Russell's Zigzag Path to the Ramified Theory of Types

Abstract

THE RAMIFIED THEORY of types was five years in the making. A curious aspect of the historical evolution of the theory is that Russell began and ended with a theory of types. In this paper 1 give a survey of the foundational schemes which Russell considered and rejected in the five years during which his ideas on logic were in a continual state of flux. One of the themes that I wish to stress is the reluctance with which Russell adopted type distinctions. I shall go into this question in some detail after discussing the first version of type theory, which is sketched in Appendix B of The Principles ofMathematics.