Re: Godel's Incompleteness Theorems

[James N Rose <***>]

Thank you Judith, thank you Tim, for the invaluable
citations, both RR's and Rashevsky's.

I wish that I had come along sooner, that I had reached
these thinkers, instead of wandering the path less taken
as I did.

I too, Judith, consider math to be simply 'another language'
as your father did.  And I can't begin to tell you how many
mathematicians/scientists balk at that notion; though some
dimly give it deference in the vocabulary of semiotics and
such.

I'm a pattern sensor, a metaphor identifier and analogue-ist.
To me, correlants are everywhere - simple patterns in alternative
guises - if you just know how to see them.

To say that such and such is 'computable' or not, is the same
as saying that memes are cross-mappable into different forms
or not, which is tantamount to saying that information is
transformable/accessible - or not - in certain conditions and
situations.

I give all due respect to Godel's incompleteness theorems, but
I've looked for and in all likelihood identified the relational
memes which the theorems discount and reject .. specifically in
order to break the strictures of Godel's "proofs" .. and get to
the operant and functional domain where natural systemic complexity
has free reign in the real/functional universe .. and could have,
should have, discussable correlations in sentient discourse and
communication.

Rosen strode in both domains of 'the real'.  Rashevsky walked
there, but capitulated to the enormity of the "unknown", finding
it comfortable to accept 'unknowability' as if it were synonymous
with unprovable/unverifiable. Too bad.

RR was excellently more meticulous in the "Syntax & Semantics"
remarks.  Because memes, sense, meaning are the substance of -all
languages- even mathematics, and even when it tries to purge
itself of 'meaning', leaving behind only the bare bones framing
armature of 'sufficiency (to prove minimum requisites of
"correlation")'.

What I don't carry well at the moment is the realization that RR
never looked to find an access route past Godel and thusly to
solidify and identify an accessibility between the world of
limited models and the extended world of the natural.

I think this is why conventional science is having such a difficult
time rising to the panoramic thinking RR was at and expressing. He
was 'there' but couldn't show others how to get there .. in terms
they'd understand.  He had had an insight and revelation, could
assert so many aspects of the differences between the limited and
the unbounded, could talk about the differential qualiae at length
and in all sorts of ways, but he had quantum leaped .. like Ramanujan
.. and couldn't identify an alternative - mundane - path for conventional
thinkers to take to join him.

Waiting for 'companions in epiphany' had to have been a very lonely wait.

What's gratifying for me though is to know that he had at least
identified the incompleteness theorems as hobbled regional
mathematics.  But, he never mounted an attack, in equations or
discourse. Strange.

Since 1995, I've seen such a counter work to be the keystone for
getting to the natural, from the priori.

The General Systems movement is the coda group which should
be championing such an effort.  It couldn't have had a better
President than it found in RR, when he served in that capacity,
but something must have a choke hold on that community and
any attempt to say, "Look, if we are going to have a universal
theorem of systems performances/behaviors, if we feel we can
reasonably identify -completely universal and pandemic- qualities
of being and performance .. in spite of all the the alternative
and new qualia arising in emergent ways .. then we are going
to have to clearly and unequivocably show that Godel restrictions
are surpassable in real, natural, provable ways .. because the
scope of 'the natural' is nothing less than the scope of the
already competently functional co-involved co-interacting
universe."

This goes to my question to Howard here last week, did he
see any 'life qualities' in the realm of physics.  He answered
'no'.  Well, that was his answer to me in 1972 also, when I was
running around talking with Walter Elsasser and I. Prigogine
also.  (I could only kick myself now for not having identified
and contacted RR back then.) 'No' is not an acceptable answer
in my book (sorry Howard).

Several things are going on here, and they all resolve around
transpositioning across Godel limitations.  In the meme sense
of things, I comfortably note that electrons filling and
emptying the valence shells of atoms are tantamount to
respiration in the higher tiers of metabolic organization.
Going so far as to say that unless atoms 'respire' in this
way on a consistant and constant basis, no living creatures
'breathes' either, because atomic respiration is the floor
phenomenon of the developed one.

That doesn't make atoms 'alive', but it semiotically and
memetically makes them PREanimate instead of INanimate.
A significant shift in paradigm.

What it also -does- is makes us re-look at a Godel
mapping of the related tiers.  Even if a system bounded
by Godel axioms exists, it does so as a -natural member-
of the extended sapce of information and relations and
proofs. It -has a relation and relevance- to the rest
of nature and information.  That pre-relevance is already
a bridge between the information domains which 'incompleteness'
rejects as accessible among one another [if it were
directly accessible then the information of the exterior would
be incorporable/incorporated and therefore make 'self-proof'
possible; however even without direct presence, just the
fact alone that there is sufficient compatibility _to_
-eventually- access such 'potential/other' information
and establish meme correlates and subsequent 'proofs'
even under alternative (expanded) conditions, is strong
enough grounds to show that some models and the natural
are compatible and relatable].

There do exist reductionist type principles I rely
upon.  I point specifically to an identifiable property
that is relevant to all tiers, systems and qualia
of existence.

One of the principles is that systems require incompleted
degrees of freedom - option spaces - to enact in.

In a sense, they require the unknown, as long as it
is knowABLE.

Conventional thought holds that anything less than completely
known, is 'incomplete' and a deficient state of being (per Godel).

In point of fact, there are knowable _characteristics_ between
the interior and exterior of Godel spaces even if specifics
aren't identified or instantiated. And that aspect is complete
and pandemically universal, which breaks the back of the
Godel paradigm.  Any system which is sufficient to have
models or subpartitionable spaces must a priorally be universally
whole in generic properties and extendedly consistent in
all regions/domains/aspects.

"Local" is insufficient to generate "global". "Global',
even if only as potential, must exist prior to any
"local".

The 'natural' has preminent requisite qualities which can
be identified, whether exhaustively accounted for or not.

Jamie