[FOM] The empty set

Richard Heck rgheck at brown.edu
Wed Feb 28 13:50:34 EST 2007

Stephen Pollard wrote:
> 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.
This assumes that {x: x<>x} exists. It's not clear why one is entitled
to assume this. It's true, to be sure, that if we use a second-order
function-symbol, a la Frege, then the standard classical treatment
requires it to be total. But as Quine long ago pointed out, this simply
emphasizes the extent to which the use of such notation hides
existential commitment.


Richard G Heck, Jr
Professor of Philosophy
Brown University
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