Discussion of the MUH
Brian Tenneson
started at sci.logic and apparently, not many logicians are interested
in Physics, or something... :P
Here is a link (two, actually) to the discussion. I don't know how to
proceed, to discuss here or there. It does not matter to me.
http://groups.google.sh/group/sci.logic/browse_thread/thread/b0ed9baa707749ad/ef7752e4bcfc2631#ef7752e4bcfc2631
<a href=""http://groups.google.sh/group/sci.logic/browse_thread/thread/
b0ed9baa707749ad/ef7752e4bcfc2631#ef7752e4bcfc2631>MUH Discussion at
Google Groups</a>
Bruno Marchal
Le 05-mars-08, à 04:15, Brian Tenneson a écrit :
>
> I'm trying to strike up a discussion of the MUH but my discussion
> started at sci.logic and apparently, not many logicians are interested
> in Physics, or something... :P
Logicians are not interested in physics, and still less in metaphysics.
Bruno Poizat (a french logician) said (in its textbook on Model Theory)
that metaphysics is what logicians hate the most. I think this is just
a result of contingent historical facts ...
And physicists have been cooled down by the logicians reaction on
Penrose's use of Godel's theorem, so that they are a bit inhibited.
Even in the field of quantum computation, which has to bring back
eventually logicians and physicists around the table, big
misunderstandings still occur.
>
> Here is a link (two, actually) to the discussion. I don't know how to
> proceed, to discuss here or there. It does not matter to me.
>
>
> http://groups.google.sh/group/sci.logic/browse_thread/thread/
> b0ed9baa707749ad/ef7752e4bcfc2631#ef7752e4bcfc2631
We have discussed this a lot on this list. I don't know if most people
have seen my point, but I can only sum up it here:
I think the physical world cannot be a mathematical structure among
others, but that physics-matter is more like a sort of border of
mathematics-mind. So the relation between math and physics are more
subtle than Tegmark seem to think. You can see this once you take
seriously the mind body problem (or the problem of relating machine's
first person talk and machine third person observations, provably so (I
think) once you assume some precise version of the computationalist
hypothesis. But Tegmark is right for its mathematicalist position.
Again: right with respect to the comp hyp.
To tackle the math of that "physical bord", I use the Godel Lob Solovay
modal logic of provability (known as G, or GL). More on this list or in
my url. You can make your point of course, or ask questions. Sometimes
but rarely, Tegmark does send a post. Try a specific question perhaps,
or consult the archive.
Bruno
dfzone-e...@yahoo.fr
> To tackle the math of that "physical bord", I use the Godel Lob
> Solovay modal logic of provability (known as G, or GL).
Can you derive any known (or unknown) physical laws from your theory?
or something that could be checked experimentally?
_____________________________________________________________________________
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Brian Tenneson
> but rarely, Tegmark does send a post. Try a specific question perhaps,
I made in the link I posted here. I'm not sure if I should cut and
paste what those questions are because they take a while to set up and
I might as well just paste the entire discussion to ask the
questions. In lieu of that, I'll just leave the link and if anyone
wants to address points made there, they can.
I probably should have posted that thread in this list but....I would
be missing out on the volumes that logicians are writing on the
subject of the MUH (joke-- no one replied to my knowledge yet)!!
Bruno Marchal
Le 05-mars-08, à 16:11, <dfzone-e...@yahoo.fr> a écrit :
>
> Bruno Marchal wrote:
>> To tackle the math of that "physical bord", I use the Godel Lob
>> Solovay modal logic of provability (known as G, or GL).
>
> Can you derive any known (or unknown) physical laws from your theory?
I am not sure we could ever *know* a physical law, but of course we can
believe or bet on some physical theory, and make attempt to refute it
experimentally.
(Also it is not *my *theory, but the
Pythagoras-Plato-Milinda-Descartes-Post-Church-Turing theory, that is,
the very old mechanist theory just made precise through digitalness).
But, yes, that digital theory makes possible to derive
verifiable/refutable propositions:
-existence of many "physical" histories/worlds, and some of their
indirect effects.
-verifiability of the many interference of the probabilities for any
isolated observable when we look to "ourselves" at a level below the
substitution level.
-observable non locality in the same conditionS.
- non booleanity of what the observables can describe (sort of Kochen
Specker phenomenon)
- It explains and predicts the first person (plural) indeterminacy (I
don't know any simplest explanation of how indeterminacy can occur in a
purely deterministic global context btw).
(+ the first person expectation like the comp-suicide and its quantum
suicide counterparts, etc.)
Of course, the problem is that, *a priori* the theory predicts too
much: the white rabbits, like I sum up usually. But then I show that
the incompleteness constraints (a one (double) diagonalization
consequence of Church thesis) explains why the presence of white
rabbits in that context is not obvious at all. If they remains, after
the math is done, then the comp hyp is refuted.
The main advantage of this approach is that (unlike most physicalist
program) the person cannot be eliminated, and the mind body problem
cannot be put under the rug. Somehow my contribution consists in
showing that the mind body problem, once we assume the computationalist
thesis is two times more difficult than without, because it leads to a
matter problem, under the form of the white rabbit problem, or, as
called in this list, the (relative) measure problem.
Do you know french? All this is explained in all details (perhaps with
too much details) in *Conscience et Mécanisme":
http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html
My "result" (not *my* theory) is that evidences accumulate in favor of
Plato's conception of matter (contra the primary matter of Aristotle).
See my Plotinus paper for more precision on this:
http://iridia.ulb.ac.be/~marchal/publications/CiE2007/SIENA.pdf
> or something that could be checked experimentally?
There is a possibility of stronger form of Bell's inequality. To
progress on this open problem you have to study the arithmetical
quantum logics I am describing in most of my papers. Eric Vandenbusch
has solved the first open problem, but a lot remains. But my modest
result is that with comp, we *have to* extract physics (the
Schroedinger equation), not a proposal of a derivation, just a reason
why we must do that, and a proposal of a path (the Loebian interview)
for doing that.
What is your opinion about Everett? You can see my reasoning as an
application of Everett's natural idea that a physicist obeys the
physical laws in the mathematician/mathematics realm (or just
arithmetics, combinators, etc.). I can understand that people in
trouble with Everett can be in trouble with the comp hyp and its
consequences.
My *type* of approach consists in just illustrating that Mechanism has
empirically verifiable consequences.
*My* theory of everything, deduced from the comp hyp is just (Robinson)
arithmetic: all the rest emerge from internal points of view. They are
similar (formally or 'relationaly') to Plotinus' hypostases.
Bruno
Brian Tenneson
your interesting but not obliviously (to me) related discussion to a
different thread. Thanks.
On Mar 6, 5:49 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Le 05-mars-08, à 16:11, <dfzone-everyth...@yahoo.fr> a écrit :
Russell Standish
>
> I would appreciate that the trolling of my thread stop. Please take
> your interesting but not obliviously (to me) related discussion to a
> different thread. Thanks.
>
Trolling! Bruno is not trolling. Whilst we all have some difficulties
fully comprehending his results, what he has to say is very
interesting, and highly pertinent to the relationship between physics
and mathematics.
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpc...@hpcoders.com.au
Australia http://www.hpcoders.com.au
----------------------------------------------------------------------------
Günther Greindl
I can assure you that Bruno is the last on this list who would "troll".
He is always very helpful and interested in serious discussion.
I suggest you look at some of his papers before accusing him of trolling.
Günther
James N Rose
Brian,
Thank you for starting this thread on Logic and
Contemporary science/math/physics.
I am amazed that there isn't more written on it,
since in my own approach - which comes at a TOE
by General Systems Theory analysis - I saw early
on that a profound relation exists from Platonic
times to now - and includes QM, Boolean thought
and even Fuzzy Logic and complexity mathematic.
The current problem is that no one has put them
all into a kladistic house - comparing relations and
definitions.
Before I jump into a random exposition of my thinking,
what are your impressions about logic, math, materiality,
et al.?
Jamie Rose
Brian Tenneson
is directly connected to any ideas in my original post.
Brian Tenneson
with my ideas, they are about Bruno's ideas, especially in Bruno's
answer to a question directed to him.
I also find it odd that Bruno suggests asking specific questions but
in the link I posted to sci.logic, there were several specific
questions.
Seems like it might just be easier to stick to sci.logic. Less
politics involved.
How is that not trolling?
Russell Standish
"An Internet troll, or simply troll in Internet slang, is someone who
posts controversial and usually irrelevant or off-topic messages in an
online community, such as an online discussion forum, with the
intention of baiting other users into an emotional response[1] or to
generally disrupt normal on-topic discussion.[2]"
It is fine to request the thread to refocus on your original question,
when you feel it is drifting offtopic. It might also help to post your
question in its original form to this list, rather than relying on a
link to another forum.
