I previously tried cutting and pasting the text instead of giving a
link no one apparently went to before replying because the formatting
was off.  So I will do that because it seems that would be prudent.  I
figured it out.  (I'm not computer guru....)




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Any interest in discussing Tegmark's Mathematical Universe

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Brian
Tenneson

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 More options Mar 1, 11:47 am


Newsgroups: sci.logic
From: Brian Tenneson <[EMAIL PROTECTED]>
Date: Sat, 1 Mar 2008 11:47:48 -0800 (PST)
Local: Sat, Mar 1 2008 11:47 am
Subject: Any interest in discussing Tegmark's Mathematical

Universe Hypothesis?
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[This post is in sci.logic because of the employment of model

theory
and discussion of abstract math structures by the author and

for other
reasons which may come up during the discussion.]
Here is a link to the article:
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0646v2.pdf
Abstract:
I explore physics implications of the External Reality

Hypothesis
(ERH) that there exists an
external physical reality completely independent of us humans.

I argue
that with a sufficiently
broad definition of mathematics, it implies the Mathematical

Universe
Hypothesis (MUH) that our
physical world is an abstract mathematical structure. I

discuss
various implications of the ERH
and MUH, ranging from standard physics topics like symmetries,


irreducible representations, units,
free parameters, randomness and initial conditions to broader

issues
like consciousness, parallel
universes and G"odel incompleteness. I hypothesize that only
computable and decidable (in G"odel's
sense) structures exist, which alleviates the cosmological

measure
problem and may help explain why
our physical laws appear so simple. I also comment on the

intimate
relation between mathematical
structures, computations, simulations and physical systems.
Quote from Intro:
The idea that our universe is in some sense mathematical
goes back at least to the Pythagoreans, and has been
extensively discussed in the literature (see, e.g., [2-25]).
Galileo Galilei stated that the Universe is a grand book
written in the language of mathematics, and Wigner reflected
on the "unreasonable effectiveness of mathematics
in the natural sciences" [3]. In this essay, I will push this
idea to its extreme and argue that our universe is mathematics


in a well-defined sense.
[End Quote]
The article linked to above is regarded by its author as a

sequel to
this:
http://space.mit.edu/home/tegmark/toe.pdf
Abstract: (sorry, some characters didn't enjoy being c&p'ed)
We discuss some physical consequences of what might be
called \the ultimate ensemble theory", where not only worlds
corresponding to say di erent sets of initial data or di erent


physical constants are considered equally real, but also

worlds
ruled by altogether di erent equations. The only postulate
in this theory is that all structures that exist

mathematically
exist also physically, by which we mean that in those
complex enough to contain self-aware substructures (SASs),
these SASs will subjectively perceive themselves as existing

in
a physically \real" world. We  nd that it is far from clear

that
this simple theory, which has no free parameters whatsoever,
is observationally ruled out. The predictions of the theory
take the form of probability distributions for the outcome of
experiments, which makes it testable. In addition, it may be
possible to rule it out by comparing its a priori predictions
for the observable attributes of nature (the particle masses,
the dimensionality of spacetime, etc.) with what is observed.
Quote:
In other words, some subset of all mathematical structures
(see Figure 1 for examples) is endowed with an
elusive quality that we call physical existence, or PE for
brevity. Specifying this subset thus speci es a category
1 TOE. Since there are three disjoint possibilities (none,
some or all mathematical structures have PE), we obtain
the following classi cation scheme:
1. The physical world is completely mathematical.
(a) Everything that exists mathematically exists
physically.
(b) Some things that exist mathematically exist
physically, others do not.
(c) Nothing that exists mathematically exists
physically.
2. The physical world is not completely mathematical.
The beliefs of most physicists probably fall into categories
2 (for instance on religious grounds) and 1b. Category
2 TOEs are somewhat of a resignation in the sense of
giving up physical predictive power, and will not be further
discussed here. The obviously ruled out category
1c TOE was only included for completeness. TOEs in
the popular category 1b are vulnerable to the criticism
(made e.g. by Wheeler [6], Nozick [7] and Weinberg [8])
that they leave an important question unanswered: why
is that particular subset endowed with PE, not another?
...
In this paper, we propose that category 1a is the correct
one.
[End quote]
I'm also interested in discussing what SAS'es might there be.

