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Lectures on the Philosophy of

Mathematics

Lectures on the Philosophy
of Mathematics

By
JAMES BYRNIE SHAW

CHICAGO
THE OPEN COURT PUBLISHING COMPANY

LONDON

1918

HARVARD COLLEGE

JAN 15 1918

LIBRARY

Bowditch found

COPYRIGHT 1918 BY
THE OPEN COURT PUBLISHING CO.

All Rights Reserved

Published January 1918

PREFACE

In the spring of 1915 the author was invited to deliver a course of lectures before a club of graduate students of the University of Illinois on the subject “The Philosophy of Mathematics.” This club consisted of students who had had an ordinary college course in mathematics, for the most part. This fact tended to narrow the field to be covered, inasmuch as the more difficult questions of mathematical philosophy had to be omitted. It tended to widen the field in the way of making it intelligible to all students of fair mathematical knowledge, which could be accomplished best by considering mathematics constantly in its historical development. This class of readers is the one directly addressed in the lectures. The large class of secondary and collegiate teachers of mathematics is also addressed to a great extent.

The author cherishes the hope that the professional philosopher too may find some interest in these lectures, even though the more delicate problems are omitted or only referred to. If the student of philosophy finds enough mathematics here to characterize the field and give him a broad view over its hills and valleys, he will see it from the mathematician's point of view. Many have already accomplished this, notably, in America, Royce, and in France a whole school, as E. Boutroux, Brunschvicg, Milhaud, LeRoy, Winter, Dufumier, not to mention the philosopher mathematicians, Poincaré, P. Tannery, J. Tannery, Picard, Borel, P. Boutroux, and others. This view is necessary adequately to account for mathematics.

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