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.

George Levy

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