🚀 go-pugleaf

In article <1992Nov20.155725.11719@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:
>>Russell's paradox denies the existence of the paradoxical set of all
>>sets.  Denial of an existential is a universal, and the universal
>>statement asserted by Russell's paradox is that every set has a
>>nonmember.  The universal set is "too big" by one element, having no
>>nonmember.  From that perspective size has everything to do with it.
>>-- 
>>Vaughan Pratt	  		A fallacy is worth a thousand steps.
>
>This is inaccurate.  Russell's paradox proves nothing except that
>there is no set which has exactly the sets which are not elements of
>themselves as members.  If the Axiom of Separation is added to one's
>theory, the paradox has the consequence indicated.  In theories where
>the Axiom of Separation does not hold (like NFU) the paradox has
>different consequences.

Good point, I hadn't spent long enough thinking about the meaning of
David Gudeman's "What if you altered ZF to contain this axiom (and
introduction of definitions)?"  I guess this must entail dropping
Separation, right?
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.