Re: Re :The empty set

On Wed, 16 Jan 2008 12:17:16 -0800 (PST), "Ross A. Finlayson"
<raf@xxxxxxxxxxxxxxx> wrote:


That is to say, there are other set theories, for example Cantor's
original Mengenlehre ("set theory"), with a universal set.

[No.] It is well known that _Cantor_ didn't consider the "totality of
everything thinkable" to be a set (but an "inconsistent multiplicity").

But the following claim would be right/correct:

"That is to say, there are other set theories
with a universal set."

Yes, Quine's NF (or NFU as well) for example.

Cantor...

I could see how he would have considered it inconsistent, as for
example the universe is a counterexample to the powerset result,

Exactly!


Cantor had a universe in his set theory, where every
thing is a set and everything is thus a set.

No. You are mixing up Cantor's theory (where there are things of our
"intuition" and/or "thought") with ZFC (where there are only sets).


Then, Cantor's "paradox" [and] Russell's [...], led to the
axiomatization [...] by Zermelo[.]

Right.


F.

--

E-mail: info<at>simple-line<dot>de
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