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.
Cheers
--
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Received on Tue Jun 14 2005 - 22:58:20 PDT