Christoph Schiller wrote:
>The universe seems to be a set only *approximately*, at energies
>or scales which are very low compared to the Planck energy or
>And that would mean that all approaches trying to describe
>the universe as some complex mathematical structure are doomed.
>the universe cannot be described with any structure which contains
>a set, or which is built on a set.
>It is not clear what the correct structure should be; but
>the structure should be very simple, and quite a bit simpler than
>a set. If you have any proposals for such a structure, I'd
>be interested to hear about them.
I agree with you that the universe cannot be a set.
Some nuances can be added because there are a a lot of approachs of
the notion of set, and perhaps by lowering some axioms of set
theory we could find some use of set in physics.
(I have proposed non extensionnal set theory for the treatment
of electronic orbital a long time ago).
Note that it is also important to distinguish ontology and
epistemology. The whole quantum field theory can be formalised
in some little enumerable model of Zermelo-Fraenkel set theory.
But this has nothing to do with the fact that the universe cannot
be considered as a set. So we must distinguish epistemological
representation (by a set) and question of ontological structure.
Now, I have shown (it seems, at least) that if we can
in principle survive with an artificial brain, then the
multiverse is much like a web of (machine's) dreams.
And this is related to the notion of observer-moment we
have discussed a lot in this ev-list.
I will say more after I read your web page ...