 Curry’s analysis of the solutions to the paradox would lead us into the realm of the theory of functionality, the history of combinatory logic and proof theory. Here it is enough to recall that according to him, a remedy would be to formulate within the system the very notion of proposition, and a way to avoid the contradictions would lead to a hierarchy of canonical propositions (or to a theory of levels of implication, already adumbrated by Church). Related ideas have been developed since the seventies by Scott 1975, Aczel 1980, Flagg and Myhill 1987, and others.