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

INTRODUCTION tI
quently, mathematics, being identical with logic, is not external to philosophy but is, strictly speaking, one of its
principal divisions; and that, accordingly, philosophers,
if they are not to be ignorant of one of the chief departments of their own subject, are obliged to be, not merely
mathematical dilettanti, but mathematical students, serious explorers of the science. Theoretically, the argument
is sound, which is the highest quality of argument as
such. I do not, however, as I have said, intend to press
it, because it imposes on the student of philosophy an
obligation that he cannot fully meet; his obligations are
many, too many and too gr-eat; he may not reasonably
hope to win the proper competence of a mathematician
in a subject where the developments, still rapidly progressing in numerous directions, have already reached proportions so great that no man, though he have the widereaching arms of a Henri Poincaré, can contrive to embrace them all.
Turning now to the second one of the two considerations mentioned a moment ago, let me guard against the
danger of being misunderstood. You are aware that, in
the view of Plato, what is peculiar to philosophy is dialectic-"the coping stone of the sciences'7; you are aware
that dialectic is the sole means by which the philosopher
may gain a knowledge of "what each thing" in the hierarchy of being "essentially is," and by which he may gain,
at length, as he ascends the scale, a vision of things supreme-absolute justice, absolute beauty, absolute truth,
absolute good; you are aware that the successful employment of dialectic requires not only native "magnificence
of tnind," but also a long course of preparation in the
subsidiary sciences; you are aware that, according to
Plato, the most indispensable of these sciences are arith