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

MORE ABOUT LIMITS 285
ideas denoted by the modest little five-lettered wordlimit.
What, broadly speaking, we may call its philosophic
significance is less well understood for the reason that it
has been neglected. It has been neglected because but
few mathematicians have been interested in it and but
few philosophers have been mathematically qualified to
treat it. If only the concept of limit and the rôle thereof
had been familiar in the days of Plato! How it would
have enriched and fortified his dialectic. In his hands
the concept would have been a new spiritual instrument
of immeasurable power; in his thought it would have
opened new ways to the inner vision of supernal light;
in his brightest pages it would have been the secret and
source of a yet stranger and brighter glory. His shining
Absolutes,-absolute justice, absolute beauty, absolute
truth, absolute good,-whose " perception by pure intelligence " brings us, said he, " to the end of the intellectual
world," would not have appeared as ends, or final terms,
of any sequences or progressions in the intellectual world
nor even as limits of such progressions but, as I intimated
in the initial lecture of the course, the absolutes would
have appeared as supernal ideals, over and above every
type of excellence in which intellectual progress is possible. And thus the Platonic philosophy would have
advanced, in even greater measure than it did advance,
the science of Idealization-the science, I mean, which
has for its appropriate subject-matter those spiritual
phenomena of life which the terms, ideal and idealization,
rightly understood, denote. In saying this, I have in
some measure anticipated the outcome of considerations
not yet adduced, and so I must ask you to reserve your
judgment for a little time,