It is not fine to accuse someone of being a troll when they're clearly not.
On Thu, Mar 06, 2008 at 06:43:33PM -0800, Brian Tenneson wrote:
>
> By trolling, I mean that by the third post in my thread, nothing there
> is directly connected to any ideas in my original post.
>
Quentin Anciaux
Good idea to propose to return where you came from.
Quentin
--
All those moments will be lost in time, like tears in rain.
Kim Jones
what I wanna talk about!!!"
The people in this forum have been having a conversation that has
lasted over a decade.
We get Tegmark on this list occasionally. He, like you, needs to
acquaint himself more with the core concepts of THIS discussion.
In his last post to us he admitted as much.
Go through the archives of this list and look at what we have been
talking about. Once you have read all of that, maybe get back to us
Kim Jones
nichomachus
I am glad to see that there are others interested in Tegmark's ideas.
I have been aware of his ideas since October but have largely agreed
with them since prior to that. by that I mean that I had reasoned to
similar conclusions prior to leaning that they had been so well
developed and articulated by Tegmark. There are a few problems that I
see with the MUH paper, although it could be that I just do not
entirely understand all of it. Before I mention those I will just say
that I believe his main thesis is correct. That is, his theory
explains correctly the relationship between mathematics and physics,
the reason why it is that mathematics has been so "unreasonably
effective" at describing natural phenomena. I with the idea that the
physical world is what Tegmark calls a mathematical structure -- a
timeless entity that exists by virtue of its own logical possibility
-- the only type of thing that truly exists. In his paper he defines a
mathematical structures perhaps overly generally as "abstract entities
with relations between them. This would seem to include a great many
things besides the type of thing we would to call a mathematical
structure. Personally I think we would want a definition that include
things like fractals, logical calculi, and the outputs of algorithms
to name a few examples, while excluding other types of things, such as
Platonic forms (which would have to be included in the definitions
provided). However, this ontology them classifies everything that we
naturally think of as real as just substructures of something that is
truly real: this universe. We ourselves are merely substrutures,
albeit the self-aware kind, of this larger, real universe, and we
therefore derive our being vicariously from it.
I would like to see that the relationship of the computable universe
hypothesis to the MUH be clarified. Is our universe's physics
classically computable at the quantum scale? If not, how does it
follow that the macroscopic universe, or the universe as a whole is
classically computable if its operation at the quantum level is not? I
apologize if this question displays my naivete on the subject, but it
is something I am currently endeavoring to more clearly understand.
I am particularly interested in information-theoretic descriptions of
the this universe, or more precisely, information theory measures of
the complexity of of this universe's presumed most basic laws (or
Grand Unified Theory, Max Tegmark's level I TOE). What exactly does it
mean to assign a value to the complexity of our still-undiscovered
GUT? Would competing notions of algorithmic complexity yield
discordant results in this case? Which measure of complexity is to be
preferred? If we defined the complexity to be the length of the
shortest possible computer program that could generate the results,
doesn't this definition imply a particular computational architecture
that would itself be necessary to account for in measuring algorithmic
complexity? Also, does having the property of universality imply a
definite lower-bound to the complexity of a hypothetical physics? once
again, probably very naive questions on my part, but I would like to
better understand these matters.
Probably what I find most appealing about the MUH is how it simplifies
things. To me it answeres the age-old question, why is there something
rather than nothing by boldly asserting that the universe is a member
of the category of being for which there is no difference between
possibility and necessity.
However, this formulation leads to speculation on the ontic status of
paraconsistent systems.
I look forward to any replies on this extremely interesting topic.
On Mar 4, 9:15 pm, Brian Tenneson <tenn...@gmail.com> wrote:
> I'm trying to strike up a discussion of the MUH but my discussion
> started at sci.logic and apparently, not many logicians are interested
> in Physics, or something... :P
>
> Here is a link (two, actually) to the discussion. I don't know how to
> proceed, to discuss here or there. It does not matter to me.
>
Bruno Marchal
Le 06-mars-08, à 21:55, Russell Standish a écrit :
>
> On Thu, Mar 06, 2008 at 08:20:52AM -0800, Brian Tenneson wrote:
>>
>> I would appreciate that the trolling of my thread stop. Please take
>> your interesting but not obliviously (to me) related discussion to a
>> different thread. Thanks.
>>
>
> Trolling! Bruno is not trolling.
Thanks to you Russell, and thanks to Günther, Kim, Quentin for noticing
that I was not trolling. I was just replying.
> Whilst we all have some difficulties
> fully comprehending his results,
I have to come back on this some day, because I try to classify the
difficulties. For example, there are people who does not understand the
notion of 1-person indeterminacy, pretending for example, that they are
in both Washington and Moscow after the usual self-duplication, like
Chalmers. Actually they have a problem with the notion of first
person/third person. They have problem with Everett too, and with the
whole of "philosophy of mind" issues. They have problem with the type
of discussion we have in this list, for sure.
But then there are those who do not understand the mathematical logic,
or point in theoretical computer science, but this means they have to
work ...
Well I say this because you say "we all". Surely every one can find
some more difficult point ...
Also, Russell, I feel a bit guilty because years ago you find a sort of
real problem in the "movie graph argument" which is so interestingly
relevant that I have never been able to finish my reply...
Unfortunately it is currently a bit out-of-topic. I will come back on
this when I will put my mind again in the movie-graph-Olympia issue.
This is really (imo) conceptually difficult ... I am not yet entirely
satisfied by my own argumentation ...
> what he has to say is very
> interesting, and highly pertinent to the relationship between physics
> and mathematics.
Thanks for saying. And sorry for Brian. I think all threads are
related, but people replies from their own theory/prejudice. If someone
is not sastified with an answer, he has to just say "you did not answer
my question, let me perhaps rephrase it more succinctly ...", or
something like that, (or ask somewhere else, of course).
(Also the web group archive is not always simple to follow, sometimes
you have to remember your password in the middle of a post reading, you
stop daring to click or just touch your mouse ... I prefer the Nabble
archive where posts are more easily individuated).
Now, I do sincerely think my reply (to dzone actually) *has* a bearing
with Brian's post or Tegmark's work.
Bruno
Brian Tenneson
>acquaint himself more with the core concepts of THIS discussion.
>In his last post to us he admitted as much.
Fuzzy Logic and the MUH that I am discussing in THIS thread?
Can we +please+ either talk about the first post on THIS thread or
anything at least somewhat related or post in a different thread?
I did not come here to argue about who is diverting the topic away.
Please don't reply in THIS thread if you aren't going to discuss THIS
topic (connections between Fuzzy Logic and the MUH). Thanks.
I did not post my ideas in a random person's thread. If I did, I
would be called a troll, perhaps, or at least, unnecessarily diverting
the thread.
It is insulting to me to be said I'm looking for attention. Why use
THIS thread's bandwidth to analyze my psychological makeup?
Thanks.
Brian Tenneson
On Mar 6, 1:46 pm, James N Rose <integr...@ceptualinstitute.com>
wrote:
I am a Platonist or Spinozist and I think logic as being of
metamathematics (the math about math). Furthermore, Fuzzy Logic is
simply a generalization of logic. I do believe that FL (Fuzzy Logic)
has the potential as providing interesting examples of mathematical
structures that Tegmark mentions in his recent Mathematical Universe
Hypothesis paper.
You see a lot of logic, ie, metamathematics, in his "beyond the
standard model" papers, and I think there is a connection to the Greek
schools of thought.
While the MUH is just a hypothesis, it is the one I personally guess,
for want of better term, is correct.
The issues is that experimental evidence has not (and can not?)
confirm or deny the MUH. To me, that is not a problem. I think we
can tell about the universe in science, philosophy, and mathematics.
Just different parts and different questions are better suited to each
discipline.
However, if the MUH is true, then the deepest nature of the universe
is a mathematical inquiry rather than a physics inquiry.
Any other questions, like for clarification about my ideas, and
especially if you spot errors in my reasoning regarding the link in my
first post, please feel free to pull no analytical punches as that's
the only way to improve.
Thanks
Brian Tenneson
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....)
sci.logic
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Brian
Tenneson
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More options Mar 1, 11:47 am
Newsgroups: sci.logic
From: Brian Tenneson <tenn...@gmail.com>
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
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More options Mar 1, 12:30 pm
Newsgroups: sci.logic
From: Brian Tenneson <tenn...@gmail.com>
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 <tenn...@gmail.com>
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 <tenn...@gmail.com> 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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More options Mar 4, 10:21 am
Newsgroups: sci.logic
From: Brian <tenn...@gmail.com>
Date: Tue, 4 Mar 2008 10:21:00 -0800 (PST)
Subject: Re: Any interest in discussing Tegmark's Mathematical
Universe
Hypothesis?
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On Mar 3, 12:38 pm, Brian <tenn...@gmail.com> wrote:
- Hide quoted text -
- Show quoted text -
> On Mar 1, 12:30 pm, Brian Tenneson <tenn...@gmail.com>
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
...
read more "
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More options Mar 4, 2:38 pm
Newsgroups: sci.logic
From: Brian <tenn...@gmail.com>
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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More options Mar 4, 3:06 pm
Newsgroups: sci.logic
From: Brian <tenn...@gmail.com>
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?
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On Mar 4, 2:38 pm, Brian <tenn...@gmail.com> 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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Russell Standish
>
> 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....)
>
Wow 1700 lines of stuff. Not well organised, slabs quoted en masse
from papers that are already fairly familiar, and duplicate
information. No wonder people find it hard to respond.
The various Tegmark papers referenced in your discussion have been
discussed on this list before. I'll comment where you seem to be
adding something.
I haven't read Daegene Song's Non-Computability of Consciousness paper
yet, but I'm sceptical it would be a strike against CUH (or COMP). I'm
also rather sceptical about purported quantum functions being
necessary for consciousness. Also, it is known that quantum computers
are classically emulable (with exponential slowdown).
Alright - I think the heart of where you wish to go is to use fuzzy
logic to describe the mathematical structure of all mathematical
structures. I don't know enough fuzzy logic. Is there a fuzzy
universal set? And can one avoid Russell's paradox in FL?
I'm not sure I would personally proceed further than this, my preferred
ontological basis differs a bit from Tegmark's, and consequently
doesn't suffer from this issue of consistently having to specify all
of mathematics. The same can be said of Bruno's ontological basis,
which differs yet again.
In your next post - there is no bird's bird. A bird viewpoint is in
fact the viewpoint of nobody. All it is a bunch of symmetries, really,
with symmetries broken in just those necessary ways to allow an
observer. See the discussion in section 9.1 of my book, in particular
about the 3rd person viewpoint, which is effectively Max's bird viewpoint.
I got lost on your speculations on the excluded middle. Perhaps you
can refine. Was it connected with your fractal musings earlier perhaps?
Cheers
Russell Standish
> I would like to see that the relationship of the computable universe
> hypothesis to the MUH be clarified. Is our universe's physics
> classically computable at the quantum scale? If not, how does it
> follow that the macroscopic universe, or the universe as a whole is
> classically computable if its operation at the quantum level is not? I
> apologize if this question displays my naivete on the subject, but it
> is something I am currently endeavoring to more clearly understand.
>
One can solve the Schroedinger equation using a classical algorithm.
> preferred? If we defined the complexity to be the length of the
> shortest possible computer program that could generate the results,
> doesn't this definition imply a particular computational architecture
> that would itself be necessary to account for in measuring algorithmic
> complexity? Also, does having the property of universality imply a
> definite lower-bound to the complexity of a hypothetical physics? once
> again, probably very naive questions on my part, but I would like to
> better understand these matters.
>
This is resolved by using the observer as the reference to measure
complexity. See my paper Why Occams Razor for a discussion.
George Levy
As Russell said, we have been discussing this topic for at least a
decade. We all respect each other. I am sure that Bruno did not mean
harm when he made his comment.
You bring up an interesting question: the relationship between Fuzzy
logic and the MUH and you state that Fuzzy logic is a superset of
deterministic logic. Isn't true that Fuzzy Logic can be implemented by
means of a Turing Machine? Since a Turing Machine is purely
deterministic it means that Fuzzy logic is actually a subset of logic.
Hence the ad hoc introduction of Fuzzy logic may be unnecessary in the
context of MUH.
I don't think that the indeterminacy that we are considering here is
fundamental or derives from an axiomatic approach. It is rather a
consequence of living in many worlds simultaneously. When "I" make a
measurement, a number of "I"'s make(s) a measurements. The result of the
measurement that each "I" perceive(s) defines the world where the "I"
actually am (is). As you can see English is not rich enough to talk
about "I" in the third person or in the plural.
If there is a need for Fuzzy Logic, it would have to be a kind of logic
adapted to deal with the MUH. I don't know enough to say if there is
such a logic.
George
John Mikes
about the 'impressions'
of concepts you mentioned and asked for, a warning:
Impressions, even definitions/identifications are very personal. A
vocabulary of one's terms can't be just 'translated': it has to be
adapted to the entire 'mindset' of the person who uses it.
You have to 'walk in my shoes' to rightfully apply MY definitions from
MY vocabulary.
George L remarked that MUH is superceding Fuzzy Logic (George, pls.
correct me if I read you wrong) as a mathematically describable
theorem, what I take with a grain of salt: maybe F.L. is based on a
root what also sprouted mathematical thinking as well? (Even if I
deckipher the M in MUH as Multiple, when in my opinion every one of
the U-multitude is fundamentally different and no individual can (in
toto) exist identically in them all or do the same activity as he
does:here(?). )
I considered the original F.L. idea as a diversion from the
quantizable (mathematical?) formal logic, just before mathematically
impaired minds adopted the idea into the math-based TOE.
(Remember: my 'everything' includes more than the ' numbers-based'
part of it and here I am still missing a (common sense) advice from
the list) how to understand 'numbers' (especially in the Bruno defined
"integers only" sense differently from "numbers - as in integers". *)
I still did not reject David Bohm's "numbers are human invention" groundrule.
So Your escapade into Fuzzy Logic is a valid one for me, irrespective
of a (narrowly cut) MUH
only I don't see the possibility of a wide-range agreement in
'concepts' among people with different - well - what? sci. worldview?
basic (sci.) philosophy? specialization? or even the not-so-obvious
"common sense".
John M
*) the statement that everything (including mentality-terms) can be
described by numbers in long enough series means in my vocabulary:
"SOMEHOW", the same as in assigning ALL mental finctionality to the
physiological neuronal brain (somehow). JM
Russell Standish
Universe Hypothesis from Tegmark's paper. Fuzzy Logic means something
quite precise - it is a mathematical theory where truth values take on
a real value in [0,1], which is called a membership function.
Brian is proposing something quite specific - to use fuzzy logic to
resolve the contradictions in merging contradictory axiom sets, which
would be needed to make Tegmark's proposal work. I am somewhat
sceptical this can be made to work, but prima facie I cannot see any
showstopper. Brian might just be right, so if he wants to pursue this
as a PhD topic, then good on him.
Cheers
--
Bruno Marchal
Le 08-mars-08, à 21:09, George Levy a écrit :
>
> Hi Brian
>
> As Russell said, we have been discussing this topic for at least a
> decade. We all respect each other. I am sure that Bruno did not mean
> harm when he made his comment.
Actually I was replying, not even to Brian. But thanks.
>
> You bring up an interesting question: the relationship between Fuzzy
> logic and the MUH and you state that Fuzzy logic is a superset of
> deterministic logic. Isn't true that Fuzzy Logic can be implemented by
> means of a Turing Machine? Since a Turing Machine is purely
> deterministic it means that Fuzzy logic is actually a subset of logic.
> Hence the ad hoc introduction of Fuzzy logic may be unnecessary in the
> context of MUH.
>
> I don't think that the indeterminacy that we are considering here is
> fundamental or derives from an axiomatic approach. It is rather a
> consequence of living in many worlds simultaneously.
This is the key point. Tegmark believes that the physical universe
could be a mathematical structure among others, which I can believe
too. But with the coomputationalist hypothesis or its many weakenings,
we have to take into account all mathematical structures supporting the
self aware entities, to derive that particular mathematical structure.
So we just cannot postulate a theory like "SWE", we have to derive it
from a sum on all (sufficiently rich) mathematical structures. We just
cannot consistently invoke a notion of existence of a "physical
universe". This gives a clue why we believe or could believe in such a
physical universe.
> When "I" make a
> measurement, a number of "I"'s make(s) a measurements. The result of
> the
> measurement that each "I" perceive(s) defines the world where the "I"
> actually am (is). As you can see English is not rich enough to talk
> about "I" in the third person or in the plural.
>
> If there is a need for Fuzzy Logic, it would have to be a kind of logic
> adapted to deal with the MUH. I don't know enough to say if there is
> such a logic.
This puts light on the reason why the "explicitation" of comp (or its
weakenings) is useful. The logic, in this case, has to be derived (by
the UDA) from the sum invoked above. When the math are done we do find
indeed a sort of quantum logic (ref in my url). It is an open problem
if this logic is a fuzzy quantum logic. Evidences add up to think it
could be a form of quantum credibility, instead of the "usual" quantum
probability theory. This is related to the fact that we get the modal B
logic (the "Brouwersche system") *without* the rule of necessitation.
Much works remain, of course.
