On Tue, Jun 14, 2005 at 09:26:54AM -0700, Brian Holtz wrote:
> Hi everyone (in this world and all relevantly similar ones :-),
> I like the solution to the Induction / Dragon / Exploding Cow problem that I
> see in work by Malcolm, Standish, Tegmark, and Schmidhuber. So I forwarded
> references to Alexander Pruss, whose dissertation raises the Induction
> Objection to modal realism. The full context is on my blog at
> http://blog.360.yahoo.com/knowinghumans?p=8.  I'm interested in how the
> folks on this list would respond to Pruss's most recent comment, below.  Can
> anyone recommend a primer on probability in transfinite contexts like ours?


I will require some thought, but the approach I take (which is
effectively identical to Malcom's), the Plenitude is a set of
cardinality c (2^\aleph_0). The argument works within such a bound. My
reading of Tegmark and Schmidhuber is that they also have a similar
cardinality bound.

Could it be extended to higher cardinality plenitudes (if such a thing
makes sense)? I don't know without giving it a lot of thought (and
even then?), but I'd hazard a guess that certain paradoxes might step
in making the whole thing untenable.


*PS: A number of people ask me about the attachment to my email, which
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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
Australia                                http://parallel.hpc.unsw.edu.au/rks
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