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Gödel's incompleteness theorem is one of the main things that I like pointing to when talking about stuff like this, thanks for bringing it up. Its a good supporting piece that helps show there are limits to logic and knowability. I think physics models will eventually have their own version that puts theories of everything in jepoardy.
I do think our current physics theories are inaccurate at the extremes. To quote Zach Weinersmith: