Re: FOL, ZFC, NGB and Prolog

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torkel franzen wrote:

"galathaea" <galath...@xxxxxxxxx> writes:
-- he was confident
-- like hilbert
-- that the process of proof could comprehend all truth

What actual statement of Godel's do you have in mind here?

-- but in his attempts to prove this assertion

When and where did he try to prove this?
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i have no first hand knowledge of the account of godel's life
i only learn from what i have read
so if you know of places where i am incorrect
i appreciate any specific corrections

however

hao wang wrote a paper that i have in my collection
(JSL vol. 46, pp. 653-659)
where godel gave recollections to hao about his process:

"He represented real numbers by formulas (or sentences) of number
theory and found he had to use the concept of truth for sentences in
number theory in order to verify the comprehension axiom for analysis.
He quickly ran into the paradoxes (in particular, the Liar and
Richard's) connected with truth and definability. He realized that
truth in number theory cannot be defined in number theory and therefore
his plan of proving the relative consistency of analysis did not work.
He went on to draw the conclusion that in suitably strong systems ...
there are undecidable propositions."

this quote i have pasted from a notebook i keep on old newsgroup
postings
where i had first learned the reference
so this should be able to be found online

although i do not consider myself a godel scholar
i have read several books and a small collection of articles on his
life
(as well as, of course, many of the actual technical papers)
and these seem to agree on his development concerning notions of truth
including the mystical later years i mentioned


torkel franzen also started up the male alpha problem with:

Your various comments seem to be based on your personal fantasies.


if there is any place you feel i have erred
i accept technical critique eagerly

however
i feel your comment is intended purely for hostility

it is comments like that
which are why i do not post often in the newsgroups
though i am an avid, regular reader

you are not normally so mean...

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galathaea: prankster, fablist, magician, liar

.

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