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

LECTURE III
Basic Concepts
PROPOSITIONAL FUNCTION AND DOCTRINAL FUNCTIONMARRIAGE OF MATTER AND FORM-ITS INFINITE
IERTILITY-PROPOSITIONS AND DOCTRINES THE OFFSPRING-VERIFIERS AND FALSIFIERS-SIGNIFICANCE
AND NON-SENSE —A QUESTION ASKED BY MANY AND
ANSWERED BY NONE.
ALL postulate systems have certain properties or
features in common. In connection with the Hilbert
system, I desire to draw your attention to such of these
features as will lead us to form a certain conception which
I think highly important and to which I have given the
name -Doctrinal Function.
As a preliminary, I must explain briefly a closely related term-Propositional Function-invented by Bertrand Russell; it is, perhaps, the weightiest term that has
entered the nomenclature of logic, or mathematics, in
the course of a hundred years. It has the rare distinction
of being, as we shall see, a perfect name for a supreme
concept. Every one is familiar with the ordinary notion
of a function-with the notion, that is, of the lawful
dependence of one or more variable things upon other
variable things, as the area of a rectangle upon the lengths
of its sides, as the distance traveled upon the rate oi
going, as the volume of a gas upon temperature and pres49