 
Summary: In the Light of Logic
by Solomon Feferman
Oxford University Press, 1998, 352 pp. $ 60.00 US,
ISBN 0195080300
REVIEWED BY ANDREW ARANA
PoincarŽe famously compared the logician's understanding of mathematics
to the understanding we would have of chess if we were only to know its rules.
"To understand the game," PoincarŽe wrote, "is wholly another matter; it is
to know why the player moves this piece rather than that other which he
could have moved without breaking the rules of the game. It is to perceive
the inward reason which makes of this series of moves a sort of organized
whole." [P, pp. 217218] The Dutch mathematician L.E.J. Brouwer took
a position similar to PoincarŽe's: genuinely mathematical reasoning is not
simply a matter of logical inference. It is, as PoincarŽe put it, a matter of
mathematical insight.
Despite those views concerning logic, PoincarŽe and Brouwer believed that
the foundations of mathematics ought to be studied, and indeed carried out
fundamental work in this area. This might strike contemporary ears as a bit
odd, but it is a consistent view. Mathematical logic and the foundations of
mathematics are frequently lumped together, as though they are the same.
