International Encyclopedia of Systems and Cybernetics

"The type of ordering in which individual elements of the system are systems of lower order, and/or the system under study appears as an element of a higher-order system" (I.V. BLAUBERG, V.N. SADOVSKY & E.G. YUDIN, 1977, p.55).

According to these authors: "Any given system can be adequately described provided it is regarded as an element of a larger system… The problem of presenting a given system as an element of a larger system can only be solved if this system is described as a system" (p.270).

The authors refer to this as the "paradox of hierarchy" and state that it "essentialy represents a statement of interdependence of the solution of two problems: 1) the description of the system as such, and 2) the description of the system as an element of a larger system" (p.271).

This looks like a practical application of GÖDEL's incompleteness theorem!

These notions are however somewhat ambiguous and questionable, when applied to real situations. For example, many consider that the member countries of the European Community are the subsystems, while the real future functional subsystems of the E.C. (i.e. its supra-national institutions) are still a-building, a process in many cases obstructed by some national negotiators or pressure groups, generally representative of the national subsystems whose power would suffer limitations from the new communitary subsystems (see "Hierarchic emergence).

From a more formal viewpoint, as stated by G. KLIR "Hierarchical organizations are important not only for reducing descriptive complexity of systems, but they play also a significant role in reducing computational complexity of some systems problems… If the partitioning of hypotheses can be arranged hierarchically on several levels, the reduction of computational complexity may be phenomenal" (1993, p.49).