Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

414 MATHEMATICAL PHILOSOPHY
to experts,-for enlightenment. For there are questions
to be asked. Generalization seems to be sometimes very
simple and sometimes very complicate. We should like
to know what mental phenomena,-what sorts of mental
activity,-are involved in it. What, if any, is the rôle
of imagination in it, and that of conception and that of
reasoning? Does generalization transcend the realm of
imagination? What is the office of logic therein? Is
generalization the end of a series of operations or is it
the beginning of a new series? Is it a conclusion forced
by reason or does it involve a creative act of will stimulated by motives but not coerced by them? What are
the actuating motives of the process? Are all generalizations essentially alike? If not, what are the kinds,
and how do they differ? How do the phenomena of
scientific generalization compare with those of idealization in other fields? Such questions are neither primarily
mathematical nor primarily metaphysical; they are psychological questions, which it is your proper function as
students of mind to investigate for your own enlightenment and for that of others. Let me cite again the
statement of that great man, Henri Poincaré: "The
genesis of mathematical discovery is a problem which
must inspire the psychologist with the keenest interest."
The things I have been saying are submitted as suggestions only; being a layman's suggestions, they are
probably very inferior to the best that could be made.
I am tempted, nevertheless, to add yet another one. It
is that a good way,-perhaps the best way,-for psychologists to advance their own subject would be to
cooperate with philosophic mathematicians and philosophic physicists in their efforts to solve the great problem
mentioned near the lose of Lecture X,-the problem, I