In part one of this series, I described a very few of Aristotle’s axioms. He believed that understanding a few primary things about being would allow us to build valid arguments and reasoning for everything that followed, which he called the posterior. To summarize that first part, “being is.”
Aristotle ran into people who disagree.
“There are some who, as we have said, both themselves assert that is possible for the same thing to be and not to be, and say that people can judge this to be the case.”-Metaphysics, book IV, part 4, Translated by W.D. Ross
This kind of assertion makes me crazy. I think it made Aristotle crazy too, and he wouldn’t stand for it. He makes a beautiful argument against this nonsense. He tells us that the instant someone makes an argument for the possibility of a thing both being and not being, he has made a positive statement that, in order to be true, must exist and can never not exist. Here’s another way of saying it. If I show that a proof exists for the ability of a given thing to exist and not exist, at the same time that proof would not exist, so this being/not being cannot be. Checkmate, game to Aristotle. Everything must be or not be.
Knowing that this is true, we can build from there.
Ari then moves on to definitions. He says that we can use a series of words to ascribe a meaning to the word “man” and define “man.”
“If such and such is a man, then if anything is a man, that will be what being a man is.”-Metaphysics, book IV, part 4, Translated by W.D. Ross
There is only one true definition for any given thing because if there were another definition neither would point to anything and would both be meaningless. They wouldn’t be definitive. “Man” has one meaning, and is predicable of one subject. There are no other words that carry that meaning or predicate that subject. There can’t be another definition that says “un-man” is a “man.” (In logic, any definition that was different than the original would be the “un-original.” Anything that isn’t cola is the un-cola.)
I think we’ve finally arrived.
We can now proclaim that A=A This is the Law of Identity.
In terms of universals, concepts, categories; a man is a man and can be no other. A=A. In terms of the particular, this baseball I hold is exactly this baseball I’m holding, and not the same as other baseballs. A=A.
This seems self evident, that A=A. That’s because it is. It’s axiomatic. It’s everywhere and it should not be ignored.
“A” is something. It stands for the subject of any assertion. For example, “Man is the rational animal.” “Man” is the subject both logically and grammatically. (Grammar isn’t a set of weird rules the 8th grade teacher laid out. Grammar is designed to carefully convey conceptual information from one consciousness to another.) “Is the rational animal.” is the predicate both logically and grammatically, because it is something predicated of “Man.” There are lots of things predicated of “Man” and all of the things predicated of “Man” can REALLY make us crazy and look like definitions if we lose sight of the logical subject and start acting like A is not A. I think the main trap here is when we think those things predicated of “Man” are definitive. They are not. There is one definition and it tells us that A=A. Don’t let the bastards tell you otherwise.