Georges Quénot wrote:
> peterdjones.domain.name.hidden wrote:
> >
> > Georges Quenot wrote:
> >> Norman Samish wrote:
> >
> >>> Where could the executive program have come from? Perhaps one could call
> >>> it "God." I can think of no possibility other than "It was always there,"
> >>> and eternal existence is a concept I can't imagine. Are there any other
> >>> possibilities?
> >> I think there is another possibility. I tried to explain it
> >> in my exchanges with John. It relies on several speculations
> >> or conjectures:
> >>
> >> - Mathematical objects exist by themeslves ("They were
> >> (or: are, intemporal) always there"),
> >> - The multiverse is isomorphic to a mathematical object,
> >> - Perception of existence is an internal property of the
> >> multiverse (mind emerges from matter activity),
> >
> > Given your commitment below, you also need to suppose
> > that perception is an internal property of maths.
>
> This logically comes with, yes. If consciousness is reduced
> (via biology and chemistry) to physics (monism 1) and physics
> is reduced to mathematics (monism 2), indeed consciousness
> is reduced to mathematics.
>
> >> - Mathematical existence and physical existence are the
> >> same ("there is no need that something special be inside
> >> particles", the contrary is an unnecessary and useless
> >> dualism, "the fire *is* in the equations").
> >
> > That can only be the case if the multiverse is isomporphic to
> > *every* mathematical object and not just one.
>
> Yes. The basic idea is that there is no difference between
> mathematical existence and physical existence. And this is
> indeed not specific to any particular mathematical object.
>
> > If it is only
> > isomorphic to some mathematical objects, that *is* the difference
> > between physical and mathematical existence.
>
> No. The idea is that *every* class of objects isomorph one
> to each other also have physical existence. Some have
> perception as an internal property and some have not (this
> does not need to be binary nor even one-dimensional).
>
> >> Some details and some (weak) arguments can be found in my
> >> recent posts to this group. Some papers from Max Tegmark
> >> are also relevant:
> >>
> >> http://space.mit.edu/home/tegmark/toe_frames.html
> >> http://space.mit.edu/home/tegmark/toe.pdf
> >> http://space.mit.edu/home/tegmark/multiverse.pdf
> >>
> >> Georges.
>
> > [...]
> > Georges Quenot wrote:
> >> Bruno Marchal wrote:
> >
> >>>> [...]
> >>>> - The multiverse is isomorphic to a mathematical object,
> >>> What do you mean? I guess this: The multiverse is not a mathematical
> >>> object, but still is describable by a mathematical object.
> >> No. I mean that there is a one to one correspondance between
> >> the "components" of the multiverse and those of a particular
> >> mathematical object and that this correspondance also maps the
> >> "internal structures" of the multiverse with those of this
> >> mathematical object. "Components" and "internal structures"
> >> should not be understood here as atoms or people or the like
> >> but only "at the most primitive level".
> >
> > That is the standard meaning of isomorphic.
>
> Yes. I explained it because this did not seem consistent
> with what Bruno said.
>
> > And if A isomorphic
> > to B, that does not mean that A is the same thing as B or
> > even the same kind of thing.
>
> Yes and no. For instance, natural numbers as seen as a
> subset of real numbers may be considered as different
> to "basic" natural numbers (for instance, considering
> the way real numbers are "built" from natural numbers).
> But as long as only the properties of natural numbers
> are considered they cannot be distinguished (and one
> could even "build" a new set of real numbers from them
> and that set would be the set of real numbers as long
> as the properties of real numbers wil be considered).
Since I don't adopt the premise that everything is
mathematical, I am no going to be persuaded that what
is true of mathematical isomorphism. Maps are isomorphic to
territories, but are not territories.
> Many sets of natural numbers (and of real numbers) can
> be thought of but what "really are" natural numbers
> or (real numbers) has nothing to do with the details
> that could make them appear different. These details
> are completely irrelevant to (and have no effect at all
> on) the way they "behave" as natural numbers. In order
> to identify or exhibit any difference between the
> elements of the class, we need to look at properties
> that are not shared in the class. Now, if we consider
> the universe/multiverse as a part of such a class, we
> would also have to look at properties outside of the
> class. But no such properties can be accessed from the
> inside of the universe.
