At 10:32 09/01/05 +0000, Alastair Malcolm wrote:

For my own part, I give strong credibility (>50%) to the existence of many
worlds in some guise or other, and in particular to the existence of all
logically possible(*) worlds (alpw).



I certainly agree. Now the problem is that there are many logics, and so
there are many notion or "logical possibility".
The choice of the logic (or logicS) will depend on some basic assumptions.
In particular with the computationalist hypothesis (comp) there is a necessity
to distinguish precisely notions like first and third person point of view and this leads
to different notion of logical possibilities. The Modal logics can help here.
You can read my papers referred in my URL below. A good book introducing
the main logics I am using is the book by Smullyan "Forever Undecided".


Actually I'm working currently with still another type of logic: the Shoenfinkel
Curry Combinatory Logics. This will help for linking my work with the
mainstream logical work of today's logicians (linear logic, for example).
Here too Smullyan wrote a very nice introductory book "To Mock a
Mockingbird". I strongly recommend it. A classical treatise is the North-Holland
book on the Lambda Calculus by Henk Barendregt.
Combinatory logics (and its "sister" the lambda calculus) has failed concerning
its initial goal to provide a logical foundation of the whole of mathematics.
But Combinatory Logics has been, and still is, very useful in the foundation
of computer science (which itself is indispensable through the comp hyp).
Not really the time to say much more now, but my point is that "logical possibility"
is a notion which we should'nt take for granted. Logic is a field full of surprise
and unexpected results.


Concerning your question of believing in the many worlds, I can only give
you a rough summary of the conclusion of the work I have done in the comp
frame. With the Church thesis (see the diagonalization posts to this list and
referred in my url) there is a universal notion of computation (unlike provability,
proofs, etc.), and all computations exist (the comp form of "everything").
Giving the discrepancy between first and third person notion (see my papers
or see my posts to the list) no observer-machine can ever know which
computations support them, and physical reality (whatever it is) must emerge
from the "interference" (in an a priori larger sense than the quantum sense)
of all the computations which are "rich enough" to support your processing.
This can be computed and compare to actual physics. Until now the
comparison tend to confirm both the quantum hyp. and the comp hyp.
Note that physics is made secondary with respect to computer science, or
logic, or arithmetics. The combinatory logics make possible, in principle,
to distinguish the apparition (in the eyes of the Lobian machine) of
classical physics and quantum physics (and this is new, I mean it is
not explicitly in my thesis).
The common point between my work, Smullyan's Forever undecided, and
Smullyan "To mock a Mockingbird" is, of course, the study of self-reference,
which is the main tool to define formally the first and third person views.
If you read the papers I am referring too, don't hesitate to ask questions.


Bruno

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



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