Perhaps
nail down axioms and/or defining traits of SAS'es.  This next

link
might be a diversion, but it is a starting point for the

discussion of
formalizing awareness:
http://cs.wwc.edu/~aabyan/Colloquia/Aware/aware2.html
I suppose the direction I'd +like+ this discussion to go is
investigation of this material as conjecture, what these

conjectures
would entail (physically, mathematically, and

philosophically), etc., +
+rather than debate as to the validity of these conjectures.++
It seems to me that, at worst, these conjectures form an

internally
consistent theory, not unlike Cantor's theory of the infinite;


whether  or not these conjectures are correct in a physics

sense as
being an accurate characterization of "reality," I would like

to view
these conjectures/hypotheses as, in this discussion at

sci.logic, at
worst, an internally consistent framework, worthy enough of
investigation because of the consistency, regardless of

physical
correctness.
Obviously, if these conjectures/hypotheses are correct in a

physics
sense, then the investigation is even more justified when

compared to
mathematical and/or philosophical justification for the

investigation.


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Brian
Tenneson

View profile

 More options Mar 1, 12:30 pm


Newsgroups: sci.logic
From: Brian Tenneson <[EMAIL PROTECTED]>
Date: Sat, 1 Mar 2008 12:30:05 -0800 (PST)
Local: Sat, Mar 1 2008 12:30 pm
Subject: Re: Any interest in discussing Tegmark's Mathematical

Universe
Hypothesis?
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The last link provided is giving me intermittent failure, so

here are
two cached versions to try:
1st cached version of aware2.html:
http://web.archive.org/web/20060827232622/http://www.cs.wwc.ed

u/~aaby...
1st link to 2nd cached version of aware2.html:
<a

href="http://209.85.173.104/search?q=cache:dil-L-g7Mj0J:cs.wwc

.edu/
~aabyan/Colloquia/Aware/aware2.html
+aware2+site:cs.wwc.edu&hl=en&ct=clnk&cd=1&gl=us">Google

cached
version</a>
Hopefully this forum will allow the html above because the

link might
be too long with wrapping and c&p'ing considerations:
2nd link to 2nd cached version of aware2.html:
http://209.85.173.104/search?q=cache:dil-L-g7Mj0J:cs.wwc.edu/~

aabyan/...
Also, a new link in the direction of the non-computability of
consciousness, which seems to be a strike against some of

Tegmark's
hypotheses (in particular, the computable universe hypothesis

in
section VII of the very first article linked to in the

previous post,
"assuming" that non-computability of consciousness implies the

non-
computability of the universe in that consciousness is

"contained in"
the universe), is here:
Non-Computability of Consciousness
http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.1617v1.pdf
Abstract:
With the great success in simulating many intelligent

behaviors using
computing devices, there has been an ongoing debate whether

all
conscious
activities are computational processes. In this paper, the

answer to
this
question is shown to be no. A certain phenomenon of

consciousness is
demonstrated to be fully represented as a computational

process using
a
quantum computer. Based on the computability criterion

discussed with
Turing machines, the model constructed is shown to necessarily

involve
a
non-computable element. The concept that this is solely a

quantum
effect
and does not work for a classical case is also discussed.


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Brian

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 More options Mar 3, 12:38 pm


Newsgroups: sci.logic
From: Brian <[EMAIL PROTECTED]>
Date: Mon, 3 Mar 2008 12:38:29 -0800 (PST)
Local: Mon, Mar 3 2008 12:38 pm
Subject: Re: Any interest in discussing Tegmark's Mathematical

Universe
Hypothesis?
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On Mar 1, 12:30 pm, Brian Tenneson <[EMAIL PROTECTED]> wrote:

- Hide quoted text -
- Show quoted text -

> Also, a new link in the direction of the non-computability

of
> consciousness, which seems to be a strike against some of

Tegmark's
> hypotheses (in particular, the computable universe

hypothesis in
> section VII of the very first article linked to in the

previous post,
> "assuming" that non-computability of consciousness implies

the non-
> computability of the universe in that consciousness is

"contained in"
> the universe), is here:
> Non-Computability of
Consciousnesshttp://arxiv.org/PS_cache/arxiv/pdf/0705/0705.161

