Russell on logical form (Bertrand Russell)

This thesis discusses the impact of Russell's paradox on Russell's thinking on metaphysics and epistemology. The period covers Russell's work on Logicism in the Principles of mathematics in 1900 to the Theory of Knowledge manuscript written in 1913. Russell's Logicism entities. Russell saw his task as identifying these objects and demonstrating their role in the generation of mathematics. Unfortunately, a number of these entities were implicated in paradoxes. This thesis provides an account of these paradoxes and Russell's attempts to avoid them. Russell's method consisted in regimenting the use of expressions designating entities. This method involved the use of ‘incomplete symbols’, the idea being that ontological complexity was to be reflected in the use of contextually defined expressions. This method would have a profound influence on the evolution of Anglo-American philosophy. Russell's considered view saw the entities required for the logical reconstruction of mathematics organized into a hierarchy. While this solution dealt effectively with the paradoxes I argue that it comes into conflict with Russell's realism. Russell held that we come into contact with entities existing independently of our mind's apprehension of them. These entities are grasped in a kind of direct contact, and knowledge of this kind is called knowledge by ‘acquaintance’. Knowledge by acquaintance is knowledge of individuals. Russell's solution to the paradoxes was to posit different types of things. However, the type of thing an individual is cannot be known by acquaintance. Knowledge of this kind is knowledge of a truth. I argue that this difficulty undermined the Theory of Knowledge manuscript and led Russell to abandon it.