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From: George Levy <glevy.domain.name.hidden>

Date: Sat, 05 Jun 2004 17:50:02 -0700

Bruno

I have read your post maybe five or six times, my hair getting grayer

and grayer everytime. This subject is undoubtedly your profession and

you are an expert at it but I have a lot of trouble following you.

Nevertehless, I have a good feeling to my stomach that you appear to be

on the right track.

You seem to say that you begin with an absolute formulation but end up

with a relative one, maybe the ultimate relative one. Not only that ,

you appear to have solved the paradox of the apparent objective reality

in the context of the ultimate relative formulation. This is good. This

is what I was hoping for. I think that philosophically, the ultimate

relative formulation is the most satisfying one. But this is only my

opinion.

I cannot lead the way but I can be a critic or a friend like Salieri to

Mozart :-). Let's me see if I can convince you to bridge the gap and

maybe take the relative formulation as a starting point. Like Socrates,

let me start with one question. How can you possibly know to begin with

this particular assumption:

* >> I take as objective truth arithmetical truth, and as third person
*

objective communicable truth

* >> the provable arithmetical propositions like "1+1=2", "Prime(17)", or
*

"the machine number i

* >> (in some enumeration) does not stop on input number j", this +
*

Church Thesis + the "yes doctor"

* >> act of faith is what I mean by comp.
*

George Levy

Bruno Marchal wrote:

