Why don’t our students learn logical reasoning? Maybe because their teachers don’t either.
Case in point: The principle of non-contradiction declares that no meaningful statement can be both true and false in the same sense at the same time – or, in its ontological form, that nothing can both be and not be in the same sense at the same time. If the door is open, then it can’t be the case that it isn’t. That’s not difficult, is it?
I can tell you the following story because the persons and places have been forgotten. But I assure you that it is true.
Some years ago, a candidate who was being recruited vigorously for a full professorship in one of the social science departments of a certain great research university made the remarkable statement that the principle of non-contradiction was false. This wasn’t an offhand remark. It was a foundational assumption of her work.
Let’s think about it. In saying that the principle of non-contradiction was false, she was saying it wasn’t true. In other words, she thought it had to be one or the other -- it couldn’t be both. But that is just what the principle declares to be true of all principles. So in the very act of denying the principle, she relied on it.
Why then did she deny it? Her argument was that everything implies its opposite, and reality is incoherent. For good measure she threw in that God is a liar.
But if this is the case, then nothing is the case. So it isn’t the case. In private conversation, I tried to explain this to her.
So she tried to prove to me that she was right and I was wrong. (Yes, I know.)
Her first proof was that “Convex and concave are opposites, but every curve is both convex and concave.”
I tried to explain that this was a fallacy of equivocation. There is no inconsistency if a man standing on the inside of the curve says the wall curves toward him, and a woman standing on the other side of the wall says it curves away from her.
Her second proof was that black and white are opposites, but if a ball were painted black on one side and white on the other, then it would be both black and white.
I tried to explain that she was equivocating again. The ball would be half black and half white, and this description is perfectly consistent.
I suggested to the people who were recruiting her that a person who cannot reason logically is unqualified to teach or do research. One of my colleagues responded that I was behind the times. “Lots of people are working on many-valued logics these days.”
That was like answering the statement “The door is open” by saying, “No, the window is closed.” Many-valued logics don’t try to do without the principle of non-contradiction. They try to do without the principle of excluded middle, which is not the same thing.
I should have answered that if it is all right to deny the principle of non-contradiction, then his view that the candidate was qualified left my view that she was not qualified still standing. But it probably wouldn’t have made any difference.
Oh, I forgot to tell you. She was hired.
Tomorrow: Dark Night of the Grad Student Soul