 The paradoxes that were discovered by Georg Cantor and Bertrand Russell in the late 19th–early 20th century both involve self-membership of a set. The ramified theory of types due to Alfred N. Whitehead and Bertrand Russell, and  ZF (the formalization of set theory named after Ernst Zermelo and Abraham A. Fraenkel) exclude self-membership. However, there seems to have been always a desire to create a theory that allows self-membership or self-application. Indeed, one of Curry’s motivations for the development of CL was the goal to construct a formal language that includes a wide range of well-formed expressions, some of which—under certain interpretations—may turn out to be meaningless. (This idea may be compared to the  von Neumann–Bernays–Gödel formalization of set theory, in which—without the axiom of foundation—the Russell class can be proved not to be a set, hence, to be a proper class.)