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

Date: Thu, 24 Apr 2003 09:26:22 +0200

At 03:46 20/04/03 -0400, Benjamin Udell wrote:

*>I notice that he does not mention universes wherein unconventional (for
*

*>our everyday purposes) forms of logic, information, or probability would
*

*>hold as most suitable. He does put predicate logic at the base of his
*

*>mathematical structure. But would variations in suitable logical structure
*

*>- different numbers of truth values, for instance - be most likely to be
*

*>found only across Level IV?
*

Tegmark is just very naive about what mathematical

reality can be. He has a 19th century philosophy of mathematics.

At least Tegmark, unlike Schmidhuber, is aware that we must

take into account some difference between point of views, but

he does not take those differences into account enough, and sweeps

(like so much "scientist") the mind-body problem under the rug.

*>More generally, _wouldn't variations in the suitable form of mathematical
*

*>logic, information, & probability & uncertainty, more plausibly reflect
*

*>something pertaining to quantum coherence, decoherence, etc., which are at
*

*>the basis for the idea of Level III, than anything pertaining to the ideas
*

*>for the other Levels?_ (Not that I know a great deal about quantum
*

*>coherence!) But Level III seems like the place for such variations, if
*

*>anywhere. No?
*

Only if you presuppose physicalism (which, BTW, has been

shown incompatible with the computationalist hypothesis

in the cognitive science, Marchal 88, Maudlin 89, see the ref

in my thesis downloadable from my URL, below).

*>Tegmark does discuss how different lightcone structures (reflecting
*

*>variation across Level II) would affect one's capacity for inference, but
*

*>inferential processes in an intelligent system are a different thing than
*

*>the subjects of mathematical theories of logic, information, probability,
*

*>& uncertainty. I mean that differences of lightcone structure would affect
*

*>intelligent (including inferential & other philosophically interesting)
*

*>processes as they would affect cybernetic, stochastic, & sensitive
*

*>dynamic processes. But these differences would not necessarily reflect
*

*>different forms of *mathematical* logic, information, or probability or
*

*>(more generally) uncertainty.
*

This depends on many possible philosophical assumptions.

*>I don't know whether variation in "most-suitable" forms of math-logic
*

*>(e.g., different numbers of truth values), math-information,
*

*>math-probability across a multiverse would tend to lead to the
*

*>"high-energy messes" that Tegmark mentions. I don't know whether they
*

*>would lead to qualitatively more universes in Level III than in Level II.
*

*>It seems to me like they might, but I'm no physicist! Maybe it would
*

*>amount to a violation of ergodicity as Tegmark warns, but perhaps for some
*

*>quantum-related reason these particular alternate kinds of universes would
*

*>be counted differently by the theory.
*

*>
*

*>As for information, probability, & uncertainty, I don't know enough about
*

*>mathematical theories of them, to know what element in them one might
*

*>consider as perhaps varying across a multiverse. Sorry, I wish I could do
*

*>better. As regards three- or higher-valued logics, where these prevail as
*

*>suitable, there perhaps they would start to impact the view of mathematics
*

*>itself in strange ways, I don't even know that much. For all I know, if
*

*>alternate forms of logic, etc., hold as most suitable in some places,
*

*>maybe this impacts those places' view of the structure of the four-level
*

*>multiverse itself. Maybe some places would regard there as being nine or
*

*>27 rather than four levels? Should predicate logic, if the root of such
*

*>radical variations, therefore be put, as Tegmark already puts it, at the
*

*>base of the mathematical structure? (On the other hand, do the four levels
*

*>have to have a rigidly Comtean hierarchy? They might have some kind of
*

*>4-chotomical structure with a subtler kind of!
*

*> hierarchicality. After all, some consider mathematical logic an applied
*

*> field while others regard it as Day One 8 a.m.)
*

Mathematical logic is just a branch of math, like topology or

geometry, etc. The idea that logic should be used as foundations

is known to be silly since the work of Dedekind, Godel, etc.

To study "variant of logics" two related roads can be used: either

by a weakening of classical logic (you can get

intuitionistic logic, quantum logic, intuitionistic quantum

logic, etc.), or by extending (classical) logic with modal connectives.

Some weak logics can be mirrored by modal logics and can

give epistemic or pragmatic interpretations to those weak logic.

Modal logic is a powerful tool to study invariant discourses

with respect to "observer's possible trips". The main

problem is how to choose a modal logic. In my work I have

shown how extract the unique possible logic for the physical

propositions from the only possible psychological propositions

you get from Church thesis and some amount of arithmetical

realism, once you postulate the computationnalist hypothesis

in the cognitive science. In french: with the comp hypothesis

the aristotelian notion of substance evaporates and physical

realities emerge from the provable coherence of machine dreams,

where a machine dream is 2^aleph_0 computations seen

from inside, and where "seen from inside" is defined through the

complete (at some level) and sound godelian logic of

self-reference.

