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

172 MATHEMATICAL PHILOSOPHY
to mathematics as such, and a certain perfection of logical
quality which neither "the literature of power" nor
(outside of mathematics) " the literature of knowledge "
attains. Pray do not fear that, in saying this, I am
speaking as a partisan. Why should I? Mathematics
and literature are, both of them, ineffably precious. I am
merely endeavoring to state an interesting fact. And if
the meaning and the truth of what I have said respecting
mathematical diction be not yet sufficiently evident to
you, they will become so if, when you have the opportunity, you will examine the matter attentively. It
would be sufficient to examine fifty or a hundred representative mathematical terms, such, for example, as the following, taken quite at random from a vast multitude:
Real - ideal - imaginary - transcendental - elliptic -
parabolic - hyperbolic - value - range field - domain - harmonic - anharmonic - symmetric - asymmetric - golden section - degrees of freedom - determination-necessary- sufficient - discriminant - determinant - variable c~ onstant - invariant - covariant -
calculus - congruent - divergent - oscillating- maximal - minimal - sheaf (of lines) - pencil (of planes) -
family (of curves) - cluster (of spheres) - asympotic contact or approach-point of osculation-conjugate (elements or figures or forms) —interval-neighborhoodcorrelation - dependent - independent - closed - open
-boundary - inside - outside - on - slope - continuity discreteness - finite - infinite - infinitesimal -
limit - chance - law. The literary significance of such
representative terms-the wealth and variety of their
general meanings, the warmth of some of them, their
colors, the imageries awakened by them, the associations
they carry-all that is evident. In addition to that, each