On 7/2/2012 2:09 PM, 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.

No. The mathematical laws of physics (e.g. the standard model) leave initial conditions undetermined, they assume inherent randomness (symmetry breaking), they don't specify why they are the laws of physics instead of some others. So the ontological difference is that some things exist and some don't. This distinction doesn't exist in Platonia: exist=having a consistent description. In physics exist=a member of the ontology of the fundamental model.

That's why Everett, to avoid having some randomness, postulated that we exist in many copies. Others have postulated multiple copies of the universe beyond the Hubble radius or in separate inflating spacetimes. Tegmark proposed "all mathematical structures". Most of this strikes me as a metaphysical stretch to equate the physical world with the Platonic. In Platonia everything not self-contradictory exists. There is no difference between logical and nomological. Our universe is 'explained' by anthropic selection from everything. So do you think there were chairs before there were people? Were there numbers before people?

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.

That's not the question. The question is whether all mathematical objects exist while only some physical ones do. In the latter case we need to find which physical ones exist and what is their mathematical description.

Does one theory explain more, does one make fewer assumptions, etc. The existence of the physical universe does not explain the existence of mathematical objects

I think it does.  See William S. Coopers "The Evolution of Reason".

, but the converse is true.

But only in the cheap sense of 'explain' like "God did it." Bruno at least limits his fundamental ontology to digital computation, but even this threatens to 'explain' too much.


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