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How exactly would you distinguish between 'proven' fundamental and merely 'considered' fundamental?

I mean, sure, some laws like Heisenberg's Uncertainty Principle can be proven mathematically from the axioms of a theory, but how exactly would that make it more fundamental than a law that is considered an axiom itself?




I'm not too knowledgeable in these things, but I'd guess it'd really just depend on the same things everything else does in science: supporting data.

Certain things have an immense amount of supporting data.




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