My message 6/11 to Alberto Gómez seems not to have gone through.
I send it again. Apology for those who did receive it.
                                                                                B.

At 09:24 06/11/03 +0100, Alberto Gómez wrote:

For me there is no bigger step between to wonder about how conscience
arises from a universe made by atoms in a Newtonian universe, particles
in a quantum universe, quarks in a quantum relativistic universe and
finally, superstring/n-branes in a 11 dimensional universe for one side
and, on the other side, to wonder about how SAS in a complex enough
mathematical structure can have a sense of conscience.



BM: I agree. It is a genuine point.


[SNIP]
AG:That must be true either in our "physical"
world or the world of a geometrical figure in a n-dimensional spacetime,
or in a computer simulation defined by a complex enough algorithm (These
three alternative ways of describing universes may be isomorphic, being
the first a particular case or not. The computability of our universe
doesn't matter for this question).


BM:I disagree, because if you take the comp. hyp. seriously enough
the physical should emerge as some precise modality from an
inside view of Arithmetical Truth. See UDA ref in Hal Finney's post.



AG:So the mathematical existence, when SAS are possible inside the
mathematical formulation, implies existence (the _expression_ "physical
existence" may be a redundancy)


BM:Same remark. What you say is not only true, but with comp it is
quasi-constructively true so that you can extract the logic and probability
"physical rules" in computer science (even in computer's computer science).
making the comp. hyp. popper-falsifiable.


AG:But, for these mathematical descriptions to exist, it is necessary the
existence of being with a higher dimensionality and intelligence that
formulate these mathematical descriptions? That is: every mathematical
object does exist outside of any conscience? The issue is not to
question that "mathematical existence (with SAS) implies physical
existence", (according with the above arguments it is equivalent). The
question is the mathematical existence itself.


BM:Now, it is a fact, the failure of logicism, that you cannot define integers
without implicitely postulating them. So Arithmetical existence is a
quasi necessary departure reality. It is big and not unifiable by any
axiomatisable theory (by Godel).
(axiomatizable theory = theory such that you can verify algorithmically
the proofs of the theorems)
I refer often to Arithmetical Realism AR; and it constitutes 1/3 of
the computationalist hypothesis, alias the comp. hyp., alias COMP:

COMP = AR + CT + YD (Yes, more acronyms, sorry!)

AR = Arithmetical Realism (cf also the "Hardy post")
CT = Church Thesis
YD = (I propose) the "Yes Doctor", It is the belief that you can be
decomposed into part such that you don't experience anything when
those parts are substituted by functionnaly equivalent digital parts.
It makes possible to give sense saying yes to a surgeon who propose
you some artificial substitution of your body. With COMP you can justify
why this needs an irreductible act of faith (the consistency of
COMP entails the consistency of the negation of COMP, this is akin
to Godel's second incompleteness theorem.
It has nothing to do with the hypothesis that there is a physical universe
which would be either the running or the output of a computer program.
Hal, with COMP the "identity problem" is tackled by the venerable old
computer science/logic approach to self-reference (with the result by Godel,
Lob, Solovay, build on Kleene, Turing, Post etc...).


Bruno

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