 Russell presented his theory of definite descriptions in “On Denoting” (1905) and it has probably been the most widely discussed application of the logic of PM. The role of the theory of definite desciptions in PM, however, is exhausted by its use in ∗30 to define what are called “Descriptive functions”. In contemporary logic it is routine to show how the notion of a “functional relation” can be used to justify the introduction of function symbols into a language with only n-place predicates. The theory of definite descriptions is essential for this argument. After ∗30 there are only a handful of occurrences of description operators in PM. What is perhaps Russell’s most valuable contribution to philosophical logic and the philosophy of language, is, here, only a device used for a technical, though programatically important, purpose. The technical purpose, however, does indicate an important distinction between the logicism of Frege and Russell. Frege’s logic is based on the notion of concept, which is a case of a function from objects to truth values. Russell’s logic can be seen as further reducing the mathematical notion of function to his logical notion of propositional function. Some logicians firmly in the tradition of mathematical logic do not find this to be an advance, but it does indicate a significant difference between the approaches of Frege and Russell (see Linsky 2009).