7v1.pdf
> Abstract:
> With the great success in simulating many intelligent

behaviors using
> computing devices, there has been an ongoing debate whether

all
> conscious
> activities are computational processes. In this paper, the

answer to
> this
> question is shown to be no. A certain phenomenon of

consciousness is
> demonstrated to be fully represented as a computational

process using
> a
> quantum computer. Based on the computability criterion

discussed with
> Turing machines, the model constructed is shown to

necessarily involve
> a
> non-computable element. The concept that this is solely a

quantum
> effect
> and does not work for a classical case is also discussed.
I recently came across an apparent rejoinder (intentional or

not, I
don't know) by Tegmark on the subject of the quantum nature of

brain
function.
http://space.mit.edu/home/tegmark/brain.html
Tegmark makes a case for brain function being modeled

adequately with
classical theoretical means (possibly such as Turing machines)

and
that brains do not function like quantum computers.

(Essentially the
main factor is that the brain is not nearly at absolute zero

degrees,
or otherwise in an environment in which superposition type

effects
that consciousness apparently mimics well enough to keep many

on the
fence, is more common than Earthly temperatures where our

brains
normally reside.)
If Tegmark does prove his point, while others in his community

remain
skeptical that brain function is +not+ an example of a quantum


computer, then the paper I cited about the non-computability

of
consciousness does not invalidate Tegmark's CUH, mentioned in

section
VII of the first link in the first post.  The

non-computability of
consciousness would seem to invalidate Tegmark's CUH

(Computable
Universe Hypothesis) in that the universe, by even a narrow

definition
of universe, must contain consciousness, and, I presume, non-
computability of consciousness would imply the CUH is false.

That is,
unless consciousness can have non-computable aspects that when


"glued" (ultraproduct or some other method of "gluing"???)

together
throughout the universe, somehow (I know this is vague) the

non-
computable aspects of various parts of the universe all

balance out to
a computable universe.  Hmm...things to think about...  Maybe

the CUH
is true and brains work like quantum computers, somehow...?
Anyway, Tegmark would be lending credence to his point by

invalidating
the proof of non-computability of consciousness for that

relies on the
"presumption" that consciousness is inherently a quantum

process;
obviously if their critical "presumption" is wrong, then their


conclusion (consciousness not being computable) isn't

necessarily so.
I think it is worth splitting hairs here about the difference

between
consciousness and brain function but as of yet am aware of

very little
of the +formal+ theory behind either of these notions,
philosophically, psychologically, or cognitive-scientifically.
I am compiling a list of other discussion points.
First on this list of discussion points, I will make a

connection to
abstract fuzzy logic and the Level IV multiverse situation.

If you
haven't read these fascinating articles yet, Level IV's brief
definition is:
Other mathematical structures give different +fundamental+

equations
of physics.
In the MUH article (first link, first post), appendix A

defines what
Tegmark means by a mathematical structure.
[Compilation Process] I'm thinking of whether or not the

aggregate of
all MS's can be "glued" together somehow (doubtfully by a

simple
union) in order to get the MS of all MS's.
This brings me to the connection to abstract fuzzy logic and

my
personal quest to continue my education in the area of Fuzzy

Logic.
(Apparently, no one in the US works specifically in the area I

want to
work in but there are many in Europe at institutions that

award
Phds.)  It also gratifies me, on a personal note, to think

that my
research, if carried out, might settle some question about

whether or
not the [Compilation Process]  is at all possible in any

"reasonable"
sense whatsoever.  It would be nice to know either way, rather

than a
"this smells like Russell's Paradox, so let's not try it" sort

of
deal.
My research would focus on somewhat recent papers on fuzzy

logic
pertaining to involving FL at the axiomatic level to create
generalizations and anti-generalizations of ZFC set theory, or

other
suitably modified set theory (eg, remove Foundation Axiom

immediately
for reasons that would be clear later).
According to the conclusion of that paper, linked to below, an

open
problem is figuring out how other axioms could be, should be,
shouldn't be, and can't be consistently added to the list of

axioms
they present in a FL-sense.
[[1]]

http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zSzzSzw

ww.cs.c...
In an effort to push question (2) in a particular direction,

let me
attempt to formulate my question/problem.  Start with the

bare-bones
fuzzy set theory presented in [[1]].  Let the truth set be

denoted D.
Consider the following axioms:
[[U.Strong]]  there is a y such that for all x, the truth

