Meno

– Shape Essay, Research Paper

“Shape is that which alone of existing things always follows color.”

“A shape is that which limits a solid; in a word, a shape is the limit of a solid.”In the play Meno, written by Plato, there is a point in which Meno asks that Socrates give a definition of shape. In the end of it, Socrates is forced to give two separate definitions, for Meno considers the first to be foolish. As the two definitions are read and compared, one is forced to wonder which, if either of the two, is true, and if neither of them are true, which one has the most logic. When comparing the first definition of shape: “that which alone of existing things always follows color,” to the second definition: “the limit of a solid”, it can be seen that the difference in meaning between the two is great. Not only in the sense that the first is stated simply and can be defended easily, while the later is more difficult to comprehend and back up; but also in the sense that the second would have to involve the defiance of mathematical theories and/or proofs in order to stand true, while the first does not. It should also be noted that in the first definition, the word “a” is never mentioned. Socrates is not making a statement about “a shape” or “a color”, but about shape and color themselves. In the definition given to please Meno, Socrates’ words are “a shape” and “a solid”. It can be taken from earlier discussions in the play that the second definition is simply a definition of a shape, rather than a definition of shape in and of itself.

In the simple sentence that Socrates originally gives to Meno, he has not given then definition of a shape, rather he has given the definition of the term shape. For example, if a person was asked what a triangle is, the response would most likely be that it is a shape, but shape would never be defined as shape itself. It is simply an object that falls under the category of shape. Therefore, in one sentence, Socrates has put a definition to shape, for without color there can be no shape, there could not even be a shape to fall under the category that would have once been known as “shape”. None of the examples that Socrates and Meno discussed could prove the definition false. If something is round, for instance, then it is a shape, and a shape cannot exist without color. Therefore, shape must be formed by color, proving that color must precede shape and that shape must proceed color. The same proves true of a square, trapezoid, cube, or any other shape that exists. For, a solid must have a specific area and volume, and the naked eye can tell that the solid is there and has color, because if it had no color it would not be visible, therefore it would not be known to exist. In order for a shape that is not a solid, such as a line, to be seen, it must be drawn or made visible in some other way. As soon as that occurs, color is what has formed it.

However, Socrates’ statement is also disputable. Take the matter of the geometric plane. It is not visible. It can be represented for any purpose by drawing it, but as soon as it is drawn, it is no longer a plane for restrictions have been put upon it. A plane continues infinitely in all directions. Although geometric planes cannot be seen, it is a mathematical fact that they exist, although it is not known for certain if they occupy a certain amount of space. Because it has these properties, it is indeed a shape, but it is a shape that cannot be seen, an infinite shape, and one that requires no color to be called so. But the mystery of the geometric plane in relationship to this definition has not been solved, for an object such as a circle cannot exist without a geometric plane, but a geometric plane can exist with an object. So, since it has been stated by Socrates that shape cannot exist without color, what should be said when a circle – existing solely because of color – is on a geometric plane? The geometric plane must exist, as the circle is on it and as the circle cannot exist without it, but is the plane considered a shape since it’s area is infinite? There is certainly the possibility that there are those who do not think of it as a shape because it has no restrictions put on it, but if this was so, why did Socrates not include this in his definition? It could have possibly been because by shape he meant objects with definite form.

There is the possibility that, in the mind of Socrates, his definition is unflawed, for it may have been that he did not view a geometric plane as a shape, but only as something that has an area which extends infinitely. If this was the case, then his statement is indisputable. However, if that was not the case, he may have stated it for the purpose of discovering how far he could stretch Meno’s logic. However, there is also the slight possibility that Socrates did not consider all of the options and examples that were filed under the category of shape, and therefore he could very well be wrong. In this situation it is difficult to tell how truthful this definition is, for what was going on in Socrates’ mind at that time cannot be known to us. It is for each to draw a conclusion from.

Then the question arises as to the truth and logic involved in Socrates’ second definition, which is given purely to please Meno. The problem that occurs when this statement is made is that it is mathematically impossible to have a finite number of sha