[FOM] The empty set

Tom McKay tjmckay at syr.edu
Wed Feb 28 16:57:04 EST 2007

Pollard's argument here seems fallacious. For the conclusion to follow, we
would have to presuppose that {x: not x=x} refers to something. If we are
really wondering whether the empty set exists, we can't presuppose that. The
following argument would make a similar mistake (and it is clearly invalid):

If x is one of the things that are non-self-identical, the x is
No thing is non-self-identical.
So some things [the non-self identical things] are such that no thing is
among them.


On 2/28/07 9:30 AM, "Stephen Pollard" <spollard at truman.edu> wrote:

>> The existence of the empty set is not a logical truth either.
> I'm inclined to agree, but here's something to consider. It would not
> be crazy to insist that one direction of the Comprehension scheme is
> a conceptual truth governing our use of class abstracts and epsilon.
> I have in mind:
> If x belongs to {x: Fx}, then Fx.
> It follows that nothing belongs to {x: not x=x}. Conclusion: it is
> conceptually true that something has no members
> Stephen Pollard
> Professor of Philosophy
> Division of Social Science
> Truman State University
> spollard at truman.edu
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> FOM mailing list
> FOM at cs.nyu.edu
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Tom McKay
Syracuse University
Syracuse, New York  13244-1170
315 443 2536
fax: 315 443 5675
tjmckay at syr.edu

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