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

Date: Wed, 21 Apr 2004 12:35:24 +0200

At 01:07 20/04/04 -0400, Wei Dai wrote:

*>This is an imaginary conversation between me and a Bayesian. His answers
*

*>are in parenthesis. Do you find this line of argument convincing?
*

*>
*

*>----
*

*>
*

*>Consider all possible worlds consistent with your memories and current
*

*>experiences. In other words, all possible worlds that contain at least one
*

*>observer with memories and current experiences exactly identical to yours.
*

*>Are there more than one such world?
*

*>
*

*>(yes)
*

*>
*

*>Is every one of these worlds isomorphic to some mathematical structure?
*

*>
*

*>(How do you define "mathematical structure"?)
*

*>
*

*>A set class.
*

Why not a category? It can be bigger. Why not the category CAT of all

categories? It is much bigger. You will meet here the problem of defining

mathematically the class of all mathematical structures.

A very old insoluble problem ... It is one of the major problem

in Tegmark approach.

The other problem which I see in your argument, and which is common

in both Tegmark and Schmidhuber (and not mentionned in Hal Finney

recent answer to your post) is that you are implicitly associating

mind and structure/universe using some form of psycho-parallelism.

Such association are incompatible with just quantum mechanics

without collapse (I think Zeh has seen this point). Actually such

association is completely forbidden with only the comp hyp as I have

argued at length before. Even the ontologically large modal realism

of David Lewis makes such association at least not-obvious.

Keeping just the class of all sets is also ambiguous by itself: which

theory of sets will you choose? If you take a theory with an

extensionality axiom (where sets are defined completely by their

elements)? In that case I don't know any "physical" object which could be

seen as a set. Do you accept the axiom of choice for non countable

sets? Are you allowing higher infinities? Which one?

More generally, how will you relate the worlds and the sets? Is a chair

described by its wave function or by more palatable observer memories

entangled with that wave function? How do you intend to relate first

and third person point of view?

[snip]

*>If you go back and look at how those principles of reasoning were derived
*

*>or justified, it was on the basis of simplicity and avoiding absurd
*

*>actions ("absurd" being defined by intuition or common sense). The
*

*>assumption that the actual world is the class of all sets is equally
*

*>justified on the basis of avoiding absurd actions and is simpler than
*

*>having a prior over possible worlds, so why not?
*

I have no clues what you mean by "absurd" here.

Bruno

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

Received on Wed Apr 21 2004 - 06:33:59 PDT

Date: Wed, 21 Apr 2004 12:35:24 +0200

At 01:07 20/04/04 -0400, Wei Dai wrote:

Why not a category? It can be bigger. Why not the category CAT of all

categories? It is much bigger. You will meet here the problem of defining

mathematically the class of all mathematical structures.

A very old insoluble problem ... It is one of the major problem

in Tegmark approach.

The other problem which I see in your argument, and which is common

in both Tegmark and Schmidhuber (and not mentionned in Hal Finney

recent answer to your post) is that you are implicitly associating

mind and structure/universe using some form of psycho-parallelism.

Such association are incompatible with just quantum mechanics

without collapse (I think Zeh has seen this point). Actually such

association is completely forbidden with only the comp hyp as I have

argued at length before. Even the ontologically large modal realism

of David Lewis makes such association at least not-obvious.

Keeping just the class of all sets is also ambiguous by itself: which

theory of sets will you choose? If you take a theory with an

extensionality axiom (where sets are defined completely by their

elements)? In that case I don't know any "physical" object which could be

seen as a set. Do you accept the axiom of choice for non countable

sets? Are you allowing higher infinities? Which one?

More generally, how will you relate the worlds and the sets? Is a chair

described by its wave function or by more palatable observer memories

entangled with that wave function? How do you intend to relate first

and third person point of view?

[snip]

I have no clues what you mean by "absurd" here.

Bruno

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

Received on Wed Apr 21 2004 - 06:33:59 PDT

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