A philosophy of systems


Copyright Graham Berrisford 2014. Last updated 02/02/2020 21:16 One of a hundred papers on the System Theory page at http://avancier.website.


A philosophy of systems should collate theories and ideas that help us understand, identify and describe systems.

Before turning to philosophy here a few basic ideas about systems.


Systems as realisations of abstractions

Gibbs defined a system as: “a portion of the ... universe which we choose to separate in thought from the rest of the universe.”

E.g. a planet, a tree, a rain forest, a tennis match, a wardrobe, a church (building or social organization), or a socio-technical entity such as IBM.

Since the 1950s, systems thinkers have separated the concept of a system from Gibb’s discrete entity.

Nowadays, a system is a particular way of looking at a real-world entity or situation.


The notion that a system is an observer’s perspective of an entity or situation is deeply embedded in the history of systems thinking.

In Ashby’s introduction to cybernetics, a system is an observer’s highly selective model of what something does.

In Forrester’s system dynamics, a system is a mathematical model of inter-stock flows that increase and decrease stocks.

In von Bertalanffy’s general system theory, a “system model” is selective perspective of a system reality.

In Ackoff’s vocabulary for system thinking, an “abstract system” idealises a “concrete system”.

In Checkland’s approach to business analysis, a “soft system” is a perspective of a real-world business.



System kind

Actors (active structures)

Activities (behaviors)

State (facts of interest)

A solar system


planets and star

planets orbit the star

positions of the planets

A windmill


sails, shafts, cogs, millstones

rotate to transform wind energy and corn into flour

wind speed, quantity of corn, quantity of flour

A digestive system


teeth, intestines, liver, pancreas etc.

transform food into nutrients and waste

quantities of nutrients and waste in the system

A church


people who

play roles in the church’s organization and services.

many and various attributes of roles and services


Note that the entity-to-system relationship is many to many.

Countless system descriptions (mental or documented models) may be abstracted from one substantial real-world entity or situation. 

You might look at a tennis match as a realisation of the laws of tennis, or as a process for displaying athleticism and ball skills.

You might look at a rain forest as a system for sustaining biodiversity within its bounds, or a system for transforming carbon in the atmosphere into tree trunks.

Countless real-world entities or situations (countless rain forests) may realise the same abstract type (“rain forest”).


Towards a philosophy of systems

A philosophy of systems must address questions debated by philosophers for millennia.

Notably, how do descriptions relate to realities? And more specifically, how to resolve "the problem of universals”?

Every possible answer can be found in some philosophy or other.

The aim here is not to say much that is new; it is to be decisive, choose between incompatible answers, and be definitive.

This philosophy of systems collates some particular views of description and reality.

It rejects some other views found in the works of Plato, Aristotle, Nietzsche and Wittgenstein.

It counters some interpretations of von Foerster's second order cybernetics.


This philosophy introduces a new device that separates and relates describers, descriptions and realities in an epistemological triangle.




<create and use>     <represent>

Describers <observe and envisage> Realities


This triangle is presented as an improvement on similar triangles, including the "semiotic triangle" and Peirce’s “triadic sign relation”.

In this paper’s conclusions, the triangle is edited to reflect the system theories of von Bertalanffy, Checkland, Ackoff, Forrester and Ashby.

Thereafter, footnotes to this paper go on to:

·       challenge several other views, including the “semiotic triangle”.

·       challenge a postmodern trend in sociology and management science towards “relativism”.

·       promote a type theory that allows for fuzziness and transience in the conformance of things to types. 

·       compare and contrast this type theory with the more rigid set theory you may be familiar with.

·       question whether mathematical concepts “exist” in a real/physical or ethereal/metaphysical sense.


