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> I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.

That's what ZFC does.

While `effing yourself with recursion is a takeaway from his finding, to me at least, it's a striking limitation of formal methods of 'sufficient ability'. There exists a completely understandable query that has no well defined answer. Back when it was felt that mathematics could somehow prove itself, this must have been a crushing blow.



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