Abstract

This chapter articulates a major theme in Russell's thought: his conception of logic and of the philosophy of logic. It begins by raising the question of the philosophical significance that logicism, the reduction of mathematics to logic, had for Russell when he first developed that doctrine. The answer is that it was part of a complex argument against Kant and post-Kantian Idealism. For this argument to work, logic must be thought of as made up of absolute and unconditioned truths. A certain conception of logic is thus implicit in the philosophical use that Russell makes of logicism. The chapter articulates this conception and contrasts it with a widely held modern conception according to which the central notion is truth in an interpretation, rather than truth tout court; the notion of an interpretation is alien to Russell's thought. It is argued that given his general conception of logic, it is natural, perhaps inevitable, that logic will be higher-order logic, equivalent to set theory. Russell's use of logicism, however, is cast in doubt by the need to accommodate the paradox that bears his name. The theory of types undermines his conception of logic as consisting of universal and unconditioned truths. The infinitude of objects can no longer be proved, but is taken as an explicit assumption when needed; this threatens the idea that it is indeed mathematics which is being reduced to logic. The magnificent intellectual achievement of _Principia Mathematica_ is thus, cut off from the philosophical motivations that lay behind Russell's initial formulation of logicism.