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

148 MATHEMATICAL PHILOSOPHY
or postulates,-which he may or may not have regarded,
and may or may not have recorded, as such; you will
probably find that he has tried to define certain of his
terms and will certainly find that other terms ostensibly
defined or not, have in fact been virtually employed, deliberately so or not, as undefined terms (primitives, or
variables); you will find that he has stated a series of
propositions which he has made some effort to prove,
to demonstrate, to deduce, by a process of reasoning,
from something or other; in a word, you will find that
within the doctrine, however formless, however ill ordered its parts, however loosely knit its texture, there is
shadowed forth more or less clearly, very dimly it may
be, something of the figure and frame of the logical prototype called doctrinal function, as if this thing were so
built into the very constitution of intellect as in some
measure to guide and shape its activity whether we will
or no.
It would amply compensate us for the toil involved,
had we the time for it, to devote one or more lectures
of this course to illustrating the truth of what I have just
said by critically examining one or more outstanding doctrines of the non-mathematical, or anautonomous, sort
with a view to discovering the presence in them of the
mentioned phenomena. But, except for a few hints to be
presently given, I must leave the task for you, commending it as being in my judgment the best possible discipline
in the great art of doctrinal criticism, for which the present condition of the world calls more loudly than ever
before and which it is your supreme privilege and supreme
duty as philosophers to master, foster, and practise.
You have the clue and the material abounds on every
hand. "I do not frame hypotheses" (Hypotheses non