Re: Is the universe computable?

From: Bruno Marchal <>
Date: Tue, 13 Jan 2004 15:03:38 +0100

At 14:08 13/01/04 +0100, Eugen Leitl wrote:

> > you be able to do a thing like that. I will not insist on this
> > startling consequence of COMP or QM, giving that you
> > postulate physicalism at the start. See my thesis for a proof that
> > physicalism is incompatible with comp. We have discuss the
> > immortality question a lot in this list.
>Do we have an experimental procedure to validate these fanciful scenarios?

What is the point? Do we have experimental procedure to validate
the opposite of the fanciful scenario? Giving that we were talking about
first person scenario, in any case it is senseless to ask for
experimental procedure. (experience = first person view; experiment =
third person view).

>If you insist to label me thusly. But, really, instead of glib assertions and
>pointers to your thesis (what has formal logic to do with reality?) you
>are not being very convincing so far.

Don't tell me you were believing I was arguing.
About logic, it is a branch of mathematics. Like topology, algebra, analysis
it can be *applied* to some problem, which, through some hypothesis,
can bear on some problem. With the comp hyp mathematical logic makes
it possible to derive what consistent and platonist machine can prove about
themselves and their consistent extension.

>My point is that formal systems are a very powerful tool with very small

But I never use formal system. I "modelise" a particular sort of machine by
formal system, so I prove things *about* machines, by using works
*about* formal system. I don't use formal systems. I prove things in informal
ways like all mathematicians.

>Because we know that QM is not a TOE. You haven't heard?

How could be *know* QM is not a TOE? (I ask this independently of
the fact that I find plausible QM is not a *primitive* TOE).

>This is ridiculous. You're referring to a specific notation, which needs
>systems to produce and to parse. Remove all instances of such systems, and
>everything is instanstly meaningless.

You believe that the theorem "there is an infinity of primes" is a human
invention? (as opposed to "a human discovery").

> > Perhaps we should put our hypothesis on the table. Mine is
> > comp by which I mean arithmetical realism, Church thesis, and
> > the "yes doctor" hypothesis, that is the hypothesis that there is
> > a level of description of myself such that I don't detect any differences
> > in case my parts are functionaly substituted by digitalizable device.
> > Do you think those postulates are inconsistent?
>I do not see how arithmetic realism (a special case of Platonic realism, is
>that correct?) is an axiom. I agree with the rest of
>your list.

Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical
Truth is independent of me, you, and the rest of humanity. There exist
weaker form of that axiom and stronger form. Tegmark for instance
defends a much larger mathematical realism (so large that I am not sure
what it could mean). As I said some ultrafinitist defends strictly
weaker form of mathematical realism.
The more quoted argument in favour of arithmetical realism is the one based
on Godel's theorem, and presented by him too) which is that any formal
systems (and so any ideally consistent machines) can prove, even in principle,
that is with infinite time and space, all the true proposition of arithmetic.
But look also to the site of Watkins
for a lot of evidence for it (evidence which are a priori not related to
my more theoretical computer science approach).
Now my goal (here) is not really to defend AR as true, but as sufficiently
that it is interesting to look at the consequences. You can read some
main post I send to this list where I present the argument according to
which if we take comp seriously (comp = AR + TC + "yes doctor") then
physics is eventually a branch of machine's psychology (itself a branch
of computer science" itself a branch of number theory.
If you find an error, or an imprecision, please show them.
Or, if there is a point you don't understand, it will be a pleasure for me
to provide more explanations.
Also, I thought you were postulating an universe, aren't you? (I just try
to figure out your philosophical basic hypothesis).


Received on Tue Jan 13 2004 - 09:03:21 PST

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