On 03 Jul 2012, at 16:33, Jason Resch wrote:



On Tue, Jul 3, 2012 at 8:39 AM, Bruno Marchal <marc...@ulb.ac.be> 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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