FOM: Russell paradox, NFU, categories

Stephen G Simpson simpson at
Tue Feb 22 11:30:25 EST 2000

Mathias, 22 Feb 2000:

 > 11. Some years ago I saw a preprint of a paper by Feferman
 > investigating the possibility of a category of all categories
 > within the framework of Quine's system of New Foundations, which
 > admits a set of all sets.  Can anyone tell me more about that ?

There was discussion of this NFU issue around May 1999 on FOM, in
connection with my Russell paradox for naive category theory.  Forster
helped me get clear on this.  As I recall, the conclusion was that my
paradox doesn't work in the setting of NFU, because my notion of
autistic category isn't definable by a stratified formula.  In NFU you
can have something called ``the category of all categories'', but at
huge cost.

I still think my Russell paradox for naive category theory is
interesting and I am thinking of writing it up for publication.

-- Steve

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