On Mon, Jan 16, 2012 at 4:56 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

" But in computability theory we have only natural numbers. A real number
> like PI or e is modeled by a total computable function from N to N."

Yes, but real numbers like PI or e are very much the exception, they are
rare, quite literally infinitely rare oddball real numbers, because nearly
all the numbers on the number line are not computable so there is no way
for a Turing Machine, or anything else, to come arbitrarily close to one
like you can for PI or e.

 " By "number" I always mean natural number."

Then numbers can not be the only thing that is fundamental.

" By mechanism I mean the idea that the brain (or whatever needed for
> consciousness) is Turing emulable."

OK. Then mechanism has not been proven and will never be proven it is just
assumed, and the ground that assumption is built on is exactly as strong or
as weak as the assumption that you are not the only conscious being in the

" we live in a non deterministic reality."

That has been known for nearly a century.

" Non determinism is a simple consequence of mechanism"

Determinism or non-determinism has nothing to do with consciousness, its

> " Universal machine can always been optimized by change of software only,
> and one way to do that is allowing the machine to believe in non provable
> propositions."

Yes that makes sense but I don't see what it has to do with consciousness,
that's true for any axiomatic system including Euclid's geometry. And there
is a danger, the reason the proposition is non-provable may have nothing to
do with Godel, it may simply be plain ordinary false. If it's false you'd
better hope it's non-provable in your logical system.

"BTW I tend to use "competence" for what you call "intelligence".
> "Intelligence" requires consciousness"

If what you call competence and Intelligence can both produce the same
behavior then you might as well say that Intelligence and consciousness are
synonyms because they are both equally unobservable and untestable. In
common usage intelligence is simply what intelligent behavior implies, and
redefining familial words in unfamiliar ways is not the path to clarity or

> " Competence needs some amount of intelligence, but it has a negative
> feedback on intelligence."

I don't know what that means.

 John K Clark

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