This volume is a collection of papers on philosophy of mathematics which
deal with a series of questions quite different from those which occupied the
minds of the proponents of the three classic schools: logicism, formalism,
and intuitionism. The questions of the volume are not to do with
justification in the traditional sense, but with a variety of other topics. Some
are concerned with discovery and the growth of mathematics. How does the
semantics of mathematics change as the subject develops? What heuristics
are involved in mathematical discovery, and do such heuristics constitute a
logic of mathematical discovery? What new problems have been introduced
by the development of mathematics since the 1930s? Other questions are
concerned with the applications of mathematics both to physics and to the
new field of computer science. Then there is the new question of whether
the axiomatic method is really so essential to mathematics as is often
supposed, and the question, which goes back to Wittgenstein, of the sense in
which mathematical proofs are compelling. Taking these questions together
they give part of an emerging agenda which is likely to carry philosophy of
mathematics forward into the twenty first century.