FOM: Russell paradox for naive category theory
Stephen G Simpson
simpson at math.psu.edu
Wed May 5 12:25:16 EDT 1999
Dear Professor Isbell,
Thanks very much for telling me what you remember of this.
If you come across anything else that's relevant, please let
me know.
Sincerely,
-- Steve Simpson
From: John R Isbell <ji2 at eng.buffalo.edu>
To: Stephen G Simpson <simpson at math.psu.edu>
Subject: Re: Russell paradox for naive category theory
Date: Wed, 5 May 1999 11:13:06 -0400 (EDT)
Dear Professor Simpson,
What Sol says is consistent with my recollection. It is not
difficult to be consistent with something as vague of my
recollection of categorical-foundations discussions of 1969,
but I think I did say that I had seen such a paradox. Even the
likeness to Burali-Forti sounds right. But I see I have said
a bit more than I remember; 'seen' may not be right. I may have
only heard a prsentation of a paradox in naive category theory.
People inclined to tell me about such ideas in the sixties,
partly because I reviewed Lawvere's 1965 La Jolla paper on the
category of categories as a foundation for mathematics and
pointed out an inconsistency in his axioms. That was not a
paradox, just a slip. But by 1972 I had decided that I was not
interested in categorical-foundations (bar some startling news)
and I can't add to the fuzzy remarks above. Sorry.
John R. Isbell ji2 at eng.buffalo.edu or just ji2 at buffalo.edu
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