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 
> 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


Dr. Russell Standish                     Director
High Performance Computing Support Unit, Phone 9385 6967                    
UNSW SYDNEY 2052                         Fax   9385 6965                    
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Room 2075, Red Centre          

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