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

LECTURE II
Postulates
CONCRETE DEFINITION OF POSTULATE SYSTEM-THE
PROTOTYPE OF PRINCIPLES OR PLATFORMS —THE
ANCIENT "CRAFT OF GEMETRY" -THE SWORD OF
THE GADFLY-CLARITY OR SILENCE-MUNICIPAL
LAWS AND THE LAWS OF THOUGHT.
THE introductory lecture has served, I hope, to indicate in a general way the aim, the spirit, and the scope of
our undertaking. In deciding to begin the work proper with
a study of the great concept denoted by the familiar term
-Postulate System-I have been guided by three considerations: ( ) every question arising in what is strictly
called the philosophy of mathematics-in the study, that
is, of its logical foundations-is connected more or less
closely, directly or indirectly, with that concept, which is
thus the central ganglion of mathematical philosophy;
(2) by means of the concept in question and without unnecessary delay, I desire to set in clear light another concept, intimately related to it, to which I have given the
name-Doctrinal Function-and which, if I am not mistaken, has great philosophic importance; (3) postulate
systems as employed in mathematics, appear there in
perfect light as systems of principles underlying and supporting definite bodies of thought, and so they serve as
a model, as an ideal prototype, for the inspiration, the
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