Thank you for the reference to the Case papers. It is ironic that his
argument makes the case for the subtle issue that I am trying to point out
to you, that there is a grave problem with your model.
In http://www.cis.udel.edu/~case/self-ref.html we find a very
informative discussion of self-reference and the way that infinite
regression is avoided by using an "external" aspect to act as a
"mirror/sketch pad" for the machine to use as a self-referential imaging
system. While I do have some reservation regarding the assumption that N ->
N functions can completely capture physics and the exclusive usage of Well
founded statements in mathematics, I propose to set them aside for the sake
of a discussion.
Your model, as I understand it, would seem to make the "mirror/ sketch
pad" to be a derivative or "epiphenomenona" of the UD, e.g. that physicality
itself is merely derived from the intetionality of arithmetic statements,
what x implies about y. My argument is that if physicality is mere
epiphenomenona, is it sufficient to merely have a "belief" by S that x
implies y to have a causal consequence on the possible behavior of S, such
that if x did not imply y behavior would be 3-person distinguishable?
What I seem to be getting at is how do you relate 1-uncertainty to
3-person belief? I see the paper by Pratt that I have mentioned before makes
some headway on this question, but have not seen any of your comments about
----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: "Colin Hales" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Tuesday, January 21, 2003 3:21 AM
Subject: Re: "I" the mirror
> At 11:59 +1100 21/01/2003, Colin Hales wrote:
> >This is a query placed as a result of failing to succeed to find answers
> >when googling my way around the place for a very long time (2 years). I
> >about to conclude that a) no such discourse exists or b) that it is
> >disguised in a form of physics/math that my searching has not uncovered.
> >I know it is off-topic but I thought I'd run it by you folk as the most
> >eclectic agglomerators of knowledge in the multiverse. Off-list replies
> >welcome - keep the noise down and all that.
> >Q. What branch of science has ascertained the role and status of the
> >in a first person perspective of a mirror? .ie. 'be' the mirror.
> >The answer 'there ain't one as far as I know' is as acceptable as
> >I just need to know what's out there. If there's nothing there then I
> >it I'm in that breezy lonely spot past the front lines of epistemology
> >trundle on assuming (a) above.
> As far as I understand the question it seems to me that the answer
> is "intensional recursion theory". My own approach to epistemology
> has been based on it, especially through the work of John Case.
> Fortunately or unfortunately, the modal logics of self-reference (G, G*)
> can be used as a sort of shortcut so that I am no more relying
> directly on the, although very beautiful, work by John Case.
> A good starting point is http://www.cis.udel.edu/~case/self-ref.html
> Note that it is not really "first person perspective of a mirror", at
> as I define "first person" because "my" first person is just invisible
> for all third persons and so cannot be seen in a mirror.
> First persons share this property with vampires!
> One day I will put my paper "amoeba, planaria,
> and dreaming machine" on my web page, because it shows the relationship
> between Case's use of the mirror in abstract biology and the loebian
> Hoping that helps.