 Fitch 1942 proposed a new approach to the problem of finding consistent combinatory logic systems, which were progressively expanded and refined over many years (until 1980). Fitch’s method to avoid paradoxes consists of the construction of suitable syntactical models, endowed with self-referential notions of class, membership and truth. Truth and membership are inductively generated by iterating rules that correspond to natural logical closure conditions and can be formalized by means of positive (i.e. negation- and implication-free) clauses. This fact implies that the generation process is cumulative and becomes saturated at a certain point, thus yielding consistent non-trivial interpretations for truth and membership. Mathematically, a collection of positive clauses always gives rise to an operator, say \(G\), mapping sets of expressions into sets of expressions and preserving the inclusion relation (i.e., monotone); the saturated sets then correspond to fixed points of the monotone operator \(G\) (i.e., to sets \(X\) satisfying \(G(X)=X)\), which exist according to a classical theorem about complete lattices (see Birkhoff 1967).