degree of
the formula "x is in y" is the maximal (in the sense

appropriate to
the type of algebraic structure D has, such as an MV-algebra,

but
definitely not Boolean as we know Russell's Paradox +will+

rear its
ugly head in the Boolean case) element in D.
In other words, if the maximal element in D is equipped with

the
baggage "true", U.S. says there is a set y for which all sets

x are
elements of y.  This is one reason to drop the Foundation

Axiom
immediately, as such a y is obviously not well-founded.  This

could be
called a (strong) universal set, with appropriate adjectives

that
reference D and the syntactical entailment axioms used, the

underlying
language, etc...
[[U.Weak]]  there is a y such that for all x, the truth degree

of the
formula "x is in y" is a designated element of D.
In words, I view the designated, anti-designated, and

non-designated
partitions of D as shades of gray of truth.  Designated means

more
light than not, where light = truth in this analogy,

anti-designated
means more dark than not, and non-designated means more gray

than
not.  So to say " 'x is in y' is a designated truth value"

would mean
something like, "it's essentially true that y is a universal

set."
One could say that y would be a weak universal set and it is

doubtful
that such a y need be unique, unlike a strong universal set

is.
That sets (pun intended) up the problem (below) that I hope to


formalize into the beginnings of a PhD thesis in the area of

FL
someday.
Let R be some type of unary predicate.
Recall that D is the set of truth degrees, with some algebraic

(eg,
MV) structure associated with it.
Consider the statement below:
[[Statement]] A fuzzy set theory, starting with the one in

[[1]],
without Foundation, plus either the strong or weak universal

set
axiom, is consistent relative to ZFC (the best situation one

can hope
for) if and only if R(D).
The question: Determine for what R is the above statement

true, if
any, or prove that for all R, the above statement is false.
Obviously, I want, at worst, an existence proof on R, that

there are
some properties D could possess that enables a fuzzy universal

set
theory that is consistent relative to ZFC.
Also, I strongly hope that the statement is not false for all

R, that
there aren't any exotic D's or structures they could be

equipped with,
to make a universal set theory as consistent as ZFC.  Clearly,

if D =
{0,1} then the set of all R's for which [[Statement]] is true

is empty
(bad but expected and well known).  In the binary logic case,
Russell's Theorem proves that the set of all R's for which
[[Statement]] is true is empty.  No properties on D make the

universal
set a possibility in classical logic (except possibly the work

of the
sort Quinne did with the New Foundations although, in NF,

Choice must
be dropped, in some sense, which is highly disadvantageous to

anyone
who enjoys using Zorn's Lemma).
(I posed this to someone known in the area of FL and he

encouraged me
to come to Europe (as apparently no one does this type of work

in FL
in the U.S.) to formally work this into a PhD thesis.)
Now, ultimately, the connection to the CUH is that if there is

an
ultimate set of +some kind+, like a strong universal set, then

perhaps
that could provide a link to the MS of all MS's, ie, the

mathematical
structure of all mathematical structures, without leading to

deals
like, "this smells like Russell's dirty laundry, so let's not

go
there."
<punchline tag>
Either that or provide an interesting, to say the least, MS (a

fuzzy
and strong universal set theory) to investigate in the context

of the
MUH, as this strong universal fuzzy set may, in fact, be a

candidate
for what the universe literally is in a physical sense,

assuming the
MUH, of course.
</punchline tag>
If I could make all of that work, I would be a very happy man.

 Even
if I could be proved wrong, at least then I can rest on this

issue in
particular.


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Brian

View profile

 More options Mar 4, 10:21 am


Newsgroups: sci.logic
From: Brian <[EMAIL PROTECTED]>
Date: Tue, 4 Mar 2008 10:21:00 -0800 (PST)
Subject: Re: Any interest in discussing Tegmark's Mathematical

Universe
Hypothesis?
Reply | Reply to author | Forward | Print | Individual message

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On Mar 3, 12:38 pm, Brian <[EMAIL PROTECTED]> wrote:

- Hide quoted text -
- Show quoted text -

> On Mar 1, 12:30 pm, Brian Tenneson <[EMAIL PROTECTED]>

wrote:
> > Also, a new link in the direction of the non-computability

of
> > consciousness, which seems to be a strike against some of

Tegmark's
> > hypotheses (in particular, the computable universe

hypothesis in
> > section VII of the very first article linked to in the

previous post,
> > "assuming" that non-computability of consciousness implies

the non-
> > computability of the universe in that consciousness is

"contained in"
> > the universe), is here:
> > Non-Computability of
Consciousnesshttp://arxiv.org/PS_cache/arxiv/pdf/0705/0705.161

7v1.pdf
> > Abstract:
> > With the great success in simulating many intelligent

behaviors using
> > computing devices, there has been an ongoing debate

whether all
> > conscious
> > activities are computational processes. In this paper, the

answer to
> > this
> > question is shown to be no. A certain phenomenon of

consciousness is
> > demonstrated to be fully represented as a computational

process using
> > a
> > quantum computer. Based on the computability criterion

discussed with
> > Turing machines, the model constructed is shown to

necessarily involve
> > a
> > non-computable element. The concept that this is solely a

quantum
> > effect
> > and does not work for a classical case is also discussed.
> I recently came across an apparent rejoinder (intentional or

not, I
> don't know) by Tegmark on the subject of the quantum nature

of brain
> function.http://space.mit.edu/home/tegmark/brain.html
> Tegmark makes a case for brain function being modeled

adequately with
> classical theoretical means (possibly such as Turing

machines) and
> that brains do not function like quantum computers.

(Essentially the
> main factor is that the brain is not nearly at absolute zero

degrees,
> or otherwise in an environment in which superposition type

effects
> that consciousness apparently mimics well enough to keep

many on the
> fence, is more common than Earthly temperatures where our

brains
> normally reside.)
> If Tegmark does prove his point, while others in his

community remain
> skeptical that brain function is +not+ an example of a

quantum
> computer, then the paper I cited about the non-computability

of
> consciousness does not invalidate Tegmark's CUH, mentioned

in section
> VII of the first link in the first post.  The

non-computability of
> consciousness would seem to invalidate Tegmark's CUH

(Computable
> Universe Hypothesis) in that the universe, by even a narrow

definition
> of universe, must contain consciousness, and, I presume,

non-
> computability of consciousness would imply the CUH is false.

 That is,
> unless consciousness can have non-computable aspects that

when
> "glued" (ultraproduct or some other method of "gluing"???)

together
> throughout the universe, somehow (I know this is vague) the

non-
> computable aspects of various parts of the universe all

balance out to
> a computable universe.  Hmm...things to think about...

Maybe the CUH
> is true and brains work like quantum computers, somehow...?
> Anyway, Tegmark would be lending credence to his point by

invalidating
> the proof of non-computability of consciousness for that

relies on the
> "presumption" that consciousness is inherently a quantum

process;
> obviously if their critical "presumption" is wrong, then

their
> conclusion (consciousness not being computable) isn't

necessarily so.
> I think it is worth splitting hairs here about the

difference between
> consciousness and brain function but as of yet am aware of

very little
> of the +formal+ theory behind either of these notions,
> philosophically, psychologically, or

cognitive-scientifically.
> I am compiling a list of other discussion points.
> First on this list of discussion points, I will make a

connection to
> abstract fuzzy logic and the Level IV multiverse situation.

If you
> haven't read these fascinating articles yet, Level IV's

brief
> definition is:
> Other mathematical structures give different +fundamental+

equations
> of physics.
> In the MUH article (first link, first post), appendix A

defines what
> Tegmark means by a mathematical structure.
> [Compilation Process] I'm thinking of whether or not the

aggregate of
> all MS's can be "glued" together somehow (doubtfully by a

simple
> union) in order to get the MS of all MS's.
> This brings me to the connection to abstract fuzzy logic and

my
> personal quest to continue my education in the area of Fuzzy

Logic.
> (Apparently, no one in the US works specifically in the area

I want to
> work in but there are many in Europe at institutions that

award
> Phds.)  It also gratifies me, on a personal note, to think

that my
> research, if carried out, might settle some question about

whether or
> not the [Compilation Process]  is at all possible in any

"reasonable"
> sense whatsoever.  It would be nice to know either way,

rather than a
> "this smells like Russell's Paradox, so let's not try it"

sort of
> deal.
> My research would focus on somewhat recent papers on fuzzy

logic
> pertaining to involving FL at the axiomatic level to create
> generalizations and anti-generalizations of ZFC set theory,

