Craig
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> [Roger Clough], [[email protected]]
> 12/31/2012
> "Forever is a long time, especially near the end." - Woody Allen
> ----- Receiving the following content -----
> From: Bruno Marchal
> Receiver: everything-list
> Time: 2012-12-30, 08:57:29
> Subject: Re: Ten top-of-my-head arguments against multiverses
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> On 29 Dec 2012, at 20:51, Brian Tenneson wrote:
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> Why not take the categories of all categories (besides that Lawyere
> tried that without to much success, except rediscovering
> Grothendieck topoi).
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> I'm more interested in the smallest mathematical object in which all
> mathematical structures are embedded but the category of all
> categories will do.
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> Except that it is too big, and eventually lawvere extract the topi
> from this, which model well, not the mathematical reality, but the
> mathematician itself.
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> Also, we have already discuss this, but the embedding notion does
> not seem the right think to study, compared to emulation, at least
> with the comp hypothesis.
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> But if you assume comp, elementary arithmetic is enough, and it is
> better to keep the infinities and categories into the universal
> machine's mind tools.
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> Enough for what, in what sense?
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> Enough for a basic ontology (and notion of existence) to explain all
> the different sort of existence, notably of persons, consciousness,
> matter appearances, etc. See my papers, as I pretend that with comp
> we have no choice in those matter, except for pedagogical variants
> and practice.
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> To have a single mathematical object that all mathematical
> structures can be embedded would give us an object that, in a sense,
> contains all structures. If one follows Tegmark's idea that ME=PE,
> then a definition for universe just might be a mathematical object
> (which by ME=PE is a physical object) that contains, in a sense, all
> mathematical objects (i.e., all physical objects).
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> I think that this is deeply flawed. We cannot identify the physical
> and the mathematical. We might try theory on the physical, or on the
> mental, or on the mathematical, which might suggest relation between
> those thing, but I doubt any non trivial theory would identify them,
> unless enlarging the sense of the words like mental, physical.
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> Isn't it simpler to assume there is only one type of existence?
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> It seems to me part of the data that this is not the case. My pain
> in a leg has a type of existence different from a quark. The game of
> bridge as a different type of existence than the moon material
> constitution.
> Then for machine, once we distinguish their different points of view
> (intuoitively like in UDA) or formally like in AUDA, we get many
> different sort of existence.
> The ontic one is the simpler ExP(x), but we have also []ExP(x),
> []Ex[]P(x), []<>P(x), []<>Ex[]<>P(x), etc. All this in 8 different
> modal logics extracted from self-reference.
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> What are the actual flaws of a mathematical universe?
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> Too big. It is a metaphor.
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> A physical system can be mathematically encoded by its corresponding
> set of world lines. This encoding is an isomorphism. A very simple
> example of what I mean is the nearly parabolic path taken by a
> projectile. The set of world lines would be some subset of R^4 or
> R^n if it turns out that n != 4. I am aware that indeterminacy due
> to Heisenberg's uncertainty principle kicks in here so we may never
> "know" which subset of R^n a physical system is isomorphic to but by
> a pigeonhole principle, the physical system must be isomorphic to
> some subset of R^n, several in fact.
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> May be. But I am driven by the mind-body problem, and what you show
> above is mathematical physics. With comp, by UDA, we have to extract
> the belief in such physical idea by ultimately explaining them in
> term probabilities on computations (that the result I invite you to
> study and criticize).
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> With computationalism, the coupling consciousness/physical is a
> phenomenon, person perceptible through numbers relations when they
> (the persons) bet on their relative self-consistency. This explains
> the appearance of the physical, without going out of the
> arithmetical. It works thanks to Church thesis and the closure of
> the comp everything (UD*, sigma_1 completeness).
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> How are you defining consciousness here?
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> I can't define it. I just hope you know what I mean. Basically
> something true but non provable about yourself, and, by comp,
> invariant for some local digital substitution.
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> It's not super clear to me that the cocompletion of the category of
> all structures C exists though since C is not a small category and
> thus Yoneda's lemma doesn't apply. I would have to fine-tune the
> argument to work in the case of the category C I have in mind.
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> The n-categories might be interesting, but we don't need so rich
> ontology. If we are machine, the cardinality of the basic TOE is
> absolutely undecidable from inside. Omega is enough.
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> Do you have an argument that proves that our minds can't transcend
> "inside"?
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> The mind can do that. Math, by diagonalization, does that, actually,
> even in a 3p way.
> But the fact that "number's mind" can do that invite us to not reify
> the transcendental. This is what lead to superstition and non
> necessarily complex ontologies.
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> If the cocompletion of C is the One, that which all mathematical
> structures can be embedded, then the parallel universe question
> would be a matter of logic and category theory; it would depend on
> how you defined "the visible universe" and "parallel" universe.
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> You will have to define an observer, its points of view, and to take
> into account its many distributions in that super-mathematical
> structure, but you can't do that, as you will need an even bigger
> structure to define and study the indeterminacy. So you will have to
> limit your notion of observer and use some "comp" hypothesis (an
> infinite variant if you want).
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> With comp, it is easier: you cannot really take more than
> arithmetic. God created the Natural Numbers, all the rest belong to
> the (singular and collective) number's imagination. If nature
> refutes this, it will still remain time to add the infinities
> needed. I think.
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> How is the arithmetical structure going to give rise to a
> description of reality that takes into account observer, its points
> of view, and its many distributions without the need to study the
> indeterminacy?
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> You might take a look on my paper(s)(?), or my posts here, as this
> is what I keep trying to explain here. I am not sure how you can
> study the relation between the first person and its possible
> realities without using the first person indeterminacy, which is the
> building block of the physical realities.
> The observer are the (Turing) universal numbers. Physics is given by
> the measure on the computations going through their state. This
> extends Everett on arithmetic. It leads to a many-dream view of
> arithmetic, and can be shown to be developed by almost all universal
> numbers.
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> Bruno
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> (?) http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
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> http://iridia.ulb.ac.be/~marchal/
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