– 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 shapes; therefore, there are an infinite amount of solids, meaning that a solid cannot be limited. A shape can look like anything; it can have any form, but the instant that even the smallest part of that shape is moved or shifted, it becomes a different shape altogether. Several examples exist that can prove this statement untrue. Take the word “round”, which Socrates used as an aid in an example that was given to Meno in a previous part of the text. A ball, for instance, is a round solid (round being any shape that has a circumference), so the conclusion can be reached that the ball is a solid and round is its shape, therefore the shape is limited by only the solidity of the ball. Thus, this does not support Socrates’ definition, for it shows that the shape is limited by the solid, not that the solid is limited by the shape. In addition to this, there is another dispute against this definition of shape using the word round. A circle is round, and yet it is not a solid. Therefore, this statement does not define the term shape; rather it defines on a certain type of shape, a solid shape.

The logic that Socrates had in stating his second answer in those particular terms could have been several. It would have followed the theme that is seen throughout the play of the Meno and Socrates mocking each other. Socrates knew that the answer that would please Meno the most would be the one that sounded the smartest but made the least amount of sense. However, Meno does not seem to realize this, and accepts Socrates’ answer. This should have made it especially interesting for Socrates, for he had agreed to give Meno this second definition in the form of Gorgias. Meno is always agreeing with him, and incorporates his points into many of the conversations that he tends to hold. Not only is Socrates secretly mocking Meno, he is also mocking Gorgias.

At first appearance, both definitions seem to hold some weight. However, upon further investigation, the second can be ruled out as truth altogether. The first holds much weight, and definitely contains a higher percentage of truth within it than the second. However, the debate about whether all shapes can fall under his original definition is still debatable; having many strong points, but one weak point. Nonetheless, the conclusion that, if one of the two had to be chosen as the truth, the first definition of Socrates would most certainly emerge victorious.