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

ESSENTIAL DISCRIMINATIONS 109
you, you doubtless see that you can make them yourselves.
I grant that the vast majority of doctrines that are constructible in the way indicated are trivial-mere weeds
of the doctrinal garden; it was, however, not our task to
estimate their worth, but to demonstrate their infinite
multiplicity.
Sense in which All Doctrines Derivable from HzF and
HAF' Are Like in Form, or Structure.-Let me request
you to remind yourselves vividly of the fact that each
of the doctrinal Functions consists of a system of propositional functions, called postulates, and a set of propositional functions logically deducible from the postulates
and called theorems. Be good enough to recall also the
fact that, if we replace the variables in the postulates
of one of the doctrinal functions by admissible constantsa term already explained-we thereby obtain a doctrine,
which is true, and then called a value of the function,
or false, according as the substituted constants verify
or do not verify all of the postulates. Because the doctrine, whether true or false, matches the doctrinal function, statement for statement, and because the statements
(propositions) composing the doctrine and the corresponding statements (propositional ft.lctions) composing
the doctrinal function are identical in respect of form, we
say that the doctrine and the function are themselves like
in form, or structure. You see that, therefore, the infinitude of values of either one of our doctrinal functions and
the infinitude of false doctrines derivable from it are all
of them like in form, or structure, for each of them is like
in form, or structure, to the function from which all of
them are derivable.
Senses in which All Doctrines Derivable from HzF and
HaF' Are Like and Unlike in Content, or Subject-matter.