COMP & Self-awareness

From: Russell Standish <>
Date: Fri, 21 Jul 2006 05:01:19 +1000

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.

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. 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.

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


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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                         	       0425 253119 (")
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Received on Sat Jul 22 2006 - 22:52:23 PDT

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