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From: Marchal <marchal.domain.name.hidden>

Date: Mon Mar 8 07:03:16 1999

James Higgo write :

*>...I am
*

*>flabberghasted that anyone could read my "Universes are related to other
*

*>universes only by correlation, which is a subjective feature...." post and
*

*>agree with it.
*

I agree with it ... relatively to my (comp-) understanding of it. (Of

course).

*> I thought it was pretty radical. Do you know of anywhere
*

*>these ideas are developed further?
*

Difficult question. My feeling is that the idea is, more or less

explicitly, in Pythagore, Xenocrate, Platon, the neoplatoniste (Plotin

...), but also in some idealist school of India and nominalist school of

China, and also in Descartes, Berkeley, Hume, Leibnitz... (you probably

knew that).

I mention http://iridia.ulb.ac.be/marchal :)

Some modern analytical approach which bear on causality or explanation

lends, more or less repulsively, to such ideas. Have you read "David

Lewis: the plurality of worlds" (Basil Blackwell 1986) or his

"Counterfactuals" (idem 1973).

Modal logic, (the science of possible "worlds"/relative truth), is, I

think, an almost unavoidable tool if we hope to make things more precise.

The best textbook, to my knowledge, is Chellas 1980 "Modal Logic, an

Introduction".

This could be premature if you are not logic-minded. Plain english is

still better than eclectic formal exercices. But I hardly imagine

many-worlders tripping seriously without modal logical tools at hands in

the long run.

*> Could you refer me to something on the Skolem paradox?
*

Mmh... It seems you are in a difficult-question mood today.

The search on the net is rather disappointing (today too).

My first encounter with Skolem Paradox (SP) is "Les limitations internes

des formalismes" from Jean Ladriere 1957. 650 pages in french.

A reinterpretation of SP with comp can be find in my

Iridia-Technical-report-1995, 750 pages in french (cruel fate!)...

I got it: I realise I have never mentionned "Boolos G.S. & Jeffrey R.C.,

Computability and Logic, Cambridge University Press, third edition 1989".

It is a very nice and clear and deep introduction to computability,

classical logic including modal and provability logic !

...and you will find in it more than two pages on

Skolem Paradox: pp. 152-155.

SP in a nutshell : the Skolem Paradox (paradox means here:

counter-intuitive result) is a consequence of Loewenheim-Skolem theorem

(LST): any first-order theory which has a model has a denumerable model

(among others).

Now take a model U of a classical first order axiomatisation of set

theory, like Zermelo-Fraenkel set theory (ZF).

Such a model U is usually called a universe (sic).

By LST there is such a denumerable universe U and even transitive one

(i.e. if x belongs to U then x is included in U). U obeys to the axioms

and theorems of set theory, so it is easy to prove the existence of a non

denumerable set y in U (Cantor theorem). So y is non denumerable and is

included in U which is denumerable.

Contradiction. Contradiction?

There is no contradiction. What happens is that bijections between y and

N (which makes y denumerable) does not belong to U. So "from inside" U, y

is correctly proved to be non-denumerable, but for an "outside" observer

of U, y is denumerable. Skolem paradox shows that notion like

"cardinality" are not absolute but are relative to a model.

*> I think I'll pass on the program-writing.
*

Cool !

*>I can't see why you need
*

*>anything more than "LET A=A+1 GOTO START" to generate the universe.
*

You are definitely in the difficult-question mood.

Besides, I tell you I do NOT need anything more than "LET A=A+1 GOTO

START" to generate the universe ...and other machines's dreams.

The problem is to made that statement both obvious and non trivial, to

make people understanding the point AND appreciating the richness of the

point.

The whole thread "information or computation" is all about that. And I

don't thing we got consensus there.

I will not repeat statements by Gille Henry or Jacques M Mallah, but most

of them are founded. Especially if you present such proposition in a so

provocative statement.

Actually, when you say "LET A=A+1 GOTO START generates the universe", I

am afraid you are saying something PRESUMPTUOUS, RIDICULOUS, ALMOST UGLY,

IMPOLITE WITH RESPECT TO DEWITT & WHEELER, Etc. Consolation: it is true,

(trivially provably so with comp).

But truth is a meager and even frustrating consolation if you are not

able to share the "tresor" with others.

You know, there is a time for coming back from the mountain, ...

Now that you pass on the program-writing I will suggest you the following

exercice (forgive my teacher-deformation) :

Exercice : From the statement

"LET A=A+1 GOTO START" generates the universe.

Prove (and make precise) that

Universes are related to

other universes only by correlation,

which is a subjective feature.

Weak anthropic principle is certainly a powerfull tool here, but that's

hardly enough.

I doubt you will ever succeed without the concept of universal turing

machines, and/or without finding some measure on the set of

computationnal histories (remember the thought experiments PE-omega), etc.

And, please, don't underestimate the hardness of making the notion of

"subjective feature" clearer.

... An explicit UD, (or a great programmer) on the contrary, makes more

explicit what is needed for the proof. It is just more pedagogical.

...Luckily enough, part of the work appears to be done in some nice books

like Li and Vityani, Boolos and Jeffrey, etc.

I want add something. When you say, in the preeceding post:

*>In an infinite multiverse universes
*

*>which appear to have any relation you like do in fact exist.
*

*> We appear to
*

*>exist in those sets of universes which can be strung
*

*> together so that the
*

*>laws of physics appear to emerge (weak anthropic principle, my dear
*

*> friend).
*

I agree so much that I believe a big part of the laws of physics can and

must be derived from

"a theory of consciousness" which itself can and must be derived, with

comp,

from theoretical computer science in the form of what machines can tell

(AND NOT TELL) correctly about themselves including their most "probable"

computationnal history.

