FOM: Re: Categorical "foundations"?

Colin McLarty cxm7 at
Fri Jan 23 12:07:07 EST 1998

Friedman wrote a reply to Pratt

        Including one important point I will reply to now. Pratt referred
to mathematical thought:

>Mathematical thought? Whose mathematical thought? Philosophers are going to
>want to understand and examine very carefully some of the relevant
>mathematical thought to see if it is conceptually coherent.

        This is crucial to the disagreement. When I say "mathmatical
thought" I mean high school math but also the thoughts of people generally
considered the best mathematicians. I do not mean that "mathematics" is just
by definition "whatever mathematicians do". I mean that I actually like, by
and large, the usual judgements: Gauss, Poincare, Hilbert, Serre, Atiyah,
Thurston are great mathematicians.

        Friedman considers much of what those people do as mere sport, "not
stupid in the ordinary sense" but also not respectable. He means a kind of
"mathematical thought" validated by a particular philosophic view. Well, I
am interested in his philosophic view. That's what interests me most on fom.
But understand that he intends it as oppositional to what nearly all
professional mathematicians mean by "mathematics".


More information about the FOM mailing list