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Re: [ontolog-forum] The notion of a "classification criterion" as a clas

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 26 Apr 2010 14:51:01 -0500
Message-id: <1272311461.2536.44.camel@xxxxxxxxxxxxxx>
On Sun, 2010-04-25 at 16:19 -0400, John F. Sowa wrote:
> Avril,
> I agree.  I was thinking of the set theories that follow Cantor's
> approach, which includes the empty set.    (01)

No set theory I know of fails to include the empty set; certainly its
existence is provable in all well-known and commonly used set theories
-- ZF, VNBG, Quine's NF and ML, Morse-Kelly, KPU, etc.  That isn't to
say one couldn't formulate one that rejected the empty set, but it would
be very hard to see the point, mathematically.  Of course, one might
have philosophical objections, but in this case the easiest thing to do
is simply let some urelement (the moon, Barack Obama, the number 17)
play the role of the empty set.  That way you can quiet your
philosophical objections and continue using the traditional set theory
of your choice.    (02)

Chris Menzel    (03)

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