Le 16-mars-06, à 22:52, daddycaylor.domain.name.hidden 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
science.
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
SWE.
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Mar 17 2006 - 08:49:44 PST