Bruno
Bruno Marchal
Le 08-mars-08, à 10:18, Russell Standish a écrit :
> And can one avoid Russell's paradox in Fuzzy Logic?
Many paradoxes leads to chaos when (re)interpreted in Fuzzy Logic.
There is a paper by Mar and Grim:
Mar, G. & Grim, P. (1991) Patterns and chaos: New images in the
semantics of. paradox. Nous 25:659–93
Bruno
Brian Tenneson
mislabeling labeling a digression as trolling. I seem to have shot
myself in the foot with that remark.
Second, I will have more to say about specific posts later today, but
I would like to clarify what I mean by Fuzzy Logic (FL), and it's
connection to Classical Logic (eg, Model Theory). On that note, fuzzy
logic truth sets need not be [0,1] but could be anything algebraically
like a Boolean Algebra. Specifically, the truth set could be what's
known as an MV-algebra, which could have some order. Chang's Theorems
relate MV-equations to equations that hold in [0,1], making the
comparison to [0,1] quite relevant, actually, but without (seemingly)
realizing it. I suggest readers interested in what I mean by Fuzzy
Logic see this paper which I referenced, and the references of the
paper I am linking:
http://citeseer.ist.psu.edu/444507.html
PDF version:
http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zSzzSzwww.cs.cas.czzSzvvvvedcizSzhajekzSzstrls2.pdf/a-set-theory-within.pdf
Recall from an earlier post that I am pushing question (2) on page 8
in reference to a universal fuzzy set axiom and this in relation to
Tegmark's MUH. Perhaps some universal fuzzy set +is+ the universe in
some sense.
Also, for my ME statements (mutual exclusivity), I am suggesting that
"locally" ME holds and maybe sometimes ME does not hold[***], within
the context of Tegmark's MUH. It seems apparent that ME is true in
the parallel we inhabit. With my D+( ) notation above, I was just
trying to formalize a conjecture along the lines of "ME seems locally
true". Discussion of what I mean by designated truth degrees can be
probably found in the references to the paper I just linked to. Also,
I suggest seeing parts of this:
A treatise on many-valued logics
by Siegfried Gottwald
http://worldcat.org/wcpa/oclc/44162540
Also, this might be worth trying for background:
http://en.wikipedia.org/wiki/Multi-valued_logic
[quote]
The first known classical logician who didn't fully accept the law of
the excluded middle was Aristotle (who, ironically, is also generally
considered to be the first classical logician and the "father of
logic"[1]), who admitted that his laws did not all apply to future
events (De Interpretatione, ch. IX).
[/quote]
MV-algebra (truth sets are these sorts of things, basically):
http://en.wikipedia.org/wiki/MV-algebra
I just wanted to clarify what I mean by F.L. before launching into how
F.L. might interact with the MUH in the sense of a "strong fuzzy
universal set" being the universe.
[***] I'm wondering, not knowing about QM much, how in some parallels
the Copenhagen interpretation could be correct and in others, the
Everett interpretation could be, in light of the MUH---if different
+fundamental equations+ of Physics are true in a Level 4 multiverse
scenario, then are different +interpretations+ of the equations
correct in different parallels?
Perhaps this paradox (and all paradoxes) could have a very
(unsatisfying?) resolution in the context of ME not being universally
"true"?
Brian Tenneson
(perhaps I should have said Many-Valued Logic or Non-classical Logic):
http://en.wikipedia.org/wiki/Multi-valued_logic
The structure of the truth set is not necessarily the interval [0,1];
it could be an MV-algebra, perhaps with some type of ordering:
http://en.wikipedia.org/wiki/MV-algebra
Chang's Theorems do, however, connect arbitrary MV-algebras with the
[0,1] interval.
<quote from http://en.wikipedia.org/wiki/MV-algebra >
Chang's (1958, 1959) completeness theorem states that any MV-algebra
equation holding in the standard MV-algebra over the interval [0,1]
will hold in every MV-algebra. Algebraically, this means that the
standard MV-algebra generates the variety of all MV-algebras.
Equivalently, Chang's completeness theorem says that MV-algebras
characterize infinite-valued Łukasiewicz logic, defined as the set of
[0,1]-tautologies.
</quote>
Also, I would like to reiterate/argue that what I mean by FL +is+ a
generalization of Classical Logic (including Model Theory). Try to
find and see this book for more details, including what I meant
earlier in my posts about "designated" truth values.
Gottwald S. 2000, S. A Treatise on Many-Valued Logics, Research
Studies Press, Baldock.
One might try this article which seems to be a tutorial on FL (Many-
Valued Logic):
http://www.uni-leipzig.de/~logik/gottwald/SGforDJ.pdf
My personal investigation is regarding some type of universal fuzzy
set, by which I mean a set U such that for all fuzzy sets x, x is in
U. Now I don't yet know whether there is a fuzzy set theory (ie, a
fuzzy set theory with suitable axioms) that is consistent relative to
ZFC (Zermelo-Fraenkel set theory, with the axiom of choice). This is
what I hope to settle in my future PhD thesis (I currently just have a
master's), maybe, if not connect this all to the MUH outright or just
confine myself to logic.
My work I think is related to Tegmark's MUH in that some universal set
is, at least in some sense, literally, the universe, assuming the
MUH. This (my) work in FL is based on this paper below which lays the
foundation:
http://citeseer.ist.psu.edu/444507.html
Abstract: This paper proposes a possibility of developing an axiomatic
set theory, as first-order theory within the framework of fuzzy logic
in the style of [13]. In classical ZFC, we use an analogy of the
construction of a Boolean-valued universe---over a particular algebra
of truth values---to show the non-triviality of our theory. We present
a list of problems and research tasks.
The aim of my research right now is to pursue question (2) on page 8
of that paper. (Here is the pdf:
http://citeseer.ist.psu.edu/rd/0%2C444507%2C1%2C0.25%2CDownload/http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zSzzSzwww.cs.cas.czzSzvvvvedcizSzhajekzSzstrls2.pdf/a-set-theory-within.pdf
)
<quote>
Which additional axioms might/should be added? Which must not be
added because they imply the crispness of everything
</quote>
As I mentioned earlier, the foundation axiom would have to be dropped,
because U would be in U, and so this is a non-well-founded type of set
theory, and leads to so called vicious circles as mentioned elsewhere,
for example:
http://en.wikipedia.org/wiki/Non-well-founded_set_theory
Hopefully, this all will shed some light on the discussion I posted a
link to:
http://groups.google.sh/group/sci.logic/browse_thread/thread/b0ed9baa707749ad/ef7752e4bcfc2631#ef7752e4bcfc2631
Brian Tenneson
In +this+ post, I am attempting to encapsulate all previous posts on
sci.logic and here.
In a nutshell, my work in FL is going to hopefully provide the
beginnings of an answer to "what is the universe" by at least making a
plausibility case for some universal fuzzy set, in conjunction with
Tegmark's (et al) MUH, as being the universe.
I would at least like to rule that possibility out, ie, settle that
question: is the universe some type of universal set?
My main dilemma is not phrasing the new or different axioms. My main
goal is that I seem to need to show that such a fuzzy set theory, one
with a "universal set," is ++consistent relative to ZFC++ or at least
prove that that's not possible (ie, prove a generalization of
Russell's "paradox"). That would make at least some of this, perhaps,
interesting to mathematicians, at least logicians, instead of just
theoretical physicists and those interested in FL. Also, if any such
fuzzy set theories actually are consistent, my problem would then be
to investigate exactly what about the axioms, or the nature of logic
itself (eg, the nature of all MV-algebras for which a set theory
'using' a logic with that MV-algebra can consistently have a universal
set), leads only some such set theories to be inconsistent, as in the
case of Russell's "paradox" and two-valued logic).
And that is why the fact that FL is a generalization of classical
logic is highly relevant. If they were unrelated, for example, a
relative consistency proof would be, I believe, completely impossible.
dfzone-e...@yahoo.fr
> My main
> goal is that I seem to need to show that such a fuzzy set theory, one
> with a "universal set," is ++consistent relative to ZFC++ or at
> least
> prove that that's not possible (ie, prove a generalization of
> Russell's "paradox").
It is proved in Paraconsistent Logic:
http://plato.stanford.edu/entries/logic-paraconsistent/#MatSig
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Envoyez avec Yahoo! Mail. Capacité de stockage illimitée pour vos emails. http://mail.yahoo.fr
Brian Tenneson
question been answered yet" as I honestly don't know for sure. I
would be really happy if it was answered, in some sense, because
whether or not I answer it, I am still curious about the answer.
Thanks for posting that.
Brian Tenneson
Does 'any theory' in the following quote include theories that involve
logics with every MV-algebra as their truth set and every set of
syntactical axioms or is this just any theory using binary logic?
