 The former project has important historical antecedents. Starting with a two-place predicate intended to express a specific notion of similarity (between total experiential states), Carnap  (1928)  defines a “quality circle”—roughly, a natural class—as a class any two members of which are similar, which is not contained in any other such class. Goodman  (1951)  influentially objected to some consequences of this definition (see the entry on  Nelson Goodman,  §4.2): for example, it implies that whenever \(A\), \(B\), and \(C\) are quality circles, \((A\cap B)\cup(B\cap C)\cup(C\cap A)\) is contained in some quality circle (the “difficulty of imperfect community”). This does not seem plausibly necessarily true, equating ‘quality circle’ with ‘perfectly natural class’. 