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

INTRODUCTION 85
In the light of the foregoing considerations, the
mathematical obligations of the philosopher appear to be
heavy. They are heavy; but they are not too heavy for
those whose native talents qualify them for a vocation
demanding "magnificence of mind." It is consoling to
know that a student who faithfully keeps the obligations
will have two great rewards: the joy of an insight and a
power not to be otherwise gained; and the joy of representing and perpetuating a noble tradition of his kind,the tradition, I mean, of mathematical competence as illustrated by the heroes of philosophy in every important
age. In relation to that tradition, it is indeed true, as you
know, that there have been many philosophers of great
learning, some of them important thinkers, whose ignorance of mathematics has been virtually complete, and
these have differed widely in kind; of their mathematical
ignorance some of them have not been aware; some have
deeply regretted it and humbly confessed it-our own beloved William James, for example; in some it has been
not only complete but shameless as well, even haughty
and defiant, as in Sir William Hamilton and Schopenhauer, whose false and malicious diatribes against mathematics I have dealt with elsewhere,l and in case also, I
am sorry to say, of Benedetto Croce,2 whose fine literary
and artistic culture and true elevation of spirit have not
availed to restrain him from speaking with strange confidence and very disparagingly of a science which his fellow countrymen, by brilliant research, have done so much
to honor and which he has not qualified himself to understand even slightly.
It is edifying to compare such representatives of phi1Human Worth of Rigorous Thinking, p. 290.
'Logic as the Science of the Pure Concept.