In Meno, Plato explores Socrates conundrum “that a man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire.” .
Meno uses the device of encountering Meno a Thessalian who is a follower of Gorgias. The conversation turns to the topic of virtue. The first question is if, and how virtue can be taught. They agree that it must be defined before any more questions are answered about it. Then they immediately run into the problem of establishing what virtue is. Meno seems at first to be confident in his ability to define virtue. Then he runs into problems as he flounders over the different qualities that are virtuous in some, but not in others. In particular, womanly virtues would not be considered such for men, and the manly virtues would be inappropriate, almost the reverse for a woman, child or slave. They progress though the conversation and Socrates likens the “swarm” of virtues to bees. Then he seeks to find the common elements that each of these qualities has that makes them a virtue. First, they attend to the common elements in each of these individual virtues that makes them a virtue. Although they are able to establish what virtue is not, they have a great deal of trouble determining what it is.
The issue of how to define defining virtue itself then turns into the problem of how to create a definition. One of the problems encountered is that the term cannot be used in the definition; an example of this is that Meno says the ability to acquire beautiful things. Socrates makes the point that this only works if the acquisition is just. However, since justice is a virtue, it cannot be used in a definition of virtue. The issue of how to define virtue itself then turns into the problem of how to create a definition.
Socrates uses geometric argument in the Meno to establish the difference between the instances of virtue represented by the different kinds of virtue that are only appropriate to a particular circumstance and virtue itself. Socrates points out that “a round, for example is ‘a figure’ and not simply ‘figure,’ and I should adopt this mode of speaking, because there are other figures.” . Later in the dialogue, Socrates goes back to the example of shape and expands it to explain if someone asked what is figure and the response was “roundness” that would only suffice for one type of figure it would not encompass all the shapes that are also figures. He treats color in a likewise manner, using what as an example of a color that does not provide a definition of the term color. Socrates revisits the notion of roundness being a figure and not the definition of figure. Further, on, he observes that although there are many different figures, and some that are at cross-purposes with each other there is a common nature that is designated as figure. That common nature includes straight as well as round, without taking away from either as within the concept of figure.
In this way, Socrates uses geometric argument to illustrate the difference between a shape and the concept of shape itself. Meno asks Socrates to define shape so that he would have an example to follow in defining virtue. Socrates agrees to define shape, as long as Meno then agrees to make another attempt at defining virtue. Socrates establishes that shape establishes always follows color. However, he had made the earlier definition of color as always following shape. Therefore, it is necessary to know a definition of one in order to establish what the other is, and Meno asks for something that gives more clarity to the situation. Socrates establishes that Meno knows what a solid is, and a surface and defines a figure to be the “limit of a solid.” . Meno is exasperated by this simplicity and chastises Socrates who then goes into a lengthy description of color in the manner of the Sophist philosopher Gorgias. In this way, he establishes how to create a definition and it is Meno’s turn to have another go at defining virtue.
The conversation then turns back to the original topic of whether virtue can be taught. In the course of this discussion, Socrates uses Meno’s slave to illustrate how we can believe we know something, but when we go into it further, we discover that we have been in error. The slave thinks he knows the answer, when put to its proof he discovers he was in error. Socrates establishes that the slave knows what a square is, then draws a square with two foot sides and the area of four square feet. Then he asks the slave how long a side would have to be in order for the square itself to contain eight square feet. The slave initially responds four feet, four being two times two and eight being two times four. However, when they look into it further and draw out the square with four feet they find that the area is actually sixteen square feet so the answer of four is incorrect. Next, the slave figures that three is half way between two and four just as eight is between four and sixteen so they put that theory to its proof and it also fails the test since a square with three foot sides has an area of nine square feet. In the course of this, Socrates points out to Meno that he is “not teaching the boy anything, but only asking him questions;” . As this progresses, he calls Meno’s attention to the slave pointing out that the boy is observing and remembering. At each step along the way Socrates calls upon the slave to remember what went before and apply that to the solution of the puzzle in order to determine what length side will yield a square with an interior of eight square feet. At one point Socrates points out to Meno, “what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a figure of eight feet: but then he thought that he knew, and answered confidently as if he knew, and had no difficulty; now he has a difficulty, and neither knows nor fancies that he knows.” . Then they go back to the geometric figure with four-foot sides and an area of sixteen square feet. Socrates draws an interior square whose corners touch the center points of each of the sides. In this manner, they are able to create a square with four equal sides and an area of eight square feet thereby solving the puzzle. Once that is done, Socrates goes back through the steps the slave used to come to his answer and established that the slave used those steps to remember that he line that made up the square was the diagonal and that the diagonal was the square root of the square. The point of course that Socrates was making of course was not to find a square with an area of eight square feet; it was to illustrate how the slave used memory to arrive at the conclusion for himself and was not “taught” the answer by Socrates.
We can call these lessons by Socrates into question. Socrates clearly led the slave in every step along the way illustrating the initial and second errors and the conclusion. However, the concept of aporia, or coming to know what one does not know was clearly established by this exercise. Socrates concludes the conversation on the topic of virtue with the following statement:
Plato. "Meno by Plato." 2012. Project Gutenberg. 14 09 2012
Stanford Encyclopedia of Philosophy. "Aristotle's Metaphysics." 11 06 2012. Stanford Encyclopedia of Philosophy. 06 09 2012