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

26 MATHEMATICAL PHILOSOPHY
that common character is sufficient; and that such knowl.
edge does not demand exploration of the continent in all
its length and breadth and height and depth, but may be
gained by examination of representative parts and especially of the elements which fundamentally compose the
whole.
That reply, if we rightly interpret the meaning of
the terms, is just. But their meaning is momentous. The
mathematical knowledge which they tell us is sufficient
for the purposes of the philosopher is neither slight nor
simple nor easy to gain. The questions it must answer
determine its nature and its scope. What are the idiosyncrasies of mathematics as a body of content? As a system of methods? As a type of activity? As a distinctive enterprise among the great kindred enterprises of the
human spirit? If the science be logical, what are its relations to Logic? If it be beautiful, what are its relations to Art? If it employ hypothesis, observation and
experiment, what are its relations to Natural Science? If
it be purely abstract and conceptual, what are its relations
to the concrete world of Sense? If it be theoretic, what
are its relations to Practical Life? If it be self-critical,
what are its relations to the science and art of Criticism?
If it be a wisdom respecting infinite and eternal things,
what are its relations to Philosophy and to Religion? If
it have limitations, what are its relations to the dream
of Universal Knowledge? To the challenge of these
great questions and their kind, no one having "magnificence of mind," no one called to be "a spectator of all
time and all existence," can fail to respond. And so we
see that the mathematical obligations of the philosopher
confront him with two difficult close-related Problems:
the problem of definition and the problem of evaluation: