On Wed, Jun 15, 2005 at 10:02:19PM -0700, Brian Holtz wrote:
> Alex Pruss wrote:
> 
> Remember that I am working in David Lewis's framework.  Each world is a
> physical object: a bunch of matter, connected together spatiotemporally.  So
> I do not need to work with specifications, but with concrete chunks of
> stuff.  There is nothing further illuminating to be said in a lewisian
> context, really, about what makes two concrete chunks of stuff the same
> chunk, is there?
> 

...

I haven't read David Lewis, and unfortunately it would be serious
distraction for me to follow his work up at this point in time. It
does strike me that "concrete chunks of stuff" is a bit incoherent, however.

> 
> My suspicion/hope is that the work I cited by Malcolm/Standish/Schmidhuber
> suggests an approach to defining such a linear order, by which we can judge
> that apparently regular worlds predominate over apparently irregular worlds.
> (Alastair, Russell -- am I reading you correctly?)
> 

Linear ordering is not needed. Rather, the fact that only finite
prefixes of the bitstrings are meaningful defines a natural topology on
equivalence classes of bitstrings having the same meaning. Such a
topology leads to an induced universal measure.

> (The one or two papers you linked to that I looked at made the assumption
> that there was a fixed maximum cardinality of things.  But why assume that?)
> 

The assumption is that the Plenitude is a particular object, the set
of all bitstrings ("descriptions"). The justification for this is
twofold:

1) All we can know about reality enters the mind as a string of data
   (a bitstring)
2) The set of all such bitstrings has precisely zero information.

No other Plenitude has these properties. It is a side effect that the
cardinality of this Plenitude is c, not an assumption that limits it.


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