Re: Goedel - interesting problem?

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

Date: 6 Jun 2004 12:36:12 -0500

Torkel Franzen <torkel@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinezapthis@partpostmark.net> writes:
>
>> I purposely set up a right to
>> argue from ignorance by characterizing the article in question as a
>> "Masterpiece of explanatory text" and not "A masterful explanation of
>> the Theorem" or even "A correct explanation of the Theorem" in
>> theoretical context. I replaced the aspect of correctness in proper
>> context, editing trade-offs having been made, with a supposed ability
>> to evaluate credentials.
>
>Ok, so you're saying that the summary you quoted is a fine one when
>we set aside the question of how it relates to Godel's theorem

IF I didn't write the article AND IF I claim ignorance of Goedel in
theoretical context, THEN my characterization of the article is
irrelevant to how well the article describes Goedel in theoretical
context.

Regardng pragmatic context then, here are two examples from my
most recent post in which I stated that there are many more than two
examples. I snip to the bone since it appears you found it too
challenging on the first read:

====================================
Excerpt:

Somebody (not to confuse the author with you):
>>Well, I get your point here, but it doesn't seem to relate at all to
>>Godel's theorem. <snip> Analogies are great intuitive tools <snip>

Me: (example #1)
But if Goedel's Theorem is a great intuitive tool, then isn't that a
use outside of the theoretical context of the Theorem? That was my
only point. <snip>

Me: (example #2)
I was reading a piece on physics quite a while ago, probably in
The Elegant Universe IIRC, and there was an entertaining part
about the relationship of physicists and mathematicians.

When Goedel's Theorem came along, in a sense it put mathematicians
(as the author described it) in the same boat as physicists - not
knowing if their proof would hold until confirmed by observations, but
even then subject to falsification somewhat like a scientific theory.
My paraphrase is probably terrible but that's the gist of it as I
recall. I remember talking about it with my wife, but she didn't know
Goedel's theorem. To bad I didn't have Kent's piece then. She would
have understood enough to follow the discussion in no time, while
everything I was able to google on the web was too lengthy or
theoretical for that use.

======================================

And in case your memory matches reading and inferential
ability, I'll repeat the summary of our previous exhanges
because the final point now seems critical!

>Torkel Franzen <torkel@sm.luth.se> wrote:

You said:
>>"Godel proved
>>that even mathematics is full of contradictions."

You snipped this from my reply:
>I would need to know if "full" is
>correct or the general concensus.

So that you could think yourself clever with:
>>It's complete nonsense, though.

I reminded you about that with:
>I did not accept "full."

To which you did not respond in your next reply.
- - - - -

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.
- - - - -

You said:
>> Since you don't claim to know anything about Godel's theorem or its
>>proof,

For which I needed to clarify your muddled logic with:
>Note that "don't claim to know anything" is not the same as, "claim not
>to know anything."
- - - - -

You said:
>>text by Kent Paul Dolan that you quote
>>promotes misconceptions quite unnecessarily.

Not being an expert in Goedel's theorem, I asserted confidence in
the author's credentials, then described sufficiency of same and asked:
>...Are you such a Phd by any chance?

To which you did not respond.

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.
- - - - -

I said:
>Stupidity is the difference between ambition and achievement.

Which you seem only too happy to continue demonstrating with:

I said:
> I wound up writing 500
> lines of explanatory support.

To which you added another unsupported opinion that:
>>... your various comments were nothing to the point, since they
>>made no distinction between accurate summaries of Godel's
>>theorem and vague or incorrect blathering about it.

*When you find yourself in a hole, stop digging!*

=======================================

Larry