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

TRUTH AND THE CRITIC'S ART 143
trine, we have seen, is one derivable from a doctrinal
function and inheriting its form. Today indeed we are
familiar with the general conception of such functions and
have numerous examples of it; and we are in some danger
of inferring or supposing that the formation of that conception and the discovery of the known functions exemplifying it have been accomplished easily. But such an inference or supposition would be very erroneous. Those
whom we conventionally call the authors of the known
doctrinal functions are not, strictly speaking, their discoverers. Far from it. The discovery of them and of
the general concept they exemplify is not the achievement
of an individual but of a very, very long series of individuals; it is, like all other forms of wealth, like all other
elements of civilization, a racial achievement-the slowly
accumulated fruit of many generations of dead men's toil.
And clear consciousness of the outcome,-of the fact and
nature of the fruit,-is of very recent date. To realize
vividly that such is the case, you need only reflect that
doctrinal functions are composed of propositional functions and that, as we saw in a previous lecture, the supremely important notion of propositional function came
to recognition and received a name only a few years ago.
Compared with the vast backward stretch of human time,
-say, a quarter or a half million years,-the interval
from Euclid's day to ours is indeed very short; virtually
we are among Euclid's contemporaries; yesterday he was
here; yet his Elements is our human race's earliest example of a doctrinal function and even it is an imperfect
example, failing, as we have seen, to state certain of the
postulates explicitly, and being in appearance, as he probably conceived it to be in fact, a specific doctrine instead
of a doctrinal function.