Math can answer almost any question
The logic question that almost everyone answers wrong
“In a previous post you spoke of quantum mechanics: here, too, there is no tertium - because quantum mechanics is pure mathematics. Indeterminacy only arises in interpretation. "
And that's where ambiguity comes in. The question is, how precisely is the puzzle posed so that the respective meta-level that the puzzle author had in mind is also accepted as such. When I say “something is”, it does not have to be clear per se which meta level and notion of “being” is meant per se. The mathematically axiomatic one? The philosophically ontological? Furthermore, QM is not pure mathematics, because it makes direct use of empiricism, like pretty much every department of physics. Their methods make use of mathematics or even inspire it. However, the time will certainly come when the interpretation of QM will leave its status as an interpreation stage and move into the regular research status. This is a common thread that has always run through physics. Incidentally, it is completely clear to me how far removed we are from the riddle here. But I don't find that any less interesting.
“The axiom of choice is also inappropriate: either you add it to the axiom system or you don't. The logic is completely unaffected. "
But I didn't talk about logic, I wanted to make a comparison. The axiom of choice was and is a break with "conventional" mathematics and even has far-reaching philosophical consequences with regard to mathematics. The break is precisely that of the mixing of the level of clarity of mathematical concepts.
"And undecidability is something completely different from the proposition of the excluded third party"
Where did I write that? But if you emphasize that: Yes, the two terms are sometimes not as far apart (I'm not talking about equality / similarity) as you think, even if not in the Gödelian sense. In the sense of the stricter logic, one sees this, for example, in Brouwer's intuitionistic logic calculations.
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