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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