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.
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).
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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