*> Hi George,
*

*>
*

*> At 15:33 03/06/04 -0700, George Levy wrote:
*

*>
*

*>> Bruno,
*

*>>
*

*>> I reread your post of 5/11/2004 and it raised some questions and a
*

*>> possible paradox involving the idea that the "notion of first person
*

*>> is absolutely not formalizable." (see below, for a quotation from
*

*>> your post)
*

*>>
*

*>> GL wrote
*

*>>
*

*>> << It may be that using the observer as starting points will force
*

*>> White Rabbits to be filtered out of the
*

*>> << observable world
*

*>>
*

*>> BM wrote:
*

*>>
*

*>> >>And again I totally agree. It *is* what is proved in my thesis. I
*

*>> have done two things:
*

*>> >>1) I have given a proof that if we are machine then physics must be
*

*>> redefined as a
*

*>> >>science which isolates and exploits a (first person plural) measure
*

*>> on the set of all
*

*>> >>computational histories. The proof is rigorous, I would say
*

*>> definitive (unless some systematic
*

*>> >>error of course), although provably unformalizable (so that only 1
*

*>> person can grasp it).
*

*>> >>2) I provide a mathematical confirmation of comp by showing that
*

*>> (thanks to Godel,
*

*>> >>Lob, Solovay ...) we can literally interview a universal machine,
*

*>> acting like a scientist
*

*>> >>---by which I mean we will have only a third person discourse with
*

*>> her. BUT we can
*

*>> >>interview her about the possible 1-person discourse. That is a
*

*>> "tour de force" in the sense
*

*>> >>that the notion of first person is absolutely not formalizable (and
*

*>> so we cannot
*

*>> >>define it in any third person way). But by using in a special way
*

*>> ideas
*

*>> >>from Plato's Theaetetus + Aristotle-Kripke modal logic + Godel's
*

*>> incompleteness
*

*>> >>discovery make the "tour de force" easily tractable.
*

*>> >>Here I can only be technical or poetical, and because being
*

*>> technical seems
*

*>> >>yet premature I will sum up by saying that with comp, the plenitude
*

*>> is just the
*

*>> >>incredibly big "set" of universal machine's ignorance, and physics
*

*>> is the common
*

*>> >>sharable border of that ignorance, and it has been confirmed
*

*>> because that
*

*>> >>sharable border has been shown to obey to quantum laws.
*

*>> >>I get recently new result: one confirm that with comp the first
*

*>> person can hardly know
*

*>> >>or even just believe in comp; the other (related to an error in my
*

*>> thesis I talked
*

*>> >>about in some previous post) is the apparition of a "new" quantum
*

*>> logic (I did
*

*>> >>not command it!) and even (I must verify) an infinity of quantum
*

*>> logics between
*

*>> >>the singular first person and the totally sharable classical
*

*>> discourses.
*

*>> >>This could go along with your old theory that there could be a
*

*>> continuum of
*

*>> >>person-point-of-view between the 1 and 3 person, and that would
*

*>> confirms that you
*

*>> >>are rather gifted as an "introspecter" (do you remember? I thought
*

*>> you were silly).
*

*>> >>But then it looks you don't like any more the 3-person discourse, why?
*

*>>
*

*>> The adoption of the first person as a "frame of reference" (my
*

*>> terminology) implies the ultimate relativization. In other words, the
*

*>> logical system governing the mental processes of the observer becomes
*

*>> part of the "frame of reference> However, we all know that human
*

*>> beings do not think according to formal systems. Human systems are
*

*>> full of inconsistencies, errors, etc... and very often their beliefs
*

*>> about the world is just wrong. Very often they even make arithmetic
*

*>> errors such as 8x7 = 65.
*

*>>
*

*>> So if we assume a relative formulation, here is the dilemma:
*

*>> 1) if we adopt a formal system such as the one(s) your have talked
*

*>> about we assign an absolute quality to the observer which violates
*

*>> our premise of relative formulation.
*

*>> 2) If we adopt a non-formal human logical system," we are left with
*

*>> an extremely complicated task of reconciling the observations
*

*>> obtained by several observers who in my terminology "share the same
*

*>> frame of reference"
*

*>>
*

*>> One of the question that arise is how fundamental should be the
*

*>> concept of "frame of reference" or of the mechanism/logic that
*

*>> underlies our thinking:
*

*>> 1) Is it governed at the atomic level by physical laws down to
*

*>> resolution of Planck's constant? The notion of observer is defined
*

*>> here with a Planck resolution. If we share the same physical laws
*

*>> then we can say that we share the same frame of reference. This
*

*>> option avoids the inconsistencies of the "human logical systems" but
*

*>> throws out of the window the relativistic formulation. In addition
*

*>> this approach provides a neat justification for the equivalence of
*

*>> the sets describing the physical world and the mental world.
*

*>> 2) Is it governed at the neurological or even at the psychological
*

*>> level? The notion of observer here has a very coarse resolution
*

*>> compared to the first option. This approach keeps the relative
*

*>> formulation but becomes a quagmire because of its lack of formalism.
*

*>> How can the notion of "objective reality" be defined? In fact, is
*

*>> there such a thing as a true psychological objective reality?
*

*>> However, the fact that a "psychological objective reality" is an
*

*>> oxymoron (contradiction in terms) does not invalidate the definition
*

*>> of the observer at the psychological level. Au contraire.
*

*>
*

*>
*

*>
*

*> -----------------
*

*>
*

*>
*

*> Remember that my starting point is the computationalist hypothesis in
*

*> the theoretical cognitive science. I take as objective truth
*

*> arithmetical truth, and as third person objective communicable truth
*

*> the provable arithmetical propositions like "1+1=2", "Prime(17)", or
*

*> "the machine number i (in some enumeration) does not stop on input
*

*> number j", this + Church Thesis + the "yes doctor" act of faith is
*

*> what I mean by comp.
*

*>
*

*> From this it will follow many things which can perhaps put some light
*

*> on your questions and dilemmas, although, as you, see my point of
*

*> departure is not a "relative formulation". What will happen is that
*

*> physics will reemerge from what is invariant from all "relative point
*

*> of view", which are themselves defined by the formal machines we are
*

*> at some, necessarily unknowable, level. Indeed, in a second step, I
*

*> interview the *sound* (by choice) universal machines on those
*

*> invariant "through all relativities". The reasoning I invite people
*

*> into occurs itselfs at a third person level, as do the interview of
*

*> the machine.
*

*>
*

*> But then, talking with the machine I need to (re)define some notion.
*

*>
*

*> I (re)define science as the third person provability: thanks to
*

*> Solovay this is formalizable by a modal logic G (+ that incredible
*

*> G* which extends it at the "truth" level))
*

*> Let us write it simply by []p. It means p is provable by me (me=the
*

*> (hopefully) sound machine).
*

*>
*

*> I define, following Theaetetus, the knowledge of p by the conjunction
