Hi Stephen, At 10:52 -0500 22/01/2003, Stephen Paul King wrote:

Dear Bruno,## Advertising

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.

BM I am not sure which "external aspect" you allude to. Case'w work relies on the second recursion of Kleene, which gives easy way to construct self-referential programs. The "mirror" is really in machine's head. The basic idea is very easy. Let D be a duplicator in the sense that the program D applied to X, written DX, gives a description of X apply to itself, that is XX. So DA gives AA. DB gives BB. DC gives CC, ... What gives DD? Yes. DD gives DD. It's an example of a duplicating program. For all transformation T you can generalize and find a program which computes T applied to itself. Simple reproduction is the particular case when T = the identity transformation: take a new "duplicator" which apply to any X, written DX, gives T applied to a description of XX, that is T(XX). Now DD gives T(DD). DD gives T applied to itself. So you get self-referential machines by the substitution of some [variable of some transformation] by duplicator applied to themselves. You could say that the self-referentiality comes from the language chosen, but working with Rogers numerical representations, the \phi_i, you can show the reasoning constructive and machine, or programming language, independent. What remains true is that any self-referential program needs a universal program to run it, for making the self-referentiality manifest. I have never deny that. What the universal dovetailer argument shows is that from the point of view of the machine, if she looks closely enough to its probable local implementation, that is near its comp substitution level, she will describe not one universal machines, but MANY one. QM confirms that. But people have invented selecting rules, like the collapse of the wave or some guiding potential, making things look more Aristotelian. But Everett comes and said "why for?". And I come, if you want, and just say that if you take seriously the Everett comp then you can ask "why for?" even for the Schroedinger Equation. Not because you should dismiss it, but because if it is true, it should be derivable from LOGIC + ARITHMETIC. That the result of the UDA proof.

SPK: Your model, as I understand it, ...

BM: But I'm afraid you miss the point. It is not a "model". It is not a theory. It is a "theorem", a deductive argument. If you don't understand it, you should tell me at which step of the reasoning you are stuck. I am not so interested in knowing if the hypotheses are true. I am enough glad for showing them refutable. When a computationalist practitioners accepts an artificial digital brain, he does not ask for a model in its head. He asks and hope for the real thing. In case he survives (= COMP) he can bet he is immaterial. He can choose is body and travel on the nets, without any stable body. The UDA result is that this imateriality is contagious, in some sense, the environment cannot be more material than himself. Descartes, Hume, and Kant have partially describe this. SPK:

would seem to make the "mirror/ sketch pad" to be a derivative or "epiphenomenona" of the UD,

BM: Why epiphenomena? They are phenomenal appearances, stable patterns in consistent machines memories. Dreams if you want, but stable dreams in which they have partial control ... And thanks to the G/G* difference we get communicable and incommunicable truth. Thanks to the Z/Z* difference we get room for both physical measure and physical sensations, as uncommunicable physical result of (self)measurement. SPK:

e.g. that physicality itself is merely derived from the intetionality of arithmetic statements,

BM: Yes. SPK:

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?

BM: ... would be 1-person plural distinguishable (for the technical reason that the quantum, seems to appear at the star level. I am not yet sure). But you are right. That is, if that is believable and consistent. It is not that mind acts on matter, but it is more like the arithmetical border of mind defines matter. Roughly speaking. SPK:

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. BM: We will come back later on Pratt. It is very technical and he redefined mind and body in a very special sense. I guess something interesting. We will see if it helps for the Z1(*) semantics ... Don't hesitate to send a readable description of Pratt's "headway" for us all, anyway. Explain perhaps enough for explaining the subtle point which, if I understand you, would make comp inconsistent, or perhaps trivial. Cheers, Bruno