**From:** Perry E. Metzger (*perry@piermont.com*)

**Date:** Sun Apr 27 2003 - 10:10:37 MDT

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geodesicallyincomplete@warpmail.net writes:

*> "Perry E. Metzger" <perry@piermont.com> wrote:
*

*> > At Level II, I must confess I don't understand the whole "chaotic
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*> > perpetual inflation" thing well enough to grok but I'd guess
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*> > "countable".
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*>
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*> Tegmark mentions in his paper that the number of Level II universes is
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*> countable if inflation is not past-eternal, and uncountable if inflation
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*> is past-eternal. I think the former is considered more likely.
*

I missed that -- could you give me a quick quote from it so I can do a

search through the paper for the section?

*> Eliezer also mentions a diversity of aleph_2, but this would depend on
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*> whether the continuum hypothesis ("the cardinality of the continuum
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*> (reals) is aleph_1") is true. This made me think about a confusing issue.
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*> If every Level IV universe is a formal system, and the continuum
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*> hypothesis is independent of the other axioms of set theory, then it
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*> might be that our universe is described by set theory with CH, or by set
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*> theory without CH. If we could somehow measure experimentally (using
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*> esoteric math-tech) the cardinality of the continuum in our world, then
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*> if the CH was among the axioms, we'd find aleph_1. If one of the axioms
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*> was "c == aleph_5", we'd find aleph_5. But the possibility of doing such
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*> an experiment should not depend on whether there is such an axiom -- so
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*> what happens if our universe is described by set theory with no axioms
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*> that determine the cardinality of the continuum?
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Eeek! A fascinating new question! Indeed, it opens up an entire raft

of new questions.

*> I'm sure I'm overlooking many subtle interpretational issues here -- when
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*> discussing this sort of thing I always feel as if carefully avoiding a
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*> giant murky swamp of decision theory and probability theory and anthropic
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*> reasoning and reference classes and SSAs and SIAs and mathematical logic
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*> and set-theoretical paradoxes.
*

Mmmm. Well, if the universe was too simple, what would we do for fun

in coming millennia? :)

Perry

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