Systems theory is a term frequently mentioned in the systems literature. As currently used, systems theory is lacking a universally agreed upon definition. Examples of multiple definitions are provided in Table I. Two of the definitions in Table I refer to General Systems Theory, a concept espoused by Ludwig von Bertalanffy, Kenneth Boulding, Anatol Rapoport, and Ralph Gerard in the original 1954 bylaws for the foundation of the Society for General Systems Research (SGSR). The aims of General Systems Theory (GST), as stated in the SGSR bylaws, were [Hammond, 2002: 435–436]:
To investigate the isomorphy of concepts, laws, and models from various fields, and to help in useful transfers from one field to another
To encourage development of adequate theoretical models in fields which lack them
To minimize the duplication of theoretical effort in different fields
To promote the unity of science through improving communications among specialists.
Table I. Definitions for Systems Theory
Peter Checkland [1993: 93] remarked that “the general theory envisaged by the founders has certainly not emerged, and GST itself has recently been subject to sharp attacks by both Berlinski (1976) and Lilienfield (1978).”
We believe that this is because GST [Bertalanffy, 1968] did not provide either a construct for systems theory or the supporting axioms and propositions required to fully articulate and operationalize a theory.
In order to improve the depth of understanding for systems practitioners using the term systems theory, we believe that a more unifying definition and supporting construct need to be articulated. Although there is not a generally accepted canon of general theory that applies to systems, we believe that there are a number of individual systems propositions that are relevant to a common practical perspective for systems theory. We therefore propose a formal definition and supporting construct for systems theory.
We propose that systems theory is a unified group of specific propositions which are brought together to aid in understanding systems, thereby invoking improved explanatory power and interpretation with major implications for systems practitioners. It is precisely this group of propositions that enables thinking and action with respect to systems. However, there is no one specialized field of endeavor titled systems from which systems theory may be derived. Rather, the propositions available for inclusion into a theory of systems come from a variety of disciplines, thereby making its underlying theoretical basis inherently multidisciplinary. This paper will (1) discuss the functional fields of science in which systems theory can be grounded, (2) provide a definition, construct, and proposed taxonomy of axioms (an axiom set) for systems theory and its associated supporting propositions, derived from the fields of science, and (3) conclude by providing an introductory view of the multidisciplinary breadth represented by systems theory.
2. INDIVIDUAL FIELDS OF SCIENCE
We propose that science has a hierarchical structure for knowledge contributions as shown in Table II. The Organization for Economic Co-operation and Development (OECD) has provided an internationally accepted classification for the fields of science [OECD, 2007]. This classification includes six major sectors and 42 individual fields of science. The major sectors and individual fields of science are described in Table III. The 42 individual fields of science in Table III serve as the source for the propositions that are brought together to form a construct for systems theory.
Table II. Structure for Knowledge Contributions
Table III. Major and Individual Fields of Science [OECD, 2007]
These structural elements constitute the major contributions on which each scientific field's body of knowledge is founded. We display this concept by using a series of concentric rings where the level of knowledge contribution (Table II) radiates from the center and each of the 42 specific fields of science (Table III) is a sector on the circle. Figure 1 is a simplified diagram of how we can account for the knowledge from within a functional field of science.
3. SYSTEMS THEORY
We believe that the underlying theoretical basis developed in this paper will provide an appropriate foundation for understanding systems. Understanding the axioms and propositions that underlie all systems is mandatory for developing a universally accepted construct for systems theory. The sections that follow will describe our notion of theory, propose a group of constituent propositions, construct a set of proposed axioms, and provide a construct for systems theory.
3.1. Introduction to Theory
Theory is defined in a variety of ways. Table IV is a collection of definitions for theory and the key elements associated with each. From these definitions it should be clear that a theory does not have a single proposition that defines it, but is a population of propositions (i.e., arguments, hypotheses, predictions, explanations, and inferences) that provide a skeletal structure for explanation of real-world phenomena. Drawing on the literature, we define theory as follows:
Table IV. Definitions for Theory
A unified system of propositions made with the aim of achieving some form of understanding that provides an explanatory power and predictive ability.
The relationship between theory and its propositions is not a direct relationship. It is indirect, through the intermediary of the axioms, where the links in the theory represent the correspondence through similarity to the empirical, real-world system. Figure 2 depicts these relationships.
