Hierarchical abstraction

Copyright 2020 Graham Berrisford. Now a chapter in “the book” at https://bit.ly/2yXGImr. Last updated 22/07/2021 12:36


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Evidently, we abstract descriptions from real-world phenomena, and abstract “higher-level” descriptions from lower-level ones, thus creating a hierarchy of descriptions. However, abstraction is not a simple or singular idea, and several kinds of abstraction hierarchy are rounded up in this chapter.



Abstraction of descriptions from reality. 1

Abstraction of types from individuals. 3

Abstraction in the hierarchy of sciences. 4

Abstraction in computer system architecture. 10

Abstraction in enterprise architecture. 11

Conclusions and remarks. 12


Abstraction of descriptions from reality

“Knowledge is a biological phenomenon” (Maturana).


The universe existed for nine billennia before the earth was formed. At that time, there was no knowledge, description, model or classification of things on earth. The earth rolled on for a while longer without life on it. Eventually, animals evolved to perceive and describe things in the world, because doing that helped them survive and thrive.


Here, cognition is not a particular biological process, but rather any process by which an organism can recognize some phenomenon in its environment, observe or envisage it, and create or use a description of it.


To recognize (to know) an object, we must have a description of it, which we can correlate (well enough) with what we observe. A description is itself a phenomenon, one that can be correlated with what it represents, near enough for some purpose.

A description need not be complete or perfect. It need only be complete and accurate enough to be helpful. In fact, it is usually very incomplete and somewhat inaccurate. To describe me as “6 foot tall” reveals very little about me, but is accurate enough for some narrow purposes.

Throughout this book, the terms description and model are used interchangeably. Moreover, the terms are used at every level of granularity - from a large and complex specification of a steam engine to a small and singular concept, property, feature, attribute or characteristic (like 6 foot tall) of any individual entity.


Wholeism (considering every conceivable aspect or element of a real-world entity) is impossible. Even a grain of sand is beyond our full comprehension. All we can understand are mental models or descriptions we abstract from phenomena we observe and envisage.


Describers <observe & envisage> Aspects of reality

Describers <create and use> Descriptions

Descriptions <represent> Aspects of reality


That is not to say (as some relativists or perspectivists do) that “perception is reality”, or that all descriptions or models of a real-world entity or situation are equally true or useful. How true or useful a model is, how closely it corresponds to reality, should be testable and verifiable. Still, two different models (e.g. of light as waves or particles) may both be verifiable and useful in different contexts.

Abstraction of structures and behaviors

The universe is an ever-unfolding process, from the big bang onwards. We observe, envisage and describe the universe by carving up space and time into discrete chunks. From the continuous expanse of space, we carve out discrete structures - entities and actors. And from the continuous flow of change over time, we carve out discrete behaviors - events and activities. This table illustrates the difference between structures and behaviors.


Structure examples

Behavior examples

Solar system







Heartbeat, life

Motor cycle

Two-stroke cylinder cycle


Billing process


Every structure has a life time over which it changes – whether cyclically or progressively. Here, an aggregate entity is a collection of elementary structures that interact – whether cyclically or progressively – and change state.


Every behavior, be it cyclic or progressive, is constrained by the laws of nature or other rules. Here, an activity system is a pattern of behavior we can observe or envisage in what one or more entities do over time.


An activity system has a structural state, which changes over time. In Ashby’s cybernetics, the state is represented by the values of some variables. In Forrester’s system dynamic, the state is represented by the quantities of some stocks (state variables) that are increased and decreased by inter-stock flows. In both schools of system thinking, different observers, with different interests, may abstract different state variables from all those that might be used to describe a given entity or phenomenon.


To some, the word “system” means an aggregate entity (sometimes, regardless of its behavior) and to others, it means an activity system (sometimes, regardless of which actors perform the activities). You might presume that one aggregate entity = one activity system, and vice-versa. However, different observers, with different interests, may abstract different activity systems from one physical entity or phenomenon. And in general, the system-to-entity relationship is many-to-many. Later chapters explore this further.


