principle of noncontradiction

The traditional source of the Principle of Contradiction is Aristotle’s Metaphysics where he gives three different versions.

ontological: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.”
psychological: “No one can believe that the same thing can (at the same time) be and not be.”
logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.”

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Ontological version is just a word play. The word "belonging" is, well, the word "belonging". It is obnoxious to ascribe physicality to it.

Psychological version is not interesting. Moreover, most of us have immense capacity to believe in outright contradictory statements. (Yes, even if we are aware of them.)

The only proper domain for this principle is logic. (In fact, this is the most basic principle of logic.)

Some physicists claim that the quantum world operates with respect to a logic that is different than that of the classical world. By ascribing physicality to logic they are effectively endorsing the ontological version of the principle of non-contradiction. I sincerely think these people are very confused. Neither classical or quantum world operates with respect to any logic. Logic is too contingency-rich to be physically embedded. The sentence (P & not P) is deemed to be false by the principle of non-contradiction. Nevertheless it is a legitimate sentence, and there is no physical counterpart to it. There is no such thing as a physical contradiction. In fact, the problem is even more basic than this disparity: You can not even write a physical sentence P. Which language will that sentence be written in? What makes you think that the reality is revealing itself in its full nakedness before your eyes?

There is a reason why "non-contradiction" is called a principle. It is taken as an axiom because it can not be proven from primitives:

As is true of all axioms, the law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the grounds that any proof or disproof must use the law itself prior to reaching the conclusion.
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Like all other principles, this one is also human, all too human. Its humanness stems from the fact that only stories can be wrong.

Perhaps we should stop using the phrase "Not Even Wrong" as a derogatory expression. Who are we to insult nature?