positive answer: learning involves recollection. They can find the thing they are looking for if they can remember what they once knew. This theory about knowledge is illustrated with the geometry problem. Socrates takes someone who has had no education in mathematics and, by asking questions, shows that this person knows how to solve a problem in geometry. How is that possible? Socrates believes that it is possible only if he already knew the answer and just needed to have his memory jogged. (80d-86c)
They then return to the questions of what virtue is and whether it can be taught. Now they are following a method borrowed from geometry that uses hypotheses (87a). They hypothesize that virtue is a kind of knowledge and, accordingly, that it can be taught. After defending this hypothesis, Socrates turns around and offers a contrary argument. If virtue could be taught, he reasons, there would be students and teachers of virtue. Since they cannot find any teachers of virtue, it seems that it cannot be taught. (86c-96d)
Finally, they take up a different hypothesis, namely, the virtue is not knowledge at all but rather “right opinion.” Those who are virtuous have the correct opinions about what to do, but they do not know why. This is why they cannot teach virtue to their children. If this is correct, then the possession of virtue is fortuitous. (97a-100b)
I want to go over how the geometry example works. Then I want to talk about what it is that we know when we see the correct way to make a square that has twice the area of another square.
Is what we know about the thing drawn on the board? If not, what is it that we know something about? Where is the square that we know about, if not on the board? And is our knowledge about a square or about something more abstract, like, squares?
Those are the kinds of questions I want to talk about.
If I am very clever, I will find a way to work Mill in too, since both he and Plato are talking about knowledge. But I have not thought of a way to do that yet.