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

INTRODUCTION 23
every type of excellence in which intellectual progress is
possible, they appear as ideals supernal-as stars beyond
the sky. I need not say that the Absolutes, thus regarded,
retain their glory unimpaired and their previous value
as sources of light and inspiration. We should not, however, fail to see clearly that, if they be thus regarded, the
philosopher is thereby confronted by a new challenge, a
new problem, a new field of study or, perhaps I should
say, by an old one seen as new. For, if the Absolutes
are not in the intellectual world but are beyond it; if they
be, in fact, not concepts, but ideals of concepts, shining
downward from above them, then obviously their origin,
the manner and genesis of their appearance, and their
significance for life, must be sought in the nature and
function of that strange and familiar spiritual process
omnipresent among the activities of the intellectual world
and known as Idealization. And now the point I am
aiming at and to which I invite your special attention is
this: In the study of this great subject-the nature and
function of Idealization-the philosopher and especially
the theologian as philosopher-for rational theology,
rightly conceived, is the science of Idealization-will
have need of mathematical discipline surpassing the
Platonic requirement and surpassing what I have deemed
essential to the education of the philosopher as a human
being. For the term "idealization" is the generic literary
term for what in science and especially in mathematics is
known as generalization by means of the method or
process of limits. In mathematics, particularly in the
modern theory of the Real Variable, in connection with
the generalization of the number concept, the essential
nature of Idealization, the pattern of it as the process
and method of directing the attention from within a given