MEANING OF WORDS A. B. JOHNSON
I am not picking on the above author, his fault is common, all too common. In trying to correct a misconception, he simply goes to another misconception. A definition is used to determine class membership, all members are equally members of a class by definition. When it is given that A = A, one can substitute any name in the equation Man = Man.
One the problems with attempting to be rational is not knowing when you are switching coordinate systems of reference, what you are comparing in making a judgment. Some men are short, but we are not then comparing men, we are comparing the height of men. etc.
This is one of the topics given in Parminides. If one uses a sail, to cover a number of men, does part of the sail cover part of the men? The question, generalized, is, can the divisor be divided? Is the boundary bounded? No. As abstraction is the inverse function of predication, one cannot predicate of a predicate.
The dialog Parmenides is designed to start the reader thinking about the principles of predication, what happens to reason when you do not know them. It is not a non-sense piece–it is a piece that is necessary to master to even begin to reason. In this piece, Plato credits Parmenides, and thus the work of Zeno as being directed to get the reader to learn from the examples they give. They are not teaches like Aristotle, for Aristotle was not on par with them.
I do fault the author in this, how is it that he believed he could write about the meaning of words, when he did not even comprehend what equality is? Why things with the same name are equal by the criterial in which they were given that name was discussed by the ancients.
How would you, or do you comprehend equality?