Re: Absolute Infinity

Shmuel (Seymour J.) Metz wrote:
> In <1131511415.526544.190120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
> 11/08/2005
> at 08:43 PM, Starbles@xxxxxxxxxxxxx said:
>
> >Why does the power set have to be strictly greater than the original
> >set?
>
> In what set theory? In the cases of GBN and ZF, it's a theorem. In set
> theories that use different strategies for avoiding Russel's Paradox,
> it might not be the case both things that are sets in GBN or ZF might
> not exist at all.
>
> --
> Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
>

In those theories, there is not a set of all sets, so, why don't you
just leave the people talking about sets of all sets, like Kant, alone.
What they say can't possibly matter to you because they discuss things
totally outside the realm of possible discourse of your ZF set theory.
To talk about a set of all sets, you are not using ZF. Classes are
non-sets.

If want to talk about the universe, as a collection, ZF is
insufficient, and where there's a domain of discourse in having a
quantifier, ZF is inconsistent.

Ross

.

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