Causality is undefinable - toward a theory of hierarchical definability

Attempts to formulate mathematically precise definitions of basic concepts such as causality, randomness, and probability have a long history. The concept of generalized definability suggests that such definitions may not exist. Furthermore, it suggests that existing definitions of many basic concepts, among them those of stability, statistical independence and Pareto-optimality, may need to be redefined. The point of departure in our approach to definability is the assumption that definability has a hierarchical structure. Furthermore, it is understood that a definition must be unambiguous, precise, operational, general, and coextensive with the concept it defines