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

INTRODUCTION I9
of geometry and algebra, if the subjects be administered
in the true mathematical spirit, with due regard to pre.
cision of ideas and to the exquisite beauty of perfect
demonstration, is sufficient to give a fair vision of the
ideal and standard of sound thinking.
Herewith, I have come to the end of what I desired
to say respecting the mathematical equipment essential
to a philosopher in so far as its measure depends upon
the fact that philosophers are human beings. It remains
to enquire what further mathematical attainments are to
be regarded indispensable to the proper equipment of a
philosopher as a philosopher. It is evident that the answer must be sought in the nature of the philosopher's
vocation. It would be presumptuous in me, a student
of mathematics, to offer to teach you, who are students
of philosophy, the nature of your vocation, but I may
remind you of it for it is necessary to have it clearly in
mind if we are to see its bearings upon the question in
hand. No one, I suppose, has conceived the philosopher's
vocation more justly and nobly or characterized it more
clearly and truly than Plato, as no other has drawn, with
such clarity and charm, with so perfect a union of finesse
and amplitude, so beautifully and so truly, the spiritual
portrait of the genuine philosopher. You are, of course,
familiar with the characterization and the portrait, which
together give for all time a vision of the great ideal:
what genuine philosophy is, and the philosopher ought
to be. I wish to remind you of such elements of it as
our present task requires.
The genuine philosopher, says Plato, "has magnificence of mind"; there is in him "no secret corner of illiberality".; he is "noble, gracious, the friend of truth, justice,
courage, temperance"; he aims at being "a spectator of