From what I've read, Godel's Theorems are able to make definite statements about mathematics because they are in fact metamathematical proofs, and thus not self-referentially subject to the incompleteness of mathematics or any rigorously logical system that they demonstrate.(adsbygoogle = window.adsbygoogle || []).push({});

What exactly frees metamathematics of the same logical pitfalls as normal mathematics, though? In attempting to answer foundation problems, it still relies on the axioms present in proof and model theory to get anywhere, and thus is still particularly subject to the second incompleteness theorem, yes? Or have I misread things somewhere/ is my interpretation or impression of Godel's work misguided?

I'd appreciate any clarification. Thanks in advance.

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# Metamathematics and Godel's Theorems

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