FOM: Russell paradox for naive category theory

Stephen G Simpson simpson at
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.

-- Steve Simpson

  From: John R Isbell <ji2 at>
  To: Stephen G Simpson <simpson at>
  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 or just ji2 at
     |                                                  |
     | Der Mensch ist nur da ganz Mensch, wo er spielt. |
     |                                                  |
     |              -- Friedrich Schiller               |

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