Re: Goedel applied to the real-world

From: Acme Diagnostics (LFinezapthis_at_partpostmark.net)
Date: 10/31/04 

Date: 31 Oct 2004 10:54:07 -0600

Torkel Franzen <torkel@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinezapthis@partpostmark.net> writes:
>
>> But like I said, Goedel's Theorem demonstrates that we can
>> discover things on this level or at least close to it. We can't
>> seem to compose a theoretical logical system of some complexity
>> that is complete.
>
> We can easily define complete systems having any specified
>complexity. Or, if you have in mind an informal sense of "complexity":
>we can define complete systems that are grotesquely complex.
>
>> But Goedel doesn't necessarily apply to the real-world and
>> we already know it doesn't apply between levels of description.

<unsnip>
>> Or so I've heard.
</unsnip>

> It makes no immediate sense to say that Godel's theorem does or does
>not apply to the real world.

Well, let's see. Follows the best short description of Goedel's
Incompleteness Theorem available anywhere, compiled by me from
Kent Paul Dolan posts. Dolan is a famous superstar poster, expert
in these subjects with many times the real-world context as
Torkel in many related subjects, most notably here the art and
technique of English explanation as can be demonstrated by
googling him and reading any 10 random posts. I add two
comments in [brackets] relevant to my two above assertions:

- - - - - - - - - - - - - - - - - - - - - - - - - - -

Goedel proved that any set of axioms at least as rich as the
axioms of arithmetic has statements which are true in that set of
axioms, but cannot be proved by using that set of axioms.

[I.e. it is "incomplete."]

That does not prevent that those true things can be proved
with a more powerful set of axioms. [Read: Higher level of
description] It only conveys that the stronger set of axioms
will in turn contain new truths which cannot be proved using
only those axioms.

Goedel's incompleteness theorem only shows that some true
math facts cannot be proved within math, not that none of
them can. (* note at bottom).

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

The above explanation can be confirmed with reasonable
paraphrasing and in some cases exact duplication of wording on
numerous academic web sites of university computer and math
departments, however none capturing the concepts in nearly
such short-copy. I've done that and have posted sample links and
googles in sci.logic. Torkel has previously implied that he
disagrees with those professors, i.e. (paraphrase) that the web
is full of crap about Goedel, in favor of *his* opinions on the
subject which he has generously published on his own web site and
in argumentative Usenet posts.

Besides being the best and most useful short description anywhere
for discussions like the one we were having about determinism, it
is probably the most thoroughly examined one as well. It has
survived the criticizm of numerous experts on sci.logic in which
Torkel contributed the least in terms of helpful explanation. I
posted a recap of that criticism and why it failed in another
long-winded post which I can link upon further interest.

But the more salient point about this particular reply is Torkel
himself, that he argues in bad faith, and is given to short
cryptic posts that add nothing but promote controversy, as
explained in this long-winded but entertaining post containing
unfair insult obviously intended for dramatic effect only:

http://google.com/groups?selm=41016d93$0$90631$45beb828@newscene.com

Applause for that post from sci.math:

http://google.com/groups?selm=_jiMc.5$Hc4.3@dfw-service2.ext.ray.com

About cryptic one-liners, and in response to the above linked
post, an additional comment from Eray (just one paragraph!):

http://google.com/groups?selm=fa69ae35.0407231821.38bc7fa7@posting.google.com

In good faith, some nice things I've discovered about Torkel, and
partly why I like him now <g>:

http://google.com/groups?selm=41028190$0$24581$45beb828@newscene.com

Larry
``
- - - - - - - - - - - - - - -

* Note: In good faith as response to criticism, I promised to
make the below qualification to Dolan's explanation whenever
presenting it in the company of experts. However the distinction
made is irrelevant in context of the determinism argument. It
only relates to the fact that a "set of axioms," while much
easier to grasp in a short piece by non-experts, is only loosely
descriptive of an axiomatic system since such systems include
other things besides axioms (as every 8th grade trig or geometry
student knows). In context of our real-world determinism
discussion, I recommend that it be ignored completely:

Without prejudice to the author: I recommend this explanation
only for dialog, not general publication. This explanation favors
reader's goals over the legitimate academic goals of experts by
approximating theoretical accuracy in favor of explanatory value
and usefulness outside of theoretical context. Upon objection of
experts, or in company of experts, you should expend some
of the explanatory excellence in their favor by replacing the 2rd
and 5th occurrences of "set of axioms" with "axiom system."

L.

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