There are many different types of plenitude. For the sake of
precision, I will be referring to the Schmidhuber plenitude, ie "all
descriptions".
I think we're mixing levels here. Individual descriptions needn't be
consistent. Whilst the description "The subset of the plenitude that
contains all subsets that don't contain itself" may be in the
plenitude, the subset referred to by the description is not.
White rabbits do exist in anthropically consistent universes, but they
are rare.
George Levy wrote:
>
>
>
> Russell Standish wrote:
>
> > ...The plenitude would include all
> > sets that don't contain themselves, as well as sets that do. We know
> > the plenitude contains itself. However, since the set of all sets that
> > don't contain themselves is a logical contradiction, it is presumably
> > excluded from the plenitude in just the same way as square circles are.
> >
> > So this still doesn't imply that the plenitude is not a set, only that
> > the set of all sets that don't contain themselves is not a subset of
> > the plenitude. (Perhaps this make it not a set ??)
> >
>
> The plenitude is the absolute whole and is complete. It is however inconsistent,
> irrational... choke full of white rabbits. It includes the barbers who shave all
> those who don't shave themselves, and those horrible sets that Russell dreamed
> about, those that include sets that do not include themselves. In biblical terms
> it is the primeval chaos ( "tohu bohu", French, Hebrew). Our world, that is our
> perception of the plenitude, anthropically constrained by our consciousness, is
> incomplete but rational and completely devoid of white rabbits.
>
> George
>
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Received on Sun Mar 11 2001 - 17:36:36 PST