Beware that some scientists speak of an aggregate entity (say a molecule) as being a system with a state, as though this is true independently of any observer. Similarly, social and management scientists often speak of a social entity or business organization as being a system, regardless of any model or description of it.

Abstraction of types from individuals

Scientific thinking involves various kinds of reasoning, and flipping from one to another.


Deductive reasoning works from the more general or universal (a theory or type) to the more specific or unique (an elaboration, an example or instance). Since the general is often seen as higher level than the specific, this is often called a “top-down” approach. 


Inductive reasoning may be called a “bottom up” approach, since it works the other way, moving from specific (lower level) observations of examples or instances to broader (higher level) generalizations, theories and types. The ability to induce a general type from observations of particular phenomena is widely considered to be a defining feature of intelligence – both natural and artificial.


Abductive reasoning, proposed by philosopher Charles Sanders Peirce, starts with some observations and then seeks the simplest and most likely explanation. Given some phenomenon, and several alternative theories, models, typifications or explanations, others speak of using Occam’s razor to choose the simplest.


A type is a concept, is a description. The philosopher A J Ayer pointed out that every description (if not pinned to one individual in time and space) typifies what it represents. A description of one apple applies to every other apple that matches the same description. Even if we see only one member of a set (one apple, or one universe), we can, from its description, envisage more members. And even if we describe only one mythical unicorn, we can envisage many of them.


So, a description is a general type (or intensional definition). It sets out descriptive properties shared by each member of a set of near-enough similar things. Not only can one type describe (characterize, represent, typify) many individuals, but also, one individual can be described by (embody, exemplify, exhibit, instantiate) many types.


The later chapter on description and typification explores the use of types further.

On the emergence of knowledge and typification

Remember that knowledge is a biological phenomenon? The evolution of human civilization from primitive forms of life can be correlated with advances in our ability to know and typify things in the world around us.


Levels of science

Knowledge acquisition tools

Management science

Information systems

Human sociology

Teaching and logic

Social animal psychology

Parenting and copying

Animal psychology




Organic chemistry


Inorganic chemistry





The types we use to classify and describe things include both numeric, quantitative variables and qualitative variables. Surely, in the evolution of description, quantities followed qualities? Countless animal species have evolved to the point their members can discriminate between object types and recognize them by smell, shape or color. Only a few species of animals can remember quantities (as their members may demonstrate by distinguishing three objects from four objects), and fewer still can communicate a quantity, one to another.


Of course, to test theories, scientists turn them into quantitative predictions about measurable variables. Even in the humanities (when, say, discussing variables such as employment, pay and poverty) science requires us to quantify the variables and the cause-effect relationships between them, and to measure them.


The later chapter on intelligence and civilization explores the evolution of intelligence.

Abstraction in the hierarchy of sciences

In seeking to describe, understand and manage nature, we impose hierarchies on it, or at least, on our descriptions of it.


This section discusses the hierarchy of sciences (from physics to the humanities). It suggests that a) each level of science can be seen as autonomous, b) the elementary parts of a system in one science may be seen in another science as a whole to be analysed, and c) complexity is most usefully assessed or computed with respect to a description or model made at one level of science.


In the 1940s, the biologist Bertalanffy sought to abstract principles and patterns common to systems in different sciences. Although he didn’t start from sociology, or analysis of human behavior, he stimulated people to look afresh at social and business systems, which they saw as higher level than biological systems.

Boulding’s hierarchy

In the 1950s, general system terms and concepts were taken up by “management scientists” concerned with the structures and behaviors of socio-technical entities that employ human actors. Kenneth Boulding is perhaps best known for his article below.


Management Science, Volume 2, Number 3, April 1956

General System Theory – The Skeleton of Science

Kenneth E Boulding, University of Michigan


Below are some of the points made in the article, which you find on pages 197 to 208 of the journal.


“Two approaches to the organization of a general system theory suggest themselves. The first approach is to… pick out certain general phenomena which are found in many different disciplines, and to seek to build up general theoretical models relevant to these phenomena.”


