FOM: Reply to Wallen on "proof"

Wed Mar 11 14:40:03 EST 1998

Thanks for your reply -- I think I will think a bit and see what other people
on FOM say before responding.  I'll say here that in the set-cat debate the
category theorists are making a "category mistake" in the philosophical sense by
answering the wrong question -- the issue is not whether categories can
theoretically provide a formal foundation for mathematics, it is that all
ordinary mathematical practice can be completely formalized much more easily in
set theory than in category theory or topos theory; and until the necessary
technical work is done in categorical foundations to allow complete
formalization of ordinary mathematical practice that does not simply
recapitulate set theory, the "foundational" significance of category and topos
theory is at best peripheral.   -- JS

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