Le 02-nov.-06, à 17:34, David Nyman a écrit :
>
>
> Bruno Marchal wrote:
>
>> I don't understand really what you mean by "AUDA is not RITSIAR". AUDA
>> is just the lobian interview, or if you prefer the complete
>> mathematical formalization of the UDA reasoning. In some sense you can
>> interpret it as the eventual elimination of the "yes doctor"
>> hypothesis
>> in the UDA argument (but here I do simplify a little bit).
>
> Yes, sorry, perhaps I should have said 'if number is not RITSIAR, is
> anything?' The intention behind the question is to find out how and
> where you would apply RITSIAR in your schema - if at all - because
> Peter has been willing to do this but you haven't. I just want to know
> why.
I recall RITSIAR = Real In The Same Sense That I Am Real (introduced by
Peter).
Now, the notion of existence is very difficult, and the notion of
"personal existence" is still more difficult, and was the object of the
debate.
Take the expression "I am real". Does it mean "I am real and this is
something I cannot doubt about", in which case "I" refer to the first
person, or is it "my physical body is real", in which case it refers
to a third person description of "I" based on some theory (for example
physics, or comp, etc.).
So RITSIAR is an highly ambiguous which presuppose many points we were
arguing about.
Let me try shortly to make it less ambiguous in the frame of the AUDA.
Now I cannot be 100% rigorous without being long and boring, so I ask
you some indulgence, and I am just trying to convey the idea.
As you know I am realist or platonist about numbers and their
arithmetical relations. For example I believe in theorem like "all
numbers can be written as a sum of four square" (Lagrange theorem). I
take such a truth as being completely independent of me, you, time,
place. I take such truth as being primitive and beyond time and space,
a-physical if you want.
Now I also believe in "1-persons, or souls, etc". I am not a solipsist,
and I really believe in my own current experience, but also in yours
even if I am currently feeling them differently.
I don't believe at all that a first person experience is a number, nor
do I believe any first person can believe to be a number. Still, I
assume comp, so there must be a relation between 1-person experience
and numbers. Indeed persons can manifest themselves relatively to me
when they are related to some computations (brain activity with comp
and some high substitution level for making things simple). Those
computations define or are defined by complex set of counterfactuals,
and UDA shows that physics emerge or should emerge (with comp) from
their structure. It is plausible because quantum logic can already be
seen as a logic of counterfactuals. How to get them, and what the
results will say for RITSIAR ?
Let me give you all the person point of views (pov), that is the
"complete science and theology" of a simple lobian machine like PA
(Peano Arithmetic). It is a fact that if M1 and M2 are lobian machine,
and if M2 has stronger provability abilities than M1, then M2 can prove
both the science and the theology of M1. But NO lobian machine can
prove its own theology without becoming inconsistent, they can only
abductively infer their own theology:
0-person pov = arithmetical truth. This can be shown "ineffable" or non
definable by the machine (Tarski theorem). In the arithmetical
interpretation of Plotinus' "TOE", it corresponds to the ONE. It is the
big unameable entity at the origin of all forms of existence.
3-person pov = arithmetical provability. It is the self-referential
godelian provability predicate. The fundamental thing here is that the
incompleteness phenomenon splits it into two parts, each of which are
captured by a modal logic: G and G* respectively. G captures what the
machine can prove about herself, and G* captures in addition what is
true about the machine but unprovable by the machine (like
self-consistency for example). G axiomatizes the self-referentially
correct "science" of the machine, and G* minus G axiomatizes the
correct "theology" that the machine can infer without proving (its
"hope-space" if you want).
In the arithmetical interpretation of Plotinus' "TOE", it corresponds
to the INTELLECT. Terrestrial or discursive = G, divine = G*.
Please note that G and G* capture self-referentially correct *3-person*
statements, like someone talking about his own brain with his doctor.
It is "I" with "I" = my 3-description of my "body". It is not the "I"
with "I = my soul, or my experiences" ...
