Russell: The Journal of Bertrand Russell Archives

Reviews 107 RUSSELes LOGICISM RUSSELL WAHL Philosophy / Idaho State University Pocanello, ID 83209, USA Denis Vernam. la Philosophie mathematique de Bertrand Russell. Paris: J. Vrin, 1993· Pp. 509· 174F. This is a massive work which details the development of Russell's mathematical philosophy from The Principles ofMathematics to the second edition of Principia Mathematica. Its thoroughness is impressive. It will make available to the French academic world the kind of Russell scholarship previously available only in English. In this way it is an importam successor to Jules Vuillemin's lefons sur la premiere philosophie de Russell (1968). Vernam begins with an extremely detailed exposition of the main points of the Principles, from the opening remarks on meaning and denotation to the discussion of geometry. He focuses on the evolution of Russell's logicism from the Platonism of the Principles through the ramified theory of types and finally to the amended logic of the second edition of Principia. Vernant argues that Russell built his various philosophical systems in response to problems which arose in the development of this logicism, and he further argues that the evolutions and modifications of Russell's philosophy are justified by these problems, and that they do not involve a rejection of the " Research supporred by the Social Sciences and Humanities Reseatch Council of Canada. 108 Reviews initial project. Throughout, Vemant is extremely careful in his exposition of Russell's various problems. Despite the fact that he does not see Russell's logicisr project as successful, Vemant is always respectful of Russell, and at pains to point out the value of Russell's work. Vemant has a clear sense of Russell's general philosophical outlook and of the project which began with the Principles. Here is his summation of Russell 's position, as opposed to Hilbert's formalism: Centreprise philosophique ne pretend pas donner de I'exterieur un sens, mais seulement reveler une signification que Ie discours logico-mathematique contient deja pour et par Lui-meme. La construction logico-mathematique se fonde sur ses propres principes et n'a pas a ttre autrement fondee. Le regard philosophique ne vise qu'a elucider ce prod~s d'auto-fimdation de La Logique en contribuant a clarifier ses principes. (P. 29) It is this aspect of Russell's logicist project that most interests Vemant, namely the notion of logic as the most general science not requiring and not being capable of a foundation other than what it itself contains, and the idea that mathematics is a part of this logic, in the sense that the mathematical notions are themselves definable in terms of logical notions, and mathematical principles are derivable from logical principles. He sees Russell's early theory of meaning as being part and parcel of the logicist project, and he sees the modifications which began with "On Denoting" as being crucial to the development of the project. With respect to his chronicling of the development of Russell's theory of meaning and denotation, Vemant gets the overall picture right. I would quibble, though, with some of the details. For example, his analysis of the main arguments in "On Denoting" relies on the outdated interpretation which "explains" the crucial part of the argument in terms of a confusion between use and mention. With respect to this part, Vemant would have done well to consult some of the manuscripts in the Russell Archives. He is clearly aware of them, and makes reference to "On Fundamentals" (1905)/3 but doesn't appear to have examined this manuscript with an eye to the arguments in "On Denoting". The section on Principia Mathematica begins with an account of the resolution of the paradoxes by the theory of types. This topic is very difficult since Russell was not always clear as to what exactly the theory was. Many commentators have, after Ramsey's work, seen the ramified theory of types as imposing the orders on a simple theory of types. Vemant appears to follow this line, introducing first the hierarchy of types (pp. 290-2) and then intro23 Now in Papers 4. Reviews 109 ducing the orders as a further refinement. However, Russell's ramified theory is better seen as beginning with the...