Dear Bruno, 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 this. Kindest regards, Stephen ----- 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 am > >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 image > >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 anything. > >I just need to know what's out there. If there's nothing there then I take > >it I'm in that breezy lonely spot past the front lines of epistemology and > >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 least > 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 machine > psychology. > > Hoping that helps. > > Bruno > >