Basic ideas about systems. 1

Memories, messages and meaning. 1

Basic ideas about data, information and knowledge. 1

Descriptions represent realities. 1

Describers observe and envisage realities. 1

Describers create and use descriptions. 1

More about the epistemological triangle. 1

Testing the truth of a description. 1

Myths relating to general system theory and science. 1

A philosophy for system theory. 1

FOOTNOTES on related and opposing views. 1

Other triangular philosophies. 1

Relativism in systems thinking. 1

The problem of universals. 1

Mathematical concepts as realities. 1

Type theory as separable from set theory. 1

A new tractacus logico philosophicus. 1

A table of philosophical dichotomies. 1


Basic ideas about systems

Having observed or envisaged a system, we can describe it by typifying its elements.

We may typify actors (structures in space that perform activities) by defining roles

We may typify activities (behaviors over time that advance the state of the system or something in its environment) by defining rules.

We may typify system state (structures changed by activities) by defining state variables.


How systems may be described

Roles, Rules, Variables

<create and use>                       <represent>

System describers <observe and envisage> Actors, Activities, State


Abstract and concrete systems

To paraphrase Ashby, the common error is to point to an entity and call it "a system".

The notion that a system is a "perspective" of a real-world entity or situation is deeply embedded in systems thinking.

An entity is only a "concrete system" when, where and in so far as it realises an "abstract system".


A concrete system is the instantiation by an entity of an abstract system.

A real-world entity or situation is describable as a system when, where and in so far as it realises a system description.

E.g. A real-world hurricane is a realisation in the atmosphere of an abstract weather system described by meteorologists.

E.g. Your beating heart behaves in accord with an abstract system known to medical science.

This table presents three more examples.


Systems thinker

Abstract system (type)

Concrete system (instance)



a musical score

a performance of the score

an orchestra

Software engineer

a program

an execution of the program

a computer

Game designer

the rules of “poker”

a game of poker

a card school


Abstract systems describe roles for actors and rules for activities that advance system state variables.

Concrete systems are realisations by real world entities or situations of abstract system descriptions.

An abstract system does not have to be a perfect model of an entity’s behavior; only accurate enough to be useful.

We can test that an entity realises an abstract system to the degree of accuracy we need for practical use.


The relationship between physical entities and abstract systems is many-to-many.

·       One physical entity (e.g. a card school) may realise countless abstract systems (poker, whist, pizza sharing).

·       One abstract system (the game of poker) may be realised by countless physical entities (card schools).


Ashby pointed out that infinite systems could be abstracted from a material entity by different observers.

IBM can realise countless different abstract systems in parallel, some of which may be in conflict.

Moreover, the systems that IBM realises may change over time. 


Abstract systems as types

A system may be envisaged in an abstract form - as in a causal loop diagram, or the rules of poker.

A system may be realized in a concrete form – as a performance of an abstract system.

Given an abstract system (a type); a concrete system is an instance of that type.


Modelling systems

Observers can use various modelling techniques to describe or model the actors, activities and state of a system.

Using Ashby’s cybernetics, observers model a system as a set of state variables advanced by processes.

Using Forrester’s system dynamics, observers model a system as a set of stocks (variable quantities) increased and decreased by inter-stock flows.

Using Checkland’s soft systems method, observers model a system as actors playing roles in activities that transform inputs from the environment into outputs for customers.


Memories, messages and meaning

As von Bertalanffy observed, system theory is much concerned with information.

Memories and messages contain structures that encode meaningful information.

In a biology, neural memories are recorded internally and privately.

In a sociology, a memory can be recorded externally, in writing or another form, and accessed by many.



The meaning of a memory or message is not in its structure per se.

Meanings only appear when memories and messages are created and used by actors.

Some promote the principle that the meaning of a message is determined only by its receiver.

Also important to the philosophy here is the meaning encoded in the message by its sender.

Since successful communication requires the two meanings (one encoded, one decoded) to match - near enough.

(Sometimes, the meaning decoded by a receiver differs from the meaning encoded by the sender.

This is a challenge for Ogden and Richards’ "semiotic triangle", and Peirce’s “triadic sign relation”.)


Describers and descriptions of reality

Memories and messages can contain decisions and directions, and questions and answers, relating to activity performed.

