What was the “Appendix B” theory of types for?: Russell’s Principles of Mathematics Revisited

In the “Appendix B” to his Principles of Mathematics (1903), Bertrand Russell developed a theory of types that is different explicitly from his so-called “ramified” theory of types in Principia Mathematica (1910). It is not easy to evaluate properly this “Appendix B” theory of types, because (A) it is sometimes thought that it is only a rough sketch added hastily, and (B) it seems to play no role for Russellʼs later theoretical developments. But in this paper, I shall show that both (A) and (B) are not correct and that the “Appendix B” theory of types played an important role for his theoretical developments leading to the ramified theory of types.