Having gotten nowhere in their attempt to define virtue, but having made the idea of a definition somewhat clearer, Socrates and Meno renew their efforts. First, however, Meno brings up a difficult question: "How will you look for [virtue]," he asks, "when you do not know at all what it is?" This is a serious paradox--if we are seeking the nature of something we do not know, how will we know when we have found it? How will we even know where to look? Socrates has a long and somewhat complex answer.
He begins with a strange reference to "priests and priestesses," "wise men and women [who] talk about divine matters." These people, Socrates says, claim that the soul is immortal, and that it is not destroyed with the death of the human body. Thus, since the soul "has been born often and has seen all things...there is nothing which it has not learned." Learning, then, is really a process of recollection in which the soul comes to remember what it already knew before its current human life span. On this model, seeking what one does not know is not a paradox because one is simply trying to remember the truth.
This claim that the soul is immortal and therefore already knows everything is one of Plato's most important ideas, and it is probably introduced for the first time here. It will play a major role in later dialogues, particularly the Phaedo and the Phaedrus. Having put this theory on the table, Socrates proposes to move on with the pursuit of the definition of virtue. Meno, however, wants evidence of Socrates' claim that learning is really a kind of recollection. Calling over one of Meno's slaves, Socrates sets about illustrating this idea. The questioning that follows provides a concise model of the Socratic elenchus, in which continuous questioning leads Socrates' subject into a state of total uncertainty (aporia) about what they thought they knew.
Establishing that the slave speaks Greek, Socrates draws a square in the dirt in front of him and divides it into four equal sections. Asking questions of the slave (and never teaching him anything directly), Socrates establishes that one side of a square four feet in area is two feet long. He then asks the slave to determine the length of the side of a square that is double the area (i.e., eight feet in area). The slave mistakenly says that such a side would be four feet, double the length of the original square (but a four foot side, of course, would yield a sixteen-foot square).
Socrates proceeds, still only through questions, to show the slave his mistake. The slave, realizing that the length he is after must be somewhere between two feet (the length of the original square) and four feet (his wrong answer), now answers that three feet must be the correct length (wrong again--that length would give a nine-foot square). Socrates points out this mistake as well, and makes a point of showing Meno that the slave is now in a state of aporia--he knows that he does not know the correct length. This state, Socrates argues, is better than the slave's original (false) claim to know the answer. Referring to Meno's earlier complaints about being "numbed" by Socrates' questions, Socrates says that "now, as [the slave] does not know, he would be glad to find out, whereas before he thought he could make many fine speeches to large audiences about the square of double size." The slave, like the ungrateful Meno, "has benefited from being numbed."
Reminding Meno that he is only asking the slave his opinion (and not teaching him), Socrates continues his examination. To the original square of four feet in area, Socrates adds three more, thus creating a square four feet on each side (and so four times the area of the original square--it may help to draw this out yourself). Drawing diagonal lines that link the centers of each side of this larger square, he asks the slave if these diagonals cut each of the original-sized squares in half. They do, of course, though it's worth pointing out that Socrates has strayed somewhat here from his policy of not teaching anything but only asking the slave's opinion.