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

CONTENTS xiii
PAGES
-Limits and Limit Processes Omnipresent as Ideals
and Idealization in All Thought and Human Aspiration
-Ideals the Flint of Reality-Genius and Generalization...,..,..................,....... 65-296
LECTURE XV
INFINITY
Mathematical Infinity-Its Dynamic and Static AspectsNeed of History of the Imperious Concept-The Rôle
of Infinity in a Mighty Poem-No Infinity, No Science.. 297-3 I6
LECTURE XVI
HYPERSPACES
Meaning of Dimensionality-Spaces pf Four or More Dimensions-The Mode of Their Existence-Distinction of
Imagination and Conception-Logical Existence and
Sensuous Existence-Open Avenues to Unimaginable
W orlds............................................ 317 —34I
LECTURE XVII
NON-EUCLIDEAN GEOMETRIES
Their Birth and Varieties-Their Logical Perfection-Their
Psychological Differences-Their Scientific and Philosophic Significance-All of Them Pragmatically TrueScience and Tragedy-A Prelude on the Popularization
of Science-Science and Democracy................ 342-365
LECTURE XVIII
THE MATHEMATICS OF PSYCHOLOGY
Backwardness of This and of the Psychology of Mathematics
-The Law of Weber and Fechner Reëxamined-Some of
the Law's Unnoticed Implications-Thought as Infinitely
Refined Sensibility................................. 366-401