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

INFINITY 299
pursue the doctrine in its elaborate and recondite developments.
To an audience of philosophical students it need not
be said that some notion of infinity has figured conspicuously, often fundamentally and dominantly, throughout
the whole historic period of philosophy, and speculation
East and West. It may, however, be said to such an
audience, and I think it should be said, that a critical history of the concept of infinity-or rather of the concepts
thereof, for there have been many of them, for the most
part but ill defined-would be an invaluable contribution
to the history of Thought-an incomparably more important contribution than the philosophical doctor dissertations commonly accepted. There can hardly be a
doubt, I believe, that the mentioned task of historical
criticism will sometime be performed. Why should it not
be done by one of you? You are, of course, aware that
the doing of it calls for an extraordinary kind of composite scholarly preparation-linguistic, historical, philosophical, scientific, and especially mathematical. Our
American universities have long been amply equipped
with adequate machinery for the giving of such preparation. Perhaps one of you will demonstrate that they have
at length acquired the necessary spirit and purpose and
atmosphere and temper.
In any adequate historico-critical survey of the rôle
which the notion of infinity has played in our human thinking, the thought of many thinkers, widely distributed in
time and in space, would have to be passed in reviewanalyzed, understood, and appraised. Among the questions which the critic would have to ask and try to answer
respecting each thinker are such as these: What did he
mean by infinite? Did he employ the term to denote a