[FOM] The empty set

Stephen Pollard spollard at truman.edu
Wed Feb 28 09:30:35 EST 2007

Robbie Lindauer 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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