 This claim that the notion of “propositional function” is subject to use-mention confusions has persisted to this day. This entry will present a modernized version of the syntax of PM, combined with an account of the notation for types in the works of Alonzo Church (1974, 1976). Modern theories of types allow for a coherent syntax for higher-order languages which many find adequate to meet these objections. The complaint about the formulation of the syntax of PM was repeated and a further difficulty was expressed by Gödel (1944) in his influential survey of PM: