[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
non-self-identical.
No thing is non-self-identical.
So some things [the non-self identical things] are such that no thing is
among them.
Tom
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
>
>
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
--
Tom McKay
Philosophy
Syracuse University
Syracuse, New York 13244-1170
315 443 2536
fax: 315 443 5675
tjmckay at syr.edu
Plural Predication
Available now through all good bookshops, or direct from Oxford University
Press at:
http://www.oup.co.uk/isbn/0-19-927814-8
More information about the FOM
mailing list