Le 16-mars-06, à 22:52, [EMAIL PROTECTED] a écrit :

> Is isomorphism or a one-to-one correspondence a mathematical concept or
> a metamathematical (or metaphysical? another complication in the
> discussion) concept?  I take them as mathematical concepts, so that
> speculating about isomorphisms of things like the multiverse is in
> itself assuming that the multiverse is mathematical.  I don't think we
> can use the one-to-one correspondence when it comes to metamathematical
> questions like the multiverse (or philosophy of everything), but this
> is simply because I assume that the multiverse (or "everything") is
> metamathematical.

Metamathematics is a branch of mathematics. It is the mathematical 
study of mathematical reasoning, proof, theories, models, etc. It is a 
part of mathematical logics. It can be identified with recursion 
theory, computability theory and evn with abstract theoretical computer 
This is of course unlike "metaphysics" which can belongs to physics 
only with supplementary metaphysical assumptions.

I do think there can be isomorphism between a physical structure (if 
that exists) and a mathematical object. I think, for example, that even 
a physicalist  could say that the quantum physical multiverse is 
isomorphic (or homomorphic) to the vector space of the solution to the 

Also something can be mathematical does not imply that there is a 
mathematical object associated to it. The simplest example is the whole 
of mathematics. This is arguably mathematical, but there is no 
mathematical object capable of representing it. There is only 
mathematical approximations.
Some philosophical assumption can add nuances.



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