Re: Godel's Incompleteness Theorems

[Tim Gwinn <***>]

Jamie,
See interposed comments.
Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of James N
> Rose
> Sent: Sunday, March 28, 2004 5:10 PM
> To: ***
> Subject: Re: Godel's Incompleteness Theorems
>
>
> Will give it a go, Tim. Using two frames of reference.
>
> My own in the first.  Russell/Godel in the second.
>
> A.  There are criterial conditions for existence.
> Even and especially for existence which includes
> 'mutual exclusives'.  [a precludes b; b precludes a;
> yet, a nor b nor not-a nor not-b are precluded;
> and, predicated condition-states exist where a and
> not-a are 'co-present' even if not simultaneously
> 'instantiated']
>
> The first pair of bracketed conditions are spatial and
> relativistic; the second statement is quantum mechanical.
>
> Both are informational.  In their description and in
> content.
>
> The extremum of the criterial conditions is 'existence'
> in which the extants are not even co-considerable - yet -
> they are posited both to 'exist' none the less.
>
> That is, there is the situation where evidencing of an
> 'a' and its 'complement-exclusive' share depictable aspects
> -and- are convivial to/within a general space where one
> or the other can/will exist when the other doesn't.
> [They are 'built' of the same 'stuff']
>
>
> There is also the situation where there is no direct
> evidencing or depictable cross translation possible
> under any circumstances, yet for there to be logical
> wholeness, both must have an existential essence in a
> space which is so wholly inclusive that they are not
> precluded there, even if they preclude one another.
> [They have no way of communicating or recognizing
> or acknowledging the other's existence, but they
> -do- "co-exist" within a space that is competent and
> prevasive enough to the extent of being able to harbor
> them none the less.]
>
> The first image would include particles and anti-particles
> which can exist independently but not together. YET are
> qualia-interactive such that they WILL interact when
> proximate to one another.  Also, waves which are both
> entity -and- environment-for-other-waves (resulting in
> normal wave-interference phenomena).
>
> The second image would include wave-energy which is so
> dis-synchronous from other wave forms that they can literally
> both inhabit some same unique space and be totally unaware
> or sensitive to the other's presence in that exact same space.
>
> The most extreme case of this would be absolute chaos vis a vis
> any degree of order (or even pervasive order).  Here, the second
> mode would include recursive patterned information, and the first,
> chaos: absolute never-possible never ever recursive in even a single
> instantiation, wildness.
>
> For there to be a viable universe, there must be qualia and conditions
> which embrace and include ALL of the above.
>
> Requisite: coherence, consistency, compatibility.
>
> At least on the Grand/Global, even if not on the Inter-Local.
>
> Therefore.  There must be properties prima-foundational
> which exist -everywhere-.  First and foremost because there
> would be -no- intertier architecture possible otherwise.
>
> The apparatus of existence as we know it would neither hold
> let alone come to be if there weren't primal-mutuals exhaustively
> and perfectly everywherewhen.


As I understand this, it is a realist metaphysical claim. Is that right?


> (Now to Russell/Godel ..)
>
> Which means two things.  First, the extended universe or statement-space
> that Godel -might- have referenced, was set aside as unimportant to him
> in his thrust to define informational insufficiency and highlight the
> limitations of lesser-frames-of-reference.
>
> What has gotten thrown out by G and his followers is that the formal
> statement space hold information COMPATIBLE with the information
> that resides in the region 'beyond its capacity to know about (and
> use in statements that -would render- complete 'selfproof or
> validation' statements.)


I think Godel's Incompleteness theorems do not make any sweeping statement
about limits on information per se. Rather, the theorems have highlighted
that formal mathematical systems are generically not complete, and so in
such systems there will be statements that cannot be decided as being either
true or false from **within that particular system**. In the mathematical
world, one can always go to some other system in which a particular
undecidable statement can be decided. (The trivial case is where the other
system is simply one in which the statement itself is added as another
axiom.)

I'd venture to say that Godel's results ruin the prospects of organizing all
information into one monolithic syntactic, axiomatic system, but does not
impact the limits of information or what can be known per se.


> We -know- something about the external statement/information space.
>
> Godel deduces that that information is not accessible or capturable
> by a lesser system.
>
> I say that that is correct when capitulating to restrictions, but
> importantly INCORRECT when emphasis is placed on compatibility and
> coherence instead.
>
> Godel: our brain processes light in one form, the outside world
> processes it differently.  We will never know true 'reality'.
>
> Rose: our brain processes light in one form, the outside world
> processes it differently. We can know - even if not 'experience'
> the alternative ; we can deduce the spectrum of reality and talk
> competently about all the alternative forms of light, because
> we can open our eyelids and identify the shared informational
> transactions of the external and internal realms.
>
> We can even make true statements on both sides of the retina,
> about both domains, because we can identify their mutuals,
> rather than their information differences.
>
> The grand-frame of reference allows proofs and truth statements
> now no matter where you are, or where you start from.  There
> are real mechanisms of information transform which now enable it.
>
> There -is- a deep group of rules and formalisms which the
> natural world -can- be addressed by, understood through.
>
> Jamie
>