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The implications are really on the concept of language. It proves that there is no language that can be complete; as such, we cannot express a complete system, even if it existed. So a unified theory of everything might well exist, but you wouldn’t be able to describe it. Which is a nice philosophical riddle.



I think that if you allow some axioms, you can describe it. But I'm not sure if it will be called complete.

I think because "(next axiom)" is not defined, it will make your language not mappable to integer numbers and you avoid Godel proof.




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