No properties of actually existing things can be
accesed from our universe. However that may
just mean that there are no actually existing things
outside our universe; what is special about
our universe is just that it actaully exists.
It doesn't need to be distinguished from other
actual universe by having different properties ,
it is already disnguished by actually having any real,
empricially detectable properties at all.
> All we can access to from the
> inside of the universe is the shared properties of the
> elements in the class. In other words: if there was
> anything special inside the particle that would make
> them "real",
Errmm..but if the universe is the set of all real
things, then they all share the "property" of realness.
Perhaps you mean: what is the difference between real
things and unreal things? Well, the difference is that
real things have properties and unreal things don't.
Thus existence is not an ordinary propery, but what
follows from the existence of any other property.
> not only we would not have any access to
> it but whatever that might be and whatever there is
> actually something or not will not make any difference
> on the way we see these particle behave (including
> their mass, charge, interaction rules, ...).
Why does the fact of existence need to be explained
by some other fact ? Well, in fact we do this
quite a lot; we say that one thing exists because
it is caused by another.
> Finally, what makes differences between the different
> versions of the sets of natural numbers is not only
> accidental and neutral from the point of view of the
> structure (or the isomorphism) but the only thing that
> is likely to have a "platonic existence" in all that is
> not any of the instances of the class but rather what
> defines the class as such, the structure that is shared
> by all the instances. This is what is usually meant
> by "there is one and only on set of natural nummbers".
> Distinguisshing instances and considering what might
> make them different one from each other migth be
> completely vaine and pointless. Indeed, that *might*
> be the case for our universe/multivers.
Assuming what you are seeking to prove, that the universe
we live in is mathematical.
> >>> Are you postulating a physical universe?
> >> This is an ill-formed question. The universe could be purely
> >> mathematical and still appear as physical from the inside.
> >
> > Things are what they are, not what they appear to be.
>
> In this context, what they appear to be actually leaves
> some indetermination.
what they appear to be is
1) temporal
2) contingent
3) causal
4) apprehended by conscious beings
all of which are quite difficult to explain
on the Mathematical hypothesis.
> I would say that both the monist
> and dualist views (and possibly still many others) seems
> compatible with how things appear to me. What they might
> "really" be is open for me (and this is the same for the
> classical "mind/matter" dualism by the way).
> >>> Arithmetical truth already contains the full description of
> >>> the deployment of a full quantum universal doevetailer, but it remains
> >>> to explain why such a quantum realm wins the "white rabbit hunting
> >>> battle" (that is how it solve the measure problem).
> >> Yes. Many things remain to be explained and we may still be
> >> far to discover which mathematical object we live in (if we
> >> do, indeed).
> >
> > If we live inside any particular mathematical object as opposed to
> > others,
> > (if one mathematical object is instantiated in reality) then we
> > don't live in a purely mathematical world, since pure maths
> > cannot explain why only one of its objects should be instantiated.
>
> None in particular is actually instanciated or all are
> (in the context of the monist view). But rather it
> makes no sense in this view to consider instanciation.
> The class or the structure is all that exists.
OK, but that approach still has problems. For one thing,
it isn't really explanatory because it doesn't say why the
world is the way it is as opposed to some other way.
> >>> I tend to criticize all *fundamental* dualism.
> >> Okham's razor doesn't like them too, especially when they
> >> appear unable to help to explain anything more.
> >
> > If mathematical "objects" do no exist at all there is no dualism.
>
> True. That also works with the mind/matter dualism.
> >>> I agree with you that the fire is in the
> >>> equation (or more aptly in their solutions,
> >
> > Why some equations rather than others ?
>
> Anthropic principle: all possible sets of equations
> exist and develops into universes/multiverses. Some
> of them only will have conscioussness as in internal
> property. Indeed, "nobody" is there to figure how
> things might appear in the others.
If every possible mathematical structure is instantiated
people with brains/minds like ours will be contemplating
very different "Harry Potter" worlds. So the multiversal
version of Mathematical Monism is not explanatory.
> Finally, please note that I do not insist that monism
> (in the sense I defined it here) must be true. I do
> not even insist that anybody must find it have sense.
> My point is that one should not say that it must be a
> nonsense to everybody.
>
> Georges.
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Received on Fri Mar 17 2006 - 11:40:48 PST