SYSTEMATICS AND SYSTEM THEORIES

* J. G. Bennett *

* Systematics Vol. 7 No. 4 March 1970 *

We are often asked how Systematics differs from other types of organization theory, and in particular from General Systems theory as developed from the work of Bertalanffy and Rapoport. There is a basic assumption in all organization theory that organizations, however diverse in external form, content and function, have certain common features that allow us to transfer knowledge gained in the study of one type of organization to another. Aristotle is probably the first natural philosopher to have stated and developed some of the consequences of this assumption, and this is one of his major contributions to Western thought over the past 2,500 years. Aristotle gave the lead in the line of thought that regards biological systems, being the most perfect form of organization, as paradigms for studying mechanical and man-made systems. It will readily occur to a biologist that a human society has much in common with a human organism, but less readily to a mathematician that a society is like the solar system. Bertalanffy was one of the first to draw attention to the threefold homology between biological, mathematical and man-made systems. In doing so, he laid the foundations of General Systems which is now a well-established discipline, particularly in the USA, and is represented by the Society for General Systems Research that has recently established a branch in Great Britain.

One of Bertalanffy's early papers drew attention to a small group of mathematical functions that can be used to represent a great variety processes. There are the constant, the linear relationship, and spatial configurations: all timeless. There are also various time systems uniform motion, accelerated motion, including circular and elliptic motions. There are rate of change functions such as power curves and exponentials and also special functions such as the Gaussian curve of error. Mere recitation of these functions evokes in the mind of a mathe matician processes that occur in nature and in human affairs, and it is very tempting to suppose that they can be used to create models of complex systems.

After many years of trying, it became apparent that natural systems are subject to constraints that call for a combination of functions generally not amenable to classical analytic treatment. Nowadays, classical models are only used for representing those aspects of an organic process that are amenable to quantitative expression such as rates of change or distribution of probabilities. Modern mathematics has developed non- numerical models that have wider applications but require quantification before they can be used in practice.

The next stage of development was the recognition that interaction of functions is a characteristic of any organic system that cannot be ignored. With this, the development of General Systems research took a new direction with the definition of a system as a complex of interacting terms. This can be represented graphically by a number of boxes with connecting lines of flow and interaction. The development of the digital computer aroused interest in this type of organizational model; because it enables processes to be analyzed into binary terms and programmes to be written that enable the computer to perform an ever-growing range of operations. It must be emphasized however that the technique is still essentially analytical. Systems are broken down into more or less invariant components, which are studied in terms of paired interactions, and changes are assumed to be occurring in some or all of the terms as a result of the interaction. Reconstituting the system so analyzed into an integral whole requires a different kind of operation.

At the other extreme has been the development of Gestalt theory applied first to psychology and later to the study of complex organizations. The principles here are that the totality of any system is its most significant feature and that the separate terms cannot be rightly understood without reference to the whole. As applied to organization theory, the concept is best described in words used nearly forty years ago by Mary Parker Follett, one of the founders of modern management.

"My point concerns the nature of the interaction if we could discover that I think we shall have arrived at something very fundamental. Suppose you have two factors (or I should prefer to say, two activities) A and B. reciprocally influencing each other. The key to our problem lies in what we mean by reciprocally influencing. Do we mean all the ways in which A influences B and all the ways in which B influences A? Reciprocal influencing means more than this, it means that A influences B and that different by A's influence, influences A, which means that A's own activity enters into the stimulus which is causing his activity."

At first, it might appear that Miss Follett's formula penetrates to the heart of the matter, and if correctly applied should enable us to study both the system as a whole and all that happens within it. There are, however two defects in the formula that describes a system as a complex of interacting parts. The first of these is that the parts or elements of the system must acquire their very character from their presence within that par ticular system. They cannot be taken out of the system and remain what they are. The second is that the parts are not only determined by their containment within the system, but also by their compresence * with all the other parts by which the system is composed. The realization that a system is very much more than a complex of interacting elements is basic for systematics.

The first axiom of systematics is that

* the elements of any complex unity* —*i.e. a system*—*derive their functional ** identity from their compresence within the unity*. *

* The word ‘compresence’ here is used in the technical sense of Bennett, Bortoft and Pledge (Systematics 3 (3), 1965). When the system coalesces the elements lose their * functional * identity and acquire a new *systemic *identity.

A simpler statement describes a system as a totality, all parts of which are relevant to one another and to the whole. It will be noted that interaction is not specified. This is because interaction is only one of the secondary modes of mutual relevance. The primary mode is the relativity of identity according to which identity is derived from member ship of a system. This is very different from the usual notion that the whole derives its identity from the totality of its elements together with some unspecified "wholeness" factor.

Systems are composed of qualitatively different terms. Terms that cannot be distinguished by some qualitative character are, for the purpose of systematics, identical and can be grouped together and treated as a single term. Systems are of different order according to the number of qualitatively distinct sets of terms they comprise. A system with only one kind of term is called a monad. A system with two sets of qualitatively distinct terms is a dyad. A three-quality system is a triad. Thus each order of system has a definite number of kinds of terms and this number is indicated by the corresponding Greek word with the suffix -ad, thus : monad, dyad, triad, tetrad, pentad, hexad, heptad, etc.

