Analysis, Mathematics, and Logic in Russell’s Early Philosophy

Abstract

russell: the Journal of Bertrand Russell Studies n.s. 36 (winter 2016–17): 163–90 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\arlene\documents\rj\type3602\red\rj 3602 134 red.docx 2017-01-09 4:03 PM oeviews ANALYSIS, MATHEMATICS, AND LOGIC IN RUSSELL’S EARLY PHILOSOPHY James Levine Philosophy / Trinity College Dublin 2, Ireland jlevine@tcd.ie Jolen Galaugher. Foreword by Michael Beaney. Russell’s Philosophy of Logical Analysis: 1897–1905. (History of Analytic Philosophy series.) Basingstoke and NewYork: Palgrave Macmillan, 2013. Pp. xii, 218. isbn 13: 978-1-137-302069 . £60; us$110 (hb). n this book Jolen Galaugher discusses a number of key turning-points in Russell’s early philosophy: his break from Idealism in 1898–99; his acceptance of logicism in the period following the International Congress of Philosophy in Paris in August 1900 at which he was impressed by Peano and his students; and his arrival at his theory of descriptions in 1905 in the context of his attempts to grapple with various versions of what Russell called “the Contradiction”. Her overall purpose is to examine the interplay between the view of the analysis of propositions that Russell accepts following his break with Idealism and his developing views within the philosophy of mathematics. The main merits of the book are the way in which it highlights unresolved issues in our understanding of Russell’s early development and brings to bear relevant evidence in attempting to address those issues. However, as Galaugher acknowledges, the book’s “arguments are complicated in places” (p. 2), and it is not an easy read. Like some other books in this series, it appears to be based on a recently completed phd dissertation, and, like some dissertations, it combines a serious engagement with recent scholarship with a manner of presentation that presumes a shared understanding with the reader of a number of central issues and positions, and so does not clearly articulate and defend her understanding of those issues and positions to the uninitiated or sceptical reader. Hence, while the book will be useful to scholars already familiar with the sorts of issues it addresses, it would be hard to recommend it to someone coming to this material for the first time. The book consists of five chapters. In the first, Galaugher outlines some f= 164 Reviews c:\users\arlene\documents\rj\type3602\red\rj 3602 134 red.docx 2017-01-09 4:03 PM central elements of Russell’s position during his Idealist period and some of the steps involved in his dismantling that position. In the second, she argues more specifically, that in rejecting Idealism, Russell was not, as it is sometimes presented, simply following G. E. Moore—that his engagement with Leibniz’s views led Russell to go beyond Moore in certain ways and to adopt his characteristic view that relations are “external”. In the third, she discusses aspects of Russell’s logicism and its development in the period following the Paris Congress. In the fourth, she focuses on Russell’s logicist definition of the cardinal number and the notion of “class” that underpins it, arguing that in the face of the Contradiction, and his changing view of class and propositional function, it becomes questionable whether Russell and Frege should be said to endorse the same definition of cardinal number. In the fifth, she examines aspects of Russell’s coming to reject the theory of denoting concepts in favour of the theory he presents in “On Denoting”, arguing that by doing so Russell reaffirms his commitment to his post-Idealist view of a “decompositional” view of analysis as opposed to Frege’s function/argument style of analysis. Each of the aspects of Russell’s views that Galaugher examines concerns issues on which Russell often changed his mind, sometimes within a quite short period of time. While much of the material relevant to understanding these changes of mind has now been published in the Collected Papers of Bertrand Russell, Russell scholars have not fully assimilated it. Galaugher not only calls attention to a number of features of Russell’s early development that are not yet fully understood...