Our notion of theory is a population of propositions that “… explains a [real system in terms of a] large set of observations or findings. Those constituent findings are the product of scientific research and experimentation, those findings, in other words, already have been verified, often many times over, and are as close to being ‘facts’ as science cares to characterize them” [Angier, 2007: 154]. Our representation of theory subscribes to the model espoused by Giere [1988: 87] where “rather than regarding the axioms and theorems as empirical claims, treat them all merely as definitions.” In this case, our model of systems theory is defined by its set of axioms and supporting propositions.
The following section will use the axiomatic method [Audi, 1999, p. 65] to articulate the accepted propositions and concepts from the 42 fields of science discussed in Section 'INDIVIDUAL FIELDS OF SCIENCE' of the paper in order to increase certainty in the propositions and clarity in the concepts we propose as systems theory.
3.2. Systems Propositions
This section addresses a proposed group of constituent propositions that we have encountered in our work with systems. Each of the propositions has an empirical basis in one of the 42 individual fields of science in Table III. While likely incomplete, this set of propositions provides a representation of real-world systems encountered during our work with systems problems. Each underlying proposition, its primary proponent in the literature, and a brief description are presented in Table V.
Table V. Alphabetical Listing of Systems Propositions
3.3. Axioms of Systems Theory
This section addresses a proposed set of axioms and their constituent propositions that we termed systems theory. The 30 propositions presented in Section 'Introduction to Theory' supported inductive development of the axioms. Using the axiomatic method [Audi, 1999], the propositions were reorganized into seven axioms as follows:
The Centrality Axiom states that central to all systems are two pairs of propositions: emergence and hierarchy, and communication and control. The centrality axiom's propositions describe the system by focusing on (1) a system's hierarchy and its demarcation of levels based on emergence and (2) systems control which requires feedback of operational properties through communication of information.
The Contextual Axiom states that system meaning is informed by the circumstances and factors that surround the system. The contextual axiom's propositions are those which bound the system by providing guidance that enables an investigator to understand the set of external circumstances or factors that enable or constrain a particular system.
The Goal Axiom states that systems achieve specific goals through purposeful behavior using pathways and means. The goal axiom's propositions address the pathways and means for implementing systems that are capable of achieving a specific purpose.
The Operational Axiom states that systems must be addressed in situ, where the system is exhibiting purposeful behavior. The operational axiom's propositions provide guidance to those that must address the system in situ, where the system is functioning to produce behavior and performance.
The Viability Axiom states that key parameters in a system must be controlled to ensure continued existence. The viability axiom addresses how to design a system so that changes in the operational environment may be detected and affected to ensure continued existence.
The Design Axiom states that system design is a purposeful imbalance of resources and relationships. Resources and relationships are never in balance because there are never sufficient resources to satisfy all of the relationships in a systems design. The design axiom provides guidance on how a system is planned, instantiated, and evolved in a purposive manner.
The Information Axiom states that systems create, possess, transfer, and modify information. The information axiom provides understanding of how information affects systems.
The specific axiom and its supporting propositions are presented in Table VI. It is important to note that neither propositions nor their associated axioms are independent of one another.
Table VI. Axioms for Systems Theory
3.4. Construct for Systems Theory
Systems theory provides explanations for real-world systems. These explanations increase our understanding and provide improved levels of explanatory power and predictive ability for the real-world systems we encounter. Our view of systems theory is a model of linked axioms (composed of constituent propositions) that are represented through similarity to the real system [Giere, 1988]. Figure 3 is a construct of the axioms of systems theory. The axioms presented are called the “theorems of the system or theory” [Honderich, 2005] and are the set of axioms, presumed true by systems theory, from which all other propositions in systems theory may be induced.
Systems theory is the unified group of propositions, linked with the aim of achieving understanding of systems. Systems theory, as proposed in this paper, will permit systems practitioners to invoke improved explanatory power and predictive ability. It is precisely this group of propositions that enables thinking, decision, action, and interpretation with respect to systems.
The axiom set in Figure 3 may be considered a construct of a system, where a construct is defined as a characteristic that cannot be directly observed and so can only be measured indirectly [Bernard, 2002; Gliner and Morgan, 2000; Leedy and Ormrod, 2001; Orcher, 2005] and a system is defined as “…a set of interrelated components working together toward some common objective or purpose” [Blanchard and Fabrycky, 2006: 2]. Thus, a system may be identified as such if it exhibits and can be understood within this set of axioms. Conversely, any entity that exhibits these seven axioms is, by definition, a system. Thus, given its testable nature, this construct can be evaluated with respect to systems under consideration in order to determine its generalizability. Further, given the multidisciplinary nature of its foundational axioms and the multidisciplinary nature under which the construct was formed, there are numerous implications for multidisciplinary application of such a construct.
