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,
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
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).