some comments from John Baldwin

[Stephen G Simpson]

John Baldwin sent me the following comments.  With his permission,
I am forwarding them to this group.

   Dave has showed me some of your correspondence with Anand et al.
   Let me try to say what I think Anand is saying.
   
   Mathematics existed for many centuries with (increasing) notions of
   rigor in establishing the truth of various assertions but without a
   single axiomatic basis for the entire subject.  One of the great
   acheivements of 19th and early 20th century mathematics was finding
   an axiomatic basis for all mathematics and finding the limitation
   to that `basis'.  However, some mathematicians (and I don't sense
   that there are more now that 40 years ago) never regarded this as a
   central problem.  They remain content with what I call `local
   proof': Make clear what the assumptions of your current situation
   are and that your deductions are sound.

and, later on the same day,

   I hope it is clear that I am only guessing at Anand's point.
   Thinking it over, he may be making a somewhat stronger point which
   I think has changed in the last 40 years.  While Bourbaki was
   rather virulently antifoundations, they did employ a more
   explicitly axiomatic method of exposition than is perhaps
   fashionable at the moment.

Also, John has now posted an HTML version of his `philosophy notes',
at 

   www.math.uic.edu/~jbaldwin/pub/phil.html

-- Steve Simpson