LS Re: The four levels


Magnus Berg (MagnusB@DataVis.se)
Thu, 2 Oct 1997 03:40:33 +0100


Hi Doug and Lila Squad!

>"In 1931, the Austrian logician Kurt Goedel devastated Hilbert's and
>Russell's hopes of creating a perfect formalization of all mathematical
>reasoning. Goedel had demonstrated that there were undecidable
>propositions in any consistent axiomatic system of the Hilbert-Russell
>sort, propositions based on famous paradoxes of logic that had plagued
>logicians ever since the Greeks...What Goedel had left unsettled,
>however, was the question of whether, given an axiomatic system and an
>arbitrary proposition in it, one could determine mechanically whether
>that proposition was undecidable in that system." Page 485.

I'll continue on the theoretical trail one moment, bear with me.

I'm not acquainted with Hilbert-Russel systems but I assume they are
not always, I think the word is, complete. A complete axiomatic
system is where every proposition is decidable. One might wonder
why anybody would want to construct an incomplete axiomatic system.
Generally, because the more powerful and expressive a system is,
the harder it is to evaluate propositions. And to describe 'reality',
very powerful systems must be used.

Now, what has this got to do with the MoQ? What we should do with
the static levels, is to construct a consistent and complete
axiomatic system in which it is possible to express any static
phenomenon. It's probably better to construct four systems, each
corresponding to one level. It's of course possible to use various
already existing systems for this. What we gain in splitting
the systems up is the same as the old 'divide and conquer' approach.
What the MoQ provides is the glue between the systems, which
must be equally waterproof.

This 'divide and conquer' approach is partly what makes the MoQ
superior to SOM in describing static phenomenon, and we must
use it wisely. We must not extend the systems beyond completeness,
because then, we're entering the domains of DQ.

This might sound as if we just think real hard, we will eventually
be able to capture DQ within these systems also. I don't think we
need to worry about that though. For example, today it looks like
quantum flux is very much influenced by DQ, (which would actually
contradict the fact that each higher level is more dynamic than
the lower, which in turn is an argument to include it in the
inorganic level... well). Maybe we'll one day be able to describe
quantum flux as complete as our description of matter is today,
but there will always be indecidable dynamic phenomenon somewhere.

Here's another big difference between the SOM and the MoQ. The
SOM either tries to explain 'reality' with one gigantic incomplete
axiomatic system, or 'gives up' and says it's impossible, don't
bother. The MoQ on the other hand has the freedom to explain as
much of 'reality' currently possible and leave the rest to DQ,
and still be amazed by and have faith in DQ.

>
>Many truths to you,

Are there more than one? ;-)

        Magnus
>

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