Bruno, do we have an agreedupon identification
"what" to call an observer? I may heve missed it on the list, if yes. Your post
below speaks about the topic, but I don't see some conclusion: is it the
unformalizable first person concept, is it upon formal, or nonformal
considerations? Is the essence of an 'observer' unresolved and so hard to
involve it in activities for conclusions?
I mean a short, concise plain language
identification.
In my (nonphysics) verbalizing I tried lately
to identify an observer with something receiving (maybe responding to) any
topically relatable information (not the 'bit' of course).
Very close to my "copout" for consciousness of
a decade ago.
Sorry for my simplistic
question....
John Mikes
 Original Message 
Sent: Friday, June 04, 2004 10:22
AM
Subject: Re: First Person Frame of
Reference
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 1person
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 + AristotleKripke 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 >>personpointofview
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 3person
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 nonformal 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 certaintyknowledge
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 selfreference 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 nonformal 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 quasiexclusively 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/
