some comments from John Baldwin
Stephen G Simpson
simpson at math.psu.edu
Tue Sep 30 16:54:06 EDT 1997
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',
-- Steve Simpson
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