If I could ask armchair physicists and amateur logicians to do one thing, it would be to put Schrödinger's cat to sleep - or just leave it a saucer of milk and ignore the damn thing. The cat is never both alive and dead. Its state is simply inaccessible to those outside of the box.
I'm tired of logicians invoking the wave-particle duality, as well. Often, it is done rashly. Take this gentleman, who says:
I'm interested in the names; and modern physical theory seems to indicate that photons for example can be both a wave and a not-wave.
Then the issue is that the current theory of physics has incorrectly explained the concept of a "wave" if they put it in an opposition to "particle" that is no longer proving trustworthy. That abductive model no longer provides consistent results. The writer here seems to be equivocating the term "particle" and "not-wave," when it seems to me that current physical theory is discovering that the divide between wave and particle was incorrect.
Can something behave both as wave and particle and not behave as both wave and particle, at that exact moment? Or, to touch on Buddhist logic, can something be both wave and not-wave yet also not be both wave and not-wave? Can an instrument in a lab record that at a single moment of observation, we find both the presence of a wave and absolutely no presence of a wave?
We can reduce this to symbolic logic. "Something is both wave and not-wave" will be symbolized A. Thus, "Something is not wave and not-wave" is not-A. So, is it "A and not-A," or is it "A or not-A," in the end?
I was likewise disappointed when S. I. Hayakawa dismissed the Aristotelian Laws of Thought by asserting that they do not accommodate the ambiguity of natural language. This is an imposition on the Laws of Thought.
When a logician of the classical bent argues that "Something either is or is not," symbolized p v ~p, she is asserting something about the term, not the language used to express that term.
As Aristotle wrote in Metaphysics:
And it will not be possible to be and not to be the same thing,
except in virtue of an ambiguity, just as if one whom we call 'man',
others were to call 'not-man'; but the point in question is not
this, whether the same thing can at the same time be and not be a
man in name, but whether it can in fact.
Clearly Aristotle is speaking of the reality of a term being described, not merely the language.
Aristotle is dear to me, but dearer still, of course is the truth. However, rejection of the Laws of Thought based on perception and expression is faulty.
Imagine that I am given a delicious chocolate cake. Sadly, however, the cake depicts Caligula sodomizing an effigy of himself while dashing infants on marble steps (those of proper age to watch HBO clips, remember this scene from Curb Your Enthusiasm?). Thus, I could say:
"This cake is good, and it is not good."
The first use of "good" implies that it is delicious, and wholesome. The cake is not rotted. It tastes like chocolate. It fits my subjective impression of what a chocolate cake should be. However, it is not morally good from my standards. It celebrates what I would consider evil. Or perhaps, I simply mean "not good" and in "not of good taste."
The ambiguity that seems to defy the Law of Excluded Middle can be cleared up by defining the terms. If we have a situation where I define an action as "moral" based on what someone argues is subjective, and someone else deems it "immoral" based on their own standard, the issue does not lie with the concept, but with our clashing perceptions.
However, I could not logically assert that "There is something on my fork and there is also in no way, shape, or form anything on my fork."
Obviously, applying the Laws of Thought to language, which is inherently ambiguous, is not always simple. Nor does the statement "A v ~A" imply that we know which side of that exclusive disjunction is true! It does, however, posit that ultimately (Law of Sufficient Reason, mayhaps?) a proposition about a term will either be true or false. Applying those Laws to the external reality that language attempts to express is necessary!
p ~p ~~p
T FT TFT
F TF FTF
However, I do agree with Einstein as he wrote to Schrödinger (wow, agreeing with two revered scientists, I'm really taking a risk here).
You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality—if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.
One must presuppose reality, and yet can only speak of what is observed. The Law of Excluded Middle simply asserts that thing perceived is or is not. Russell declared this axiomatic.
"Fuzzy logic" does not get around the problem. Fuzzy logicians reject a clear, crisp definition of the A in "A or not-A." So what's the issue?
"A thing either is in some way, or is entirely not."
This is the principle of a contradiction as demonstrated on the Square of Opposition.
"Either this dish contains some amount of meat, or it is meat-free."
Furthermore, fuzzy logic in the wrong hands attempts to do more than simply provide a mathematical model for vagueness. Fuzzy logic still runs into the same sorites paradox of classical logic. By attempting to move beyond the simple values of "True," "False," or their temporary companion "At this moment unknown," fuzzy logic simply introduces a range of partial truth values that still depend on being able to articulate how much something possesses.
"The grand aim of science is to cover the greatest possible number of experimental facts by logical deduction from the smallest number of hypotheses or axioms." - Albert Einsten
Pardon any vitriol and bile on my part. I do not wish to be counted with the rash commentators on logic who assert that those who deny various axioms are attempting to somehow destroy morality or society. I'm working through proofs and I'm simply wondering if the rejection of the Law of Excluded Middle by folks who are not trained intuitionistic logicians comes from a misunderstanding about its claims. Once again, wiser folks would be welcomed to instruct me.