or other
> suitably modified set theory (eg, remove Foundation Axiom

immediately
> for reasons that would be clear later).
> According to the conclusion of that paper, linked to below,

an open
> problem is figuring out how other axioms could be, should

be,
> shouldn't be, and can't be consistently added to the list of

axioms
> they present in a FL-sense.
>

[[1]]http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zS

zzSzwww.cs.c...
> In an effort to push question (2) in a particular direction,

let me
> attempt to formulate my question/problem.  Start with the

bare-bones
> fuzzy set theory presented in [[1]].  Let the truth set be

denoted D.
> Consider the following axioms:
> [[U.Strong]]  there is a y such that for all x, the truth

degree of
> the formula "x is in y" is the maximal (in the sense

appropriate to
> the type of algebraic structure D has, such as an

MV-algebra, but
> definitely not Boolean as we know Russell's Paradox +will+

rear its
> ugly head in the Boolean case) element in D.
> In other words, if the maximal element in D is equipped with

the
> baggage "true", U.S. says there is a set y for which all

sets x are
> elements of y.  This is one reason to drop the Foundation

Axiom
> immediately, as such a y is obviously not well-founded.

This could be
> called a (strong) universal set, with appropriate adjectives

that
> reference D and the syntactical entailment axioms used, the

underlying
> language, etc...
> [[U.Weak]]  there is a y such that for all x, the truth

degree of the
> formula "x is in y" is a designated element of D.
> In words, I view the designated, anti-designated, and

non-designated
> partitions of D as shades of gray of truth.  Designated

means more
> light than not, where light = truth in this analogy,

anti-designated
> means more dark than not, and non-designated means more gray

than
> not.  So to say " 'x is in y' is a designated truth value"

would mean
> something like, "it's essentially true that y is a universal

set."
> One could say that y would be a weak universal set and it is

doubtful
> that such a y need be unique, unlike a strong universal set

is.
> That sets (pun intended) up the problem (below) that I hope

to
> formalize into the beginnings of a PhD thesis in the area of

FL
> someday.
> Let R be some type of unary predicate.
> Recall that D is the set of truth degrees, with some

algebraic (eg,
> MV) structure associated with it.
> Consider the statement below:
> [[Statement]] A fuzzy set theory, starting with the one in

[[1]],
> without Foundation, plus either the strong or weak universal

set
> axiom, is consistent relative to ZFC (the best situation one

can hope
> for) if and only if R(D).
> The question: Determine for what R is the above statement

true, if
> any, or prove that for all R, the above statement is false.
> Obviously, I want, at worst, an existence proof on R, that

there are
> some properties D could possess that enables a fuzzy

universal set
> theory that is consistent relative to ZFC.
> Also, I strongly hope that the statement is not false for

all R, that
> there aren't any exotic D's or structures they could be

equipped with,
> to make a universal set theory as consistent as ZFC.

Clearly, if D =
> {0,1} then the set of all R's for which [[Statement]] is

true is empty
> (bad but expected and well known).  In the binary logic

case,
> Russell's Theorem proves that the set of all R's for which
> [[Statement]] is true is empty.  No properties on D make the

universal
> set a possibility in classical logic (except possibly the

work of the
> sort Quinne did with the New Foundations although, in NF,

Choice must
> be dropped, in some sense, which is highly disadvantageous

to anyone
> who enjoys using Zorn's Lemma).
> (I posed this to someone known in the area of FL and he

encouraged me
> to come to Europe (as apparently no one does this type of

work in FL
> in the U.S.) to formally work this into a PhD thesis.)
> Now, ultimately, the connection to the CUH is that if there

is an
> ultimate set of +some kind+, like a strong universal set,

then perhaps
> that could provide a link to the MS of all MS's, ie, the

mathematical
> structure of all mathematical structures, without leading to

deals
> like, "this smells like Russell's dirty laundry, so let's

not go
> there."
> <punchline tag>
> Either that or provide an interesting, to say the least, MS

(a fuzzy
> and strong universal set theory) to investigate in the

context of the
> MUH, as this strong universal fuzzy set may, in fact, be a

candidate
> for what the universe literally is in a physical sense,

assuming the
> MUH, of course.
> </punchline tag>
> If I could make all of that work, I would be a very happy

man.  Even
> if I
...
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Brian

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 More options Mar 4, 2:38 pm


