Re: SUO: Echos
At 03:20 PM 2/15/01 -0500, Jon Awbrey wrote:
>¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
>Ah, Set Theory, How Do I Love Thee!?
>Let Me Just Try To Count Thy Weighs:
>
>There's the set of things that are abstract.
>...
No there isn't. You are talking about something that is equinumerous with,
e.g., the collection of all sets, namely a "proper class" (von Neumann),
"ultimate class" (Quine), "megacollection" (Langendoen and Postal), or,
perhaps best of all, an "inconsistent multiplicity" (Cantor's 1899 letter
to Dedekind). According to Fraenkel, Bar-Hillel, and Levy, "The only
difference between proper classes and sets is that, because of the
antinomies, the proper classes cannot be members of classes whereas sets
can." (_Foundations of Set Theory_, North-Holland Publishing Co.,
Amsterdam, 1973, p. 137.) Some authors take a dimmer view of "proper classes".
Josh Tonkel
Farance/Edutool