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).
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. 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", 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, ...).
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.
>>> 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. 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.
>>> 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.
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 - 04:13:11 PST