Library of Philosophy
EDITED BY J. H. MUIRHEAD, LL.D.
INTRODUCTION TO MATHEMATICAL
PHILOSOPHY
By the same Author.
PRINCIPLES OF SOCIAL RECONSTRUCTION.3rd Impression. Demy 8vo. 7s. 6d.net.
"Mr Russell has written a big and living book."—TheNation.
ROADS TO FREEDOM: SOCIALISM,ANARCHISM, AND SYNDICALISM. Demy 8vo.7s. 6d. net.
An attempt to extract the essence of these three doctrines,first historically, then as guidance for the coming reconstruction.
London: George Allen & Unwin, Ltd.[Pg iii]
INTRODUCTION TOMATHEMATICAL PHILOSOPHY
BY
LONDON: GEORGE ALLEN & UNWIN, LTD.
NEW YORK: THE MACMILLAN CO.[Pg iv]
First published May 1919
Second Edition April 1920
[All rights reserved][Pg v]
PREFACE
THIS book is intended essentially as an "Introduction," anddoes not aim at giving an exhaustive discussion of the problemswith which it deals. It seemed desirable to set forth certainresults, hitherto only available to those who have masteredlogical symbolism, in a form offering the minimum of difficultyto the beginner. The utmost endeavour has been made toavoid dogmatism on such questions as are still open to seriousdoubt, and this endeavour has to some extent dominated thechoice of topics considered. The beginnings of mathematicallogic are less definitely known than its later portions, but are ofat least equal philosophical interest. Much of what is set forthin the following chapters is not properly to be called "philosophy,"though the matters concerned were included in philosophy solong as no satisfactory science of them existed. The nature ofinfinity and continuity, for example, belonged in former daysto philosophy, but belongs now to mathematics. Mathematicalphilosophy, in the strict sense, cannot, perhaps, be held to includesuch definite scientific results as have been obtained in thisregion; the philosophy of mathematics will naturally be expectedto deal with questions on the frontier of knowledge, asto which comparative certainty is not yet attained. Butspeculation on such questions is hardly likely to be fruitfulunless the more scientific parts of the principles of mathematicsare known. A book dealing with those parts may, therefore,claim to be an introduction to mathematical philosophy, thoughit can hardly claim, except where it steps outside its province,[Pg vi]to be actually dealing with a part of philosophy. It does deal,however, with a body of knowledge which, to those who acceptit, appears to invalidate much traditional philosophy, and evena good deal of what is current in the present day. In this way,as well as by its bearing on still unsolved problems,