Re: Is the universe computable?

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Wed, 14 Jan 2004 11:49:56 +0100

I agree with you Ben, you make a point. My objection admits indeed
your wonderful generalization. Thanks.

Bruno


At 11:07 13/01/04 -0500, Benjamin Udell wrote:
>[Georges Quenot]>>Some people do argue that there is no arithmetical
>property independent of us because there is no thing on which they would
>apply independentkly of us. What we would call their arithmetical
>properties is simply a set of tautologies that do come with them when they
>are considered but exist no more than them when they are not considered.
>
>[Bruno Marchal]>But then what would be an undecidable proposition?
> >You know, about arithmetic, and about machines btw, a lot of people
> defends idea which are just no more plausible since Godel has proved its
> incompleteness theorems.
> >Arithmetical proposition are just not tautologies. This is how Russell's
> and Whitehead logicism has break down. There is a ladder of arithmetical
> propositions which ask for more and more ingenuity to be proved. Actually
> arithmetical truth extend far beyond the reach of any consistent machine
> (and consistent human with comp). There is an infinity of surprise in there.
> >I guess you know that there is no natural number p and q such that
> (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why
> did the pythagoreans *hide* this fact for so long? So those propositions
> are neither tautologies, nor conventions.David Deutsch, following
> Johnson's criteria of reality, would say that such propositions kick back.
>
>Since Georges Quenot's objection claims that nothing exists when
>unconsidered, be it a mathematical structure or concrete singular objects
>to which it applies, isn't the objection too broad to be singling out any
>particular physics-based cosmology as objectionable? The objection seems
>too powerful & broad, & seems to apply with equal force to all subject
>matters of mathematics & empirical research, from pointset topology to
>Egyptology. I wouldn't demand that a philosophical objection, in order to
>be valid at all, offer a direction for specific research, but I'd ask how
>it would at least help research keep from going wrong, & I don't see how
>the present objection would help keep any kind of research, mathematical
>or empirical, from getting onto excessively thin ice, except perhaps by
>inspiring a general atmosphere of skepticism in response to which people
>pay more attention to proofs, confirmations, corroborations, etc. -- not
>that any such thing could actually overcome such a !
>radical objection.
>
>And the objection is stated with such generality, that I don't see how it
>escapes being applied to itself, since, after all, it is about things &
>relations. If there's nobody to consider concrete things or mathematicals,
>then there's nobody to consider the objection to considering any
>unconsidered things to exist. The objection seems to undercut itself in
>the scenario in which it is meant to have force. Unless, of course, I've
>misunderstood the argument, which is certainly possible.
>
>Best,
>Ben Udell
Received on Wed Jan 14 2004 - 05:49:28 PST