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

110 MATHEMATICAL PHILOSOPHY
The doctrinal functions, we have seen, have no specific
content, no definite subject-matter, and are neither true
nor false. On the other hand, each of the derivable
doctrines has specific content, or subject-matter, and is
true or else false. Being, as we have seen, like in form, or
structure, the doctrines are discriminated among themselves solely by differences of content, or subject-matter.
Now, their contents, or subject-matters, differ in respect
of what we may call their meanings. Query: Is there any
respect in which the contents of the various doctrines are
identical? The answer is that the contents of all of the
true doctrines,-of all of the values of the doctrinal function concerned,-are identical in the respect that the
various contents equally verify, or satisfy, the postulates
of the function; but such partial identity of content can
not be affirmed of two of the false doctrines. Let us now
confine our attention to the true doctrines for it is these
that we value. It is perfectly clear that the meaning of
the content, or subject-matter, of such a doctrine,-the
meaning, that is, of the things which the doctrine is a
doctrine of or about,-is not exhausted by the requirement
that the things shall be verifiers of the postulates. Ordinary points and lines, for example, or number dyads and
dyad systems, have countless uses and significances over
and above the service they render by satisfying the
postulates of HAF. The meaning that the content of a
true doctrine has beyond that it must have to verify the
postulates of the function of which the doctrine is a value
may be called the content's, or subject-matter's, excessive
meaning. Thus you see that the infinitely many diverse
doctrines having a given doctrinal function for their
common matrix are discriminated from each other by
diversities in the excessive meanings 0f their contents,