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

28 MATHEMATICAL PHILOSOPHY
counted among the mathematical scholars of their day.
It must be noted, however, that, though the advancement
in question was made by mathematicians, it was made' by
them, not in their character as mathematicians, but in
their capacity as philosophers. There is nothing in the
fact to astonish. For a man is greater than any occupa,
tion, and a mathematician, like a physician or lawyer or
poet or statesman or farmer, may be-indeed he must be,
in some measure-a philosopher as well. It is not, then,
strange or a matter for wonder that there have been
mathematicians who, in relation to their proper subject
taken as a distinctive whole, have sometimes taken the
attitude and played the rôle of philosopher. Nay, even
within the subject, in relation to its parts, the rôle is very
common; for whenever a mathematician, having acquired
competence in two or more branches-say algebra and
geometry-pauses to compare them, seeking to ascertain
the essential nature of each, what they have in common,
their respective worths and their joint significance as
forms of activity, his interest and his attitude have then
become for the time, whether long or short, those of the
philosopher. The fact is that such minor alternations of
the scientific and the philosophic interests may be constantly witnessed even in the activity of such mathematicians as ignorantly affect to spurn philosophy and to
scorn its achievements; but they are not aware of it.
Of the two tasks with which, as we have séen, the
mathematical obligations of the philosopher confront him,
the task of definition is far more advanced than that of
evaluation; and, though the work of the former is not yet
complete, we know much better today what mathematics
is than what it is worth. That it should be so is natural,
for a just appraisement of worth depends, of course, upon