[FOM] Bressoud vs Corfield

[Peter Smith]

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.

Peter S.

-- 
Dr Peter Smith
Faculty of Philosophy, University of Cambridge
www.logicbook.net
www.phil.cam.ac.uk/Smith