Could Russell have proved anything in the context of even
paraconsistent logic, not to mention all non-classical logics (such as
those that were revealed in the 50's or so), using what he might have
known at his time?
<quote>
As was discovered by Russell, any theory that contains the
Comprehension Schema is inconsistent. For putting 'y not-element y'
for A in the Comprehension Schema and instantiating the existential
quantifier to an arbitrary such object 'r' gives:....
</quote>
dfzone-e...@yahoo.fr
> involve
> logics with every MV-algebra as their truth set and every set of
> syntactical axioms or is this just any theory using binary logic?
my guess is: just any theory using binary logic.
Brian Tenneson
physicists and even more engineers and even more laymen would say that
'just' is a huge, huge understatement.
However, from the perspective of Non-Classical logic (be it
paraconsistent or fuzzy), that sentence was perfectly formulated, in
my humble opinion, and that article was not written with all forms of
non-classical logic in mind.
What I need to show is that the answer is different or the same in all
MV-Algebras. My guess is looking at just [0,1], as proofs done in
[0,1] can sometimes be carried over to all MV-algebras using Chang's
theorems, mentioned above, which connect just [0,1] to all of these
types of fuzzy logics, would be a big step towards settling my
investigation for all MV-algebras.
In other words, I want to investigate Russell's "paradox" for as many
types of logic that already have been developed, to determine how
"true" Russell's "paradox" is for any logic that is not binary logic.
I don't know, it could be false in +all+ logics that could be
reasonably called logics or, more interestingly to me, true in some
but not all. Then, in that event, the investigation would be to find
out in which logics Russell's Theorem (ie, no universal set exists in
that logic-set-theory combo) is true and in which is false. Then I'd
like to know why Russell's Theorem is true sometimes and why not
sometimes. Or why it's always true. Why being the main question for
me. I think the physicist would mainly be interested in whether any
universal (fuzzy) sets can consistently exist, and the logician more
interested in why it exists. However, why it exists is, I think, also
interesting to the philosopher in that it is like asking "why does the
universe exist" assuming the MUH and that any universal sets can
consistently exist.
James N Rose
Your inquiries about FL is an uncharted but important one.
I'd like to suggest though that your approach is too
conventional and 'consistency' is not the ultimate
criteria for evaulating it's connection with validity
or more importantly - feasability - in context with
'logic' - and mathematical value judgements.
I've taken a wholly different/radical approach which
has been productive. "Existential Probability" is a
strong and broader base to use and in general is
an umbrella-space for all logic systems. I call the
most generalized form "Stochastic Logic". It has the
interesting attribute of placing FL and QM on a par,
in the scheme of things, with direct connection with
Boole, and Aristotelian logic before-that.
In historical framing, it can be seen that the earliest
logics were limited-specific-condition logics and that
each new step was toward 'improved generalization'.
The leap that FL makes is removing the boundaries of
the probability space and pushing toward a 'logic'
system that copes with Cantorian infinities and
transfinites. It pushes towards plural-criteria
logic (what you've indicated as akin to Multi-modal).
It is a critically important step that out-paces
all the conventional analysis. Think of it as the
tool to developing utile computation/description
methods for 'logic' evaluation of the (so far)
intractible "many bodied" problem. Complexity math
is one way of coping with -some- factors of many-bodied
systems, but even that math hasn't been fully scrutinized
or (logically) evaluated for kladistic characteristics
yet. I've looked some of the equation forms and found
some interesting things going on in 'recursion' equations
that relate to breaking away from 'zero to one' boundary
restriction.
I discuss a bit of it in general vernacular at
<http://www.ceptualinstitute.com/uiu_plus/uiu05charting.htm>
Feel free to contact me directly at integrity @ prodigy.net
(remove the spaces) if you'd like to discuss in more detail.
I made an effort several years ago to get Lotfi Zadeh speaking
with Herb Simon (just before he died) in the hopes that traditional
and leading edge probability theories could find commonality.
They did talk some but nothing definitive or fruitful came
from it - mainly because each had too much vested interest
in separate academic venues. And because second and third
generation 'probabilists' were so dedicated to their particular
stances on 'how the math "should" be done', instead of opening
themselves to combining the methodologies into a grander
schemata - it's going to take someone or someones with -your-
sensibility and intuitions to make it happen. :-)
Jamie Rose
Brian Tenneson
breath, as it were.
1. It is nice to hear a human say this is uncharted territory. Since
I am not in a graduate school now and have no affiliation, my research
resources are limited compared to having free access to basically any
relevant publication. I really had no idea if this was charted
territory; if it was, that shoots down it being potentially used as
part of a PhD problem (which I'm considering going for, but others
have convinced me I'd have to move to Europe which is exceptionally
logistically hard for me due to strong unmovable attachments, if you
will -- I'm +not+ a 20-something person without a family, and such).
2. I appreciate immensely the last line of your message. Over the
years, I've asked many authors something like, "do you think Russell's
paradox might be false in other logics" I got, let's say, an extremely
condescending response, and so forth. I'm not expecting praise, by
God, just to not be condescended to. I suppose that is why I was
touchy when I perceived someone totally derailing this line of
discussion and that being continued by the third poster. My bad. I
think my main improvement, while not really coming close to really
answering my question, was changing the goal from prove Russell's
Theorem is not always true to asking the question "Is Russell's
Theorem true in all logics?" A bonus seems that now there is a
theoretical physics, by way of the MUH, motivation for answering this
question.
3. On that note, Physics/Philosophy actually what inspired me to go in
this direction. I was mainly, back then when this idea of trying to
find a consistent universal set theory occurred to me, trying to
answer a intended-to-be serious argument against the existence of the
universe.
I was stunned at the notion that someone was trying to prove the
universe does not exist. I think they were asserting some form of
solipsism.
In a nutshell, here was their argument. My opinion is that it is not
at all formal but very clever and probably persuasive but, ultimately,
like the many clever "proofs" that 1=2 and such. It's just going to
be convincing to those who aren't vigorously attacking the argument,
which I soon did.
<begin their argument for the non-existence for the universe>
Definition: To contain means <insert something most people would
accept here>. The notation and word for 'is contained in' is
is<in.
Thing and exists are undefined or ... acceptably defined only be
common intuitive sense of what a thing is, but neither formally (in
her argument)
Definition: the universe (call it U) is a thing that has the property
that it contains all things, notated by (x) (x is<in U), where x is a
thing.
Theorem: If the universe exists then the (three or so) axioms of
binary logic are inconsistent.
Proof: The method is to show that if U exists then there is a logical
statement (ie, a WELL FORMED formula) that is true if and only it is
false, being simultaneously, to abuse language, true and not true,
which violates the +definition+ of the words not and and.
Suppose U exists. Then apply Russell's approach. Given how broad and
vague 'thing' is defined, let's discuss the thing, call it S, this
thing called S is the thing that contains all things that don't
contain themselves. In the notation, let S be the thing (given the
vagueness of 'thing', S is a thing) such that
(x) (x is<in S if and only if x!<x).
In other words, S is the thing such that for all things x, x is
contained in S if and only if x is not contained in x.
Since we wrote (x), then apply to S by an application of some
universal quantifier rule, which most people would accept (and maybe
they should qualify the universal sometimes) to S. Then you get, just
as Russell's approach:
(S is<inS if and only if S!<S).
This contradiction proves the theorem. That if the universe exists,
then binary logic is inconsistent.
Corollary: The universe does not exist.
"Proof:" Binary logic is consistent, therefore, by contraposition of
the theorem, the universe does not exist.
<end their argument for the non-existence for the universe>
I've been banging away at this keyboard for a while so I'll post this
and take a break.
The idea came to me when I tried basically to prove her argument that
the universe does NOT exist, wrong. It occurred to me that three
truth values are sufficient to make the usual proof by contradiction
+not a tautology+. And, therefore, even in 3-valued logic, her
argument fails.
Obviously, that doesn't prove the universe does exist, it just proves
her argument that is doesn't is wrong.
<end their argument for the non-existence for the universe>
On Mar 23, 2:14 am, James N Rose <integr...@ceptualinstitute.com>
wrote:
Russell Standish
Maybe it instead proves that "things" like S do not exist in the
universe. OK, it means we have to change the definition of universe a
bit, but this is not so strange as universe really just means all that exists.
So, yeah, I'd say it was a bit of linguistic sophistry, rather than
being too profound.
Anyway, the question of whether Russell's paradox can be found to not
hold force in non-standard logic seems interesting, and potentially
well motivated for the MUH case which ab initio would include things
like S in the level 4 "multiverse".
Cheers
James N Rose
Brian Tenneson wrote:
>
> Thanks for your reply. I have a lot to say, so let me try to rate my
> breath, as it were.
>
> 1. It is nice to hear a human say this is uncharted territory.
