"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...
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