On Mon, Jan 13, 2003 at 07:36:40AM -0500, John Cowan wrote:
> Jordan DeLong scripsit:
[...]
> > He doesn't have a power set function in his system, but it can be
> > created using his abstraction stuff. For set of all subsets of x:
> > =E2(a < x)
> > ('<' as containment). So it would certainly be a problem for the
> > system if the power set of a set is an element (which I am not adept
> > enough to determine).
>
> That's Cantor's paradox: the set of all sets must contain its power set
> as a member, which is impossible. The whole point of Quine abstraction
> is that it's eliminable *without* reifying over sets.
I dunno what 'eliminable' means.
But I do know that many sets in Quine are members of V (the set of
all elements). In fact V is a member of itself. Furthermore his
quantifiers do go over sets, so Ex(x = V) is true, etc.
See the thing is that 'V' is not truely a 'set of all things' (or
of 'all sets'), but a set of all 'elements'. I'm not sure, but I'm
guessing cantor is avoided (like russell) by making a power set not
count as an element. I ought to try to prove that though....
--
Jordan DeLong - fracture@allusion.net
lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u
sei la mark. tuen. cusku
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