*>What got me asking these questions was that Tegmark's four-level
*

*>multiverse picture struck me as seeming to reflect, somewhat, a structure
*

*>of the fields of research as I had pictured them.
*

*>
*

*>If all possible universes exist, & if the idiosyncrasies of histories are
*

*>reflected at Level I, & the far reaches of abstract mathematics at Level
*

*>IV, one might well wonder whether there is a reflection, a similarity to
*

*>be seen, between the set of the four Levels of multiverses & the outlines
*

*>of the most general kinds of research -- science, mathematics, &
*

*>intermediate fields. A similarity between multiverse "constellations" &
*

*>the "city" of research. This would require at the least that researches
*

*>collectively have developed to a point where their "natural" (unplanned,
*

*>but persistent & making some kind of sense) outlines could be seen. And of
*

*>course who knows what multiverse-theory will be like (if it persists at
*

*>all) in even only a few years. So in a way this is a lark.
*

I doubt it. Not only there are too many evidences for multiverse

theories, but there are no evidence for 1 universe theory,

and strictly speaking there is only 0 universes-theory or

many-universes theory in the literature. Of course a lot of

people believes that classical physics, for example, is a

1-universe theory. But this is logically untenable, and is

just a form of wishful thinking in naive cosmology.

Reality is like the Chinese TAO. Give it a name and then

it multiplies.

*>I wanted to pursue the analogy, because it seemed to be roughly
*

*>working for Levels I, II, & IV. Tegmark's III & my "III", if they do
*

*>roughly match up, are less than obvious about it to me.
*

*>
*

*>Tegmark's multiverse levels:
*

*>I. Different initial conditions, different histories.
*

*>II. Different constants.
*

*>III. Different quantum branches.
*

*>IV. Different mathematical laws. STRUCTURES
*

*>
*

*>Arrangement of areas of research:
*

*>I.. Empirical sciences/studies (from human/social studies to physics).
*

*>II. Mechanical/systems/process theoretical research with generalized
*

*>applicability (e.g., philosophy itself?, cybernetics, statistical
*

*>mechanics, complex (conditions-sensitive) mechanics).
*

*>III. Applied yet mathematically deep fields (math. theories of logic,
*

*>info., probability, & perhaps some other mathematical theories of
*

*>uncertainty, like possibility theory).
*

*>IV. Pure mathematics.
*

*>
*

*>Actually I tend to put these fields of research in exactly the reverse
*

*>order, it's become a habit. My habits are a unusual kind of subject,
*

*>marked as they are by the fact that, about them, I actually know something.
*

*>
*

*>Thank you for your patience, anybody who has read all this, & any
*

*>responses will be appreciated.
*

*>
*

*>Benjamin Udell,
*

*>Lifelong layperson who likes 4-chotomies, reads some philosophy, & enjoys
*

*>articles on cosmology for the educated public.
*

You are welcome, You will find links to more of

what I have said in my URL below, including some

contributions to this list.

Bruno

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

Received on Thu Apr 24 2003 - 03:27:42 PDT

Date: Thu, 24 Apr 2003 09:26:22 +0200

At 03:46 20/04/03 -0400, Benjamin Udell wrote:

Tegmark is just very naive about what mathematical

reality can be. He has a 19th century philosophy of mathematics.

At least Tegmark, unlike Schmidhuber, is aware that we must

take into account some difference between point of views, but

he does not take those differences into account enough, and sweeps

(like so much "scientist") the mind-body problem under the rug.

Only if you presuppose physicalism (which, BTW, has been

shown incompatible with the computationalist hypothesis

in the cognitive science, Marchal 88, Maudlin 89, see the ref

in my thesis downloadable from my URL, below).

This depends on many possible philosophical assumptions.

Mathematical logic is just a branch of math, like topology or

geometry, etc. The idea that logic should be used as foundations

is known to be silly since the work of Dedekind, Godel, etc.

To study "variant of logics" two related roads can be used: either

by a weakening of classical logic (you can get

intuitionistic logic, quantum logic, intuitionistic quantum

logic, etc.), or by extending (classical) logic with modal connectives.

Some weak logics can be mirrored by modal logics and can

give epistemic or pragmatic interpretations to those weak logic.

Modal logic is a powerful tool to study invariant discourses

with respect to "observer's possible trips". The main

problem is how to choose a modal logic. In my work I have

shown how extract the unique possible logic for the physical

propositions from the only possible psychological propositions

you get from Church thesis and some amount of arithmetical

realism, once you postulate the computationnalist hypothesis

in the cognitive science. In french: with the comp hypothesis

the aristotelian notion of substance evaporates and physical

realities emerge from the provable coherence of machine dreams,

where a machine dream is 2^aleph_0 computations seen

from inside, and where "seen from inside" is defined through the

complete (at some level) and sound godelian logic of

self-reference.

I doubt it. Not only there are too many evidences for multiverse

theories, but there are no evidence for 1 universe theory,

and strictly speaking there is only 0 universes-theory or

many-universes theory in the literature. Of course a lot of

people believes that classical physics, for example, is a

1-universe theory. But this is logically untenable, and is

just a form of wishful thinking in naive cosmology.

Reality is like the Chinese TAO. Give it a name and then

it multiplies.

You are welcome, You will find links to more of

what I have said in my URL below, including some

contributions to this list.

Bruno

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

Received on Thu Apr 24 2003 - 03:27:42 PDT

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