FOM: query on quote: Feferman?

Torkel Franzen torkel at
Tue Nov 18 03:15:40 EST 1997

  Colin says:

   >I believe Sol Feferman somewhere argued against categorical
   >foundations for math, saying something like: it is impossible to define
   >linear transformations before defining linear spaces. (I had thought this
   >was in the Midwest Category Theory Seminar of 1969, in his paper with an
   >appendix by Kreisel, but it is not.) Can anyone help me with a citation?

   It's probably not the passage you have in mind, but there is a comment
in a similar spirit in "Proof theory: a personal report":

        For example, some mathematicians espouse category theory
        as a new, purely mathematical foundational scheme. But what
        has been done is to take relatively sophisticated
        structural notions (category, functor) defined (informally)
        in terms of ordinary unstructured mathematical notions
        (class, function) and attempt to kick away the traces -
        'explaining' the latter in terms of the former. Whatever
        the organizational power of category theory in different
        parts of mathematics, this attempt at foundations is an
        exercise in self-deception.

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