I'll talk a little more about Meno now. It's been a long time since I read it in its entirety, so take what I have to say at this point with a grain of salt. If I'm off the mark, please correct me in the comments section. My understanding is that Socrates is saying that when we figure something out, when we discover a solution through reasoning our way to an answer, what we're doing is remembering or recollecting. I suppose that's his answer to the paradoxical question I mentioned yesterday, how can we find a solution if we don't know what to look for?

Socrates demonstrates the process of discovery through recollection by questioning a servant, a child who has not had any formal training in mathematics. Through a series of questions, the boy is able to figure out how to calculate the area of a square.

Since there is a lot of information and guidance in Socrates' questions, is this really a matter of recollection? At first, it seems that Socrates is teaching the boy by providing information in the questions. But it seems that the servant already has knowledge of the fundamental concepts. The first questions are, "Tell me now, boy, you know that a square figure is like this?" and "A square then is a figure in which all four sides are equal?" The boy answers yes in each case, so he already has knowledge of what a square is. Since a square (i.e., a two-dimensional object with perfectly straight and equal sides) is never seen in nature, how can he know what it is? We could say that someone taught him this, but then the question would be, how could he know what a perfectly straight, abstract line is?

As the series of questions demonstrates, the child not only knows what a square is, he knows enough to learn how to manipulate it. My guess at this point is that the child does learn something through Socrates' instructive guidance; he is learning a procedure for manipulating the square and discovering its properties. But maybe Socrates is saying that the properties discovered, as opposed to the procedure for discovering them, are recollected, not learned through instruction.

The child understands from the get-go that a square is divided into four parts when two lines are drawn through the middle, as shown in the diagram of the dialog. Where does this understanding come from? I have a hard time convincing myself that it came from Socrates. Socrates draws a figure, and the child naturally sees that one square is divided into four. He naturally sees that a figure can be decomposed into smaller, identical pieces. It's as if we are already born with knowledge of concepts such as one-as-many and division.