Maybe we should start a new thread on this topic.
Here are just a few preliminary comments:
The law of excluded middle is as follows:
For any statement, S, Either S or ~S. (I’m using ~ to represent the negation function).
Or, to put it in terms of properties:
For any object, o, and any property P, either Po or ~Po.
In essence, this law tells us that either a statement or its negation must be true (or, either an object has the property or it lacks that property).
Here is my point: Either the law of excluded middle is a good law (it is a true law of logic) or else it is not. If there is a realm where it does not apply, then it is NOT a law of logic. Some philosophers think that it is false. Of course, there is a great deal of uncertainty. But if it is false, then it is false and it is not a law of logic.
The only disagreement we have here is your insistence on universality. Formal logic only applies to propositions—statements that can have a definite truth value. Not all statements fall into that category. Excluded middle (along with identity and contradiction) define for us what it means to have a (formally) logical discourse. (There are also some mathematicians who don’t allow excluded middle in proofs, but they are a very small minority.) (One area where none of the laws of logic apply universally is in magical discourse. Now we can say that that’s because magical thinking is incorrect thinking, but try to tell that to an advertising executive .)
What we want to say is that either the cat is dead or she is alive. However, because the wave-function has not collapsed until an observation is made, we are told (by some interpreters) that the cat is neither dead nor alive.
I am very skeptical of this interpretation. But I am the furthest thing from an expert. So, let’s grant that it is correct. Does it show that the LOEM is false? I don’t think so.
Note that ‘is alive’ and ‘is dead’ are NOT logical opposites. The law of excluded middles applies only to logical opposites.
Let A= The cat is alive
D= The cat is dead.
The LOEM does NOT tell us that either A or D.
What LOEM tells us is, Either A or ~A. And also, Either D or ~D.
Why does LOEM not tell us that either A or D? Because ‘is alive’ and ‘is dead’ are NOT logical opposites. Since they are not, we cannot get from ‘X is not alive’ to ‘X is dead’. In other words, the following principle does NOT hold in general:
Principle AD: If X is not alive, then X is dead.
Principle AD is NOT true. There are many things that are not alive but are not dead. Rocks, for example, are not alive, but nor are they dead. The sun is not alive, but it is not dead. And so on . . .
So, we know that ‘is alive’ and ‘is dead’ are not logical opposites, and thus we know that Principle AD is NOT true.
For the same reasons, we can’t get from ‘X is not dead’ to ‘X is alive.’ Thus the following principle is also false:
Principle DA: IF X is not dead, then X is alive.
Rocks are not dead, but nor are they alive, and so on.
Now, the following principle IS true:
Principle DL: If X is dead, then X is not alive.
Principle LD: If X is alive, then X is not dead.
Remember, the LOEM tells us that both of the following are true:
Either A or ~A.
Either D or ~D.
Because DL and LD are true, it cannot be that A is true and D is true. So one or the other must be false.
The Schrodinger experiment tells us (allegedly) that the cat is neither dead not alive. So, if this is correct, we know that both A and D are false. Thus, in order to fulfill LOEM, the only option left for us is for both ~A and ~D to be true. Can this be the case?
Well, logically speaking, because DA is false, we certainly can have ~D and ~A (my point here is that nothing about LOGIC rules this possibility out).
Now I think that this might suggest to us that there might be states somewhere in between life and death. Perhaps such states are rare and only occur in such bizarre circumstances as those in the experiment. But there is nothing that rules out the possibility of such states (certainly nothing logical rules out the possibility).
Suppose the cat were in such a state between life and death. Would the cat be alive? No, that is the thing about this state (if it exists); an animal in such a state is not really alive, but nor is it dead. Is the cat dead? Here again the answer must be, NO. The cat, on this theory, is in some kind of limbo (quasi-life, quasi death), in which it is neither alive but nor is it dead.
Thus, if any of this makes sense, then both ‘A or ~A’ and ‘D or ~D’ are true. The cat is not alive AND the cat is not dead. (in other words ~A is true AND ~D is true)
Conclusion: The fact that Shrodinger’s cat is neither alive nor dead (if it is a fact) does not prove LOEM false. The cat can be neither alive nor dead. Since this is a possibility that is not ruled out by anything in quantum mechanics (at least as far as I know), we should conclude that Schrodinger’s cat does NOT disprove the Law of Excluded Middle.
The three possibilities are (a) the cat is either dead or it is alive; (b) the cat is both dead and alive; (c) the cat is neither dead nor alive. The first case is the one we would logically assume, throwing out the second as contradictory. (On your argument, however, taking dead as not the opposite of alive, would it not be correct?) If the cat is neither dead nor alive, I agree this is strange, but may not violate excluded middle. But boiling it down to more elementary quantum entities, what about a photon that seems to have followed two distinct paths through an experimental apparatus? The basic point is not that quantum mechanics rules out excluded middle (or identity, or contradiction) as conditions of our empirical descriptions, but the actual entities seem to operate on a different set of logical principles. (Identity is particularly disturbing, the inability to say that this electron here is the same electron as the one that we observed earlier, even though we know that it ought to be…).
I wonder if we are talking across each other. All I’m saying is that the axioms of formal logic apply to propositional discourse and that is all they apply to; but that is not all there is. That, I think, is why logically oriented people get frustrated talking to theists.