Le 20-juil.-06, à 21:01, Russell Standish a écrit :

>
> On Sat, Jul 22, 2006 at 04:49:04PM +0200, Bruno Marchal wrote:
>>
>>
>> Le 20-juil.-06, à 13:46, Russell Standish a écrit :
>>
>>> Bruno, I know in your theory that introspection is a vital component
>>> (the Goedel-like constructions), but I didn't see how this turns back
>>> onto the self-awareness issue. Did you develop this side of the
>>> argument?
>>
>>
>> Yes sure. The Goedel-like construction can handle only a 3-person
>> discursive self-reference.
>> A little like if you where reasoning on some 3-description of your
>> brain or body with your doctor, although it could be also an high 
>> level
>> 3-description (like I have a head).
>>
>
> ... Removed for brevity
>
>>
>> I will come back on the correspondence later. The key point is that 
>> the
>> nuance between
>> p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, are imposed by the incompleteness
>> phenomenon, and self-awareness corresponds to the one having " & p" in
>> their definition. It is the umbilical chord between "truth" and
>> intellect of the "reasonable" first person.
>>
>> Bruno
>
> How do we get the "& p" part corresponding to self-awareness? That
> doesn't seem to make sense at all!
>
> We could of course be foundering upon my major problem with your
> work. I have no problems with your UDA, and even think it could be
> generalised to the functionalist position, but where I come to grief
> is the latter Theatetical arguments.


Functionalism is the same as comp, except that functionalist 
traditionally presuppose some knowable high level of substitution (and 
then like materialist presuppose a physical stuffy level).
So I would say comp is just the "old functionalism" corrected for 
taking the UDA consequence into account (the level of substitution is 
unkowable, and physical stuff is either contradictory or devoid of 
explanation power and redundant).


>
> I have studied the book by Boolos, and can appreciate the power of
> modal logic to handle reasoning about provability. I can also see how
> you (and others) have extended these logic systems to the Theatetical
> notion of knowledge (adding the &p), but my (physicist's) intuition
> riots against this definition capturing what we mean by knowledge. At
> best, I consider it a description of _mathematical_ knowledge, where
> indeed we can never know something unless proved.


It depends what you put in the "B". It is indeed a sort of scientific 
knowledge when starting with B = the provability predicate of some 
fixed theory like Peano arithmetic, but such a theory can 
(autonomously) transcends itself in the (constructive) transfinite, and 
the "arithmetical" meaning of "B" will evolved, letting invariant the 
modal logic G, G*, S4Grz, ...
Then the justification is that it works. It gives an unameable creative 
subject which lives in a non describable temporal structure, etc. You 
can take this as a simplification. With comp the simple first person 
already leads to a notion of arithmetical quantization. Then sensible 
matter is also given by adding "& p" , but on "Bp & Dp", ...
I will say more in the road map ...


> General scientific
> knowledge doesn't seem to work that way, let alone knowledge of
> humanities or other types (echoes of John Mike's criticisms here, I 
> know).
>
> Parenthetically, what about scientific knowledge being captured by
> DB-p & -B-p? In other words, "falsifiable, but not falsified", a
> statement of Popper's principle.
>
> Substituting D=-B-, we get -BDp & Dp, which has a similar Theatetical
> structure about a statement being possibly true.


Except that Dp always entail ~BDp (by second incompleteness). This 
would make your refutability notion much too large.


>
> Anyway, thats by the bye. If I accept the Theatetical notion for the
> sake of argument (since I can see how it might work for mathematical
> knowledge), I still struggle to see how the "&p" part leads to self
> awareness.

To be just a little bit more specific, "Bp" is 3-self-referential (the 
machine proves correct proposition on any of third person description 
made at some level, correctly chosen in a serendipitous way).
But by adding "& p", by a theorem similar to Tarski theorem, we are 
lead to a first person  self-reference (Bp & p) without any nameable 
subject. It is the "I" which has no name. That "I", somehow, could 
correctly said about himself that he is not a program, that he is not 
duplicable (and indeed the first person is not duplicable from its 
first person point of view (despite Chalmers).
The heart of my critics to non computationalist is that they confuse Bp 
with Bp & p. (or Bp with Bp & Dp). Easy confusion given that G* 
justifies it, but then G* justified also that the machine cannot access 
that equivalence.
Feel free to propose other definition of person point of view 
(intensional variant of G). The key is that they are all G* equivalent 
and none are G-equiavlent reflecting an explanation gap between 
communicable, intelligible, sensible etc.

Bruno




http://iridia.ulb.ac.be/~marchal/


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