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

INTRODUCTION 9
ning of it. Nevertheless, I am disposed to think that a
preliminary discussion of the matter will be of some service. A complete discussion would involve many considerations differing greatly in weight. I shall ask your
attention to such of them as seem to me cardinal and
decisive.
The first consideration grows out of the fact that a
philosopher is a human being. It is immediately evident
that the proper equipment of a philosopher must include
as much mathematical training as is essential to the appropriate education of men and women as human beings.
How much is that? Be good enough to note what the
question precisely is. I am not asking how much mathematical discipline is essential to a "liberal education" for
this fine term, though clearly defined long ago by Aris.
totle in terms of spiritual interest and attitude, has in
our day lost its significance even for the majority of academic folk, who ought to be ashamed of the fact. That
great man, the late Lord Kelvin, used to tell his students
that among the "essentials of a liberal education is
mastery of Newton's Principia and Herschel's As.
tronomy." On the other hand, such educators as Mat.
thew Arnold, John Henry Newman, Thomas Huxley,
though differing infinitely in their outlooks upon the
world and in their estimates of worth, yet unite in deny.
ing Kelvin's contention impetuously or even with scorn.
Let us so frame our question as to avoid that debate. The
question is: How much mathematical discipline is es.
sential to the appropriate education of men and women
as human beings? This exceedingly important question
admits of a definite answer and it admits of it in terms of
a supremely important and incontestable general principle. A clue to the principle is found in the phrase I