Newsgroups: sci.logic
From: Brian <[EMAIL PROTECTED]>
Date: Tue, 4 Mar 2008 14:38:26 -0800 (PST)
Local: Tues, Mar 4 2008 2:38 pm
Subject: Re: Any interest in discussing Tegmark's Mathematical

Universe
Hypothesis?
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A paradox???
http://www.torrentreactor.net/torrents/1588942/Parallel-Worlds

-Parall...
There is one part when Tegmark is speaking, around the 27-30

minute
mark or so, that they give a visual clue about parallel

universes that
was perhaps more interesting than the director realized,

unless the
director's assistant was Tegmark himself.
When they showed two universes splitting, in one parallel, the


Copenhagen interpretation is correct...and in the other, the

Many
Worlds interpretation is correct.
There is a QM formula with [[[EXCEPT DURING OBSERVATION]]] in

one half
of the screen
and
in the other half of the screen, [[[EXCEPT DURING

OBSERVATION]]] is +
+crossed out++ by Tegmark.
Interestingly, part of Tegmark's work says just that: not only

do
physical things split into parallels, but the laws of physics
themselves are different in different universes.
+++Therefore, The Copenhagen view is correct and the Many

Worlds
interpretation is correct.+++
But which is correct in THIS universe?
Or, maybe, that is a loaded question.  More details on why

that might
be a loaded question has to do with my crew's speculation

about there
not just being parallel universes but also "overlaying" (or
overlapping) of parallels, where the aggregate of parallels

(aka, the
universe) are (is) very much like the water system on earth:

separate
at times and other times, quite combined and overlaid upon one


another.  Indeed, if one "frog" is floating on the river, the

"bird"
sees the "frog" actually pass from the North Pole somehow

through down
to the Nile, passing thousands of different waterways in

between, and
the "frog" just thinks he has been in one body of water all

along,
which couldn't have been more wrong, at least, as far as the

"bird"
sees things.
Then again, is there a bird's "bird?"
And a bird's bird's bird?
And a bird's bird's bird's bird?
And do frogs have pets?
Do those pets have pets?
Do those pets have pets that have pets?
Sound familiar?  To me it sounds like a self-similar fractal

and the
way the universe would look if you started at a string and

zoomed out
to view the universe from the boundary of the universe, which

might
not "exist", unless the boundary of the universe exists
mathematically, of course!  I suppose one might want to push

the
envelope of mathematics to determine what the boundary of the

universe
is, to mightily abuse language.
Well, assuming the MUH, this overlaying of parallels +must+ be

the
case due to the hierarchical nature of mathematics.  Set

theory is on
a +somewhat+ lower echelon in the hierarchy than Category

Theory,
which is, on a lower echelon than Logic which is, in turn, on

a lower
echelon than Fuzzy Logic, a generalization of Logic.  Perhaps

instead
of the ultimate set, I need to search for the ultimate math,

but I
think Logic and Model Theory and/or Cat might be that, except

Logic
does have its limitations, in some sense.


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Brian

View profile

 More options Mar 4, 3:06 pm


Newsgroups: sci.logic
From: Brian <[EMAIL PROTECTED]>
Date: Tue, 4 Mar 2008 15:06:35 -0800 (PST)
Local: Tues, Mar 4 2008 3:06 pm
Subject: Re: Any interest in discussing Tegmark's Mathematical

Universe
Hypothesis?
Reply | Reply to author | Forward | Print | Individual message

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message | Find messages by this author
On Mar 4, 2:38 pm, Brian <[EMAIL PROTECTED]> wrote:

- Hide quoted text -
- Show quoted text -

> A paradox???
>

http://www.torrentreactor.net/torrents/1588942/Parallel-Worlds

-Parall...
> There is one part when Tegmark is speaking, around the 27-30

minute
> mark or so, that they give a visual clue about parallel

universes that
> was perhaps more interesting than the director realized,

unless the
> director's assistant was Tegmark himself.
> When they showed two universes splitting, in one parallel,

the
> Copenhagen interpretation is correct...and in the other, the

Many
> Worlds interpretation is correct.
> There is a QM formula with [[[EXCEPT DURING OBSERVATION]]]

in one half
> of the screen
> and
> in the other half of the screen, [[[EXCEPT DURING

