[FOM] FOM: Infinite sets and plural reference

[Neil Tennant]

On Mon, 10 Feb 2003, Dean Buckner wrote:

> As it happens, set theory assumes a set is not identical with its elements.
> {Alice} is not the same thing as Alice, for instance.  {} has no members to
> be identical with.  And from the mere existence of Alice and Bob, we cannot
> infer the existence of {Alice, Bob}. 

I thought set theory contained the pair-set axiom:

	for all x for all y there exists z z={w|w=x v w=y},

i.e.,

	for all x for all y there exists z z={x,y}.

Now assume that Alice exists and Bob exists. Even in free logic, universal
elimination (twice) would then yield

	there exists z z={Alice, Bob}.

Neil Tennant