cat-dist@mta.ca writes:
Date: Wed, 13 Mar 1996 13:40:25 -0800 From: james dolan <jdolan@math.ucr.edu>
-This is an interesting example. You state a question in mathematical -English, and then criticise ZF for being able to express this question, -while category theory cannot.
i at least am curious just what is this mathematical question you claim to have in mind which zf can express but which category theory can not. obviously it wasn't "Does any simple group appear as a zero of the Riemann Zeta function?" since that is mere gibberish and not a
This question clearly is mathematical English, in the sense that it is in the English language, and uses mathematical jargon. It doesn't make sense. I wasn't arguing with that. Ruling out statements from being "mathematical" *merely* on the grounds that they offend your mathematical taste, quickly becomes disasterous. Especially when we're (implicitly) talking about a formalisation in a formal language such as that of first order set theory. Anyway, as a good example, take a set-theoretic proof of Borel determinancy. Can anyone give a reasonable category theoretic proof of Borel determinacy? [This is a result that Friedman showed is a theorem of ZF but not of Z, if my memory serves me correctly.] This could well suffice to answer my concerns w.r.t. the adequacy of category language, by showing how even arguments needing replacement can have category theoretic analogues. Ralph. P.S. My personal opinion on foundations is fairly agnostic, in case anyone mistakes my concerns with rejection of category theoretic foundations.