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From: Scott H on 23 Sep 2009 22:35
Well, I hoped you'd like it.

If you see an actual error in the essay, feel free to let me know.
From: Scott H on 23 Sep 2009 22:36
Well, I hoped you'd like it.

If you see an actual error in the essay, feel free to let me know.
From: Newberry on 23 Sep 2009 23:38
On Sep 23, 6:40 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Scott H <zinites_p...(a)yahoo.com> writes:
> > On Sep 23, 5:46 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> >> As said, I can't really fathom the exact nature of your confusion --
> >> taken literally much of what you write is simply nonsense [...]
>
> > It isn't nonsense. I've read Goedel's manuscript and the proof I've
> > given follows his.
>
> You haven't presented any proof in the usual mathematical sense, at
> least in the essay on your site. The incompleteness theorems appeared
> very advanced, difficult to follow, at the time they were presented. As
> usual with such things, they are now regarded as commonplace, and
> various matters that were once obscure have been clarified through
> decades of subsequent work in proof theory and recursion theory. Gödel's
> original paper is not best source for learning this stuff. (And your
> quoting Gödel's original statement of the incompleteness theorem in your
> essay is bafflingly pointless.)
>
> > Your attitude reminds me of something Wittgenstein wrote about the
> > Liar Paradox: that "it was a useless language game, and why should
> > anybody be excited?" To date, I don't know why we shouldn't.
>
> Anyone is of course free to be excited about anything. As to the liar,
> pondering it has led to many important insights, in philosophy and in
> logic, including Tarski's theorem on undefinability of truth, Kripke's
> theory of grounded truth, etc.
>
> My attitude is not of much general interest, but my suggestion is by no
> means that we shouldn't think about various logical conundrums, or
> reflect on the possible philosophical significance of this or that
> technical result in logic. I only suggest that if one is to contribute
> meaningfully to our understanding of these matters, in the sense of
> technical philosophy or mathematical logic, it is necessary to take into
> account the work that's already been done, relating one's insights and
> ideas to the actual intellectual interests of professional philosophers
> and logicians. In case of "infinite reference", for example, one would
> expect to see some mention of Yablo's paradox and such matters. (Yablo's
> paradox, like many other paradoxes, can be made to do actual
> mathematical work, e.g. in establishing the closure ordinal for various
> kinds of inductive definitions.)
>
> From what you say I presume you're an autodidact when it comes to the
> incompleteness theorems. One of the dangers in being an autodidact --
> and I say this as a fellow autodidact -- is that it is often very
> difficult to assess with any accuracy whether some idea, some line of
> thought, that springs to mind, is likely to have any significance or
> interest, from the point of view of the professional researcher; without
> feedback from those in the know

Jargon and group think will not help us to solve the outstanding
problems of the foundations of mathematics.

> it's very easy to get stuck on some
> apparently brilliant but in reality vacuous insight, thinking it the
> bee's knees, basking in the warmth of the feeling of having really
> gotten to the heart of something. The possibility that this might have
> happened to you is something you'd do well to consider.
>
> --
> Aatu Koskensilta (aatu.koskensi...(a)uta.fi)
>
> "Wovon mann nicht sprechen kann, darüber muss man schweigen"
>  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

From: Frederick Williams on 24 Sep 2009 04:27
Scott H wrote:

> My proof is based on the one in Goedel's original manuscript.

Have you read it? Did you understand what you read?

--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.
From: Frederick Williams on 24 Sep 2009 05:55
Aatu Koskensilta wrote:
>
> ...
> cleared up -- but perhaps, having died over fifty years ago, you no
> longer recall Kreisel's explanation...

What?!

--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.
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