If you can prove it's undecidable, it creates the same paradox.
What makes you say this?
If I can prove that the problem is undecidable, so can H. H searches through all possible proofs, which must contain that proof too.
If a problem is undecidable, that means no proof exists either way. Otherwise it would be decidable, in principle.
If no proof exists either way, and H searches through all possible proofs, then it will not halt. It will keep searching forever.
Therefore, if you can prove that it is undecidable, then you can prove that H will not halt. And H can prove this too.
So H has proved that it will not halt, and returns false. This causes a paradox.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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