The 1-person point of view. I identify him/it/her with the
"incorrigible knower". By Godel's second incompleteness theorem, no
correct machine can prove its own incorrigibility. But that fact makes
it possible to define the knower by making the explicit conjunction of
truth and provability, for example by defining a new modal connector
like Kp = Bp & p. This is what actually Theaetetus has proposed to
Socrates when Socrates asked him to define knowledge. Kp makes both
truth and provability participating in the knower, like in Plotinus. In
fact, quite amazing things appears here. First "Bp & p" cannot be
directly defined in the language of the lobian machine, making the
"soul" or the first person unnamable, like the big ONE. Secondly the
logic of Kp (which *is* completely *defined* in G and G*) appears to be
a temporal logic of a self-extending self, and it can be related the
brouwer "creative subject" philosophy in intuitionistic logic. This is
confirmed also by the fact that G and G* completely agree on Kp. G*
does not add anything: the soul of the machine is bound up to confuse
proof and truth, the Kp logic (already known in the logician literature
as S4Grz) does not split into two like the intellect.
In the arithmetical interpretation of Plotinus' "TOE", it corresponds
to the "ALL SOUL" or "universal SOUL". It is a good candidate for a
simple form of first person pov.
The 1-person plural pov. This is the consistent believer. It is defined
by Cp = Bp & ~B~p. Or equivalently Bp & ~B~t. (with t = any tautology)
Again by incompleteness, although it is equivalent with both Bp and Bp
& p at the G* level, it obeys different logic, and here the G and G*
difference does again split it into two. In the arithmetical
interpretation of Plotinus' "TOE", it corresponds to the "INTELLIGIBLE
MATTER". It is here that a logic of counterfactual, or a quantum logic
appears. It is the logic of probability on observable proposition.
Actually the quantum appears only at the G* level, and this can be used
to show that "we" (the first person plural) share the quantum
splitting: here we recover Everett. The price of that is that the
"quanta" have to be just a case of sharable qualia. Note that it is the
difference between the 1-person and the 1-plural person which prevents
comp from solipsism. I call its modal logic Z.
The incorrigible 1-person plural pov. This one is again an "intensional
(modal) variant" of G. It is defined by Op = Cp & p = Bp & ~B~p & p. It
is also split into two by G and G*. In the arithmetical interpretation
of Plotinus' "TOE", I would say it corresponds to the "SENSIBLE
MATTER", its G* part gives an astonishing non trivial notion of
"correct qualia" (showing the existence of possible non correct qualia
in the intelligible matter, this can be used to explain phantom limb,
phantom body, phantom universe).
To sum up, and to relate this with RITSIAR, I would say that the
unnamable reality (of the lobian machines PA, (resp. ZF ...)) is
arithmetical truth, (resp. set-theoretical truth, ...) which is somehow
beyond existence, and all form of existence are internal modalities of
arithmetical (set theoretical, ...) truth.
Does this help a bit?
To be short I have not mentionned that the quantum appears only when I
translate the comp hypothesis in the language of the machine. Now comp
can be translated in G (and G*) into the formula "p -> Bp", so what I
say above is true with G1 = G + "p -> Bp". To explain why comp is
"p-> Bp", we should dig deeper in recursion theory/computer science (cf
the Wi and the Fi for those who remembers those posts). Of course you
can also interview non computationalist machine, if you desire (good
subject for a PhD thesis!).
Perhaps I could compare this with Spinoza Neutral Monism. The big
0-person view (cf Nagel's view from nowhere) is truth, and all the form
of existence (quanta, qualia, space, time, taxes, death ...) emerges
from relatively canonical views from inside. Incompleteness makes this
approach consistent, and comp makes it provable by any lobian machine
M1 for any machine M2 when M1 is sufficiently stronger than M2. Then
M1, by postulating comp, can lift abductively (and thus
interrogatively) the M2 theology to itself.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Nov 03 2006 - 06:34:30 PST