Introduction to mathematical philosophy. With a new introduction by John G. Slater. 2nd reprint of the 1956 9th impression. (English) Zbl 0877.03001

London: Routledge. 208 p. (1995).
[This review has been erroneously combined with the Dover reprint of Russel’s Introduction to mathematical philosophy (1993; Zbl 0865.03001). In fact, the review was written for the Routledge reprint, which differs from the Dover edition in some respects. In particular, the Introduction by J. G. Slater is especially written for the present edition.]
This is a further volume of Routledge’s meritorious series of cheap reprint editions of classical works by Bertrand Russell. “Introduction to mathematical philosophy” was written during the summer of 1918 when Russel was in prison having been summoned by the authorities and charged with making a statement insulting a war-time ally of Great Britain. During his six months of imprisonment he wrote this book as a popular introduction to Principia Mathematica, his seminal co-production with A. N. Whitehead (3 vols., Cambridge University Press: Cambridge 1910–13. It first appeared in 1919 (see JFM 47.0036.12).
This reprint is accompanied by an interesting new introduction by John G. Slater who gives the details of the remarkable context in which the book emerged.
The conception of the book and it contents may be best characterized with a statement by Russell himself which appeared only on the dustwrapper of the first impression of the first edition (quoted in the “Introduction”): “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 the 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.” Given this scope, Russel’s book never lost its significance.


01A75 Collected or selected works; reprintings or translations of classics
03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations