Re: OT: Quine; Cantor (was Re: [jboske] Aristotelian vs. modern logic)

[John Cowan <cowan@ccil.org>]

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."

> 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.

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