Date: Sun Apr 27 2003 - 13:30:46 MDT
"Perry E. Metzger" <email@example.com> wrote:
> I missed that -- could you give me a quick quote from it so I can do a
> search through the paper for the section?
"Indeed, if this exponential growth of the number of bubbles has been
going on forever, there will be an uncountable infinity of such parallel
universes [...]" (pages 5-6 of the .pdf)
> Mmmm. Well, if the universe was too simple, what would we do for fun in
> coming millennia? :)
It's not so much the possibility that there might be a lot more to think
about that bothers me (that's a good thing) as the possibility that all
these ideas are going in completely the wrong direction and will collapse
because of various paradoxes lurking on my horizon of comprehension.
A few comments on formal systems.
It's not obvious to me they should all have a finite number of axioms.
Googling, I see people talk about "recursively axiomatized formal
systems", which means that their set of axioms is recursive, which means
it doesn't have to be finite. Their number remains countable, though.
By "mathematical structure" Tegmark means an equivalence class of formal
systems. This is explained further in his older paper at
In the same paper, he argues set-theoretic models (which are themselves
formal systems) have the same physical existence as the formal systems of
which they are models. In that sense, the universe (and others) can be
seen as a set.
Nus (prophet of the universal quantifier)
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