They can also contain descriptions of reality.

Epistemology is about what we know of reality, through observation, testing, reasoning and learning from others.

The triangle below identifies and relates three epistemological concepts.




<create and use>        <represent>

Describers <observe and envisage> Realities


In this triangle, describers are actors that create and use descriptions.

Descriptions are created to remember or convey meaningful information about some aspect or portion of reality that is observed or envisaged.                                              

Basic ideas about data, information and knowledge    

In natural language, the terms data, information and knowledge are often used interchangeably.

In science, Shannon’s “information” theory is about data structures in signals; it is not about the information or meaning contained in the signals.

This section distinguishes data, information and knowledge using a simple WKID ontology.





the ability to respond effectively to knowledge in new situations


information that is accurate enough to be useful


any meaning created or found in a structure by an actor


a structure of matter/energy in which information has been created or found



Any structure can be used as data structure or signal. E.g.

·       The shadow on a sundial may be used to represent the time of day

·       The state of your office door (open or closed) may be used to tell people whether you are open to visitors or not.

·       Dance movements are used by honey bees to tell other bees about pollen locations.


Any structure or motion that is variable - has a variety of values – can be used to convey information/meaning.

Here, the term structure embraces data structures and process structures like the honey bee’s dance.

Humans can - with almost no effort - form infinite data structures using words.

We use speech to convey data structures, and use the written word to preserve data structures in shared memory spaces.



There is no information or meaning in a structure (shadow, office door, dance movement or words) on its own.

Actors must perform processes to a) encode/create some meaning in a structure, and b) decode/find some meaning in a structure.

So, data is structure or signal, and information is meaning that only exists at the moments (and in the contexts) that actors encode or decode structures/signals.


(However, in most practical business and IT system design, the terms data and information are interchangeable.

Because it is taken for granted that receivers will decode the same meanings from structures/signals that senders encoded in them.)



Knowledge is information (created or found in a memory or message) that is accurate enough to be useful.

E.g. the knowledge of where to find some pollen can be communicated by one honey bee to another.



To complete the WKID hierarchy, wisdom is the ability to respond effectively to knowledge in new situations.

The application of wisdom to knowledge implies a higher level of intelligence than simply remembering and communicating.


To recap (because it is counter intuitive) there is no information/meaning in a data structure/signal on its own.

Information/meaning exists only when actors create and use data structures/signals.

And knowledge exists only when that information is useful.


Consider the transmission of an SOS message, broadcast by a sender to any and every actor able to receive it.

It is only understood by receivers who can decode the message, using the language it was created in.

It is intended to convey the meaningful information that help is needed.

But it might be a fake, intended to waste the time of its receivers – which is to say it conveys misinformation rather than knowledge.


The following sections explore the three-part relation in our epistemology triangle.

Descriptions represent realities

This section focuses on the middle part of this triangular relation.

“Describers <create and use> Descriptions <that represent> Realities <observed and envisaged by> Describers.”

This section looks at description from the viewpoint of Darwinian biology.

It takes the view that description and knowledge are instruments that emerged as a side effect of biological evolution.

And they have evolved in richness and sophistication alongside life.




<create and use>        <represent>

Describers <observe and envisage> Realities


“Knowledge is a biological phenomenon” (Maturana, 1970).

In thinking about how we create and use descriptions of the world, you might be drawn to a study of linguistics.

This philosophy of systems rejects the idea that communication started with words.

Because social animals described things to each other for eons before verbal language.

And animals recognized things for eons before they attempted to communicate much more than mating intentions.


Why did processes for encoding and decoding memories and messages evolve in animals? Because they proved helpful.

Animals remember things in the world because it helps them to react appropriately to them.

The members of a social species communicate and cooperate because it helps them live better than they can do alone.


To know something of a reality, an animal must have access to a description of it

The description may be fuzzy and flawed; it need only represent a reality well enough to prove useful later.


