Boundaries in Systems Science
From Philosophical Debate to Practical Necessity
Last week the ISSS Research Towards General Systems Theories SIG held a lively conversation on the concept of boundedness.
Since I was moderating the discussion, I was more focused on facilitating productive conversation than on sharing my perspective. Here are a few of my personal thoughts on the importance of boundaries as a systems concept.
Philosophy and Worldviews
A significant aspect of the conversation was the philosophical one. A decent amount of time was spent considering questions such as:
Do real “objective” things exist outside of our perception?
Does it make sense to treat humans as being “separate from nature”?
For me, this highlights the importance of making our philosophical assumptions and worldviews explicit. The goal isn’t to form consensus, but rather to make it as easy as possible for others to understand where we are coming from.
My current philosophical stance is best described as “Bertalanffian Perspectivism”, as summarized in General Systemology (p.39).1
I believe that there is a universe that exists independently of the observer and that the scientific method can reveal aspects of reality’s nature. I also believe that science is limited in what it can reveal, and that the unique cognitive capacities and purposes of different agents condition the observations, models, and theories that they make.
I also largely agree with the following seven tenets of a “General Systems Worldview” as outlined in General Systemology (p. 68) :
We can progressively gain more complete real knowledge of the real world.
A real concrete world underlies some of our experiences, but experiences can also be distorted, or constructed, or hallucinated.
Nothing supernaturalistic exists, but concrete phenomena cannot all be reduced to Physics.
The concrete world is inherently systemic (but we can also project systemicity onto our experienced world).
Every concrete thing (i.e. everything that has causal powers) is always a real system or part of one.
Values are largely constructed via cultural processes, but natural systemic processes also influence them.
We have the capacity and freedom for un-coerced choices and actions, but our choices and actions can also be conditioned by natural and cultural factors.
These philosophical assumptions inform how I approach the topic of boundedness.
Systems Science Requires Boundary Identification
In General System Theory (p. 215), Bertalanffy states that “any system as an entity which can be investigated in its own right must have boundaries, either spatial or dynamic.”2
While I don’t hold a strong position on whether or not boundedness is an essential systems concept from the perspective of a pure theorist — I do believe that the development of General System Theory must be informed by feedback from the practice of systems science.
I don’t see how a general science of systems can progress and provide meaningful empirical data to advance theory if systems scientists don’t develop formal methods for identifying boundary conditions in all of the traditional scientific domains.
Mathematical Definitions of Boundary
So, how can we develop such formal methods?
My current focus is on developing formal frameworks for the analysis of real world systems which can inform the design of ultra-realistic computational models and simulations. As a result, I’m most interested in exploring the various mathematical definitions of boundary that have been proposed by systems theorists and scientists that can be used in the creation of these tools.
Theoretical physicist and systems philosopher Mario Bunge argued that the concept of a boundary belongs in general topology. He proposed a set-theoretic definition of a “boundary component” as an element whose every neighborhood contains at least one system component and at least one thing from the environment of that component. A boundary of a system is then defined as the set of all its boundary components.3
Andrew Cavallo argues that Bunge’s definition is deficient because he made the error of including “the environment of a system in the general definition of system.”4 He goes on to propose a slightly refined version of Bunge’s definition.
George Mobus has proposed a set-theoretic definition of an “effective boundary” that is produced by some kind of internal binding between a special set of a system’s components. A boundary, then, consists of a set of properties (such as porosity and perceptive fuzziness) and a set of interfaces that are responsible for determining whether or not substances are allowed to pass in and out of a system.5
Formal mathematical definitions like these provide essential frameworks for studying real-world systems that can support systems scientists in the important process of boundary identification.
From the perspective of a General Systems Theorist, I could probably make an argument for boundedness not being an essential systems concept. But as a systems scientist, I see no choice but to treat boundedness as a first-class and essential systems concept. Without boundaries, there are no separate distinguishable systems for me to study.
Rousseau, D., Wilby, J., Billingham, J., & Blachfellner, S. (2018). General Systemology: Transdisciplinarity for Discovery, Insight and Innovation (Vol. 13). Springer Singapore. https://doi.org/10.1007/978-981-10-0892-4
von Bertalanffy, Ludwig. General System Theory: Foundations, Development, Applications (p. 215). George Braziller Inc.
Bunge, M. (1992). SYSTEM BOUNDARY. International Journal of General Systems, 20(3), 215–219. https://doi.org/10.1080/03081079208945031
Cavallo, A. M. (2012). On Mario Bunge’s Definition of System and System Boundary. Science & Education, 21(10), 1595–1599. https://doi.org/10.1007/s11191-011-9365-0
Mobus, G. E. (2022). A Model of System and a Language to Represent It. In G. E. Mobus (Ed.), Systems Science: Theory, Analysis, Modeling, and Design (pp. 177–225). Springer International Publishing. https://doi.org/10.1007/978-3-030-93482-8_4