[FOM] The empty set

[Neil Tennant]

On Wed, 28 Feb 2007, Stephen Pollard wrote:

> 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

This last conclusion is fallaciously drawn. The correct claim "nothing
belongs to {x: not x=x}" has the logical form

	not exists y (y belongs to {x: not x=x}).

And this could hold by virtue of the non-existence of {x: not x=x}. For,
if it did not exist, then nothing could belong to it.

Neil Tennant