> .
> .
> I think my main improvement, while not really coming close to really
> answering my question, was changing the goal from prove Russell's
> Theorem is not always true to asking the question "Is Russell's
> Theorem true in all logics?" A bonus seems that now there is a
> theoretical physics, by way of the MUH, motivation for answering this
> question.
>
This is an important task. As I mentioned, the direction of
concepts-progress is: 'towards maximum generalization' -- even
absolute generalization, if you will. An encompassing single
notion, or limited group of notions, that imply 'all else'.
Simplest principle(s). Matching the sensibility connected
with a 'theory of everything'. Simplest qualia.
> 3. On that note, Physics/Philosophy actually what inspired me to go in
> this direction. I was mainly, back then when this idea of trying to
> find a consistent universal set theory occurred to me, trying to
> answer a intended-to-be serious argument against the existence of the
> universe.
>
> I was stunned at the notion that someone was trying to prove the
> universe does not exist. I think they were asserting some form of
> solipsism.
>
> In a nutshell, here was their argument. My opinion is that it is not
> at all formal but very clever and probably persuasive but, ultimately,
> like the many clever "proofs" that 1=2 and such. It's just going to
> be convincing to those who aren't vigorously attacking the argument,
> which I soon did.
>
> <begin their argument for the non-existence for the universe>
> Definition: To contain means <insert something most people would
> accept here>. The notation and word for 'is contained in' is
> is<in.
>
> Thing and exists are undefined or ... acceptably defined only be
> common intuitive sense of what a thing is, but neither formally (in
> her argument)
>
> Definition: the universe (call it U) is a thing that has the property
> that it contains all things, notated by (x) (x is<in U), where x is a
> thing.
This in itself is a problematic conjecture (presumption). So fundamental
in fact that no past or current analysis has enunciated the criteria-error.
(The reason for this is illuminated by Benj Whorf's linguistics analysis
circa 1936 ... which paraphrasedly states that, absent experiential recognition,
systemic information self-insulates on itself.) In this case, the presumption
is that perfect quantification is possible; and in -that- basis, that probability
valuations are designatable (fixed), for all situations and scenarios possible.
That is -not- the 'generalized case'. Those presumptions, which classical non-FL
math is built on, is closely-defined and therefore godelianly incomplete.
Specificly - there are at least two non-considered factors in conventional
computation: all possible simpletemporal-conditions, and, gross-set and
sub-setS of relations that 'exist' when the entire spectrum of simpletemporal
conditions are included.
This situation stems from the mathematical principle: "Simplfy". Yes, it
helps remove extranous information-noise and makes some certain relationship
clear and identifiable. But it also -removes- from thoughtful consideration
the information resident in and analytically important about - the total
mathematical environment.
Let me give you a pragmatic example with at least two ramification
implications that conventional analysis/presumptions -totally miss-.
Consider the gaussian-mean curve. It has been classically analyzed
to death; all things about it considered: complete/known.
That is a major deficiency/error.
Consider the equation form that produces the standard-deviation
curve. It is known; isolated, independent.
Now consider any 'real events' that produce and mimic/map the curve.
I like to use two, each which highlight two missing-consideration
factors. First, is random test results from some 'standardized'
exam. If you set up a criteria for accurate/innacurate answers,
the resulting spectrum is typically the standard deviation curve.
The time sequence of the answers registered is open, just the net
patterned result. In otherwords, the distribution curve misses
two essential input-factors: the reason the testing event happened,
and, the time frame of measurement. The testing event is 'factored
out' -causal impetus/energy- brought to zero/one, the time frame of
testing is 'factored out' (brought to zero/one).
Second is a pachinco apparatus, with balls falling though a
matrix of pegs. Run enough sample events and you reproduce
gaussian mean-distributiuon curve. But there are at least
two missed factors/presumptions. One is the presumption of
component ordered-relations. And relatedly, the presumption
of a stable universal impetus-field being present; it is
assumed, taken for granted, and ... 'factored out'. The
gravity/gradient field the apparatus resides in.
Take the pachinco apparatus made of wooden pegs. Placed the
board non-orthogonal to the gravity gradient field. Run
samples with matched-to-pegsize ball bearings and you get
the traditional result.
Run the sampling again, but use bowling balls. The 'standard
mean' curve is now and every time - a straight line. This is
an extreme, but ALSO IMPORTANT limit potential of the
standard deviation. Run the sampling again, using perfectly
elastic/reflective particles and some runs produce the
refraction patterns seen during the early atom-nucleus
investigations - particles curved or shadowed by their
reaction to encounters with the form or fields of the
atomic nuclei. Run the sampling again with the balls and
pegs matched as originally, but place the board flat on the
ground orthogonal to the 'motivation' field of earths gravity;
or place the apparatus in far outerspace in the appropriate
'initial configuration for starting a test run'. In both these
environmental situations/orientations -- nothing happens. No
'curve' or results get done. In otherwords, absent an
impetus/gradient, no 'standard deviation' profile is produced.
This means that there is a MISSING FACTOR which we discount
in computation work, because we presume SOME gradient or impetus
is 'always present' and need not be considered for existing ot
not. It means that for general statement accuracy a 'g' gradient
factor should be always written and stated ahead of the standard
equation form, to prevent its presence and potential impact on
evaluation be missed, dissed, and left out for those critical
conditions where the 'rate of event' or 'production of event
conditions' is ignored and remissly overlooked.
So right off the bat, the analysis of statistical potential
IN ALL THINGS is deficient by not correctly including one or
more time parameters (which coincides with: simultaneous
consideration of all-states, both when an entity or relation
is identifiably present, AND, when it/they are NOT.) This means,
that standard traditional statistical analysis is a SUBSET,
a limit set, of QM statistics which considers both existential
and neg-existential factors (potentia) .. SIMULTANEOUSLY.
Calculations are already deficient by not counting null-state
as a unit factor possibility. and null-state for each and
every non-null option.
When this is done, factorial enumeration counts become
insignificant. When null states are -included- in states
count, by the time you get to three existential non-null
count, the statistical alternatives of combinatoric options
is OVER 100 alternative distinct 'relations states with
considered potentials'.
And this is just with re-analysis of -standard- non Fuzzy Logic
(which I prefer to call Zadeh Logic in respect and honor of
its delineator/designer).
When you open the option parameters beyond 0,1 (which is no
less important than Complexity which now explores and uses
non-wholenumber 'dimensions' in exponents .. 'fractal dimensions')
you explore the fuller Stochastic space that logic must obligatorally
address and speak to as well.
.
.
.
.
Consistency and completeness then require re-review in a fuller
and larger context. that the previous bounded-logics were, and are not,
capable of dealing with.
There is no longer: A and not-A. There is conditional-A, probable-A,
never-A, partial-A, and ... each of these if/when/ever in union with
time parameter(s). I.e., non-Abelian sequencing alternatives of all
factors needs to be included as well. (got a headache yet? :-) )
For example, consider the 'options space' and 'options-potentials space'
of the universe at any given moment (this generally ties in with
multi-verse concepts, but puts a bit more meat on its bones ; and with
critically present errors in entropy analysis as its currently performed).
At any given moment, scenario events and causal results-states, not only
open up and future enable potentials that did not exist moments before,
there is the SIMULTANEOUS extinction, preclusion, closure and PREVENTION
of equally or larger domains of states-options can can no longer possibly
exist.
Current analytical methods totally ignore considering such plural unbounded
potentials subsets; especially on a scale that includes cybernetic relations
and transfinite spaces for existence, and alternative-existences, states,
and for relations/performance spaces concurrent with 'extancy'.
Re-worded: at any given moment and depending on which parameters and
extancy/potential set one uses as criteria for analysis .. some relational
entropies are increasing, while others are proportionally DEcreasing.
Entropy is not monolithic, there are categorical sub-domains, AND, there
are local regional proportionally changing domains. AND entroepy is not
exclusively 'thermodynamic'. Probability states differentials are evaluable
and patternable .. there is gradientable sensibility assignable to all
sorts of parameters. Each and every one has its own, and comparable to others,
entroepy aspect/gradient.
These and more are absolutely Zadeh Logic options, that standard logic,
computation, physics, conventional analysis is not built to evaluate;
and are deficient because of that.
Godelian incompleteness theorems - when generalized - wholly miss
important information, ignore relational constants, that are
superior and universal.
.
.
.
I know I didn't address your 'universe doesn't exist' logic review.
You were exampling a viable logic/analysis that is problematic and
illuminates for you the possibility that logic as currently practiced
harbors inconsistencies and errors, and you want to explore other
possibilities. I understand that. I agree with the anomaly you
identify and gave you reason to explore 'something else' and question
the 'what is'.
My above remarks showcased a few of the anomalies -I- recognized and
the conclusions I reached on re-review of ideas/understandings.
