If the plenitude is a set, then the power-set of the plenitude is not
contained in the plenitude.
Saibal
Russell wrote:
> I'm not sure that it would actually. 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 ??)
>
> Cheers
>
> Brent Meeker wrote:
> >
> > Hello Russell
> >
> > On 07-Mar-01, Russell Standish wrote:
> >
> > >> From the dim recesses of my memory, "the set of all sets" is a
> > >> logical
> > > contradiction, although I can't remember why. Is the plenitude like
> > > the "set of all sets" in some way?
> >
> > It would include the set of all sets which are not members of themselves
> > - but the existence of this set is self-contradictory.
> >
> > Brent Meeker
> >
>
>
>
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Received on Fri Mar 09 2001 - 07:23:36 PST