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

BASIC CONCEPTS 69
Function. The same name must, of course, apply to the
function body consisting of the postulates of any other
postulate system together with the theorems logically
deducible from them. It can hardly escape your attention that just as a propositional function has true propositions for its values, a doctrinal function has true doctrines for its values; that just as we viewed a propositional function as the matrix of all the propositions (true
or false) derivable from it by substitution of admissible
constants, so we may view a doctrinal function as the
matrix of all the doctrines (true or false) derivable from
it in like manner; and that just as a given propositional
function and the propositions derivable from it are identical in form, so a given doctrinal function and the
doctrines derivable from it are the same in respect of
form; they are isomorphic, as we say. In marriage with
subject-matter, a Doctrinal Function becomes the matrix
of an infinite family of doctrines; the children inherit the
form of the mother.
It will be convenient to say that we are interpreting
a given doctrinal function whenever we derive from it,
in the way now familiar, one of its values, or true doctrines; and these values, or true doctrines, may be conveniently called interpretations of the function.