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.

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.



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