·       A cat remembers a mouse's features well enough that the cat can spot and catch mice

·       A honey bee remembers and communicates the location of some pollen well enough that later, other honey bees can find that pollen.

·       Newton's laws of motion are accurate enough that you can use them effectively.


Descriptions of material things are massive simplifications – barely scratch the surface of the infinitely complexity of reality.

A description does not have to be perfect or complete, only useful

Does it help us to understand, predict and manipulate things in reality?


The approach here is Darwinian; the premise is that there was no description of reality before life.

Consider some stages in the evolution of knowledge.

1.     Molecular memory: organisms recognize molecular structures.

2.     Neural memory: animals remember things they have seen, heard or otherwise perceived

3.     Messaging: social animals share descriptions of things in fixed format messages (e.g. gestures and alarm calls)

4.     Speech: humans encode descriptions in words

5.     Writing: humans record descriptions in an external persistent form.

6.     Science: humans learn to form theories, predict outcomes and test them in reality.

7.     Machine learning: humans create machines that can abstract descriptions from realities.

Describers observe and envisage realities

This section focuses on the last part of this triangular relation.

“Describers <create and use> Descriptions <that represent> Realities <observed and envisaged by> Describers.”

It discusses how describers observe and envisage realities.

The focus is on natural describers, but describers can be artificial intelligences.




<create and use>     <represent>

Describers <observe and envisage> Realities

Observing actualities and envisaging possibilities

For sure, stuff does actually exist out there.

We may observe a house, a horse, and the largest known prime number, which all exist in time and space, in material reality.

The types “prime number” and “largest known prime” exist in countless minds and records.

But the latest instance of “largest known prime” exists only in records, because it is too large to remember (in 2018 it had more than 23 million digits).


We can also envisage stuff that might possibly exist.

We can envisage a unicorn, and the next prime number beyond today’s largest known prime.

None of those exist in material reality today, but we can describe them, and infinite other possibilities.

We can describe the process for generating the next largest known prime, starting from the one known today.


The realities of interest to us here include whatever is

·       observed (including observed describers and descriptions) or

·       envisaged (including envisaged describers and descriptions).


Some portions or aspects of the cosmos that exist, in the everyday sense, may never be envisaged or observed by describers.

Conversely, some “realities” envisaged by describers will never actually be realized in the cosmos.

They will only “exist” in so far as describers envisage and create descriptions of them.

Yes, to call them “realities” is questionable, but to call them anything else would obscure this philosophy of systems.

Perception is realistic rather than illusory

According to research discussed in this Anil Seth talk, human perception combines:

·       Observation: sensing information input from what is out there.

·       Envisaging: making a best guess as to what has been sensed, with reference to what is expected.


That does not mean what you perceive and remember is purely an invention - or does not inform you about the external world.

It only means your brain (given the time and resources at its disposal) makes the best bet it can as to what your senses tell you about the world.


What we expect to see is not purely fanciful (invented out of nothing); it is what a mix of inheritance and experience predicts is likely to be true.

Thus, the brain optimises its matching of perception and experience; else, it would have the hopeless task of analysing each perception from scratch.


Perception and sensation

Perception is the end-to-end process that turns an input message into a sensation (model or image) an animal can respond to and/or remember.


In biology, a sensor (e.g. the eye) is a machine that can detect qualities or changes in a reality.

It responds by firing messages into a nervous system.

The eye’s lens may do little to modify the signal received.

As the input message progresses through the nervous system, processes can be applied to it.

E.g. The retina of a cat's eye is especially sensitive to thin wiggly lines - like mouse tails.

Further into the brain, cognitive processes may reshape the incoming message.


A sensation cannot be the observed entity – it can only be a model of some of its features.

That does not mean (as Seth seems to imply) that perception is hallucination, and the entity does not exist.

The survival of every social animal depends on the presumption that:

·       things exist out there

·       our memories of those things are useful models of them and

·       we can share features of those models by translating them into and out of messages.


The sensation created by a perception may be fuzzy, incomplete and malleable.

