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 > > > > > > -------------------------------------------------------------------------- -- > Dr. Russell Standish Director > High Performance Computing Support Unit, Phone 9385 6967 > UNSW SYDNEY 2052 Fax 9385 6965 > Australia [EMAIL PROTECTED] > Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks > -------------------------------------------------------------------------- --
