Thank you for your responses, Bruno.
I will reply in return.
As an overview to my original theme, I believe you
missed several key notions. First, yes, I am bothered
by interpretations of Godel's Incompleteness Theorems,
but I avoid getting entangled in debating 'interpretations'
by getting to deeper theorems-criteria and analyzing
those.
When I read the Theorems - which I do not have at hand
to quote - it was apparent that invariant - systemwide
information compatibility was and is a founding requirement --
when attempting to assess and invoke those -situations and
conditions- whereby 'some' information becomes segmented and
partitioned away, producing a 'self-evaluation incompleteness'.
Godel expressed the projection that non-present data or rules
may at some future time be made present and then-inclusive,
allowing for satisfactory completion of true-false statement
assessments; with the always receding horizon ... where new
true-false assessments arise that are undecidable under the new
added information/relations expansion.
But the scenario depends upon the criteria presumption that
no information is permanently incompatible with any other
information.
That is, he begins and foundations his entire assessment
on a true-false statement that is most definitely
Intuitionist. And a constructive keystone as well --
because invariant induction is at the heart of
existence and of mathematics -- before any 'local'
differentiations produces conditional-incompleteness states.
A mathematics and systemic analysis that key on
alpha-omega compatibility are far superior and
more productive than those built on 'incompleteness'.
But I see that no one is doing that, and they
are missing critically important new understandings
because they are not doing that.
As far as your reaction that some of my statements
were 'vague'. You might try re-reading and re-interpreting
them. They were in fact rather explicit. There are
very real relational analogues that scale very nicely
and exactly between tiers of existence and different
fields/subjects/topics also.
You need to think of metaphors as a real-form
of transduction, with all mapping validity retained.
Best of luck Bruno ; someday 'the lightbulb'. :-)
James
Bruno Marchal wrote:
>
> Le 09-juil.-06, à 17:20, James N Rose a écrit :
>
> >
> > from July 2, 2006 (lightly amended and then addended)
> >
> >
> > Bruno,
> >
> > I have found myself in this lifetime to be a staunch
> > OP-ponent and challenger to Godel's incompleteness theorems.
>
> Are they other math theorems you are opposed too?
> To be frank, I could imagine that you believe having find an error. If
> that is the case let me know or try to publish it. I doubt it of
> course. Until now I have been able to find the error of all those who
> have pretended to me having finding such an error.
> Sometimes people does not challenge Godel's proof, but some
> interpretation of it. That is a different matter, and obviously less
> simple.
> Did you realize that I have, just last week, give an astonishingly
> simple proof, based on Church thesis, of a stronger form of Godel's
> incompleteness? Did you try to follow it?
>
> >
> > In the way that they are structured - with the premises
> > Godel preset: of initial boundaries for what he was
> > about to design by 'proof' - his theorems -are- both
> > sufficiently closed and constituently -accurate- in
> > their conclusion and notions.
>
> OK you are cautious. So you criticize an interpretation of Godel's
> theorem.
>
> >
> > _But_ what I find disturbing about them is that they are
> > RELIANT on a more formative -presumption-, which presumption
> > enables an analyst to draw quite a -contrary result- to what
> > Godel announced. A self-discontinuity _within_ his theorems,
> > as it were.
> >
> > Clearly, this:
> >
> > He tacitly identifies any information resident -outside- any that
> > current/known, as -eventually accessible, connectible, relatable-;
> > even if it means restructuring known-information in regard to
> > alternative/new criteria and standards definitions, descriptions,
> > statements. A presumption/definition of universal information
> > compatibility - of all information - whether known or unknown.
>
> You could say this about my proof, or about Emil Post's one, or about
> some simplified version of it. But it is 99% unfair to say Godel made
> those presumptions. You could argue like that a little bit by invoking
> its use of the omega-consistency notion, but then that case is closed
> after Rosser's amelioration of Godel's proof. The Godel-Rosser proof
> does not rely in any way on any semantical notion, not even AR.
> Godel's proof is even constructive and completely acceptable, even for
> an intuitionist.
