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If you could prove reductionism comprehensively you could win not just a nobel prize but probably every nobel prize from now until the end of the institution. "You don't understand, it's true but we don't have the computational power reeeeeeeeee!" All you have is intuition.
It's not like there aren't other valid systems of math. You're just taking a small number of cases and generalizing that everything can in principle be solved this way. It's a circular appeal to the way human cognition works, not a valid inductive proof of universal properties.
