Bruno Marchal wrote:
> [...]
> I should have said that the appearance of a universe cannot entirely be 
> a mathematical object from the internal (first person) point of view. 
> Arguably so with comp or with weaker hyp.

I feel a strong ambiguity about the possible sense of
"appearance" here. Indeed, the universe *can* appear as a
mathematical object and it certainly does to at least a few
people (whether this appearance is correct or not and even
whether it is sound or not). Whatever sense you choose I
don't understand your point.

>>>> [...]
>>>> - 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".
> It seems that this is just a precise formulation of what I did 
> understand, except that I still don't know if you postulate the 
> existence of a physical universe.

I do (in the context of these speculations) in a monist sense
which means I do not in a dualist sense (see below).

> If not, what is the difference 
> between being a physical object and being a mathematical object ?

At the level of the whole universe (or multiverse) I don't see
any (and this is what I call a monist view in this context).
Everything else that appears to us as a "physical object" is
unlikely (possibly even electrons) to individually correspond
to a mathematical object. These (other) "physical objects" only
appear as such as (formally ill-defined) emerging properties.

>> *If* comp is true. I am not sure of that.
> Me too. But it is the theory I am studying. Also comp provides some 
> neat "etalon philosophy" to compare with other theories. The advantage 
> of comp (which I recall includes Church thesis) is that, at least, many 
> fundamental questions can be addressed.

Which one for instance (that is not addressed in the view of
the universe/multiverse as a mathematical object)?

>>> But then: What is mind, what is matter, what is activity?
>> I would say for all three: emerging properties that appear
>> as such when "viewed from the inside" of the universe.
> All right, but then you should make clearer what you mean by 
> "universe". I do think like you that mind, matter, activity, ... are 
> emerging from an inside view (actually it needs to be so once comp is 
> *postulated*),

It also needs to be so once it is postulated that the universe
(or multiverse) is a (particular) mathematical object.

> but at least with comp we can say more. Mind matter 
> activity arises from the collection of all the "inside view" (sometimes 
> refer too in terms of observer-moment in this list) which are all 
> implicitly defined in the Arithmetical Platonia.

I do not see how this says more.

> Kronecker said: God created the natural numbers, all the rest has been 
> invented by humans.

If God did create the natural numbers, He did not have much
choice while doing so. Possibly so little choice that nothing
was left for Him to create. He could ne create them with the
Fermat's therorem being false for instance.

Last but not least: time seems to be a *local* property
*within* a universe (there do not seem to exist a global time
within the universe and it it is even harder to imagine a time
outside of it). How can have He creat*ed* numbers, especially
if they are a requisite for a universe with a time flow to

> But with comp you can say: God has created the 
> natural numbers, all the rest has been invented by the natural numbers.

 From the "mathematical object" perspective, it can also be
argued that real numbers, Hilbert spaces, etc. also come with
natural numbers. God had not much (if nay) choice than men
about their properties.

> Of course here "God creates X" means that we cannot even conceive how X 
> could have appeared or have been created.

I can conceive (yes, I can be wrong) of natural numbers (up
to Hilbert spaces and higher) as necessary beings by themselves.
"... have appeared or have been created" sounds to me like an
anthropomorphism. They just "are" in an intemporal sense and
questionning their appearance or creation is a nonsense.

>>> 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.
> That what I think. By default I tend to use the expression "physical 
> universe" as a short form for "Aristotelian physical universe", that is 
> one in which there is a primary matter, that is a notion of primitive 
> matter which would not be reducible to anything else.

I mentionned that these reflections questions the meaning that
"physical existence" may have. I agreed (and mentionned) that
the default sense did correspond to a dualist view ("there
needs to be some special substance in particles", which seems
equivalent to what you call an "Aristotelian physical universe").
But I also suggested that it could also have another sense
corresponding to a monist view. From the inside, both should
be undistinguishable (and that was my point, with in addition
Okham's razor in favor of monism). So I guess that you meant
that comp is incompatible with a physical universe in the dualist
sense but not it might not be with the monist sense. To your
question "Are you postulating a physical universe?" I would reply
"No" in the dualist sense and "Yes" in the monist sense.


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