>There are three essential errors the author makes. The first error is using an incorrect statement of Gödel’s theorem. The second error is working in a meta-system that implicitly assumes its own consistency. Although non-obvious, it is well-know to mathematicians that such a system is inconsistent. Thus it is not surprising that the author is able to derive results that contradict Gödel’s results.
>The third error is his attempt to find a flaw in Gödel’s Proposition V. As the author notes, Gödel omits the details of this deduction, leaving it for the reader to fill in. Unfortunately, the author has not correctly filled in the details himself. Perhaps Gödel (and other writers) could have been more clear about the distinction between the sub-language of ‘number-theoretic relations’ and its interpretion as a relation in the meta-language by explicitly writing out the uses of the ‘evaluation’ function converting the sub-language into the meta-language. It is indeed tricky to get this part right. I refer the reader to any one of the formal computer-verified proofs to see the details about how this can be done properly.
> ...finding an error in the original proof is uninteresting (from a mathematical perspective). Even if Gödel’s orginal proof contained a minor error, there are plenty of modern (and computer verified) proofs that establish the theorem.
Shockingly, there appears to be a fatal error in Godel's famous Incompleteness Theorem. Read more at the link above, and for more details see also: https://www.jamesrmeyer.com/ffgit/godels_theorem
