[FOM] FOM: Infinite sets and plural reference
Neil Tennant
neilt at mercutio.cohums.ohio-state.edu
Mon Feb 10 23:19:16 EST 2003
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
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