The Origin of the Theory of Types

抄録

Bertrand Russell presented the very first theory of types in the appendices of The Principles of Mathematics. I will argue that he was led to the theory due to Frege's argument against any philosophical account of classes that assimilates a singleton with its sole member. By so doing I will attempt to show that the original theory of types was not meant to be a mere technical solution to the set-theoretic paradox but a philosophical account of what classes are in themselves.