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

LECTURE IV
Doctrinal Interpretations
A MOTHER OF DOCTRINES MISTAKEN FOR HER ELDEST
CHILD-INFINITELY MANY INTERPRETATIONS OF ONE
DOCTRINAL FUNCTION-ORDINARY GEOMETRY BUT ONE
OF THEM-OTHER INTERPRETATIONS GEOMETRIC,
ALGEBRAIC AND MIXED-IDENTITY OF FORM WITH
DIVERSITY OF CONTENT-DISTINCTION OF LOGICAL
AND PSYCHOLOGICAL-PROJECTIVE GEOMETRY THE
CHILD OF ARCHITECTURE-A SCIENCE BORN OF AN
ART-INFINITE POINTS AND THÈ MEETING OF PARALLELS-POLE-TO-POLAR TRANSFORMATIONS-LOGICAL
USE OF PATHOLOGICAL CONFIGURATIONS.
IN the following discussion, I shall assume that you
have before you the Hilbert postulates as restated in
terms of the variable-symbols, vi, V2, V3, V 4, R and R2.
It will be convenient to call the doctrinal function consisting of these postulates and their consequent theorems
the "Hilbert doctrinal function" and to denote it by
H^F'. Now be good enough to note very carefully that,
if we omit from the postulates all reference to points not
in a given plane, the remaining postulates together
with their theorematic consequences constitute another
doctrinal function and that this is included in HaF'.
Let us denote the minor function by HAF. The
purpose of this lecture is to present or rather to indi60