[FOM] The empty set

[Neil Tennant]

A brief reply to Professor Pollard:

I don't think anyone would grant any relevance, to this discussion, of
what Kummer did. Your respondents pointed out a simple fallacy in your
argument about the empty set. No red herring from the history of
mathematics will alter the fact that it was fallacious.

In the post containing the fallacy in question, you 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

Later you wrote that you 'had offered (without endorsement) an argument
for the conceptual truth of "something has no members."' Granted, the
illocutionary force of "it would not be crazy to insist that..." is
different from straightforward assertion; but what, then, would be its
interest? Why should anyone pay attention to what fills the three dots,
when all they are told is that insisting on it would not be crazy? There
are, no doubt, many others on this list beside myself who would find
but cold comfort in the assurance that, if they were to insist that [...],
they would not be thought *crazy*.

Neil Tennant