Re: An All/Nothing multiverse model

From: Georges Quenot <Georges.Quenot.domain.name.hidden>
Date: Wed, 17 Nov 2004 20:44:49 +0100

John Collins wrote:
>
> 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.

I was not thinking of that one but rather to the inconsistency
that appears when one wants to consider things like "the set of
all sets that do not containe themselves".

> 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)

This is the first time I heard of such things as 'urelements'
and I haven't that faintest idea of what that might be but,
for sure, I must be severely "computationally-minded".

> 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...

I have heard of the first two but not on that topic.

Georges.
Received on Wed Nov 17 2004 - 15:17:55 PST