Is it possible to reject the law of non-contradiction?
I had a conversation with my teaching mentor on wednesday. She rejects the law of non-contradiction, or so she claims. She would probably not put it like that, saying instead that the law of non contradiction does not hold in all circumstances, but when I talk about THE law of NC (as opposed to a law of NC) I mean the one that says "X and not-X are never in any circumstances both true at the same time and in the same sense."
I presume she is being honest when she says she rejects that. Since she has a PhD in Philosophy I can assume that she understands what she is saying. So it would seem that she really means what she says.
But is it even possible to reject the law of NC? I can't imagine what it would be like to reject it. I'm not saying it's logically impossible. I can't imagine what it's like to be a bat, but it is logically possible for something to experience bat-life. However, in a weaker sense it is not possible for a human being to experience what it is like to be a bat, just as it is impossible for a human being to swim across the Atlantic Ocean. That's the kind of impossibility I'm talking about.
I can't imagine what it's like to reject the law of NC. I can imagine believing a lot of nonsense: that I am made of glass, that 2+2=579, that I don't exist. I can imagine believing individual contradictions, so long as I don't admit that they are contradictions. I can imagine not understanding the law of NC; I can imagine understanding it, but withholding jundgment; but to actually disbelieve it? It's not just that nothing could convince me that the law is false, I don't even know what it is to hold a belief like that.
So what am I to make of the many educated people who claim to reject the law of NC? Either they have some cognitive faculty that I lack, or else they are deeply mistaken about their own beliefs: they honestly report what they think their belief is: that the law is not true. But they are wrong: as a matter of fact they don't believe that. That's the only way I can make sense of the situation.
If this is correct, a question arises: why do so many people have this misperception of their own minds? I think I can understand why sophomoric relativists think that way: they want to be tolerant and are either too stuborn to think the matter through, or else they just haven't been taught to think clearly. But what about the highly educated thoughtful people--people who are quite capable of rational thought, and who have thought about and seem willing to continue thinking about the law of NC, but still claim to reject it?
Posted by mccartney at February 6, 2004 2:25 PMI've been trying to think of a case where the law of non-contradiction (LNC) doesn't hold (it's pretty dang hard). If there is such a case, then your teacher would be justified in believing that the LNC doesn't hold in all cases. The following counterexample doesn't work, but it is sort of interesting.
Case #1:There is an imaginary sphere that is half red and half black.
Let X1 be the sentence: "the sphere is half-red." X1 is true for Case #1. Let X2 be the
sentence: "the sphere is half-black." X2 is true for Case #1. X2 is equivalent to the sentence ~X1: "the sphere is not half-red." ~X holds because the black half is not red. Therefore, for Case #1, both X1 and ~X1 hold.
Subcontrary.
Posted by: Kevin at February 11, 2004 5:18 AMPaul's logic is caught up in the symbols of language.
You say that it is possible for the sphere to be half red and not half red at the same time. But that word "half" is referring to two different halves--not the same half.
ergo, the law holds.