Boulding (1956) pointed to some ideas shared by many sciences. He began with a population of individuals of a given type, which grows and shrinks as individuals are added and subtracted. The individuals behave in ways that affect each other, and other populations. These ideas are reflected in Ashby’s cybernetics and Forrester’s system dynamics.


“A second possible approach to general system is through the arrangement of theoretical systems and constructs in a hierarchy of complexity of the individuals of the various empirical fields. This approach is more systematic than the first leading towards a “system of systems”.


Boulding proposed a hierarchical classification of system types that places socio-cultural systems near the top.



System type


Symbolic systems


Socio-cultural systems






Lower organisms


Open systems


Control mechanisms


Clock works


Static structures


Boulding implied that moving up the hierarchy implies increases in both scale and complexity. Each higher-level population (say molecules, or social entities) contains many individuals of a different type at a lower level (think atoms, or people). Higher-level individuals are seen as larger than lower-level ones, and each higher-level population adds some new complexity to what is evident at lower levels of thinking.


“Each individual is thought of as a structure or complex of individuals of the order immediately below it. The behavior of each individual is explained by the structure and arrangement of the lower individuals from which it is composed”.


Bertalanffy didn’t like some directions in “the system movement” he helped to initiate. In 1968, he wrote that Boulding’s hierarchy was “impressionistic and intuitive with no claim for logical rigor.” 


Aside: In ascending from level 1 to 9, are the levels steps in complexity (simple to complex), steps in scale (smaller/narrower to larger/wider), steps in time (in the evolution of the universe), or all three at once? Curiously, the hierarchy stretches from static structures (at 1) through clocks, organisms and humans to their language-based products (at level 8), which are static structure. Note that a clock (at 2) is an open system (4), since it consumes energy from a winder, and gives that energy to the hands on a clock face viewed by observers. And the interactions between cells in an organism (5) might be seen as more complex than interactions between animals in a socio-cultural system (8).

Bertalanffy’s hierarchy

Bertalanffy recognized the significance of arranging sciences in a hierarchy.

“We presently "see" the universe as a tremendous hierarchy, from elementary particles to atomic nuclei… to cells, organisms and beyond to supra-individual organizations.” Bertalanffy 1968


The table below is my attempt to outline the “tremendous hierarchy” of sciences. From bottom to top, it can be seen as a history of the universe from the big bang to human civilisation.


Science level

Elements or actors

Interact by

Management science

Human organizations

Information encoded in writings

Human sociology

Humans in groups

Information encoded in speech

Social animal psychology

Animals in groups

Information encoded in signals

Animal psychology

Animals with memories

Sense, thought and response


Living organisms

Sense and response. Reproduction

Organic chemistry

Carbon-based molecules

Organic reactions

Inorganic chemistry


Inorganic reactions


Matter and energy



Evidently, scientists in higher level sciences think and work without reference to laws established in lower-level sciences.


“We cannot reduce the biological, behavioral, and social levels to the lowest level, that of the constructs and laws of physics.” Bertalanffy 1968

Anderson’s hierarchy

In the 1970s, the physicist Anderson (probably unaware of Boulding and Bertalanffy) wrote a famous paper called “More is different” on the emergence of new laws as we move up the hierarchical structure of sciences: P W Anderson, Science 4 August 1972, Volume 177, Number 4047


Anderson’s paper is erudite, informative and admirable. However, readers may draw questionable conclusions from it, such as “reductionism is bad” or “larger is more complex”.


“one may array the sciences roughly linearly in a hierarchy, according to the idea that the elementary entities of science X obey the laws of science Y… At each stage [in the hierarchy of sciences] entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry.”


The elementary entities of

Obey the laws of

solid state or many-body physics

elementary particle physics


solid state solid or many-body physics

molecular biology


cell biology

molecular biology



social sciences



A different perspective is possible. Consider planet earth as an elementary part of our solar system. The whole system is studied in astrophysics; the earth is analysed in geology and biology. Consider a rider and bicycle as elementary parts of a system. The motion of the whole is studied in physics; the behavior of a person is analysed in psychology and biology.


