I think it’s generally rejected because there is an easy proof that if “P /\ ~P” were true, anything could be proven. Observe:

1.P /\ ~P … Given
2.P … Separated from 1
3.P / Q … From 2, disjunction introduction
4.~P … Separated from 1
5.Q … From 3 and 4.

Since Q is not dependent on any given, it can represent any statement. So if we allow P / ~P, absolutely everything is true and false (e.g., (P / ~P) / ~(P / ~P)).

Sorry, did you comment on my proof? Which part of my proof is wrong?

The contradictory nature of, well, nature. . . is still up for debate. Under the Copenhagen Interpretation, it is contradictory, but there is at least one other interpretation I am aware of that is empirically indistinguishable from the CI that does not involve contradiction (I mean the Multiple Worlds Interpretation, of course). The contradiction of the CI is one of its greatest shortcomings.

-(P/-P) in English reads: â€œIt is not the case that (both) P and not P are trueâ€.

As usual Carleas analysis is correct.

Additionally, I do not know of any case in Quantum mechanics where this logical statement is violated.

The article referenced by Ladyjane does attack the law of the excluded middle. P = - (-P), and it is true that Quantum behavior appears to validate â€œQuantum logicâ€ or multivalued logic.

The rejection of bivalent logic in Mathematics has enormous ramifications.

Perhaps Ladyjane simply applied the wrong logical statement?

Divid Bohm developed an alternative description of the quantum phenomenon in his book “Quantum Theory” which does not depend on the Copenhagen Interpretation. As I understand it his model produces the same predictions of quantum behavior.

The law of non-contradiction and the law of the excluded middle are both logical assumptions; logic is a form of language, it does not make positive propositions, it expresses them. That is all.

Thanks for the recommendation, Ed, I’ll add it to my reading list. But it’ll probably be a while before I get to it, I just got Conrad Black’s book on FDR.

Can you give us a specific example of how it shows this? I’m somewhat familiar with quantum weirdness, but I don’t know of any definitive instance that shows P and not P for some statement P. The closest thing I know of is Schrodinger’s Cat, and, as I mentioned, there are other interpretations that do not include that contradiction.

You can’t disprove the law of non contradiction. It claims nothing about reality. A particle can be in two places at once: sure! It’s like the cat thing: it’s not both alive and dead and therefore violating the law. It’s in a superposition of states: if you violate the law of non-contradiction, it means your linguistic model of reality is inconsistent and therefore you should revise what you mean by p because if it were really the case that p it couldn’t be the case that ~p.

This is a prior language stuff. Linguistic deconstruction is one thing but I’ve heard too many people try to peddle some kind of notion that an a posteriori physics can have somehow “disprove” a language.

Imagine!
I eat apple - English
I apple eat - Japanese

Now who’s going to argue that their is some kind of true way the words should be arranged? Or the words should be pronounced? Logic is in principle no different.

No, it hasn’t. Wave-particle duality is a metaphore. The thing is not actually either a whole lot of water crashing in the ocean and a tiny ball shooting through space. Wave-particle duality just means that the particle behaves as both a wave and a particle. That would be absurd on the macroscopic scale, so we call it ‘paradoxial’.
Furthermore, even if you want to push this issue, it doesn’t get you what you want. A “wave” is not the same as “not a particle”. That’s just saying “P /\ Q”, not P /\ ~P.

I’m familiar with the principles of quantum theory. My point is that your (and everyone else who I’ve heard say this) position is a priori absurd.

And don’t make particles into things which are also waves. Quantum theory is just a set of equations which make predictions. Anything beyond that isn’t science. As one quantum physicist supposedly responded when asked what they were really doing by one of his students: “Shut up and calculate.”

Ok, did ladyjane really just claim that being a particle was logically equivalent to not being a wave?
p=light is a particle which is logically equivalent to light is not a wave
~p=light is a wave.

What? So we can take any 2 properties A,B which no object can possess together and say possessing A is equivalent to possessing not-B? Thats retarded. The object could be not-B and not-A. In the context of our example, light could be not a wave or a particle. It’s like a shape can’t be red and green at the same time, so being red is equivalent to being not-green, so because the sky isn’t green it’s red. That, essentially, is your argument ladyjane.

Ok, thats a new low here.

Light isn’t a particle or a wave, it exhibits wave-like characteristics and it exhibits particle-like characteristics. You can’t call it either.