I -know- you are on a correct path of thinking/exploring.
Lots of great possibilities are ahead of you.
I found some wonderful things, like how to determine the
ratio of any-dimensioned sphere, volume::surface area,
without having to do any exotic calculus calculations.
I discovered that the Heisenberg Uncertainty principle
is a direct statement of spacetime geometry, a particular
limit equation of relativity options. In otherwords,
QM has a direct connection with Relativity. (!)
All sorts of new-realities are in the math. The uncourageous
and overly habituated practitioners could never discover them.
Good luck on -your- journey of discovery.
Jamie Rose
cc: RR list
Brian Tenneson
further study. Therefore, a delay may occur between now and a
substantive reply.
On Mar 23, 8:46 pm, James N Rose <integr...@ceptualinstitute.com>
wrote:
Bruno Marchal
Your idea of a universal set, in case it works, would indeed meet one
of the objection I often raised against Tegmark-like approaches, mainly
that the whole of mathematical reality cannot be defined as a
mathematical object. Of course this is debatable, and a case can been
made that such a universal set can exist (see the Forster reference
below).
Nevertheless I have no clues why do you want such an universal set to
be fuzzy, except perhaps by the analogy which can exist between the
empirical multiverse and some sort of fuzzy physical universe. A
problem with fuzzy set is that there are many approaches, and they do
not seem to converge on some standard apprehension. Perhaps you know
better. Have you written a longer text?
Now, once you assume the computationalist hypothesis in the cognitive
science (NOT in the physical science!) and once you are aware of the
mind-body problem (or the first person/third person relationship
problem) then you will be confronted with my other objections to
Tegmark, mainly the fact that the mind-body problem is still somehow
put under the rug. I suggest you read my texts (url below, or see the
Archive of this list) for appreciating that a universal structure
definitely cannot exist. Like in Plotinus or Cantor the big whole
cannot be made first order citizen.
Of course with comp (actually with only Church's Thesis) we do have
some "universal structure" like the universal *machine* or the
universal dovetailer, and those are embedded in the structure they
deploy. That is why comp works. But of course a universal machine does
not describe a universal set in your sense.
For the existence of a universal set in the context of Quine New
Foundation set theory (NF) I suggest you consult the book by
T. E. FORSTER, Set Theory with a Universal Set. Oxford Science
Publications, 1992. Oxford.
Bruno
http://iridia.ulb.ac.be/~marchal/
Le 23-mars-08, à 05:46, Brian Tenneson a écrit :
nichomachus
point because I fail to see why this is such a damning criticism of
the MUH. How is in inconsistent to affirm the existence and reality of
mututally exclusive axiom sets? I realize how that sounds so I would
like to amplify this point with the example that a mathematical
platonist may believe in the independent existence of both Euclidean
and non-Euclidean geometries. Each system is defined by its own set of
axioms and though any two may be mutually inconsistent, any one alone
may be entirely self-consistent. In other words, we don't merge the
axiom sets. Rather, each set defines one mathematical object or entity
that exists independently and in its own right. This is the way that I
read Tegmark's work anyway. I am interested to get other takes on this
point.
> Mathematics
> Australia http://www.hpcoders.com.au
> ----------------------------------------------------------------------------- Hide quoted text -
Russell Standish
>
> I have been following this discussion and I wanted to respond to this
> point because I fail to see why this is such a damning criticism of
> the MUH. How is in inconsistent to affirm the existence and reality of
> mututally exclusive axiom sets? I realize how that sounds so I would
> like to amplify this point with the example that a mathematical
> platonist may believe in the independent existence of both Euclidean
> and non-Euclidean geometries. Each system is defined by its own set of
> axioms and though any two may be mutually inconsistent, any one alone
> may be entirely self-consistent. In other words, we don't merge the
> axiom sets. Rather, each set defines one mathematical object or entity
> that exists independently and in its own right. This is the way that I
> read Tegmark's work anyway. I am interested to get other takes on this
> point.
>
Tegmark is unfortunately ambiguous on this point. I read Tegmark as
you do, that the ensemble is the union of all finite axiom systems,
which is of course enumerable (over a given alphabet). This
formulation then connects with the dovetailer approaches of both
Marchal and Schmidhuber.
However, there is an alternative interpretation that Tegmark's
ensemble contains all of mathematics, and then Russell's paradox does
present a problem, which Brian is attempting to find a solution.
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
James N Rose
Brian Tenneson
It's not a new idea, no. However, I find the classical logic
restriction to make set theories with a universal set as unnatural
(e.g., some automatically sacrifice choice) as one that uses FL might
seem to others. I mainly want to know if Russel type paradoxes are
completely universal, which would be interesting, in all
generalizations of classical logic or even logics without excluded
middle. W/o Em, I think no paradoxes are even paradoxes, though.
(Boring w/o Em?)
Not as interesting when one changes logic, maybe to some. But to me,
changing the logic, it's like non Euclidean geometry. Why assume (not
you, but the mathematical masses) that non-classical logic need be
uninteresting? It seems to have been quite opposed until recently
(ie, basically less than a century).
I have been mainly working on different approaches recently. Now I'm
trying to stay in classical logic and challenge your valid objections
to Tegmark-like mathematizations of physics, based on Russell-style
lines of thought. The idea is that a non-well founded set theory,
where a set could easily be an element of itself, is all I really need
to resolve (seemingly?) the objections.
This post at "project virgle" might be interesting as some of Rose's
ideas are invoked:
http://groups.google.com/group/virgle/browse_thread/thread/76f99835bbfc9b30/4c617765852ced87?hl=en&lnk=gst&q=tenneson#4c617765852ced87
Bruno Marchal
Le 10-avr.-08, à 04:35, Brian Tenneson a écrit :
>
> Hi Bruno,
>
> It's not a new idea, no. However, I find the classical logic
> restriction to make set theories with a universal set as unnatural
> (e.g., some automatically sacrifice choice) as one that uses FL might
> seem to others.
Although I feel certainly being a platonist with respect to the
arithmetical reality and machines, I am not sure about sets. The notion
of set is far too rich.
> I mainly want to know if Russel type paradoxes are
> completely universal,
It is hard for me to figure out what you mean here. In both NF, or in
computability theory you can give meaning to V is-in V. In Quine New
Foundation you have model with V-is-in V, but nobody knows if NF is
consistent. In computability V is-in V (for example the universal
dovetailer does run the universal dovetailer), and this does not lead
to paradoxes or contradictions but only to infinities or non stopping
machines.
> which would be interesting, in all
> generalizations of classical logic or even logics without excluded
> middle. W/o Em, I think no paradoxes are even paradoxes, though.
> (Boring w/o Em?)
?
>
> Not as interesting when one changes logic, maybe to some. But to me,
> changing the logic, it's like non Euclidean geometry. Why assume (not
> you, but the mathematical masses) that non-classical logic need be
> uninteresting?
I wrote in some paper that the beauty of classical logic is that it
forces us to see the beauty of non-classical logics.
Classical logic is the simpler and common way to describe what is a
non-classical logic. Like common sense is the best tool to go beyond
common sense.
You will not find a fuzzy book on fuzzy logic, with fuzzy theorems and
fuzzy price.
> It seems to have been quite opposed until recently
> (ie, basically less than a century).
Even that could be a matter of debate, but ok: formal non classical
logic is a recent development. Yet there is a sense to say that very
old mathematics and engineering were primarily intuitionistic.
Classical logic could be attributed to the greeks. The main power of
classical logic is that it allows the possibility of having partial
information, and allowing ignorance. It makes possible the theological
reasoning.
I guess you know Garden's proof of the existence of irrational numbers
x y such that x^y is rational. It illustrates how simple and powerful
and tolerant classical logic can be. But Garden's proof can be replaced
by a constructive proof. Yet this one is hard and can be communicated
only to expert in number theory. Then, in theoretical computer science,
and even more in theoretical artificial intelligence, most proofs are
*necessarily* not constructive. Those vast landscape are threw away, or
made less accessible when you weaken the logic.
Also, most weakened logics can get some sense by having epistemical
interpretations in classical logic. It is one of the main use of
(classical) modal logic.
In my (humble) opinion: believing that a non-classical logic can be
"fundamental" or absolute is the same as Berkeley, Wittgenstein, or
Brouwer's type of mistake: mainly to confuse the unknown reality with
one of its many mode of apprehension. Like in "esse est percipi".
>
>
> I have been mainly working on different approaches recently. Now I'm
> trying to stay in classical logic and challenge your valid objections
> to Tegmark-like mathematizations of physics, based on Russell-style
> lines of thought.
OK.
> The idea is that a non-well founded set theory,
> where a set could easily be an element of itself, is all I really need
> to resolve (seemingly?) the objections.