For sure, generally speaking, the elementary parts of a system in one science may be seen in another science as a whole to be analysed, and reduced to the parts of interest in that science.


Complexity is asymmetry?

Anderson compared molecules of different sizes and noted that larger ones are more asymmetrical. He proposed that increases in asymmetry at larger scales lead to the emergence of new scientific laws. He suggested this shift from symmetry to asymmetry may help to explain why the laws of higher-level sciences cannot be constructed from the laws of lower-level sciences.


For sure, symmetry-breaking does generate complexity. Given a symmetrical structure, introducing some asymmetry increases its complexity. But can we say the converse, that complexity is loss of symmetry? Is asymmetry the one and only measure we make of complexity? People do measure complexity in other ways – not reducible to asymmetry.


Complexity is a function of scale?

Anderson explained that at the level of physics and chemistry, symmetry breaking occurs as we change scale. But he went on to say:

“There may well be no useful parallel to be drawn between the way in which complexity appears in the simplest cases of many-body theory and chemistry and the way it appears in the truly complex cultural and biological ones…


It seems Anderson did not presume his idea is general to higher levels of science, except…

…. except perhaps to say that, in general, the relationship between the system and its parts is intellectually a one-way street.”


By “one way street”, Anderson wrote that whereas top-down analysis (which usually means dividing a whole into parts) is possible, bottom-up synthesis (which usually means combining parts to whole) is all but impossible. Did he mean reductionism is possible and holism is not? No, he meant the rules that govern the behavior of parts in higher-level sciences cannot be constructed from the rules that govern the behavior of parts in lower-level sciences.


On the emergence of complexity

“The reductionist hypothesis does not by any means imply a "constructionist" one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society.”


In 1972, Anderson was not aware of the term emergence. The idea that new, emergent, properties can be explained by holistic thinking, had long been promoted by system theorists; and is sometimes presented as the opposite of reductionism. Anderson didn’t so much reject reductionism as reject constructivism that says we can start from the laws of physics and construct or reconstruct the laws of higher-level sciences from there.


“The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.” Ibid.


Twinning of scale and complexity?

Boulding and Anderson correlated higher levels of science with increased scale and complexity. Hmm… in what sense is larger twinned with more complex? What it means to speak of increasing scale and complexity at higher levels of science is not obvious.


It is easy to rank a molecule, a virus, a planet and the solar system in order of size. However, that order does not match the hierarchy of the sciences that study them. And how to rank them in terms of complexity? Consider these three kinds of hierarchy.


In a composition hierarchy - larger entities contain smaller ones. A large and complex software system is typically composed of smaller (sub)systems, each a black box, defined only by its interfaces to other subsystems. This top-down decomposition may continue for several levels, using abstraction-by-encapsulation of black boxes at each level. When discussing a system at one level, we usually ignore the internal complexity of its subsystems. After studying both, we might find a system at a higher level to be simpler than a system at a lower level.


In a delegation hierarchy - client entities depend on server entities. In a client-server hierarchy, client components (in a higher layer) depend on server components (in a lower layer). Consider for example the client-server stack in layered software design (UI, business logic and data server layers), in network communications (the TCP/IP stack), or in business supply chain. In discussing a client component, we usually ignore the internal complexity of its server components. After studying both, we might find a client system to be simpler than a server system.


In the science hierarchy - entities in one science are often composed of entities discussed in other sciences. Moreover, one entity may be viewed in different  ways in different sciences. For example, a sociologist may see a person as an atomic entity that consumes and produces messages in a social system; whereas a biologist may see person as an atomic entity that consumes oxygen and produces carbon dioxide and waste products in a biosphere system. The sociologist’s system may be simpler than the biologist’s system.


The three hierarchies above might better be seen as hierarchies of abstraction rather than size or complexity. We can only measure the scale or complexity of some entity or phenomenon with respect to a description or model of it that we find useful. When discussing an entity or phenomenon in one science, we usually ignore what is better explored in another science. So, a system at a higher level of science can be simpler than a system at lower levels. Rather, entities in different sciences are differently complex.


