This is debunked, but maybe a comment about how this relates to Godel's theorems: 1) the first Godel's theorem says that if a theory of arithmetics is complete

This is debunked, but maybe a comment about how this relates to Godel's theorems: 1) the first Godel's theorem says that if a theory of arithmetics is complete then it must be inconsistent, 2) the second is that a theory of arithmetics cannot prove its own consistency, specifically if it proves its own consistency then it is actually inconsistent. This thesis (with an invalid proof) says "no consistent theory of arithmetics can exist", regardless of whether it's completely complete.