George Levy wrote:
>
> Saibal wrote:
>
> > George Levy wrote:
> > Even with the null set I have my doubt. Why not use the Not(null set)
> ..... which is the plenitude eh??? :-)
>
> > How do you avoid Russel's paradox?
>
> The Plenitude is not a set.... so strictly speaking the operation Not(null set) cannot be performed using
> the set operator "Not".... The fact that the result of the operation does not fall into the domain of sets
> indicates incompleteness of the sets just like taking the square root of a negative number indicates
> incompleteness of the reals. The solution for the square root problem is to invent imaginary numbers and to
> continue doing square roots. I am not sure what the solution for the sets would be.... invent an object of
> the class Not(null set)???
> I guess this would lead to logical contradictions.....The fact is that the plenitude in its entirety does
> include contradictions...What restores rationality is the presence of consciousness....it is a rational
> locus in the plenitude, imposed by the anthropic principle....
>
> George
>
I have often said myself the plenitude is not a set, however when
trying to write up some of this work for another audience, I tried
following up the web documents on set theory, I came up with nothing,
so in the end simply didn't raise the issue.
>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?
In any case, I believe this issue should be settled once and for all,
and added to the FAQ Hal is writing. Have you got a definitive on this
George?
Cheers
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
----------------------------------------------------------------------------
Received on Wed Mar 07 2001 - 21:41:12 PST