By “more is different”, Anderson didn’t mean changes in scale that merely result in more of the same. He meant changes in scale that result in something new emerging. Say, the properties of a molecule rather than an atom. Or the behavior of a colony of animals rather than one individual animal on its own.


My discomfort with Boulding and Anderson correlating higher levels of science with increased scale and complexity is that this is only meaningful to somebody thinking of a higher-level entity or phenomenon in terms of the quantity and complexity of atomic particles and structures – which is simply irrelevant in any higher-level science (psychology, sociology or economics) that regards a person as an elementary entity.


Seems to me that in so-called complexity science, the notion of complexity is hopelessly ambiguous. The later chapter on complexity science explores the topic of complexity further.


Perhaps all we can say for sure is that a) each level of science can be seen as autonomous, b) the elementary parts of a system in one science may be seen in another science as a whole to be analysed, and c) complexity is most usefully assessed or computed with respect to a description or model made at one level of science.

On reductionism

"The anti-reductionist stance described by Anderson [is] not some uninformed and poorly thought-out gibberish condemning science that unfortunately one finds too much of."  Commentary on Anderson’s paper


Many social systems thinkers resist following the disciplines of harder sciences, which they reject as “reductionist”, and promote “holism”. However, the reductionism they condemn seems to be either ill-defined or mythical. Consider three possible definitions.


Reductionism (1) reducing all to physics; explaining higher-level biological, psychological and social phenomena in terms of the rules governing interactions between atomic "particles". Whoever does that? Nobody. The quantity and complexity of molecules is irrelevant in the systems of interest to higher-level sciences (psychology, sociology or economics) in which a person is an elementary entity.


Reductionism (2) analysing and describing a whole thing (be it simple or complex) in terms of "parts" appropriate to the level of thinking. The parts can be particles in physics, cells in biology, motors and wheels in engineering, people in sociology, and buyers and sellers in economics. OK, but whoever does that without considering interactions between the parts?


Reductionism (3) in one respected source, is defined as analysing and describing a whole thing in terms of interactions between its parts. Surely that is better called holism?

Abstraction in computer system architecture

Within each science, hierarchies may be defined. In physics, there is a composition hierarchy that descends from galaxies through solar systems and planets down to atomic particles. In biology, a body is successively decomposable into organs, cells, organelles and organic chemicals.


System modelling of the kind in enterprise, business and software architecture features abstraction of several kinds, including the four particular varieties in the table below.








Atomic part













Service provision


A composition hierarchy (as in a description of the human body) groups atomic or finer-grained components into a coarser-grained component, which may in turn be further composed with others into an even coarser-grained composite.


A generalization hierarchy (as in the classification of species) relates similar things to one type, then relates similar types to a supertype, and so on. A subtype “inherits” the properties of any supertype above it, and “extends” them with additional properties.


An idealisation hierarchy may be seen as a special kind of generalization in which, from the bottom up, one first describes the properties of a thing in some detail, then removes what might be called physical properties to form a slimmer, more logical or conceptual, description.


A delegation hierarchy is a client-server structure in which actors or components at a lower (or platform) level serve the interests or aims of actors or components at higher levels.  Structuring the components of a complex activity system into client-server layers is a powerful way of simplifying a system, and often used by business, computer and software architects


Business architecture

Software architecture

Computer architecture

Network architecture


User interface

Programming language


Core functions

Business logic

Operating system


Support functions


Device drivers and

CPU instruction sets




Logic gates







Might the hierarchy of sciences at the start of this chapter be viewed as a delegation hierarchy?

Abstraction in enterprise architecture

The four kinds of abstraction above appear prominently in languages like ArchiMate (which has a symbol for each kind), and in EA frameworks like TOGAF.


It is common for business and software system architects to define composition and delegation hierarchies. Consider a conventional management structure. Seen as a hierarchical decomposition, it may divide a business into divisions, then departments, then teams. Seen as a delegation hierarchy it is a client-server structure in which the manager of a lower-level component serves the interests or aims of a manager in a higher-level component.


