FOM: Russell paradox for naive category theory

Thomas Forster T.Forster at
Thu May 6 12:42:41 EDT 1999

I'm not sure what Steve means by saying that NF does not accept
the Russell paradox.  It's true that you can't have a universal
set if you have full separation - that's beco's of the Russell
paradox.  I can't see offhand why one shouldn't have a category
of all categories by means of some NF-like ruse - indeed Sol
Feferman tho'rt this years ago and circulated a manuscript
(now repudiated) in which he developed such a treatment in NFU
(NF with Urelemente, which is known to be consistent).  I'm
not sure why he repudiated it (perhaps he is listening and can 
tell us) but i don't think it was beco's that course of action
leads to paradox.
   (I confess i haven't been following this thread as closely
as i might. I've assumed that Steve's manifestation of Russell's
paradox in Cat. theory is just what he says - Russell's pdox in
Cat. theory - in which case it should yied to stratification
in the same way it does in NF)
        Thomas Forster

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