The second axiom of systematics introduces the notion of qualitative properties. We make the assumption that there are qualitative and non- qualitative distinctions. Thus A and B may be distinguished solely by the property that A is not-B and B is not-A. This distinction can be used to generate the numbers and arithmetical operations; but not systems. The qualitative distinction takes the form A differs from B in respect to the qualitative property Q. For example, when we say A is larger than B we imply the phrase "in respect to the qualitative property size" The second axiom of systematics asserts that

* every qualitative property encountered in our experience requires ** for its manifestation a system comprising as many terms as there ** distinctions within the quality. *

* *This can best be understood by considering a few examples. Wholeness can be manifested in all systems including the monad. The same is true of non-qualitative difference, i.e. the class-concept that includes or excludes an element in a monad. Qualitative distinction requires at least a dyad for the property Q cannot have two values in one and the same term. Relatedness requires three terms A and B are related through Q and Q itself acquires its qualitative character because it is different in A from what it is in B. Dynamism, interaction, modality are other qualitative properties that require at least three terms. Directed or goal-seeking activity cannot be described with fewer than four terms: two to prescribe direction and two to distinguish between instruments and operations. The notion of identity or 'sameness in change' cannot be reduced to fewer than five terms.

It is interesting to note that the monad can generate the cardinal numbers and the operations of arithmetic and formal logic. This is because a set of monads constitutes a class in the sense of Russell and Whitehead's *Principia. *The numerical universe has quantity but not quality except the quality of wholeness. The dyad is the simplest system that permits qualitative differences. It generates ordered series and hence intensive magnitudes of all kinds. 'More and fewer' is a non-qualitative distinction; but as previously noted, 'greater and lesser' is qualitative. In general, dyads can be partitioned into subordinate, but similar dyads, as a piece of steel manifesting the qualitative property of ferro-magnetism can be partitioned so that each part remains a complete magnet.

The triad is not quantitative in either extensive or intensive modes. It is the system of basic relatedness. The terms of a triad have no identity apart from the triad and this makes the concept very hard to grasp for anyone accustomed to thinking in terms of 'entities' that carry with them their own identity. For example, in the triad 'Father-Mother-Child' Father is a meaningless word when taken out of the system of parenthood. A very important quality associated with the triad can be described 'strategy'. This refers to the types of relationship that can be set up within a system undergoing transformation. The concept of strategic options has been outlined in an earlier paper (*Systematics 5 *(4) March 1968 "Hazard and Progress" J. G. Bennett).

The tetrad is basically associated with order. An important quality is that of directedness or purpose which has no meaning unless combined with the operational constraints. Directed activity cannot be described with fewer than four qualitatively distinct terms. The tetrad is the appropri ate system for investigating the ways in which values and fact influence one another within a human organization.

One more system must be considered in order to give an adequate notion of Systematics. The notion of identity, not as an abstract concept, but as a qualitative property of the world of concrete experience, is by no means simple. Static identity is an abstraction. Concrete identity requires a recognizable persistence of sameness within a totality undergoing change in an environment that is itself changing. This homeostasis requires both inner and outer adjustment. There must be inner and outer limits or constraints and these in turn must be qualitatively different from the unchanging self-sameness of the system. There are thus five quali tatively distinct terms. This observation has proved to be very fruitful for the study of organizations as ecological phenomena.

Without carrying the descriptive series further, these illustrative examples should suffice to support the claim that systematics can do for qualities what mathematics does for quantities. Here 'quantity' is not restricted to numbers and their operations but rather taken to mean the totality of non-qualitative properties of the natural order. It is usual to say that mathematical logic is concerned with truth-functions: it is necessary to observe that in this context truth is non-qualitative. Qualitative judgments are of a different kind, they cannot be verified by any procedure analogous to those by which we justify mathematical operations. Nevertheless, qualitative judgments can be just as rigorous as non-qualitative ones: but on condition that we avoid linguistic fallacies. Common fallacies are to talk about qualities in terms of a system to which they are not applicable and to use the (incompatible) languages of systems of different orders in the same context.

We believe that General Systems theory is basically non-qualitative, qualities being introduced from outside, whereas systematics is basically qualitative—qualities being inherent in the system. This distinction is implied in the basic definitions. General Systems Theory defines a system in terms of interaction, a non-qualitative concept and Systematics in terms of mutual relevance, a qualitative concept. For this reason Systematics should be able to do in the field of value judgments and decision-making, what General Systems Theory has done in the field of non-qualitative evaluation. The technique is very difficult to use, chiefly because we are unaccustomed to rigorous thinking in making qualitative judgments. Our languages—particularly the Indo-European family – are constructed to express factual statements. They adapt with difficulty to the requirements of precision in qualitative judgments. The difference between mathematics and Systematics is akin to that between Wittgenstein’s *Tractatus *and the *Philosophical Investigations. *

Earlier papers have developed the properties of systems in various ways. Recently a programme of research has been initiated at the Institute directed at the application of systematics to the problem of organization with special reference to corporations in commerce and industry. The research has been sponsored by a group of British and Canadian corporations and was initiated by a seminar held at Glyn House, Ewell, Surrey by the courtesy of the Surrey County Council. The foregoing notes are based on the introductory lecture. The research programme is under the direction of Mr. Bennett assisted by Mr. Peter Barker, Senior Lecturer at the Brixton School of Building presently seconded to Brunei University. The research is being conducted by four small syndicates who are investigating the systematic structuring of a small number of large and small corporations. Readers interested in this project are invited to write to Mr. P. H. Barker, 23 Brunswick Road, Kingston upon Thames.