*Post by Khong Dong*https://qr.ae/pNvAdF

which should be a *summary* of why Gödel's 1931 incompleteness paper is

an invalid argument (1st Incompleteness statement anyway).

There are more reasons than those detailed in the summary, but if you'd like to correctly, technically counter argue the summary as it is, you could of course

make yourself be heard.

Comprehensive reply from Alex Eustis, Ph.D. Mathematics, University of

California, San Diego (2013)

No, that's not possible. Even without fully understanding the substance

of your complaint, I can surmise that you're wrong, and with as much

certainty as it is ever possible to have about anything.

If all of Gödel's results happen to be complete bunk because he wrote <

instead of >

or something like that, then there is absolutely no chance that nearly a

century's worth of scrutiny by the whole worldwide Mathematical

community somehow missed this — and yet you, some random dude with a

B.A. in Mathematics and an inflated ego, are the first person to notice

this error. I mean, how arrogant is that?

This paper was a breakthrough — it more or less kicked off the entire

study of Incompleteness, Independence, provability logic, and so forth.

But just as we can do Galois Theory without having to refer back to

Galois’ original notebooks that he frantically scribbled the night

before his fatal duel, we can today do Incompleteness Theory and prove

the independence of various statements from certain axiomatic systems

without directly citing Gödel's 1931 paper.

For instance, according to Wikipedia,

Stephen Cole Kleene (1943) presented a proof of Gödel's

incompleteness theorem using basic results of computability theory.

Franzén (2005, p. 73) explains how Matiyasevich's solution to

Hilbert's 10th problem can be used to obtain a proof to Gödel's first

incompleteness theorem.

Smorynski (1977, p. 842) shows how the existence of inseparable

sets can be used to prove the first incompleteness theorem.

Chaitin's incompleteness theorem gives a different method of

producing independent sentences, based on Kolmogorov complexity.

So even if you happen to be right (which you aren't), and there is some

fundamental, uncorrectable error with Gödel numbering (which there

isn't) — can you find an ingenius rebuttal for all these proofs, and

more? Can you single-handedly overturn a century of Mathematics?