On Mon, Jul 24, 2006 at 01:30:34PM +0200, Bruno Marchal wrote:
> I am afraid your solon will just have this application: to give a non  
> standard meaning to functionalism. Even a strict catholic can be a  
> functionalist in that sense: just imagine that the solon, thanks to  
> their non-comp (by construction) feature are connected to "Descartes'  
> God".

Only if the Catholic notion of soul is that it is composed of
intechangable parts like I described, which I doubt, but then IANAC!

And is it really a nonstandard meaning to functionalism? I have read
a bit on the subject - eg Dennett, Chalmers and than Plato.Stanford
article, and nothing there indicates that there is something wrong
with my interpretation. But I don't claim to be an guru.

> >> 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 can (sort of) see this. However, it is only one model, and not even
> > a terribly convincing one (to me at least).
> I don't think it is a model. Once we say yes to the doctor, it is  
> normal to be interested in what any machine (perhaps ideally correct)  
> can prove about herself, and then we inherit of the nuances *forced* by  
> incompleteness. 

The model is that knowledge is characterised by Bp & p - the Theatetus
step. I have to take this with a grain of salt - it doesn't seem at
all obvious to me, but I don't have any other proposal either.

> We just cannot threw them in the trash, and then it is  
> just an amazing news that they behave like we were expecting. I have  
> worked with more complex definition (based on Kleene realizability and  
> on Hyland effective topos until I discover the variant of provability  
> were quite enough for distinguishing in number-theoretic terms the  
> notion of persons corresponding to their use in the UDA.
> This does not preclude more fine grain "model" of course, but let us  
> first extract all the juice from simpler idea before. No?
> > Do you have any uniqueness
> > results showing that the &p is necessary for obtaining the unamable
> > creative subject or the temporality?
> For Bp & p, I mentionned the appendix "Artemov" thesis of my text  
> "conscience et m├ęcanisme", here:
> http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/ 
> 6%20La%20these%20d'Artemov.pdf

Ah yes, I must get around to reading the Brussels version one day!

> >> 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).
> >
> > You would need to be more specific in your claims, but that would
> > probably be the subject of a full scientific paper, and perhaps you
> > are only speculating at present anyway. I will need to be patient.
> The whole thing is already in my SANE paper:
> http://iridia.ulb.ac.be/~marchal/publications/ 
> SANE2004MARCHALAbstract.html

I read that paper, but didn't get anything about self-awareness there.

> >
> > But even so, I don't see anywhere the necessity of 1st person
> > self-awareness, which is what I was driving at.
> What difference are you doing between self-awareness and
> consciousness.

Consciousness is the state of "being like something" to use Nagel's
term. It is also the characteristic of the "reference class" in
Anthropic reasoning.

Self-awareness is being aware of oneself as a distinct thing different
from the environment.

It is not immediately obvious that these are identical - but perhaps
I'm overlooking something.

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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
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