Re: The Difference between a Set and an Element

On 17 Jan 2007 04:41:02 -0800, Paul Holbach
<paulholbachDELETETHENAME@xxxxxxxxxx> said:
Chris Menzel schrieb:
...
I can see a philosophical role for concepts of some sort, but I can't
imagine what it buys you to have a disjunctive concept
correspondingly uniquely to every set beyond a lot of metaphysical
bloat. But then again, I'm not very imaginative.

Indeed, the universe of concepts becomes "bloated" thereby. This is
already a consequence of Frege's comprehension principle for concepts
[EFAx(Fx <-> phi(x))], which G. Frege uses in his proof

I don't usually think of comprehension as having any implications for
the existence of concepts at all (though of course they played a role in
Frege's own views); the existential quantifier there is ranging over
classes. But suppose we assume a countable language and that every
formula with at least one free variable signifies a concept. On those
assumptions, there are at most countably many concepts, which is an
extremely *sparse* view of concepts compared to the proper-class-size
universe you envision above that contains infinitely disjunctive
concepts, one (at least) for each set.

.