You can take "theory of consciousness" just in the sense of a theory

of what you call "subjective feature".

And I hope you agree that a subjective feature, is a feature relative to

a subject (alias a person, an observer, a point of view, an "angle"...).

Bruno.

Received on Mon Mar 08 1999 - 07:03:16 PST

Date: Mon Mar 8 07:03:16 1999

James Higgo write :

I agree with it ... relatively to my (comp-) understanding of it. (Of

course).

Difficult question. My feeling is that the idea is, more or less

explicitly, in Pythagore, Xenocrate, Platon, the neoplatoniste (Plotin

...), but also in some idealist school of India and nominalist school of

China, and also in Descartes, Berkeley, Hume, Leibnitz... (you probably

knew that).

I mention http://iridia.ulb.ac.be/marchal :)

Some modern analytical approach which bear on causality or explanation

lends, more or less repulsively, to such ideas. Have you read "David

Lewis: the plurality of worlds" (Basil Blackwell 1986) or his

"Counterfactuals" (idem 1973).

Modal logic, (the science of possible "worlds"/relative truth), is, I

think, an almost unavoidable tool if we hope to make things more precise.

The best textbook, to my knowledge, is Chellas 1980 "Modal Logic, an

Introduction".

This could be premature if you are not logic-minded. Plain english is

still better than eclectic formal exercices. But I hardly imagine

many-worlders tripping seriously without modal logical tools at hands in

the long run.

Mmh... It seems you are in a difficult-question mood today.

The search on the net is rather disappointing (today too).

My first encounter with Skolem Paradox (SP) is "Les limitations internes

des formalismes" from Jean Ladriere 1957. 650 pages in french.

A reinterpretation of SP with comp can be find in my

Iridia-Technical-report-1995, 750 pages in french (cruel fate!)...

I got it: I realise I have never mentionned "Boolos G.S. & Jeffrey R.C.,

Computability and Logic, Cambridge University Press, third edition 1989".

It is a very nice and clear and deep introduction to computability,

classical logic including modal and provability logic !

...and you will find in it more than two pages on

Skolem Paradox: pp. 152-155.

SP in a nutshell : the Skolem Paradox (paradox means here:

counter-intuitive result) is a consequence of Loewenheim-Skolem theorem

(LST): any first-order theory which has a model has a denumerable model

(among others).

Now take a model U of a classical first order axiomatisation of set

theory, like Zermelo-Fraenkel set theory (ZF).

Such a model U is usually called a universe (sic).

By LST there is such a denumerable universe U and even transitive one

(i.e. if x belongs to U then x is included in U). U obeys to the axioms

and theorems of set theory, so it is easy to prove the existence of a non

denumerable set y in U (Cantor theorem). So y is non denumerable and is

included in U which is denumerable.

Contradiction. Contradiction?

There is no contradiction. What happens is that bijections between y and

N (which makes y denumerable) does not belong to U. So "from inside" U, y

is correctly proved to be non-denumerable, but for an "outside" observer

of U, y is denumerable. Skolem paradox shows that notion like

"cardinality" are not absolute but are relative to a model.

Cool !

You are definitely in the difficult-question mood.

Besides, I tell you I do NOT need anything more than "LET A=A+1 GOTO

START" to generate the universe ...and other machines's dreams.

The problem is to made that statement both obvious and non trivial, to

make people understanding the point AND appreciating the richness of the

point.

The whole thread "information or computation" is all about that. And I

don't thing we got consensus there.

I will not repeat statements by Gille Henry or Jacques M Mallah, but most

of them are founded. Especially if you present such proposition in a so

provocative statement.

Actually, when you say "LET A=A+1 GOTO START generates the universe", I

am afraid you are saying something PRESUMPTUOUS, RIDICULOUS, ALMOST UGLY,

IMPOLITE WITH RESPECT TO DEWITT & WHEELER, Etc. Consolation: it is true,

(trivially provably so with comp).

But truth is a meager and even frustrating consolation if you are not

able to share the "tresor" with others.

You know, there is a time for coming back from the mountain, ...

Now that you pass on the program-writing I will suggest you the following

exercice (forgive my teacher-deformation) :

Exercice : From the statement

"LET A=A+1 GOTO START" generates the universe.

Prove (and make precise) that

Universes are related to

other universes only by correlation,

which is a subjective feature.

Weak anthropic principle is certainly a powerfull tool here, but that's

hardly enough.

I doubt you will ever succeed without the concept of universal turing

machines, and/or without finding some measure on the set of

computationnal histories (remember the thought experiments PE-omega), etc.

And, please, don't underestimate the hardness of making the notion of

"subjective feature" clearer.

... An explicit UD, (or a great programmer) on the contrary, makes more

explicit what is needed for the proof. It is just more pedagogical.

...Luckily enough, part of the work appears to be done in some nice books

like Li and Vityani, Boolos and Jeffrey, etc.

I want add something. When you say, in the preeceding post:

I agree so much that I believe a big part of the laws of physics can and

must be derived from

"a theory of consciousness" which itself can and must be derived, with

comp,

from theoretical computer science in the form of what machines can tell

(AND NOT TELL) correctly about themselves including their most "probable"

computationnal history.

You can take "theory of consciousness" just in the sense of a theory

of what you call "subjective feature".

And I hope you agree that a subjective feature, is a feature relative to

a subject (alias a person, an observer, a point of view, an "angle"...).

Bruno.

Received on Mon Mar 08 1999 - 07:03:16 PST

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