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 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/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
