System

We now arrive at the concept of the system, which we obviously do not take to be fundamental. The definition of "system" is of course one of the great philosophical issues of Cybernetics and Systems Science. A common definition is "a group of units so combined as to form a whole and to operate in unison" \cite{WEB89}. But there are dozens of definitions in the technical literature, reflecting a wide range of philosophical perspectives:

• A technical definition similar to the common one, but not very specific, is offered by Hall and Fagan: "A system is a set of objects together with relationships between the objects \cite{HAAFAR56}".
• Beginning with Ashby \cite{ASR56}, systems theorists have been inclined towards antirealist definitions, avoiding ideas about entities with objective attributes. Instead they define systems in terms of the perceptions and distinctions drawn by people. In that direction, Rosen \cite{ROR86b} has emphasized that systems are cognitively constructed entities, created by people and only partially referring to "real" systems, or things. Systems are defined on things, and we should clearly distinguish between physical, "thinghood" and logical, "systemhood" properties. Brian Gaines reaches the solipsistic limit of this trend, defining a system as "what is distinguished as a system \cite{GAB79}".

• Formalists have been satisfied with a very simple and general definition: given a family of sets X_1, \ldots, X_n and their cartesian product X = \times_{i=1}^n X_i, then a system S is any relation in X: S \sub X \cite{MEM64b}.

• Constructivists decry the formalist strategy \cite{KAG89}, emphasizing that the natural world of evolving, emergent systems can never be captured by formal systems with fixed, finite, a prioiri universes of discourse. Instead they suggest open-ended systems which define their own elements and universes of discourse through the emergent processes of their own self-creation and self-modification.

Leaving aside issues of objectivity and subjectivity, realism and antirealism, and formalism and constructivism, there are some common characteristics which we can discover in all these definitions. System requires at least the following:

• A variety of distinct entities called elements.
• These elements are involved in some kind of relation.
• This relation is sufficient to generate a new, distinct entity, at a new, systemic level of analysis.

Thus in the concept of the system we see the unification of many sets of distinctions: the multiplicity of the elements and the singularity of the whole system; the dependence of the stability of the whole on the activity of the relation amongst the entities; the distinction between what is in the system and what is not; and finally the distinction between the whole system and everything else. In the activity of the relation which creates a stable whole, we recognize a closure. Therefore, we define a system as that distinction between the variety and stability of a closure on some multiple other distinctions. We call the stability of the whole the persistence of the system: as long as the multiple distinctions participate in the relation resulting in the stability of the whole system, then the system exists, and persists.