Caught on tape by an undercover CIA agent were William Elliot's words:
 BS> It seems to be the same problem many people have with the idea of
 BS> God.  They cannot or will not believe in what they cannot empirically
 BS> perceive.
 WE> The same paradoxes about god are the same that have bother infinity.
 WE> Can god do something greater than anything an omnipotent being can do?
 WE> Can the set of all sets not belonging to itself, belong to itself?
 WE> Can there be an infinite ordinal greater than all infinite ordinals?
 WE> Can an infinity bigger than anything be bigger than infinity?
    I think God is limited to doing things that not logical
 contradictions.  In other words, divine omnipotence doesn't mean there
 are no limits to what an omnipotent being can do, but as Thomas Aquinas
 said, "God can do all things that are possible."  That means he cannot
 make a rock too big for him to lift, or make a round square, etc.
 Indeed, why the hell would he want to?
 BS> Sorry.  All this contemplation of infinities makes my brain hurt.
 BS> It's a small wonder Cantor went insane.
 WE> What?  You know his history?  Please tell.
 ---------------------------------------------------------
 Excerpted from Compton's Interactive Encyclopedia
 Copyright (c) 1994, 1995 Compton's NewMedia, Inc. All Rights Reserved
   Cantor was born on March 3, 1845, in St. Petersburg, Russia. In 1856
   the Cantor family moved to Frankfurt am Main, Germany. Before Georg
   was 15 years old, his talent for mathematics became evident. Choosing
   a career as a mathematician, he studied at the universities of
   Zurich, Berlin, and Gottingen. At Berlin, where he received a
   doctoral degree in 1867, his professors included the noted
   mathematicians Karl Weierstrass, Ernst Eduard Kummer, and Leopold
   Kronecker. He taught at a girls' school in Berlin, then in 1869
   joined the faculty of the University of Halle in eastern Germany. The
   salary he earned there was never great, but he inherited enough money
   from his father to build a comfortable house for himself and his
   family.
   From about 1884 until he died Cantor suffered occasional mental
   illness. Persons familiar with his life have suggested that these
   attacks were brought on by the difficulty of his research and by
   the unwillingness of other mathematicians (Kronecker, in
   particular) to accept his unusual results. Cantor died on Jan. 6,
   1918, in the psychiatric institute at Halle.
 WE> I read his original thesis
 WE> upon transfinite numbers when a kid.  Thanks to you, -) I'm borrowing
 WE> a library copy of his original work.  Maybe it will have some insights
 WE> to help you.  I'll look.  It should make interesting discussion. 
 WE> Maybe even philosophical.
    I'm looking forward to it.
 WE> The interesting thing about proving cardinality of P(S) > cardinality
 WE> of S is it's similarity with the Russell paradox:  Can the set of all
 WE> sets not belonging to itself, belong to itself?
    Does the barber shave himself?  ;^)
 BS> I know.  It still doesn't make it easier on a common sense level.
 BS> And it makes my brain hurt to try to make sense of it on that level.
 WE> Infinity is paradoxical.  You did understand how A0 + A0 = A0, so you
 WE> see you do understand some paradoxical things about infinity.
    I understand it on a purely logical level, but I don't understand it
 on a practical level, I think is what I'm trying to say.  I can't see
 it empirically, therefore it doesn't make sense on a more basic level.
 I don't grok it, if you'll pardon the Heinleinism.
 WE> For example, as Hindu scriptures say, 'From fullness take fullness and
 WE> fullness remains.'  That was centuries before Cantor showed that
 WE> taking odd integers away from all integers leaves the even integers
 WE> leaving as much as what you started with.  So you see, Cantor is a
 WE> late comer to this realm.
    That's interesting!  So, you think the Hindus already had a good
 grasp on infinity a few millennia back?
 WE> The infinite is beyond comprehension is what Christian mystics say.
 WE> What mathematicians say is there are some infinities so big that they
 WE> are inexpressible by any formulas.  They are called inaccessible
 WE> cardinals.  That is a profound and philosophically insightful
 WE> discussion for another post.
    Wouldn't that be Absolute Infinity?  Or is that the beginnings of the
 aleph-n, for all n > 1?
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... Certe, Toto, sentio nos in Kansate non iam adesse.
--- PPoint 2.05
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