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

138 MATHEMATICAL -PHILOSOPHY
trinal function includes a postulate system as its logical
base and since pure mathematics, as we have seen, consists of doctrinal functions, such a volume might be appropriately entitled: The Rôle of Pure Mathematics in
the Criticism of Thought; or, better perhaps, Pure
Mathesis in the Rôle of Critic. Possibly, one of you will
one day undertake the production of such a work. The
entire present course of lectures evidently bears upon the
task but the bearing is, in the main, implicit. In what
remains of the hour, I desire to discuss the subject, very
sketchily indeed, but explicitly and in terms. And I will
begin with a word regarding
Autonomous Truths and Autonomous Falsehoods.We have repeatedly spoken of the logically organic body
of propositional functions constituting a doctrinal function as being an autonomous form. We have done so, as
you know, because the thing presents a certain aspect of
self-sufficience or independence. If such a function be
included in another one, it does not owe its existence, its
unity or its integrity to that relation. It stands alone,
erect, eternal, holding its principles, its base,-the postu'
lates,-within itself, as it contains within itself the logical
lien binding its elements into one solitary, self-sufficing,
indestructible whole. A doctrine derived from it (in the
way now familiar) is not so pure as the function whence
it was derived; it is, so to speak, the doctrinal function
dipt-dipt or immersed in subject-matter, in a kind of
material giving each of the propositional functions significance, each of them thus loaded being a proposition
and, as such, true or false; hence, we cannot say that the
doctrine is form but. as we have seen, it has form, and
the form it has is precisely that which the doctrinal function is; and so we say that such a doctrine, too, is autono