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

170 MATHEMATICAL PHILOSOPHY
ingly important fact that the meanings of the great terms
-transformation, relation and function (in ordinary
sense)-are essentially identical.
The Rhetoric of Mathematics.-Before closing this lecture I wish to say something about the psychology of
the mathematician's use of the word transformation and
in connection therewith to speak briefly of what may be
called the rhetoric of mathematics, a subject worthy of
much fuller treatment than we have time to give it here.
Are mathematicians rhetoricians? Rhetorician? "That
is, of all things "-the mathematician will say-" exactly
what I most certainly am not." And he should not be
harshly blamed for disowning the character; for, by
empty-headed advocates of good causes and by fullheaded advocates of bad ones, the art of rhetoric has
been so much abused in the world that " rhetorician"
has come to be, oftener than not, a term of reproach.
Nevertheless Rhetoric is a perfectly good name for the
greatest of all the arts-the art of expression by speech.
" Thought," said Henri Poincaré, " is only a flash of light
between two eternities of darkness, but thought is all
there is." How much poorer we should be, had the great
thinker not expressed this thought, so beautiful and so
poignant, all will know who have worthily meditated upon
life and the world. Thought unexpressed is thought concealed, and concealed thought-light hid under a bushelfades and perishes with the thinker. Expressed, however, it lives and grows, engendering its kind, adding its
flame to the flame of other thought, and so that radiance
which is " all there is " increases and tends to abide: it is
expression, and especially expression in speech,-expression
by the art of rhetoric,-that gives increase and perpetuity
of light to the narrow vale between the dark eternities.