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

viii PREFACE
psychology of mathematics or in the mathematics of
psychology.
To such sociologists as desire to conceive the nature of
our humankind justly —in accord with the mathematical
principle of " logical types " or dimensionality.
To the rapidly increasing class of engineers who are
learning to conceive engineering worthily, as the science
and art of directing the civilizing energies of the world
to the advancement of the welfare of all mankind including
posterity.
Finally, to all readers who desire to acquire a fair
understanding of such genuinely great mathematical
ideas as are accessible to all educated laymen and to
come thus into touch with the universal spirit of the
science which Plato called divine.
In closing this preface I desire to record my gratitude
to Mr. John Macrae, vice-president of E. P. Dutton &
Company, for his generous encouragement in this enterprise.
CASSIUS JACKSON KEYSER.
Columbia Uniwrsoty,
New York, January II, 1922.