OBSERVATION]]] is +
> +crossed out++ by Tegmark.
> Interestingly, part of Tegmark's work says just that: not

only do
> physical things split into parallels, but the laws of

physics
> themselves are different in different universes.
> +++Therefore, The Copenhagen view is correct and the Many

Worlds
> interpretation is correct.+++
> But which is correct in THIS universe?
> Or, maybe, that is a loaded question.  More details on why

that might
> be a loaded question has to do with my crew's speculation

about there
> not just being parallel universes but also "overlaying" (or
> overlapping) of parallels, where the aggregate of parallels

(aka, the
> universe) are (is) very much like the water system on earth:

separate
> at times and other times, quite combined and overlaid upon

one
> another.  Indeed, if one "frog" is floating on the river,

the "bird"
> sees the "frog" actually pass from the North Pole somehow

through down
> to the Nile, passing thousands of different waterways in

between, and
> the "frog" just thinks he has been in one body of water all

along,
> which couldn't have been more wrong, at least, as far as the

"bird"
> sees things.
> Then again, is there a bird's "bird?"
> And a bird's bird's bird?
> And a bird's bird's bird's bird?
> And do frogs have pets?
> Do those pets have pets?
> Do those pets have pets that have pets?
> Sound familiar?  To me it sounds like a self-similar fractal

and the
> way the universe would look if you started at a string and

zoomed out
> to view the universe from the boundary of the universe,

which might
> not "exist", unless the boundary of the universe exists
> mathematically, of course!  I suppose one might want to push

the
> envelope of mathematics to determine what the boundary of

the universe
> is, to mightily abuse language.
> Well, assuming the MUH, this overlaying of parallels +must+

be the
> case due to the hierarchical nature of mathematics.  Set

theory is on
> a +somewhat+ lower echelon in the hierarchy than Category

Theory,
> which is, on a lower echelon than Logic which is, in turn,

on a lower
> echelon than Fuzzy Logic, a generalization of Logic.

Perhaps instead
> of the ultimate set, I need to search for the ultimate math,

but I
> think Logic and Model Theory and/or Cat might be that,

except Logic
> does have its limitations, in some sense.
The only problem is that Aristotle's mutual exclusivity might

not
actually be universal, to resolve this apparent paradox.  But

even
within one parallel (mathematical structure?), ME (mutual

exclusivity)
might be true in one region of space (ie, the context between

and
containing mathematical structures), false in another, both

true and
false in still another part of that parallel, and absolutely

all
values of truth between true and false elsewhere in that

parallel
universe.  It seems somewhat mind boggling when pondering

that.
In our "neck of the woods," I think ME is "almost" (sort of in

a
Lesbegue measure sense) true.  In other words, locally to

myself and
probably you as well (whatever that might mean), the

pseudo-well-
formed-formula below has a ++designated++ truth value in some

truth
set D:
 '   for all wffs f, ( f & not(f)   ||-->    ^D)   '
where ^D is the minimal element in D, or an arbitrarily chosen


representative of the ones of equally least value, respective

of the
order on D.  ^D is interpretable as the qualia FALSE.
In fewer words (in English):
"locally,"   D+( W(f)-->( f & not(f) ||--> ^D) )
where D+(  ) means, "the truth degree of what follows is

designated,"
and W(  ) means, "what follows is a well formed formula," and

||-->
means there is a fuzzy logical sort of valuation function

being
applied, and --> is the standard (in a fuzzy logical sense, of

course,
but the truth set of this symbol definitely need not also be

D--too
bad tex is not available to my knowledge here, that would make

this
notation less unappealing to the eye) conditional connective.

(I
think all of this is formalizable.)
I think in our dreams (double entendre intended), ME is

"almost"
false, ie, D-( W(f)-->( f & not(f) ||--> ^D) ) where D-(  )

means,
"what follows has an anti-designated truth degree."
Perhaps that could be related to the true difference between

conscious
and unconscious.
Conscious could mean something like
X( D+( W(f)-->( f & not(f) ||--> ^D) ) )
and
unconscious could mean something like
X( D-( W(f)-->( f & not(f) ||--> ^D) ) )
where X( ) means something like, "in the context of the the

parallel
network SAS labeled X is embedded or embeddable within, the

following
is true."


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