Le 09-juil.-06, à 17:20, James N Rose a écrit :
>
> Bruno, I reviewed the archive and found no reply.
> I will repeat it again, hoping for your thoughts:
>
>
>
>
>
> 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 Tue Jul 11 2006 - 04:14:01 PDT