Re: Goedel - interesting problem?

From: Acme Diagnostics (LFinezapthis_at_partpostmark.net)
Date: 06/06/04 

Date: 6 Jun 2004 12:49:12 -0500

Chris Menzel <cmenzel@remove-this.tamu.edu> wrote:
>On 5 Jun 2004 13:23:08 -0500, Acme Diagnostics
><LFinezapthis@partpostmark.net> said:
>>
>> Torkel Franzen <torkel@sm.luth.se> wrote:
>> You said:
>> >>there are statements that can be formulated within the theory, but
>> >>neither proved nor disproved in the theory
>>
>> Which is superseded in all respects of explanation by Dolan's:
>> >>>Goedel's incompleteness theorem only shows that some true
>> >>>math facts cannot be proved within math, not that none of
>> >>>them can.
>
>Acme, in all sincerity, Torkel's formulation is about as accurate a
>statement of Godel's theorem as you'll get in nontechnical language.

Well for my own personal use, that is a useful confirmation. I will
therefore put his statement in my own inventory, perhaps use it in
proper context.

But for the intended readers of the article, it is left vague whether
that refers to some statements or all statements. Not vague to you
because you knew the answer intuitively. Not vague to you because you
will interpret "there are" in the particular immediately and
intuitively, whereas the intended reader will probably not be a
logician, and may be e.g. a music major. The author (also myself) is
experienced in removing these intuitive assumptions of experts in
explanation. His sentence is oodles more logically explicit for
wide-application.

"Theory" is simply not good enough for intended readers. If you ask
100 people of a wide variety of fields what a "theory" is, you'll get
80 Relativity's, 15 "Evolutions", 5 others, and not one "a math." But
if you asked the 100 what is a "set of axioms" you'd get 80 "math's"
but they will know it's not exactly "math," but that it's a sort
of a "math or something" and that's the most they can possibly
understand anyway in the time it takes to read the article.
Probability is integral to inferencing in context, which is what
"useful in argumentation" is, i.e. how I characterized the article.

"Set of axioms" is about as precise a 13-char term as you're going to
get in context.

Chris, in all sincerity, this is why a master of language, but who
additionally understands the theorem very well, is the much preferred
writer, not a logician. And certainly not Torkel who is, in most
proximate evidence, too inferentially challenged for this job
regardless of how theoretically true his statement. It's probably a
problem of objectivity rather than ability (as usual), but the result
is the same.

>Dolan's "explanation" is really quite bad. Most notably, the reference
>to theories -- sets of axioms -- in Torkel's version, as opposed to the
>ill-defined "math" in Dolan's, is absolutely essential to getting the
>theorem right.

(redundant, answered above)

Ok, you simply do not understand the concept of context. We can never
agree in written English because understanding language in the
real-world requires context, context is purposely removed from
theoretical logic, and that is the only way you choose to think in
this instance.

>But this is one of those things that require some study
>to appreciate.

Another David Longley! Here's a quote from Captian Kook of
comp.ai.philosophy: "A little research into areas you know nothing
about may lead you to look at all of this from an entirely new
perspective." You are in fine company! Anybody can say that to
promote any kook theory! Next you'll be posting Quine excerpts!

Upshot: If you can't explain it and defend it in cooperative dialog,
stop with the professor bit. This is the real-world. No privileged
positions here. Put up or shut up, etc. You don't win or cooperatively
analyze a chess game by telling your opponent to go read a book.

>Without it, you'll just be drawn to whatever happens to
>tickle your ears, with no basis for distinguishing truth from fiction.

Ditto. More kook talk. Explain or refrain!

Explain the effect of Goedel's theorem to a music major, etc., who has
never heard the name "Goedel" before in no more words than Kent used.
Make is *useful* in a wide-variety of argumentation, some only touching
upon Goedel in passing, and with the reader never having heard of
Goedel before. And don't forget I lifted the piece out of two posts
long after the fact. He composed his version in no more time than he
would take with any two short newsgroup posts. Piece of cake, eh? All
you need to do that is a clear theoretical understanding of the
Theorem, eh?

>> Upon more criticism of the author's piece, I asked:
>> >I notice that you did not claim a phd, support of a university, etc.
>> >Do you have some pertinent credentials that I could find reliable
>> >in comparison to the author's, some of which I've mentioned?
>>
>> To which you again did not respond.
>
>Google.

Who does that apply to? If Torkel, read my reply to him just preceding
this post. Check logic in the first two paragraphs. Also the
included summary of dialog at the end. Torkel has a major ax to grind
here. He is being too unobjective and there is no way he can tell. He
is too invested in the result. Ability does not apply in that case. I'm
also unfortunately invested because I made a claim which I strongly
believe is correct. That's why cooperative dialog is so important. It
is the only way to overcome our unobjective POVs. But it requires that
you are more invested in the process (dialog) than the result. I am. I
worship at the alter of logic. I would rather be proven wrong in any
issue than denigrate the logical process. If I did that, all would be
lost. But theory isn't enough, and make no mistake, that is the major
rub here, less so the article in question. Theory is subject to paradox
and incompleness. That's what we're arguing about. That's the threat
that I represent to your and Torkel and probably others in this group.

But at the end of the day, we have to seek the facts as they are, not
as they should be. If you refuse to accept that, you will lose in the
eyes of the great majority and in the eyes of the people who matter
most. You will lose credibility.

Larry

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