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

24 MATHEMATICAL PHILOSOPHY
domain of operation to the existence and the character
of outlying domains, comes into perfect light. It is in
mathematics and not elsewhere that Idealization is beheld in its purity; and unless the philosopher becomes
familiar with it there in its purity, his endeavor to study
thc great process elsewhere, amid the many disguises half
concealing its subtle ramifications throughout the shadowy
world of general thought, will encounter serious difficulties, if not defeat.
The considerations I have now advanced, though they
are subordinate, are weighty, and I commend them as
worthy of your further reflection. Let us proceed, without further delay, to the heart of the matter.
We have seen that the genuine philosopher "has magnificence of.mind"; that there is in him "no secret corner
of illiberality"; that his vocation requires him to be "a
spectator of all time and all existence"; and that the wisdom he seeks is the wisdom which consists in knowledge
of whatsoever is eternal. It is these great things-the
highest distinctive marks of the genuine philosopher —
that determine the character of his mathematical obliga.
tions and enable us to measure them. For what is mathematics? What is that science which Plato1 called "divine,"
which Goethe called "an organ of the inner higher sense,"
which Novalis called "the life of the gods," and which
Sylvester called "the Music of Reason"? The question
is not intended to call for a complete description of the
science, much less for a definition of it. What it seeks is
a partial description. I wish merely to draw your attention to one feature of mathematics —to that feature of
it which all competent judges agree in signalizing as the
chief aspect of the science viewed as an enterprise. The
aspect in question 1 endeavored to point out some years
1See Memorabilia Mathematica by Professor Moritz,