In Meadows’ description of a system, the actors are the most concrete and tangible elements, the activities are harder to see, and the aims are even harder to see. In EA, business architects often try to make actors, activities and aims visible by drawing composition hierarchies of the kinds below.


·       An actor hierarchy – as in a management structure.

·       An activity/ability hierarchy - a functional decomposition or capability map.

·       An aim hierarchy – this decomposes grand aims or goals into finer-grained objectives.


Sometimes one hierarchy corresponds closely to another. Sometimes the three hierarchies differ. See the later chapter for further discussion.

Abstraction hierarchies in TOGAF

This table below shows abstraction hierarches found in the architecture framework called TOGAF.













Common system

Industry domain


Requirements and context

Architecture continuum

Solution continuum

Deployed solutions

Service provision





Abstraction by idealization also appears in the Zachman Framework (a 6 by 6 grid for classifying the artifacts that describe a particular enterprise and its business operations) and in data architecture scheme of conceptual, logical and physical data models.


Mapping levels of idealization to levels of generalization

TOGAF’s "enterprise continuum" can be seen as 4 by 4 grid that classifies the artifacts that describe a particular enterprise and its business operations, into 3 degrees of generalization from the particular business organization, and 3 degrees of idealization from real-world business operations.












Requirements and context





Architecture continuum





Solution continuum





Deployed solutions






Although TOGAF encourages architects to classify descriptive artifacts in the two ways shown above, the enterprise continuum is probably more a teaching device than a practical repository classification tool.

Conclusions and remarks

Abstraction is not a simple or singular idea. This chapter discusses many different kinds of abstraction. In describing some aspect of reality, or in further simplifying that description, we often use several kinds of abstraction at once.



A description (which is itself a reality) does not create the reality it represents. Rather, it is an abstraction created by an actor, that can be correlated with some aspect of reality, well enough to be useful.


By the way, "information" means different things in different sciences. In the social sciences, it typically refers to descriptions, decisions and directions that are remembered in memories and communicated in messages by actors. Gathering, manipulating and using descriptive information - as computer does as a matter of course – does not imply consciousness.



A thermometer can be read by an actor (human or machine) as describing some aspect of reality. A thermostat can react to that descriptive information in a pre-defined way, to switch a heater on or off. You might argue that means the thermostat “knows” the state of the heater, and is “disposed to” or “decides” what to do in response to that knowledge. But that falls short of the consciousness and decision-making ability exhibited by intelligent animals.


It seems it is our ability to predict the future, and creatively determine our behavior in the light of that prediction, that distances us from the mechanically deterministic behavior of the thermostat. Description making and consciousness combine to give animals the ability to compare descriptions of the past, present and future, and creatively plan their future actions.


And beyond predicting the future?



"Some people say that being able to predict the future is what’s key for AI, or being able to have common sense, or the ability to retrieve memories that are useful in a current situation. But in each of these things, analogy is very central. You can show a deep neural network millions of pictures of bridges, for example, and it can probably recognize a new picture of a bridge over a river or something. But it can never abstract the notion of 'bridge' to, say, our concept of bridging the gender gap. These networks, it turns out, don’t learn how to abstract. There’s something missing. And people are only sort of grappling now with that. Analogy isn’t just something we humans do. Some animals are kind of robotic, but other species are able to take prior experiences and map them onto new experiences. Maybe it’s one way to put a spectrum of intelligence onto different kinds of living systems: To what extent can you make more abstract analogies?" Read more: https://lnkd.in/eN99T5U


Analogies imply typification, and the principle is easily exemplified.

1) Take a description “Richard is strong and brave”.

2) Find another with the attributes of the same type: “Strong, brave, animal”.

3) Change the description “Richard is like a lion”.



1) Take a direction: “Close the gap between the rich and the poor”.

2) Find another of the general type that “Close the gap” exemplifies.

3) Change the direction: “Bridge the valley between the rich and the poor”.


The practical difficulty is to do this in a fluent and human-like way. The second analogy is obscure, since it depends on understanding that a bridge shortens the valley crossing. But who said AI would be easy?