Joined: Oct. 2006
I finally got around to taking Barry's quiz, but I'm not making any efforts to post my answer at UD. Here it is (also cross-posted at The Skeptical Zone):
In my view the differences in this discussion turn on the following distinction.
StephenB wants to argue that it is impossible for the moon to simultaneously exist and not exist. The proposition "The moon exists" and the proposition "the moon does not exist" cannot be simultaneously true, due to the resulting violation of the LNC. Therefore, by the lights of classical logic, "The moon simultaneously exists and does not exist" must be false. Further, any analogous statement regarding any other entity, quantum or otherwise, must also be false. To state otherwise is to abandon all rationality.
However, I would argue not that "the moon simultaneously exists and does not exist" is false, but rather that, within the framework of classical logic, it is unintelligible. It is not impossible that the moon simultaneously exits and and does not exist; rather, that statement is simply unintelligible. Were someone to insist that "the moon simultaneously exists and does not exist" in a conversation about actual astronomical bodies I simply would be unable to unpack what is meant.
Propositions that are unintelligible are neither true nor false. Further, the negation of an unintelligible proposition is not a true proposition, but rather another unintelligible proposition. Therefore, the negation of "the moon simultaneously exists and does not exist," namely, "the moon doesn't simultaneously exist and not exist" is equally unintelligible.
With respect to the relationship between the LNC and quantum phenomena such as superposed states, the question therefore becomes, "have we discovered phenomena that are unintelligible within the framework of classical logic?" Obviously the answer is yes, which is why the implications of quantum mechanics, when expressed in ordinary human language, and reasoned over employing classical forms of reasoning, are so difficult to grasp. Hence the statement often attributed to Feynman, "If you think you understand quantum mechanics, you don't understand quantum mechanics."
Yet the mathematical and empirical foundations generating this unintelligibility are unassailable.
Does it follow from the observation that we have discovered quantum phenomena that are stubbornly unintelligible when expressed verbally due to violations of the classical LNC that quantum phenomena cannot exist? It does not. Indeed, when stated this way, it strikes me as a startling hubris to insist a priori that a system of logic devised by Aristotle must be capable of expressing every possible true state of affairs, and that phenomena that are inexpressible within that system therefore cannot exist.
This, of course, is the conclusion that StephenB and BarryA strive to avoid, as it exposes leaks within what they suppose to be an airtight argument compelling belief in the existence of God.
So we return to BarryA's test question. "Can the moon exist and not exist at the same time and in the same formal relation? The answer to this question is either 'yes' or 'no.'"
My response to BarryA is that he is mistaken to assert that the only answer to this question is "yes" or "no." Indeed, the correct answer to his question is, "this is not an intelligible question."
Myth: Something that never was true, and always will be.
"The truth will set you free. But not until it is finished with you."
- David Foster Wallace