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

INTRODUCTION l
precision of ideas, perfect clarity of expression, and perfect allegiance to the eternal laws of thought. In mathe.
matics the name of the muse is familiar: it is RigorLogical Rigor, which signifies a kind of silent music, the
still harmony of ideas, the intellect's dream of logical
perfection.
Can the dream be realized? I am well aware that
most of the things which constitute the subject-matter of
our human thinking-that most of the things to which
our thought is drawn by interest or driven by the exigencies of life-are naturally so nebulous, so vague, so
indeterminate that they cannot be handled in strict
accordance with the rigorous demands of logic. I am
aware that these demands can not be fully satisfied even
in mathematics, the logical science par excellence. Nevertheless I contend that, as the ideal of excellence in thinking, Logical Rigor is supremely important, not only in
mathematical thinking, but in all thinking and especially
in just those subjects where precision is least attainable.
For without this ideal, thinking is without a just standard
for self-criticism, and without light upon its course; it is
a wanderer, like a vessel at sea without compass or star.
Were it necessary, how, easy it would unfortunately be
to cite endless examples of such thinking from the multitudinous writings of our time. Indeed, if the pretentious
books produced in these troubled years by men without
logical insight or a sense of logical obligation were
gathered into a heap and burned, they would thus produce,
in the form of a bright bonfire the only light they are
qualified to give. "Logic," it has been said, "is the child
of a good heart and a clear head." We know, however,
that an evil heart is not essential to a fool and that, on