International Encyclopedia of Systems and Cybernetics

Character of a system devoid of any internal contradiction.

In J.L. CASTI words: "We… call the system consistent if a statement S and its negation are not both theorems of the system" (1994, p.139). As noted by CASTI, the consistency condition is closely related to GÖDELs Incompleteness theorem: "Construct an arithmetical statement asserting that "arithmetic is consistent". Prove that this arithmetical statement is not provable, thus showing that arithmetic as a formal system is too weak to prove its own consistency", is a significant step in GÖDEL's proof (p.142).

The concept has also been discussed by M. MESAROVIC, on the base of three, interrelated sets of systems inputs and outputs:

In short, consistency may not be compatible with completeness.

It has been observed that "when a group of models, each of them internally consistent, is aggregated into a single composite model, there is no assurance of conservation of overall consistency"(J. WARFIELD, after G. FRIEDMAN pers. comm.)

This possible lack of compatibility results of the fact that some specific model may well ignore constraints that are taken into account in another model when connected, implicit contradictions may emerge.

F. HARARY enounced and demonstrated in terms of Boolean algebra a "Theorem of Model consistency" stating the conditions in which consistency is conserved (1965)

- the set of acceptable inputs

- the set of undesirable outputs

- the set of desirable outputs

No consistent system can produce at the same time desirable and undesirable outputs. (A curious consequence is that nearly all of our human systems are inconsistent…).

MESAROVIC enounced the following theorem: "A system for which the set of undesirable outputs Wand the set of acceptable inputs X' are specified is either inconsistent (contradictory) or incomplete" (1968, p.367-71).

There is anyhow some doubt that any system can be devoid of some internal contradictions. According to H.G. BURGER, who created the concept of agonemetry, consistency may be only a strain, not an attainment (1967, p.221).

G. BROEKSTRA observes that the rationality of equilibrium in human organizations led to the belief: "… that fluctuations in the form of misfits, inconsistencies, paradoxes or contradictions, had to be dampened or suppressed & driving an organization towards a particular stable attractor state (configuration). However, although a tight fit may lead temporarily to excellence… paradoxically, in the long run, fit may lead to failure" (1993, p.76).

BROEKSTRA understands that consistency should "… be reconceptualized in terms of the concept of autopoiesis, or rather, for social systems, as a case of organizational closure" (p.78).

In short, resilience is better than strait-jacket consistency for the survival of any system.

→ Incompatibility (Principle of)