 The issue with respect to defined expressions, including the “incomplete symbols” for classes and definite descriptions which are explained below, is still problematic for interpreting PM. The difficulty is that certain defined expressions such as the notation for definite descriptions, class abstracts and even the identity symbol ‘\(=\)’, are not specified in the initial description of the syntax of the theory, nor are they shown to be validly used as instances of the axioms with their apparent syntax. The method of “contextual definition” used in PM is difficult to formulate rigorously and is not used in contemporary logical theories. The modern presentation of PM in this entry includes the symbols for descriptions and classes, thus differing from the completely rigorous presentations of Church (1976), for example, who avoids both definite descriptions and class expressions, and takes identity as an undefined primitive.