FOM: Russell paradox for naive category theory

Stephen G Simpson simpson at
Mon May 3 19:14:23 EDT 1999

Carsten Butz writes:

 > On Mon, 3 May 1999, Stephen G Simpson wrote:
 > > As I think about this, it seems to me there is an analog of the
 > > Russell paradox for naive category theory.  I outline it below.
 > [...] 
 > My words. Of course there is. I guess most people know this. ...

You seem to be suggesting that the argument which I outlined in 3 May
1999 12:08:23 is well known among category theorists.  (If it has been
published, I'd appreciate a reference.)

But then, why do people keep talking about ``the category of all
categories''?  Note that, in some cases at least, such talk seems to
be quite serious and literal.  For instance, there is Feferman's FOM
posting of 25 Jan 1998 16:53:04, where he explores the possibility of
a conceptual foundation or framework for category theory in which
something like a ``category of all categories'' would literally exist.
Such a framework would of course have to be inconsistent with the
usual VNBG framework, because in VNBG there is no class of all
classes.  However, my argument seems to indicate restrictions that are
considerably more severe ....

By the way, Feferman's posting contains a reference to a 1974 abstract
which mentions NFU.  I don't understand much about NFU, so tell me:
how is Feferman's 1974 abstract related to McLarty's result which was
referenced by you in 29 Apr 1999 20:35:16 and Mossakowski in 30 Apr
1999 12:32:43.  And how is it related to Holmes 30 Apr 1999 15:20:45?

-- Steve

More information about the FOM mailing list