grace2u writes:
Lets go through this again(in as simple terms as possible)
A=spin of an elementary particle .
x=spin up
y=spin down
{A=x or y}... {A=x|y}... {A=x+y} depending on how you want to put it.
It seems that you don't understand how superposition works. The three statements on your last line do not express the same thing.
grace2u writes:
Reality says that A can be x or y as my equation demonstrates. The identity theorem does not say that x needs to equal y.
This is what I mean when I say it seems you don't understand how superposition works. A = X and A = Y are BOTH TRUE to certain degrees, yet if the identity axiom (it's not a theorem, BTW) held this would be impossible. They would have to be ONLY one or the other since X <> Y. Yet the eigenstate, superposition, the state of simultaneously existing in multiple non-identical states, is the natural state of the particle.
grace2u writes:
How is {the spin of a particle} not equal to {the spin of a aparticle}????
Because 'spin up' does not equal 'spin down' yet both must be included in a complete description of the state of the particle. Look at it this way. Let's assign numbers to the truth values. Let True = 1 and False = 0. Then, A = ('spin up' or 'spin down') = 1, A = 'spin down' = 0, and A = 'spin up' = 0. If we were to allow fuzzy truth values, then we might say that A = 'spin up' = 0.5, and A = 'spin down' = 0.5. If the identity axiom were universally true, then A = 'spin up' and A = 'spin down' could not have identical truth values.
grace2u writes:
You have demonstrated by this statement that you do not fully grasp the concepts I am describing.
Now if THAT isn't irony at its finest...
Now, what I was REALLY hoping for was a direct answer to these questions:
If logic were indeed universal, then we would expect that there would exist no statement X such that X is a well-formed statement and yet we can not prove X true or false logically, do you agree? In other words, assuming that logic is universal, absolute and fixed, we would expect that every conceivable statement is theoretically decideably true or false, right? A simple yes or no will suffice. If your answer is no, please explain how logic can be universal, absolute and fixed and yet there exist well-formed statements which it cannot prove true or false.
So what is it? Yes or no.
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