>
> >
> > It is through this process of "add then re-evaluate" that new
> > paradigms are achieved. But, it is dependent on the compatibility
> > of the -whole- scope of all the information present at that moment of
> > evaluation; and the eventual capacity to coordinate statements with
> > all content addressable by statements.
>
> That is a little vague for me.
>
> >
> > So, his thesis that at any given moment in time,
>
> The only paper where Godel mentionned time is his general relativity
> paper about its rotating universes. Its goal was to convince Einstein
> that "time" could not be a serious primary concept of physics.
>
> > not all information
> > is present or gathered, and that this makes for limited statement
> > making, where some evaluation statements in the data-set may instead
> > be reliant on future/other yet-to-be-included information .. is a
> > worthy logical notion. A closed system may not completely evaluate
> > itself -- some evaluations are indeterminant.
>
> In that vague sense I could agree with you, but we are lingering on
> many ambiguities.
> It is no more clear why you say you challenge Godel, at this stage.
>
> >
> >
> > But, instead of focusing on the random evaluation moment, think
> > about what that presumption of 'eventual includability' dictates:
> >
> > It heavily defines that we -can- (right now) state -something specific
> > and projective- about the qualia and nature of knowledge and
> > information
> > -- currently -beyond- the bounds of actual experience and encounter and
> > access.
>
> You jump from mathematical logic into the cognitive field. For this you
> need to say exactly how you do that. What are your bridges? (I show
> comp makes such an endeavor possible, but I agree that in the
> literature such a step is most of the time made in an wrong way ... We
> need to be very careful here.
>
> >
> > It also asserts: information 'unknown' is compatible with and
> > eventually relatable with information 'known'.
>
> Godel just says that: IF a proposition p is undecidable in a theory T,
> then you can add p, or add ~p, as possible new axioms for T without
> making the new theory inconsistent.
>
> >
> > The first foundation of Godel's '"I can't decide about that" Theorems'
> > is the contrary moot statement: 'I -can- decide about -everything- and
> > here's why'; -- which is a contradiction of logic.
>
> The negation of ~Bp is Bp (not B~p). (Bp abbreviating I can prove p).
>
> > That is:
> >
> > The "limited" set can make true-false statement about the -totality-
> > of existence (internal and external to its bounded known-ness); but,
> > it cannot guarantee it's own true-false statements (without some
> > added 'external' information, made eventually internal to a boundary).
> > At which point, some/all old non-decidables would be rendered
> > decidable,
> > and, -new- undecidables would arise, apparently.
> >
> >
> > I would say, the logic of future science and knowledge is
> > -incorrectly- contrained and defined by current interpretion
> > of Godel's Incompleteness Theorems.
>
> Frankly this will depend strongly on hypotheses in fields which are
> outside mathematics.
>
> >
> >
> > Rather, the logic of future science and knowledge
> > is premised in Information and Performance Holism.
> > The unitary interactional and information accessible
> > quality of Existence.
>
> Too vague too me, sorry.
>
> > Which fundamental notion is what
> > Godel ignores and rejects and tries to discredit.
>
> ?
>
> >
> >
> > Where, we CAN in fact make DECISIVE STATEMENTS -about that which-
> > the incompleteness theorems 'conclude': we should not be able
> > to say -anything- at all.
>
> Too vague. A pity, because it looks like a point I make which is that
> on some question the first and third persons will remain mute ...
>
> >
> > You can absolutely place me in the community of thinkers
> > who do not "swallow the incompleteness phenomena".
>
> Not really. I was thinking to mathematicians who just did not take the
> time to study it and to think of its consequence for the natural
> science once they postulate comp (like many materialist
> mathematicians).
>
> > Because
> > my statements/logic are not incorrect
> > and they do identify the
> > flaw/weakness/incorrectness in Godel.
> >
> > He used not a tautology but a self-contradictory tautology logic.
> >
> > If A then not-A ; if not-A, then never an inclusive
> > (A & not A) as long as not-A exists; and since not-A
> > always exists then A is not accessible to evaluate
> > not-A, or perfectly assess itself, (A); HOWEVER, A -can-
> > assert (A¬A) and assess (A¬A) which includes (not-A).
