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On Tue, Jan 14, 2003 at 11:07:33PM -0500, John Cowan wrote:
> Jordan DeLong scripsit:
> > Well, it's a little more complicated than that. Rewriting to "All
> > x such that x is even" has problems with russell sets, etc.
>
> That is the distinction between *talking* of sets and *quantifying over*
> sets. You can eliminate talk of sets, by rewriting "2 in '{x|x is even"
> as "Ex: x = 2 & x is even", because there is no set which is the object
> of quantification. "To be is to be the value of a variable."
Actually he rewrites "2 in '{x|x is even}'" as
Ey(2 e y . (z)(z e y -> z is even))
which plainly requires that the set be the value of the variable y.
> > However, sets *are* possible values of variables in Quine[1]... So
> > I still don't know what you mean.
>
> When doing actual set theory. Quine's point is that much talk of sets
> can be paraphrased away without having to actually assume the existence
> of sets with all their problems.
Maybe he changed his system or something over the years. In the
(single) book by him that I've read[1], sets can be values of
variables. Some of them can also be members of other sets (for
example, it is a theorem that (x)((Ey)(y e x) -> empty_set e x)).
[1] Mathematical Logic, 1940.
--
Jordan DeLong - fracture@hidden.email
lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u
sei la mark. tuen. cusku
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