At 10:32 09/01/05 +0000, Alastair Malcolm wrote:

For my own part, I give strong credibility (>50%) to the existence of many worlds in some guise or other, and in particular to the existence of all logically possible(*) worlds (alpw).

I certainly agree. Now the problem is that there are many logics, and so

there are many notion or "logical possibility".

The choice of the logic (or logicS) will depend on some basic assumptions.

In particular with the computationalist hypothesis (comp) there is a necessity

to distinguish precisely notions like first and third person point of view and this leads

to different notion of logical possibilities. The Modal logics can help here.

You can read my papers referred in my URL below. A good book introducing

the main logics I am using is the book by Smullyan "Forever Undecided".

I certainly agree. Now the problem is that there are many logics, and so

there are many notion or "logical possibility".

The choice of the logic (or logicS) will depend on some basic assumptions.

In particular with the computationalist hypothesis (comp) there is a necessity

to distinguish precisely notions like first and third person point of view and this leads

to different notion of logical possibilities. The Modal logics can help here.

You can read my papers referred in my URL below. A good book introducing

the main logics I am using is the book by Smullyan "Forever Undecided".

`Actually I'm working currently with still another type of logic: the Shoenfinkel`

Curry Combinatory Logics. This will help for linking my work with the

mainstream logical work of today's logicians (linear logic, for example).

Here too Smullyan wrote a very nice introductory book "To Mock a

Mockingbird". I strongly recommend it. A classical treatise is the North-Holland

book on the Lambda Calculus by Henk Barendregt.

Combinatory logics (and its "sister" the lambda calculus) has failed concerning

its initial goal to provide a logical foundation of the whole of mathematics.

But Combinatory Logics has been, and still is, very useful in the foundation

of computer science (which itself is indispensable through the comp hyp).

Not really the time to say much more now, but my point is that "logical possibility"

is a notion which we should'nt take for granted. Logic is a field full of surprise

and unexpected results.

Curry Combinatory Logics. This will help for linking my work with the

mainstream logical work of today's logicians (linear logic, for example).

Here too Smullyan wrote a very nice introductory book "To Mock a

Mockingbird". I strongly recommend it. A classical treatise is the North-Holland

book on the Lambda Calculus by Henk Barendregt.

Combinatory logics (and its "sister" the lambda calculus) has failed concerning

its initial goal to provide a logical foundation of the whole of mathematics.

But Combinatory Logics has been, and still is, very useful in the foundation

of computer science (which itself is indispensable through the comp hyp).

Not really the time to say much more now, but my point is that "logical possibility"

is a notion which we should'nt take for granted. Logic is a field full of surprise

and unexpected results.

`Concerning your question of believing in the many worlds, I can only give`

you a rough summary of the conclusion of the work I have done in the comp

frame. With the Church thesis (see the diagonalization posts to this list and

referred in my url) there is a universal notion of computation (unlike provability,

proofs, etc.), and all computations exist (the comp form of "everything").

Giving the discrepancy between first and third person notion (see my papers

or see my posts to the list) no observer-machine can ever know which

computations support them, and physical reality (whatever it is) must emerge

from the "interference" (in an a priori larger sense than the quantum sense)

of all the computations which are "rich enough" to support your processing.

This can be computed and compare to actual physics. Until now the

comparison tend to confirm both the quantum hyp. and the comp hyp.

Note that physics is made secondary with respect to computer science, or

logic, or arithmetics. The combinatory logics make possible, in principle,

to distinguish the apparition (in the eyes of the Lobian machine) of

classical physics and quantum physics (and this is new, I mean it is

not explicitly in my thesis).

The common point between my work, Smullyan's Forever undecided, and

Smullyan "To mock a Mockingbird" is, of course, the study of self-reference,

which is the main tool to define formally the first and third person views.

If you read the papers I am referring too, don't hesitate to ask questions.

you a rough summary of the conclusion of the work I have done in the comp

frame. With the Church thesis (see the diagonalization posts to this list and

referred in my url) there is a universal notion of computation (unlike provability,

proofs, etc.), and all computations exist (the comp form of "everything").

Giving the discrepancy between first and third person notion (see my papers

or see my posts to the list) no observer-machine can ever know which

computations support them, and physical reality (whatever it is) must emerge

from the "interference" (in an a priori larger sense than the quantum sense)

of all the computations which are "rich enough" to support your processing.

This can be computed and compare to actual physics. Until now the

comparison tend to confirm both the quantum hyp. and the comp hyp.

Note that physics is made secondary with respect to computer science, or

logic, or arithmetics. The combinatory logics make possible, in principle,

to distinguish the apparition (in the eyes of the Lobian machine) of

classical physics and quantum physics (and this is new, I mean it is

not explicitly in my thesis).

The common point between my work, Smullyan's Forever undecided, and

Smullyan "To mock a Mockingbird" is, of course, the study of self-reference,

which is the main tool to define formally the first and third person views.

If you read the papers I am referring too, don't hesitate to ask questions.

Bruno

http://iridia.ulb.ac.be/~marchal/