*

*> of []p and p. That is "I know p" = []p & p". Now the machine is
*

*> sound, in particular the "truth theory" G* (the one I called the
*

*> guardian angel sometimes) prove that
*

*>
*

*> []p is equivalent to []p & p
*

*>
*

*> So, from the *true* point of view: scientific provability and
*

*> knowledge are equivalent. But, keep attention because here is the
*

*> goedelian crux:
*

*>
*

*> The sound machine itself does not, and cannot, prove or know that
*

*> ( []p is equivalent to []p & p ). That is, the knower (or
*

*> first person) defined by []p & p
*

*> cannot know its "objective frame" from which []p has been defined. The
*

*> first person cannot know, neither proves, that she is any machine,
*

*> although with comp
*

*> the machine can still infer the existence, or even bet on some
*

*> presentation, of a machine through which he/she could hopefully survive.
*

*>
*

*> This is important because although the knower and the "scientist
*

*> machine" will know/prove the same arithmetical propositions, the logic
*

*> of those
*

*> knowable, respectively provable, propositions differs considerably.
*

*> "[]p" obeys to G (and G*), "[]p & p" obeys to the time/consciousness
*

*> logic S4Grz.
*

*> G describes a sort of buddhist heraclitean (irreflexive) path where
*

*> you can die, dream, get things wrong (like 8x7 = 65) at each instant,
*

*> but S4Grz
*

*> describes ever evolving certainty-knowledge states.
*

*>
*

*> (Do you see why the sound machine cannot prove that ( []p is
*

*> equivalent to []p & p ) ? Because if the machine proves that, then
*

*> the machine
*

*> will prove that []p -> p, in particular the machine will prove []false
*

*> -> false, that is the machine will prove NOT [] false, so the machine
*

*> will prove her
*

*> own consistency, which no sound machine can do by Godel's second
*

*> incompleteness theorem.)
*

*>
*

*> You see, I take the self-reference logic as a sort of "exact third
*

*> person psychology/theology". It cannot be normative because we cannot know
*

*> ourselves as consistent machine, and thanks to the difference of
*

*> behavior between []p and []p & p, there is room for subtle inside
*

*> views of arithmetic.
*

*>
*

*> For the laws of physics it is the G*-equivalence between []p with the
*

*> big nuance []p & <>p which plays the main role; and which will correspond
*

*> to the observable invariant relative to the consistent state of the
*

*> machine. (Although since recently S4Grz does say interesting things
*

*> too, I realize)
*

*>
*

*> I mean, all the relative aspects of reality are captured by point of
*

*> views (modalities) from inside arithmetical truth, which I take as
*

*> absolute.
*

*> It is counterintuitive because the inside views will appear bigger
*

*> than the outside view (like in Alice in Wonderland, Yellow Submarine,
*

*> etc.),
*

*> but logicians are used to such relativity of views. They traditionally
*

*> handle them with "model theory", or, in some case like our's "modal
*

*> logic".
*

*>
*

*> So to answer precisely your first dilemma between (I quote you):
*

*>
*

*> << 1) if we adopt a formal system such as the one(s) your have talked
*

*> about we assign an absolute quality to the observer which violates our
*

*> premise of relative formulation.
*

*> 2) If we adopt a non-formal human logical system," we are left with an
*

*> extremely complicated task of reconciling the observations obtained by
*

*> several observers who in my terminology "share the same frame of
*

*> reference" >>
*

*>
*

*> My answer is that we can take both. The formal []p and the unformal
*

*> []p & p. They are the same, the guardian angel says. But the
*

*> machine cannot know that, there is a necessary ignorance which must be
*

*> taken account. It is good because the UDA did show that physics
*

*> emerges from such an ignorance.
*

*> *We* can do that, because through comp we reason at the upper purely
*

*> arithmetical and third person communicable level.
*

*>
*

*> Mmmh ... I certainly should explain better why []p is formal, and []p
*

*> & p is unformal. The fact is that []p interprets the arithmetical
*

*> beweisbar Godel's provability, so you can translate []p in arithmetic,
*

*> but to translate []p & p you would need an arithmetical truth
*

*> predicate which does not exist by Tarski (see the thesis for a
*

*> rigorous argument). At the higher level of description of course []p &
*

*> p is formal. Yes, G and G* are so powerful as being able to
*

*> "metaformalize" unformality!
*

*>
*

*> Concerning your other dilemma:
*

*>
*

*> << 1) Is it governed at the atomic level by physical laws down to
*

*> resolution of Planck's constant?
*

*> 2) Is it governed at the neurological or even at the psychological
*

*> level?" >>
*

*>
*

*> We will never know that. Some will bet on low level (meaning saying NO
*

*> to the doctor for a very long time), other will bet on high level
*

*> (saying quickly YES to their doctor). In all case it will be at their
*

*> risk and peril, forever undecided. The reasoning I propose, and its
*

*> translation in arithmetic, does not depend on the choice of the level,
*

*> only on its existence.
*

*> Now, obviously, observation and introspection will give strong
*

*> *evidence* for some levels, but on that matter cautiousness will
*

*> *always* be needed.
*

*>
*

*> Note I was assuming comp throughout.
*

*>
*

*> I hope I have not been too technical, and that this helps a bit, and
*

*> also that you are not too much disappointed that my approach relies so
*

*> heavily and quasi-exclusively on the insane belief in the third person
*

*> communicability of elementary arithmetic, but I know you knew that :)
*

*>
*

*> Bruno
*

*>
*

*>
*

*> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
*

*>
*

Received on Sat Jun 05 2004 - 20:53:08 PDT

Date: Sat, 05 Jun 2004 17:50:02 -0700

Bruno

I have read your post maybe five or six times, my hair getting grayer

and grayer everytime. This subject is undoubtedly your profession and

you are an expert at it but I have a lot of trouble following you.

Nevertehless, I have a good feeling to my stomach that you appear to be

on the right track.

You seem to say that you begin with an absolute formulation but end up

with a relative one, maybe the ultimate relative one. Not only that ,

you appear to have solved the paradox of the apparent objective reality

in the context of the ultimate relative formulation. This is good. This

is what I was hoping for. I think that philosophically, the ultimate

relative formulation is the most satisfying one. But this is only my

opinion.

I cannot lead the way but I can be a critic or a friend like Salieri to

Mozart :-). Let's me see if I can convince you to bridge the gap and

maybe take the relative formulation as a starting point. Like Socrates,

let me start with one question. How can you possibly know to begin with

this particular assumption:

objective communicable truth

"the machine number i

Church Thesis + the "yes doctor"

George Levy

Bruno Marchal wrote:

Received on Sat Jun 05 2004 - 20:53:08 PDT

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