If you could build a machine that was able to generate every relevant scientific fact from first principles, do you think it would be done at some point, or that it would never stop?
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I am not sure I follow. He proved in a consistent system there are unreachable truths. So we agreed to not always have to stay in the system. and so new proof techniques were ok once they made sense to us.
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No, he and Turing have shown that the classical mathematical notion of truth was not self consistent and had to be changed. Values are only equivalent to functions if the function is actually computable.
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I don't mean to suggest that reality does not accord with mathematics, rather quite the opposite. Physics as a mathematical system can surely hold under Gödel. But the only way to 'verify' maths are through logic. But given an extra 'constraint' of reality, can we generate->
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physical theories that are not physically verifiable? Also, are there examples of physical theorems that are unverifiable mathematically, but are physically? Or that are not verifiable either through maths or observation? Does Popper say anything about this?
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