« This book is intended for those who have no previous acquaintance with the topics of which it treats, and no more knowledge of mathematics than can be acquired at a primary school or even at Eton. It sets forth in elementary form the logical definition of number, the analysis of the notion of order, the modern doctrine of the infinite, and the theory of descriptions and classes as symbolic fictions. The more controversial and uncertain aspects of the subject are subordinated to those which can by now be regarded as acquired scientific knowledge. These are explained without the use of symbols, but in such a way as to give readers a general understanding of the methods and purposes of mathematical logic, which, it is hoped, will be of interest not only to those who wish to proceed to a more serious study of the subject, but also to that wider circle who feel a desire to know the bearings of this important modern science. » [Russell’s blurb from the original dustcover]. – Contents : – Preface. – Editor’s note. – Chapter i: The series of natural numbers; – Chapter ii: Definition of number; – Chapter iii: Finitude and mathematical induction; – Chapter iv: The definition of order; – Chapter v: Kinds of relations; – Chapter vi: Similarity of relations; – Chapter vii: Rational, real, and complex numbers; – Chapter viii: Infinite cardinal numbers; – Chapter ix: Infinite series and ordinals; – Chapter x: Limits and continuity; – Chapter xi: Limits and continuity of functions; – Chapter xii: Selections and the multiplicative axiom; – Chapter xiii: The axiom of infinity and logical types; – Chapter xiv: Incompatibility and the theory of deduction; – Chapter xv: Propositional functions; – Chapter xvi: Descriptions; – Chapter xvii: classes; – Chapter xviii: Mathematics and logic. – Index. M.-M. V.