FOM: Re: Categorical "foundations"?

[Colin McLarty]

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".

Colin