Re: Relation between sets and their elements

> G. Frege wrote:
> > "Paul Holbach" <paulholbachSPAMBAN@xxxxxxxxxx> wrote:

> > "The set and its members are not distinct existences."

> Well, one certainly might claim that a set is "determined" by it's
> members. (Principle of extensionality.)

And of what kind might the ontological relation between 'determinantes'
(elements) and 'determinatum' (set) be?

> > "There could be no set of cookies if there were no cookies [...]."

> Nonsense. Of course, there would be a _set of cookies_ if
> there were no
> cookies - but it would be empty.

At first Priest's statement struck me as highly implausible too, but
now I'm not so sure anymore.

If the set of dinosaurs now exists, although there now are no dinosaurs
anymore, then, for obvious reasons, the set of dinosaurs and the
dinosaurs could hardly have been identical.

The problem I sense is that the empty set of dinosaurs is necessarily
identical with the empty set, the only empty set there can be. So any
statement about the set of dinosaurs is a statement about the empty
set, which is necessarily empty. That means that the seemingly true
statement "There was a time when the set of dinosaurs was non-empty" is
in fact false, for the the set of dinosaurs now *is* the empty set, and
there was never a time when the necessarily empty empty set was
non-empty!

All sets except the empty set depend for their identity on their
members, and as Quine has taught us: no entity without identity. So all
sets who lose all their members lose their identity as individual sets,
and, hence, their entityhood as things distinct from the empty set.
That does seem to mean that the existence of the set of cookies as an
individual does depend on the existence of its elements, the cookies.

Two crucial general questions are how we could possibly individuate
more than one empty set, and how we might differentiate between two
kinds of empty sets: contingently empty ones and necessarily empty
ones?

Regards
PH

.

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