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

40 MATHEMATICAL PHILOSOPHY
guidance and the criticism of every rational 'enterprise,
whether of philosophy, of science, or of life in general.
A subject so fundamental, many-sided, and far-reaching will naturally detain us for some time. The wisdom
we seek is golden, but it cannot be gained by any of the
get-rich-quick methods characteristic of our industrial
and neurasthenic age; the way to it is a little long and I
may as well warn you that in these lectures I intend to
pursue it in a leisurely fashion. The study is not so "entertaining" as a "movie" nor so easy as the life of "maggots in a cheese" or that of summer birds in a valley of
fruits. It demands some patience, hard work and endurance. It will quickly weary such as are content with
a little phraseological facility in matters they do not
understand, but not those whose curiosity is deep and
genuine, for they will be sustained by the dignity of the
task and the joy of the game.
Let us now enter upon it. What are we to understand by the term postulate? You are aware that a
branch of mathematics (or, for that matter, of mechanics
or of physics or of any other science), if the branch be
ideally constructed, is autonomous: it consists, that is, of
a body of propositions of which a few are assumed-not
proved in the branch but taken for granted there-and
the rest are deduced from them as logical consequences.
To students of philosophy, I need not say that to suppose
all the propositions of an autonomous theory to be pro.ved
in it, plainly involves circularity and a contradiction in
terms. In accordance with current usage, which I intend
to follow in this matter, any proposition thus taken for
granted in a given branch is called a postulate, or assumption, or axiom, or primitive proposition, or fundamental
hypothesis, of the branch; these terms being used inter