Re: on formally describable universes and measures

From: Russell Standish <>
Date: Thu, 8 Mar 2001 16:20:22 +1100 (EST)

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
Room 2075, Red Centre
Received on Wed Mar 07 2001 - 21:41:12 PST

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