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So 'logical' is obviously not the correct term I was looking for, in relation to the two-slit experiment or Schrodinger's cat.Quantum theory is logical. So is Schrodinger's Cat. They describe things in terms of probability, which puts them firmly within the fields of inductive logic and statistical analysis. Quantum physics does not violate any rules of logic, although it is also a relatively young field of study that we still have much to learn about.

I see a lot of abuses of supposed "logic" from people in this thread. I wonder if I accidentally caused that. I'll say that I've formally studied symbolic and modal logic at a university and I've gone beyond just what I learned in class. When I use the word, I mean it in a much stricter sense than just "reasonable."

I will say that, according to epistemic logic, we know that the impossible does not exist. So any claims about a being that can "do the impossible" are, by their very nature, illogical. There's not really any way to have a logical conversation about a conception like that.

There are some forms of nonclassical logic like paraconsistent logic where these discussions could take place but paraconsistent logic is often considered to be outdated in favor of multi-value logic and Bayesian analysis. These forms of nonclassical logic aren't meant to imply the existence of the impossible, either, but to help form an understanding when there are apparent contradictions in our data.

ETA: I should point out that this doesn't mean that conversations about things outside of logic are unproductive or can't be meaningful. That position is called "Logical Positivism" and it's been debunked for nearly a century now. It's just that this is more about theology and scriptural interpretation than logic.

Aesthetics and ethics are also examples of fields outside of logic, or that are "illogical" and I don't think it's reasonable to discount these entirely, either.

Non-intuitive, perhaps?

Would the same categorisation apply to the principle of the Trinity?