There do exist consistent approaches to set theory where you do have a
universal set and can therefore consider taking complements to be a
sinle-argument operation. to bypass the obvious paradox (that any set can be
used to make a necessarily larger powerset) you need to concoct a map from
the universal set onto its own powerset. The easiest way to do this is to
have lots of 'urelements' or' indivisible but somehow different sets, which
can then be mapped to larger sets in the powerset. If you find urelements
philosophically objectionable (which most computationally-minded people do)
then there exist other more difficult approaches: Try a google search for
"Alonzo Church", "Willard Quine" or "Thomas Forster" to see some people who
have tried...

--Chris Collins

----- Original Message ----- 
From: "Georges Quenot" <[EMAIL PROTECTED]>
Sent: Wednesday, November 17, 2004 10:36 AM
Subject: Re: An All/Nothing multiverse model

> Hal Ruhl wrote:
>  >
> > Hi George:
> Hi Hal,
> > At 09:13 PM 11/16/2004, you wrote:
> >
> >> Hal Ruhl wrote:
> >>>
> >>> My use of these words is convenience only but my point is why should
> >>> existence be so anemic as to prohibit the simultaneous presence of an
> >>> All and a Nothing.
> >>
> >> The "prohibition" does not "come from" an anemia of existence
> >> (as you suggest) but rather from the strength of nothing(ness),
> >> at least in my view of things.
> I am not sure I understand where we disagree (and even if we
> really disagree) on this question of the "{something, nothing,
> concept, existence}" question.
> Even if we consider that defining something automatically
> defines (a complementary) something else, this happens at the
> concept level. It might well be that both defined concepts
> simultaneously exists (say at least in the mind/brain of a
> few humans beings) but this says noting about whether either
> one or the other actually gets at something that would exist.
> Even if the *concepts of* something (or all) and nothing do
> need to exist simultaneously for any of them to exist, it
> (obviously ?) does not follows that something (or all) and
> nothing also needs to exist simultaneously (or even simply
> makes sense in any absolute way).
> Last but not least, what is the complementary concept of a
> given concept is not that obvious. Let's consider the concept
> of a "winged horse". Regardless of whether it actually gets
> at something or not, it can be considered to be opposed to
> "non winged horses" or to "winged things that are not horses"
> rather that to "anything that is not a winged horses". In
> set theory, a complementary of a set is always considered
> only within a given larger set and never in any fully open
> way (and there are well known and very good reasons for that
> whatever common sense may say). Similarly, defining an all
> or something in a fully open way is likely to be inconsistent.
> The situation is different here from the case of the winged
> horse and probably from all other cases and there is no reason
> that common sense be still relevant (like in the set of all
> sets paradox). This might be a case (possibly the only one)
> in which defining/considering something does not automatically
> make appear a complementary something (even simply at the
> concept level).
> >>> This would be an arbitrary truncation without reasonable
> >>
> >> Just as the opposite.
> >
> > I provided a justification - a simple basis for evolving universes -
> > which does not yet seem to have toppled.
> It might be not so simple. I went through it and I still can't
> figure what "evolving universes" might get at. Up to this point,
> I did not find something that would sound to me as a (more)
> reasonable justification. This may well comme from me.
> What appears reasonable or not or what appears as an actual
> justification or not is certainly very relative. Currently, I am
> still in the process of trying to find some sense (in my view of
> things) in what you are talking about (and/or of trying to
> figure out what your view of things might be). *Not* to say it
> necessarily hasn't.
> Georges.

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