With the comp assumption we do not need more that the fact that some
number n belongs to the domain of the nth partial functions (n is-in
W_n, or f_n(n) converges). Now I have no conceptual objection against
non-well founded set theories.
Hmmm .... except that I don't really believe in sets, ...
It is ok if you like sets. I am personally problem driven, and try to
avoid discussion on theories. They are like people who discuss days
after days about which programming language is the better and who never
programs, or like people who discuss about which car they like the most
and never drive.
A theory is just a source of light to see in the dark 'reality', and
should not be confused with the "reality" itself. Except in
metamathematics were the (formal or mechanical) theories are the object
under study. (yes theories and machine also belong to "reality"). In
that case, they are all interesting a priori. For me, axiomatic set
theories are just good examples of very strong lobian machine, capable
of knowing the whole of the "theology" of much simpler lobian machine
like Peano arithmetic. (Lobian machine are, roughly speaking, universal
machine capable of knowing that they are universal; they obey Lob's
theorem (a generalisation of Godel's theorem). Such machine knows that
thay are terribly ignorant: Lob's theorem is a self-modesty result.
I love machine for their unbounded imagination ...
Best,
Bruno
Bruno Marchal
hmmm.... I am not sure .... Perhaps a duality, or a Galois connection
of some sort. I'm afraid that an *equivalence* would show up only in
the case where "I" am the "world" or comp is false or in the case where
the comp level of substitution is infinitely low, roughly speaking.
In that case ASSA and RSSA are plausibly equivalent, and the indexical
comp (what I am used to call comp and which asserts that "I" am a
machine) is then plausibly equivalent with Schmiduhuberian form of comp
(the universe is a machine).
About Bostrom's unification/duplication, I think that from the first
person point of view we can have unification when the two identical
brains are running identically during a period of time dT, although
duplication---during that very period of time dT--- has still to be
considered when some histories, going through the identical states
during dT, differentiate later. This is what I like to sum up by
Y = II,
which means that a differentation/bifurcation change the measure on
states in the "logical past", a little like if the "first amoeba" did
get a high measure in the past thanks to her many descendants today.
This entails a form of anthropic teleology about which I lack the tools
for making things more precise.
I think you could make your point clearer by trying to be more precise
on what you consider to be a world and a (first person) observer moment
perhaps. Modal logic could help you here I guess.
Bruno
Youness Ayaita wrote, the 07 Apr 2008:
An Equivalence Principle
Youness Ayaita
Mon, 07 Apr 2008 07:51:31 -0700
By this contribution to the Everything list I want to argue that there
is a fundamental equivalence between the first person and the third
person viewpoint: Under few assumptions I show that it doesn't matter
for our reasoning whether we understand the Everything ensemble as the
ensemble of all worlds (a third person viewpoint) or as the ensemble
of all observer moments (a first person viewpoint). I think that this
result is even more substantial than the assumptions from which it can
be deduced. Thus, I further suggest to reverse my argument considering
the last statement as a principle, the equivalence principle.
Let me first present and explain the two viewpoints:
1. The ensemble of worlds
This approach starts from the ontological basis of all worlds (or
descriptions thereof). I am not precise to what exactly I refer by
saying "worlds" and "descriptions" for I don't want to lose wider
applicability of my arguments by restricting myself to specific
theories of the Everything ensemble. But admittedly, I mainly think of
theories similar to Russell's ideas. However, the crucial property of
theories starting from the ensemble of worlds consists in their third
person viewpoint. The ontological basis does not explicitly refer to
observers nor to observer moments. Observers are regarded as being
self-aware substructures of the worlds they inhabit.
Coming from the sciences, this approach is very natural. In the
sciences, we are used to the idea of a physical reality independent of
us humans. We are studying phenomena happening in our universe. Thus,
when we invent a theory of the Everything ensemble, we are naturally
driven to the idea that not only our universe, but a multiverse
consisting of all possible worlds exists. We already know how
observers come into the scene: As an emergent property, a huge number
of the fundamental building blocks can constitute an observer. In
order to understand this, one has to introduce a semantic language
which describes the emergent phenomenon. The description of the world
itself is expressed in the syntactic language (I adopt Russell's
nomenclature). The link between between these two languages is some
kind of neurological theory explaining how the states of the
fundamental building blocks (more precise: the description of the
world) lead to mental states (or the emergence of an observer).
Though, finding such a neurological theory is a very difficult task.
In this world, we are facing the so-called hard problem of
consciousness. And even if neurologists, psychologists and
philosophers will finally succeed to find an adequate theory in this
world, it is not clear whether we can apply the theory to other
worlds.
So, to conclude, this approach has the great advantage of being very
close to the structure of the physical worlds. The explanation of
observers and observer moments seems to be possible, but surely is
very complicated and difficult.
2. The ensemble of observer moments
When I first thought of the Everything ensemble, I did not come from
the sciences, but from philosophy. I judged that the concept of
absolute "existence" was a dubious extension of the concepts of
subjective accessibility and perceptibility. So, it was natural for me
to start from the ensemble of observer moments, a first person
viewpoint. The class of all observer moments constitutes the
ontological basis of this second approach. Later, I realized that the
theory of the Everything ensemble could be used to draw conclusions
about the physical world. But this seemed to be unfeasible starting
from observer moments: the relatively simple laws of nature that we
find in our universe are obscured by the complex properties of our
senses. Starting from observer moments seemed to be a complication.
Consequently, I switched viewpoints and studied the ensemble of
worlds. I always hoped that both approaches would finally turn out to
be equivalent.
Even in principle, it is very difficult to think of "worlds" when
starting from observer moments only. This task is similar to
understanding observer moments when starting from the descriptions of
worlds. Starting from worlds, we must identify the observer moments as
substructres. Starting from observer moments, we must somehow extract
information that allows us to meaningfully talk about a world. From
the sciences, we know how difficult this is because there we try to
find a description of our world given our observer moments. We see how
complementary the two approaches are: The first approach needed some
kind of neurological theory to explain the appearance of observer
moments within a world, the second approach needs some kind of
physical theory to explain the appearance of a world when first
studying observer moments. The two approaches are another
manifestation of the deep connection between laws of physics and
properties of an observer.
The assumptions
My first assumption is related to our reasoning. The equivalence of
the two approaches does not mean that they are identical. I will say
that they have identical implications for our reasoning. To clarify
this, I must first explain how we shall reason. Here, I take the ASSA
(maybe we can check during the discussion whether or not my argument
generalizes to other versions of the self-sampling assumption):
'Each observer moment should reason as if it were randomly selected
from the class of all observer moments.'
The second assumption is more subtle. Suppose we take the first
approach, with all worlds as ontological basis. We explain observer
moments with the help of some neurological theories. At first, it is
not clear whether we can find every possible observer moment under
these emergent observer moments. The assumption is that we can. Every
possible observer moment is realized in at least one world.
Perhaps, some of you remember that I wrote about this topic September
last year. At that time, I came to the conclusions that the
equivalence did not exist. But yesterday, I read Bostrom's paper that
is currently analyzed on this list ("Quantity of experience: brain-
duplication and degrees of consciousness") and I understood that
September last year I took for granted what Bostrom calls
"Duplication". His arguments in favor of Duplication didn't convince
me, quite the opposite happened: I have adopted the other position,
"Unification".
The question Bostrom raises is the following: "Suppose two brains are
in the same conscious state. Are there two minds [Duplication], two
streams of conscious experience? Or only one [Unification]?"
This may seem to be a matter of definition. But let us return to the
ASSA: Which measure should be assigned to each observer moment? Given
Unification it is natural to assign a uniform measure: no observer
moment is more likely to be selected than any other. Given Duplication
it is natural to assign a measure to each observer moment proportional
to the number of its occurences in the Everything ensemble.
I assume a uniform measure. Surely, we can soften this assumption.
Nonetheless, it is decisive that the measure does not fundamentally
depend on the worlds but can also be deduced when taking the class of
observer moments as ontological basis. This is why I think that the
RSSA does not do any worse than the ASSA.
The equivalence principle
'Our reasoning does not depend on whether the ensemble of worlds or
the ensemble of observer moments is considered fundamental.'
I assumed that our reasoning should follow from the ASSA (or any other
version of the SSA compatible with my argument). Due to Unification,
we cannot detect any difference between the two different approaches:
The measure for each observer moment is the same.
The equivalence principle is a fundamental expression of what Russell
so eloquently explained in his book: "Not only is our psyche emergent
from the eletrical and chemical goings on in our brain, but the laws
governing that chemico-electrical behaviour in turn depend on our
psyche."
I speculate that both approaches to the Everything ensemble, the
ensemble of worlds and the ensemble of observer moments, are two
different windows to the same theory.
Youness Ayaita