"Most" scholars? Russell himself didn't think it was invalid even though he had the most at stake (and he was one of the more arrogant and defensive philosophers of modernity). In fact Russell gave up mathematical logic as a result of Godel's work, and admitted that it's impossible to prove the lack of contradictions in an infinite system, which is a tacit acceptance of Godel.

Furthermore, it's openly acknowledged that Godel's theorem can only apply internally to a system in which proof comes from within the system. This not only absolves Godel's theorem from the critique you raise, but it also shows how it is applicable to mathematics, which is a system whose logic is only derived internally.

What Godel did is invalid as he uses invalid axioms so you cant then say he proved anything


It is a shame the theorem is named after Godel as what Godel proved was invalid. When Dean says Godels theorem is invalid he is refering to what Godel himself did and the theorem that Godel himself proved is invalid

When Godel got his theorem it was the first one on the market and if people had of looked at his proof for the theorem at the time they would have seen it was invalid as he used invalid axioms thus making his theorem invalid

Godel himself proved nothing -irrespective of what others have done- as his proof was based on invalid axioms

You cant say Godel proved this he proved that as he proved nothing as his proof was based on invalid axioms


It maybe openly acknowledged that Godel's theorem is applicable to systems that is not the point. The point is how Godel proved his theorem is invalid as his proof is invalid thus the theorem he got from his proof is invalid-irrespective of what others have shown or done

As I say its a pity the theorem is named after Godel as what he did is invalid

There's no path to enlightenment as effective as repetition. I love nothing more than to flog my brain continuously with the same utterance until it is reduced to a fine grey mush.

Please sir/mam I beseech thee: Pummel us about our heads and faces with that sweet, sweet, wisdom until we see the face of god!

I don't know what your problem is with G?del, nor do I have sufficient expertise in this domain to provide an academic argument. You'd think that if true such a major development in the history of math and symbolic logic as an invalidation of G?del would make somewhat of an impact in the academic world -- and yet Colin Leslie Dean does not have any journal publications that I can find using various academic search indexes (JSTOR, ISI, and PubMed). But as much as you underline, bold, and italicize your point that his theorem is invalid, your point is NOT shared by many people in academia. In fact, to the best I understand it, the whole idea of Godel is that it is anti-axiomatic, that's the whole point. In other words, proofs are possible within self-contained mathematical systems, but that doesn't make them generally true.

You assert that Russell had rejected G?del, but here is what Russell himself said about him (from a letter written in 1963):


If you're interested, here are a few references from the academic literature that give a pretty good appraisal of G?del and his importance, without resorting to judgements of validity or lack thereof (which is to some degree besides the point). I have PDF files of all of these, but you should be able to get them if you have online access to a university library.

1. Kurt G?del: Separating Truth from Proof in Mathematics
Keith Devlin Science, New Series, Vol. 298, No. 5600. (Dec. 6, 2002), pp. 1899-1900.

2. The Reception of G?del's Incompleteness Theorems
John W. Dawson, Jr. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1984, Volume Two: Symposia and Invited Papers. (1984), pp. 253-271.

3. What the G?del Formula Says
Hugh Lacey; Geoffrey Joseph Mind, New Series, Vol. 77, No. 305. (Jan., 1968), pp. 77-83

4. G?del's Theorem and Postmodern Theory
David Wayne Thomas PMLA, Vol. 110, No. 2. (Mar., 1995), pp. 248-261.

5. Future Tasks for G?del Scholars
John W. Dawson, Jr.; Cheryl A. Dawson The Bulletin of Symbolic Logic, Vol. 11, No. 2. (Jun., 2005), pp. 150-171.

i did not say Russell rejected Godel

what I said was Russell abandoned the axiom of reducibility he took it out of 2nd ed PM following - following criticisms of it from Wittgenstein- but Godel still uses it
as he states -

As I say Russell took it out of 2nd ed PM

and AR is considered invalid -then and now