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

298 MATHEMATICAL PHILOSOPHY
phers and some of them by distinguished mathematicians.
One of the best expositions I have seen is that by Professor E. V. Huntington in his The Continuum and Other
Types of Serial Order where, moreover, you can learn
what mathematicians mean by the highly important term
"continuum,"-the Grand Continuum as Sylvester called
it,-an idea with which for lack of time I was unable to
deal in the two preceding lectures-and where, too, you
will find an introduction to the transfinite numbers of
Georg Cantor, masterful primate among all who have
contributed to our understanding of mathematical infinity.
For another excellent account I may refer you to the
already mentioned Fundamental Concepts of Algebra and
Geometry by Professor J. W. Young. Clear indication
of the philosophic significance of the idea in question is
found in an article on the "Concept of the Infinite" by
the late Professor Royce (Hibbert Journal, Vol. I) and
in the Appendix to The World and the Individual, by the
same author. Perhaps no one else has treated the matter with so much deserved emphasis and with so much
freshness and facility as Bertrand Russell in his more
popular works. For some indication of my own views
respecting the bearings of the concept upon certain fundamental questions of philosophy, theology and religion, I
may be permitted to refer you to Science and Religion;
to The New Infinite and the Old Theology; and to the
articles-"The Walls of the World," "The Axiom of Infinity," and "Mathematical Emancipations"-contained in
The Human Worth of Rigorous Thinking. In the foregoing works, you will find an ample clue to the extensive
literature of the subject, both that which is more popular
and that which is, I will not say more scientific, but more
technical, if indeed you should, fortunately, desire to