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