 but also there is no indication of the logical type of the function “\(\hat{x}\) is mortal”. The project of PM is to reduce mathematics to logic, and part of the view of logic behind this project is that logical truths are all completely general. The derivation of truths of mathematics from definitions and truths of logic will thus not involve any particular constants other than those introduced by definition from purely logical notion. As a result no notation is included in PM for describing those types. Those of us who wish to consider PM as a logic which can be applied, must supplement it with some indication of types.