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

TRUTH AND THE CRITIC'S ART 131
We have seen that a doctrinal function is, like the
propositional functions composing it, neither true nor
false; and that a doctrine derived from it, is, like each
of its component propositions, either true or else false.
We have seen that a doctrinal function gives rise to
an infinitude of true doctrines,-values of the function,and an infinitude of false ones.
We have seen that a doctrinal function, owing tô the
presence of the variables in its propositional functions,
has no specific or definite, but only an ambiguous or undetermined, subject-matter; and that, on the other hand,
a doctrine, owing to the presence of the "substituted"
constants in its propositions, has a specific, or definite,
kind of subject-matter.
We have seen that, in respect to structure or form, a
doctrinal function and all of the derivable doctrines are
identical, while, in respect to content, or subject-matter,
no two of them are identical.
We have seen that, in the case of a doctrinal function, the theorems, (which are forms) are logically deducible from the postulates (which are forms)-the
deduction being purely formal; and that, in the case of
a derived doctrine, the propositions matching the theorems can not be logically deduced as propositions from
the other propositions as propositions but only as forns,
in which respect, however, the propositions and the corresponding propositional functions are, as we have seen,
identical; so that, in any and all cases, it is the form of
the premises, and never their subject-matter, that determines their logical consequences.
Hereupon, there supervenes an important critical
question: Given a doctrinal function and one of the
doctrines derivable from it, which of the two things ought