Le 12-juil.-05, à 20:09, [EMAIL PROTECTED] a écrit :

Tom: My exception to your hypotheses was supposedly independent of Church's thesis or arithmetic realism, but the objection was regarding your definition of physics, which seems too narrow to me. But now I am pondering your rebuttal of this exception, and I'm realising that there is some background that I need to become more familiar with. It's just that at first reading, I got a gut feeling that you unknowingly limited physics a priori, thus leading to the conclusion that physics is limited in that way.



That is a good constructive remark. I should be (still more) cautious. To bad I have just finished a paper, but then I don't really defined physics in it I hope :). Sometimes it is simpler to just say physics, hoping people will see the point by the reasoning. I guess that *is* the danger of trying to define physics at the beginning. I mention the notion of *correct by definition*-physics, so that there is no a priori limitation of what physics can be, at all ( other that "I am turing emulable").




Tom: Have you considered translating the UDA into mathematics?


Yes. (Without having done this I could hardly pretend having test it, no?).

And I make regularly some tiny attempts to convey the math in this list, but the branches of math relevant are not very well known (mathematical logic, modal logic, and theoretical computer science).

What I call the interview of the Lobian Machine (on UDA) *is* the translation of the UDA in mathematics.

The result is that "comp-physics" is given by the composition of three mathematical transformations operating on the "well-known" modal logic of self-reference (called G by Solovay, Smullyan, Boolos 79, etc.).


To test comp: compare physics and comp-physics.

If you like formula, here is the most fundamental perhaps:


           COMP-PHYSICS   =    SOL(THEAE(COMP(G))),



where SOL corresponds to a trip from provability to truth, made possible by the theorems of Godel, Lob, Solovay (SOL is for SOLOVAY 1976)

THEAE is put for the use of Theaetetus's definition of a knower, which looks vacuous until you realize their are non trivial again as consequence of Godel incompleteness. (Here there is really a family of theaetetical variants, giving some nuances).

And finally COMP is the translation of comp in the language of the Lobian Machine.(COMP is also non trivial by Godel's theorem!).


But now I hope I am not discouraging you because you can imagine there is a need of some amount of work, including grasping Godel's theorem and its generalizations.

But Smullyan's book "FOREVER UNDECIDED" is a quite nice recreative introduction to the modal logic G. The modal logic G, as it appeared in the formula above, is the basic pillar of the whole enterprise.

I intend to explain (or argue) that Stathis Papaioannou has (re)discovered, in his "death thread", my old initial theory of "life and death" or "consciousness", C, which is a simpler subtheory of G (meaning the theorems of C are included in the theorem of G).


Bruno



http://iridia.ulb.ac.be/~marchal/


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