Re: My investigations into Godels Incompleteness Theorem

Peter_Smith wrote:

So reasonably enough I thought it was the argument starting from
w-consistency you were talking about as not being well represented. I
gave evidence that it was well-represented. And so I was consequently
puzzled by the fact that the first quote you gave to support your case
mentioned w-consistency!

Yes - they all explained that they weren't going to include this
stronger theorem (which was my contention, not to be contentious, of
course.)

Around here, the working rule is that if it is published it must be
true, and if it hasn't been published then the author is a crank. So I
first listed some instances where the author himself admitted that he
was not including the stronger theorem. (Then I listed some examples
where Rosser's theorem was not mentioned at all.)

I like incompleteness in logic, not incompleteness in texts. For 40
years Gregory Chaitin has been bragging that he made an improvement to
Godel's weaker theorem, never mentioning Godel's stronger theorem or
Rosser's stronger yet. Now does that make any sense?

That's why I said I was lost. Now you are
talking about the Rosser proof, it seems. Well, whatever.

My sense is that the mathematically ept student who wants to get to
grips with incompleteness proofs is stunningly well provided with a
range of wonderful textbooks (with different emphases to be sure).

"Emphases", 'eh? What a euphamismm for an incomplete text.

A situation to celebrate rather than carp about, I think :-)

No carping here - simply trying to set the record straight.

C-B

(Speaking of which, these other theorems are not actually stronger.
They merely use different premises. This become clear if we formalize
the proofs, by expressing them in any Computationaly Based Logic.)

.