On Sun, Jul 23, 2006 at 04:38:01PM +0200, Bruno Marchal wrote:
> 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).

Hmm - you use the term functionalism quite differently to my
understanding. My take is that functionalism implies if you replace
the parts of my brain with things which were functionally equivalent,
you would end up with a copy of my consciousness. The description
given by Janet Levin on plato.stanford.edu seems to be in agreement
with this notion (even though she uses different words).

Nowhere in this discussion is an assumption of a level of
substitution, nor of stuffy matter.

Suppose I had a non Turing-emulable soul, composed of identical non
Turing-emulable particles called "soulons". Functionalism would imply
I can copy my brain by adding in an appropriate arrangement of
physical particles, as well as an appropriate arrangement of
soulons. Yet, by construction, this theory is not computationalist!

So I stand by my remarks that computationalism is a specialised
variant of functionalism.

> >
> > 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 can (sort of) see this. However, it is only one model, and not even
a terribly convincing one (to me at least). Do you have any uniqueness
results showing that the &p is necessary for obtaining the unamable
creative subject or the temporality?


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

Oh, well another idea bites the dust!

> >
> > 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).

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.

But even so, I don't see anywhere the necessity of 1st person
self-awareness, which is what I was driving at.

> 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.

OK - but I hope I'm not doing that.

> 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

I wish I shared your certainty that any n-person POV can be captured
by means of a modal logic. But I don't. All I can say is that I find
it unconvincing, whilst admitting that perhaps you have a point.

*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
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