On 03 Jul 2012, at 16:33, Jason Resch wrote:
On Tue, Jul 3, 2012 at 8:39 AM, Bruno Marchal <[email protected]>
wrote:
On 02 Jul 2012, at 23:09, Jason Resch wrote:
To summarize our conversation up to this point:
BM: Do you really not see any difference between tables and chairs
and people and numbers,
JR: Chairs and people are also mathematical objects, just really
complex ones with a large information content. This is the
necessary conclusion of anyone who believes physical laws are
mathematical.
BM: No, it's a necessary conclusion of anyone who cannot distinguish
a description from the thing described.
JR: I think the identity of indiscernibles applies: If no
distinction can ever be made (by observers within a mathematical
universe and observers within a physical universe) then there is no
distinction. You are using "physical" as an honorific, but it adds
no information.
BM: I can point to a chair and say "This!"
JR: Yes, but how do you know you are pointing to a "physical chair",
rather than a "mathematical chair"?
BM: I know I'm pointing at a chair. I don't know what at
'mathematical chair' is. Can you point out how it is different from
a chair?
I think we both agree that if the universe follows mathematical
laws, then observers can make no distinction between whether they
exist in a platonically existing mathematical object, or a physical
universe. If you agree with this, then there is no fundamental
ontological difference between chairs, people, and numbers, that I
can see.
Comp allows a big flexibility for the initial basic reality. If we
choose the natural numbers, then people and chair must be explained
from them, and usually will not be numbers.
I agree that chairs, people != numbers, but I think they exist in
the same way numbers exist.
In which theory? What is a chair?
Facing the question: is the universe a mathematical object, or a
physical one, we must evaluate the two candidate theories as we
would any other.
With comp, the "universe" is neither primitively physical, nor
primitive mathematical. It is a mental object, or a theological
object. It exist as an object of thought in the mind of believing
machines (relative numbers).
I assume the comp hypothesis, all experiences are the results of
computations.
This is ambiguous, as computation of unction gives results. I guess
you mean that consciousness can be related to computation. (The nature
of that relation is different than we usually think when we abandon
the physical supervenience thesis).
What I mean by a mathematical universe is any mathematical object
that implements the computations necessary to contain observers.
Any given observer, of course, may exist in an infinite number of
such objects (universes) and there is no one universe the observer
can rightfully be said to belong to.
Yes there is one. In fact many. In fact all universal systems can do.
I use the tiny universal fragment of arithmetic to fix the thing.
Does one theory explain more, does one make fewer assumptions, etc.
That is the right attitude.
The existence of the physical universe does not explain the
existence of mathematical objects, but the converse is true.
Yes. And not only with comp, but with most of his natural weakening.
If we have to explain the existence of both: mathematical objects,
and the physical universe, the simpler theory is that mathematical
objects exist, as it also explains the appearance of the physical
world. If one accepts mathematical realism, then postulate the
physical world as some other kind of thing, in addition to its
mathematical incarnation, is pure redundancy.
OK.
I think that the idea of a primitive universe is a dogma. Of course
it is only a superfluous (redundant with comp) hypothesis.
Now the idea that the physical universe is "only" a mathematical
object among others is false too. It is a mental phenomenon as lived
by internal creature and provably made non mathematical from their
points of view. The relation between mind and matter, but also
between physics and the mathematical reality are more subtle than a
simple mathematicalist shift. The physical reality "needs" the
consciousness of *all* (universal, Löbian) machines to exist in some
sense, even if locally, large part of that physical reality will be
independent of the local conscious creatures embedded in it. Physics
is really the result of an epitemological process, which exists by
the nature of the arithmetical relations.
What do you think about the existence of mathematical objects that
do not contain observers?
They exist like the object of the term of my (first order
specification) of my initial universal theory.
With arithmetic, it means that they exist like the numbers exist.
Is their type of existence somehow different from those that can/do
contain observers?
They are not different. Non universal numbers exists in the same sense
that universal numbers. Note that in that theory infinite set simply
does not exist, except in the (fertile) imagination of the universal
numbers.
With comp, the idea that there is anything more than non negative
integers is just absolutely undecidable.
The more interesting existence appears in the dreams, theologies, and
truth quests of the numbers trying to understand themselves. Even
Cantor paradise is not enough big to describe the internal realms.
Bruno
http://iridia.ulb.ac.be/~marchal/
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