[FOM] Bressoud vs Corfield
ps218 at cam.ac.uk
Fri Oct 17 20:05:47 EDT 2003
I, for one, found Corfield's book very frustrating. We are repeatedly told
that it would be salutary for philosophers of mathematics to take a hard
look at some contemporary real mathematics. And various examples are
mentioned, but never in enough detail to get much clue as to what
philosophical lessons are there to be drawn.
I've just stumbled across another book (by a mathematician, and without
overt philosophical pretensions: it's not in Corfield's bibilography),
David Bressoud's Proofs and Confirmations (CUP, 1999). Apologies if it is
already well known, but it was new to me. From the blurb, "This is an
introduction to recent developments in algebraic combinatorics and an
illustration of how research in mathematics actually progresses." The focus
is the Alternating Sign Matrix Conjecture, and so far the book seems very
accessible. The book starts by referring to Lakatos, and (skipping to the
very end) finishes with some general reflections about what we can learn
from the story about about the nature of mathematical discovery and the
nature of mathematical explanation -- among Corfield's topics (not f.o.m.
of course, but interesting all the same) but seemingly MUCH better done.
Dr Peter Smith
Faculty of Philosophy, University of Cambridge
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