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

LECTURE IX
Truth and the Critic's Art
MATHEMATICAL PHILOSOPHY IN THE ROLE OF CRITICA WORLD UNCRITICISED, THE GARDEN OF THE DEVIL
— "SUPERSIMIAN" WISDOM-AUTONOMOUS TRUTH
AND AUTONOMOUS FALSEHOOD-OTHER VARIETIES
OF TRUTH AND UNTRUTH —MATHEMATICS AS THE
STUDY OF FATE AND FREEDOM-ITS PURE BRANCHES
AS DOCTRINAL FUNCTIONS-ITS APPLIED BRANCHES
AS DOCTRINES-THE PROTOTYPE OF REASONED DISCOURSE OFTEN DISGUISED AS IN THE DECLARATION
OF INDEPENDENCE, THE CONSTITUTION OF THE
UNITED STATES, THE ORIGIN OF SPECIES, THE
SERMON ON THE MOUNT.
WE have seen that a doctrinal function is composed
of two sets of propositional functions: an assumed set,
-fertile, compendent, compatible, sometimes independent, sometimes categorical,-called a system of postulates; and a set logically deducible from the postulates,
and called theorems.
We have seen that an autonomous doctrine,-a doctrine derivable from a doctrinal function by replacing the
variables in the postulates with admissible constants,-is
composed of two sets of propositions: a set derived from
the postulates-one for each postulate; and a set similarly
matching the theorems.
130