Burgess's comments on anti-foundationalism
Stephen G Simpson
simpson at math.psu.edu
Tue Sep 30 16:42:50 EDT 1997
I asked John Burgess what the postmodernists have to say about
foundations of mathematics. He sent me the following response and
asked me to forward it to this group.
I'm not sure whom you're counting as post-modernists, but I know of
none of the usual suspects who has anything much to say about
mathematics, except insofar as it is included in their general
(negative) orientation towards science (as in the Sokal hoax). Gross
& Levitt ("Higher Superstition") is probably the best source to
consult if you're really interested. It has a section on "feminist
algebra". Also there was a review in the JSL a while back of a book
by someone named Nye called "Words of Power: A Feminist History of
Logic". I myself reviewed Tiles "Mathematics and the Image of
Reason", a much more moderate works, but not uninfluenced by Paris
fashions, in the Math Monthly a few years back. For the most part,
"Anti-Foundationalism" in philosophy of mathematics is a home-grown
phenomenon, not a French import. It is represented by Tymoczko,
ed., "New Directions in Philosophy of Mathematics", various works of
Philip Kitcher, and especially by Davis & Hersh, who are
professional mathematicians and amateur philosophers. I reviewed
their book (negatively) in a recent issue of Philosophia Mathematica
(this was paired with a positive review by a British
social-constructivist). Other public manifestations of
"anti-foundationalism" among mathematicians can be found in some of
the responses to the controversial piece on "Theoretical
Mathematics" in the AMS Bulletin a couple years back. Since the
appearance of the notorious Scientific American article on "the
death of proof", some of these people have backpedaled a bit to say,
well, they didn't really mean THAT. Tymoczko and I (representing
the opposite sides) were to have edited a special issue of
Philosophia Mathematica on the role of proof in mathematics (whether
and if so how it matters), but this was prevented by his premature
death.
I must have overlooked the "theoretical mathematics" article in the
AMS Bulletin, and the response to it. Ditto for the "death of proof"
article in Scientific American. John, can you supply volume and page
numbers?
-- Steve
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