4. MULTIDISCIPLINARY IMPLICATIONS OF SYSTEMS THEORY
We have presented a construct for systems theory, proposed a set of seven axioms and group of supporting propositions from the 42 fields of science. Our construct for systems theory is the unified group of propositions, linked by an axiom set that aims to achieve understanding of systems that provides improved explanatory power and predictive ability. It is precisely this group of propositions that enables thinking, decision, action, and interpretation with respect to systems.
We believe that systems theory is the foundation for understanding multidisciplinary systems. Practitioners can benefit from the application of systems theory as a lens when viewing multidisciplinary systems and their related problems. Systems theory and the associated language of systems are important enabling concepts for systems practitioners. The set of seven framework axioms and associated group of propositions that we designate as systems theory allow systems practitioners to ground their observations to a rigorously developed systems-based foundation.
Behaviors expected from systems should be described by the axioms proposed in this paper. For example, any system should exhibit suboptimization. For a system as complex as a Boeing 747, this means trade-offs between increased cargo carrying capacity and maximum airspeed, whereas a simpler system such as a laptop computer may require that the heating system be suboptimal (i.e., larger than ideal) in order to support a faster processing chip. While this simply illustrates the use of one of the propositions described herein, each axiom and its associated propositions provides insight into the behavior of the system. Understanding of the proposed construct of systems theory affords systems practitioners greater overall system understanding.
Finally, the propositions from the seven axioms, described briefly in Table V, can be superimposed on the Depiction of Knowledge and the Fields of Science presented in Figure 1. Figure 4 presents systems theory as the intersection of a number of well-defined multidisciplinary propositions by distinguished authors from the 42 fields of science.
It is clear from viewing Figure 4 that systems theory and its theoretical foundation are inherently multidisciplinary. Contributions to our perspective of systems theory are incorporated from each of the major fields of science with the exception of agricultural sciences (most probably due to the darkness proposition). This multidisciplinary construct ensures widespread applicability of this theory and removes barriers that traditional engineering-centric views of systems place on approaches to problem solving. The lack of a prescription regarding domain applicability further ensures that systems theory is multidisciplinary in both its theoretical foundations and application.
We have proposed systems theory as a unified group of specific propositions which are brought together by way of an axiom set to form the construct of a system. This construct affords systems practitioners and theoreticians with a prescriptive set of axioms by which the system operation can be understood; conversely, any entities identified as a system may be characterized by this set of axioms. Given its multidisciplinary theoretical foundation and multidisciplinary framework, systems theory, as developed in this paper, is posited as a general approach to aid in understanding system behavior. This formulation is in its embryonic stages and would be well served from feedback and challenge from systems practitioners to test this proposed construct and encourage future development of systems theory as a coherent, multidisciplinary endeavor.
Kevin MacG. Adams is a Principal Research Scientist at Old Dominion University's (ODU) National Centers for System of Systems Engineering (NCSOSE). Dr. Adams retired from the U.S. Navy in 1996 after 25 years of service. He received his PhD in Engineering Management and Systems Engineering from ODU in 2007.
Patrick T. Hester is an Assistant Professor of Engineering Management and Systems Engineering and Chief Scientist at the National Centers for System of Systems Engineering at Old Dominion University. He received his PhD in Risk and Reliability Engineering from Vanderbilt University in 2007.
Joseph M. Bradley is a Principal Research Scientist at Old Dominion University's (ODU) National Centers for System of Systems Engineering (NCSOSE). Mr. Bradley retired from the U.S. Navy in 2004 after 26 years of service. He is a doctoral candidate in Engineering Management and Systems Engineering at ODU.
Thomas J. Meyers is a Principal Research Scientist at Old Dominion University's (ODU) National Centers for System of Systems Engineering (NCSOSE). He served 25 years in the U.S. Marine Corps and received his PhD in Systems Engineering from ODU in 2007.
Charles B. Keating is a Professor of Engineering Management and Systems Engineering and Director of Old Dominion University's (ODU) National Centers for System of Systems Engineering (NCSOSE). Prior to joining ODU, he served over 12 years in the U.S. Army and private industry. He received his PhD in Engineering Management from ODU in 1993.