Re: on formally describable universes and measures

From: Marchal <marchal.domain.name.hidden>
Date: Sat Feb 24 10:04:46 2001

Juergen wrote:

>Bruno, I am usually skipping those of your paragraphs that contain
>sentences such as "physics is a branch of machine's psychology" because
>I have no idea what that is supposed to mean.

It is something the reasoning itself should clarify (hopefully).
The expression gives the idea of the counter-intuitiveness
(and "out-fashion"
in the current philosophy of mind, where materialistic
naturalism get the main attention today).

It is a way of not hiding we are going toward a form of idealism.
I try to explain that comp leads necessarily to some (rational)
idealism.

You can also got some "intuition" through poetical sentences. For
exemple: "Life what is it but a dream" (Lewis Carroll).

>Still, I feel you do have
>something nontrivial to say,
>I just have not been able to figure out
>what exactly it is. Maybe if I knew why "I genuinely fail to understand
>the invariance lemma" - please show me!

Actually I guess your constructive philosophy will not help you
to understand what I try to show. I hope I am wrong here.

But even if that is true, you can
maybe still put yourself at the place of a classical logician and accept
that with comp and some amount of classical (non constructive) logic
I am correct. In that case, for those who believe it is necessary to
be insane for believing in the physics/psychology reversal, my work will
appear as an argument for your constructivisme!

>But any finite future is computable by a long program as well.
>The problems arise with infinite futures.

We will come back on this (in some futur).

>No, it isn't, since "generating an individual real" is not equivalent to
>"generating all prefixes of all reals." "Generating an individual real"
>means "generating all prefixes of that individual real, AND NOTHING
>ELSE".

All right. I was using generate in a more general sense. To help us
preventing that confusion again I will say "surgenerate" instead.
So a program surgenerates a real if it generates all the prefix of that
real AND *SOME*THING ELSE.
I hope you agree that the DU surgenerates all the reals. I will not be
vexed if you anwer me "trivial".

(later it will be necessary to understand that from the first-person
point of view we cannot know if we "belong" to a "real" which would be
generated or surgenerated ...).


>The best you can achieve is an algorithm that outputs at least the
>computable infinite reals in the sense that it outputs their
>finite descriptions or programs.

I am not sure I understand you here.
Are you aware that the set of descriptions of computable reals
is not closed for the diagonalisation procedure.
That is: you cannot generate all (and only) descriptions of
computable reals. The algorithm you are mentionning does not exist.
You can only generate a superset of the set of all computable reals.
That set (of description of all computable reals) is even
constructively not *recursively enumerable* in the sense that,
if you give me an algorithm generating the (description of)
computable real, I can transform it for building a computable
real not being generated by your algorithm. I guess you know that.

That is why most formal constructivists consider their "set of
constructive reals" as subset
of the Turing computable reals. For exemple you can choose the
set of reals which are provably
computable in some formal system (like the system F by Girard,
in which you can formalize ..., well Hilbert space and probably
the whole of the *constructive* part of Tegmark mathematical ontology!
That is very nice and big but not enough big for my purpose which
has some necessarily non constructive feature.
About natural numbers and machines I am a classical
platonist. About real numbers I have no definite opinion.

Can you imagine yourself as a Platonist for a while, if only
for the sake of the reasoning?


>If it just means you don't know in advance in which possible future you'll
>end up, provided there is a nontrivial distribution on the possible
>futures, then this is ok (and trivial).

Are you saying that *without* distribution I would be less ignorant?
I was just saying "you don't know in advance in which possible future
you'll
end up". Comma.

> Do I need any additional
>preliminaries to realize why I "genuinely fail to understand your
>invariance lemma"?

Sure. The "delays" question for exemple. Let us follow Jesse Mazer
idea of torture. Suppose I duplicate you and reconstitute you, not
in Washington and Moscow but in some Paradise and some Hell.
Would you feel more comfortable if I tell you
I will reconstitute you in paradise tomorow and in hell only in
3001 after C. ? Is that what you would choose?

An honest computationalist will never suggest
that such a delay should make yourself feeling more
comfortable. Despite the third person local appearances.

After the delays, there is the virtual/"real" preliminaries.
The first person cannot see the difference.
And then the "more difficult" arithmetical/virtual preliminaries.
First person cannot makes the differences ....

Are you willing to accept that, although our brain is a
kind of pointer to our mind, our mind points only on possible
brains, a *big* collection of possible brains, possible
worlds, possible histories.
With comp you can attribute a mind to a machine, but you
cannot attribute a machine to a mind. Just a *big* fuzzy set
of possible "machine".

It is not a question of preliminaries, it is a question of
a whole reasoning.
The first part of the french text is a whole reasoning and that
reasoning needs your
quasi-personal implication (under the form of an imaginary
act of faith: saying yes to the doctor!).
You can get the concreteness of the idea "Dobell institute" on
the net. Computationalism is more a human right than a doctrinal
truth. The implication are big in all directions.

The second part is the best I have been able to do in
substituting *you* by "any sound (godel-lobian) machine" capable
of talking about arithmetic and descriptions of themselves.
I ask the universal machine. (And thank to Godel, Lob, Solovay
I ask its "truth theory" (alias the Guardian Angel) too!

Listen to the machine. What a simple and naive idea, isn't it?
The guardian angel helps only for not misinterpreting the
silences of the (hopefully) consistent machine.

Bruno
Received on Sat Feb 24 2001 - 10:04:46 PST