>
> Concerning your use of the word "proposition", I don't understand
> exactly what you mean by the words "exists" "accessible" "perfectly
> accessible", .... The whole sentence is rather hard to follow.
> Godel used this:
> From A -> B and A -> ~B, infer ~A.
>
> Godel did not really use the non intuitionist principle (but readily
> accepted by arithmetical platonist):
> From A -> B and A -> ~B, infer ~A.
>
> Of course Godel was platonist (even set-platonist), but he did it to
> satisfy as much as possible the finititary requirement imposed by its
> goal to solve (negatively) Hilbert's problem.
> Of course with Church thesis, all this is made much simpler.
>
> >
> > All Godel did was give a validation for information
> > hiding and manipulation -- something useful to politicians
> > and economic manipulators and spiritual advocates: You can
> > keep people trapped and powerless by limiting their
> > access to added (ostensibly important) information,
> > that would otherwise allow them to make decisions, which
> > an outer-heirarchy might not want them to make.
>
> You are very unfair to what Godel did.
>
> >
> > Godel's Incompleteness Theorems didn't do Science or
> > Math or Logic any favors.
>
> ?
>
> >
> > Nor the societal future for that matter.
> >
> >
> > The first order rule of 'universality' is
> > requisite non-excludable compatibility and
> > consistency. Even if subset incompatibilities
> > are conditionally allowed, (say matter and
> > anti-matter mutual anihilation)
>
> How do you hope to convince anyone in any fields when you jump from one
> field to another one without giving some bridge(s). Well even when you
> give the bridges, it is hard to get scientist really listening to
> interdisciplinary stuff..., but without the bridges it is akin to
> nonsense, and this can add to the (relatively) sane skepticism of
> scientists in front of interdiscisplinarity .... You don't help me or
> us!
>
> > the fact that
> > they interact at all indicates they -share-
> > 'reaction' parameters; they may not survive
> > interaction but they are 'interactionable'
> > due to shared scope of qualia.
>
> ?
>
> >
> > The most extreme form of universality is forms
> > that 'exist' but cannot even communicate (interact);
> > The possibility of co-existing in the same domain
> > but perfectly non-interactive. "Universality" allows
> > this -and- by doing so completes perfect self-definition.
> > Non-information transferability is umbrellaed in
> > 'the universal' and affirms that there is an ultimate
> > holistic compatibility state for all extancy of any
> > sort or non-sort.
> >
> > The ultimate/absolute "invariance rule".
> >
> > After this, partitioning gets you to
> > mini-rules (like the Godel Incmp Thms).
> >
> > But first and foremost: nothing exists absent
> > of co-existence or 'environment'.
> >
> > With the corrolary: nothing is perfectly self-definied -
> > companion existence is included even if sufficiently
> > distanced to be functionally disregarded for local purposes.
> >
> > Which then leads to the logical deduction that no
> > 'clone' or -seemingly- "duplicate" can ever be.
>
> ?
>
> > No 'perfect replicate' persona is possible -- without
> > the perfect replication (without ANY variance) of the
> > entire rest of the universe as well. No matter how
> > uncannily close in replication, each individual must of
> > needs, be its -own persona-.
>
> ?
>
> >
> >
> >
> > But the first order of business is to clean
> > house and get out from under Godel's mis-leading
> > authority & ideas. !
>
> Godel was a modest researcher who solved one of the most hard question
> by Hilbert.
> He was so modest that although a high percentage of its writing is
> philosophical, he will rarely publish them because he was not
> personally satisfied.
> Godel's theorems in logic has been very fertile, a big part of
> mathematical logic borrows from Godel ideas.
> His incompleteness 1931 paper is still today one of the better
> presentation of its first incompleteness theorem.
> As a mathematician, he has been a giant, even if you forget its
> "incompleteness" contribution.
> How can you make so big statement?
>
> Have you read any book by Hao Wang? It is a very good expert on Godel's
> life and work.
> Do you know the work of Judson Webb? [ref in my thesis]
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
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Received on Thu Jul 13 2006 - 03:46:29 PDT