Still, the accuracy of this information (is it knowledge?) can be tested by using it.



Humans acquire various kinds of knowledge in various ways; we can:

        Learn lessons from perception and physical sensation (e.g. that it hurts to fall over)

        Learn how to perform a physical process (e.g. to walk, to swim, to play music).

        Learn descriptive facts (e.g. the colors of the rainbow)

        Learn cultural procedures (e.g. to say please and thank you) and logical procedures (e.g. multiplication, algebra).

        Abstract a general pattern or type from data gathered or remembered (cf. “machine learning”).


This philosophy of systems is about “explicit knowledge”, which is explicable and shareable.

Polanyi said "tacit knowledge" (e.g. “know how” such as the ability to swim or play music) cannot be shared,

And moreover: "in the end all knowledge is personal and tacit".

While true in one way, it is misleading to interpret Polanyi as meaning no knowledge is shareable 

And we do teach people to swim and play music, so even tacit knowledge can be partly codified.


Recognizing things by comparison with memories

Actors can recognize a thing by comparing a new sensation with an inherited or remembered sensation.

To do this, an actor must access a stored description that represents the thing and/or similar things.


Sharing information by coding and decoding

Actors can store data in shared memory spaces, and send descriptive information in messages.

Ashby used a gale warning broadcast to illustrate the sharing of a description via coding and decoding translation steps.

1.     The broadcaster intends to share a description of the coming weather with listeners.

2.     The broadcaster translates a psychological representation of an envisaged reality into a communicable representation.

3.     Between the broadcaster and each listener, the message passes through a long series of coding and decoding translation steps.

4.     It reaches a listener who translates the message back into an internal psychological representation.

5.     Soon thereafter, a listener can verify the accuracy of the warning message they have remembered.


Failures in perception and memory

Actors may misread a message, or find it to be a poor representation.

They may hallucinate (perceive something where there is nothing); they can miss-remember or forget a memory.

But still, neural systems evolved to perceive what does exist out there.

And the survival of an actor depends being able to do this reasonably well, most of the time.

Describers create and use descriptions

This section focuses on the first part of this triangular relation.

Describers <create and use> Descriptions <that represent> Realities <observed and envisaged by> Describers.

In the creation and use of descriptions, as Ashby observed, “coding is ubiquitous”.




<create and use>     <represent>

Describers <observe and envisage> Realities

Memories must be encoded and decoded

To remember a thing, animals encode a representation of some of its features in a neural memory.

And to recall that thing, they decode that memory.

Nobody understands the processes by which higher-level knowledge and consciousness emerge from our biochemistry.

But we do understand those processes exist.


A brain’s biochemistry, a cave wall drawing, a word expressed in sound waves, a honey bee’s wiggle dance.

Each is a physical data structure that an actor can use to encode some information, to remember it or communicate it.

But the structure is meaningless on its own; it is only meaningful to the actor who creates it, and any actor who uses it.

So, in short, there is no meaning in data per se.

Meaning only exists in the processes of encoding and decoding data structures.

Meaning exists when a data structure is encoded or written, and when it is decoded or read.

To encode or decode data, an actor must use a code.


In the 1940s, Turing proposed how a machine could read and respond logically to inputs.

McCullough and coresearchers realized that cyclic networks of artificial neurons could act as a system with memory.

At first, some hoped they were identifying mechanisms used by the brain, but by1960 it was clear that brains work differently.

Experiments show that people find it difficult to apply the rules of logic.

The brain does not store persistent data structures as a computer does, its mental images are incomplete, fuzzy and malleable.


Nevertheless, the brain is not empty; it does remember some features of entities and events it has perceived.

It evidently processes representations of those features when it remembers and recalls them.

You surely recall a dollar bill is rectangular, and green, and has the number one on it.

How information is stored is a mystery, perhaps it is stored in bio-electro-chemical processes.

If no information was stored how, would you describe a dollar bill or a friend to somebody else?

Messages must be encoded and decoded

For an act of communication to succeed in conveying information, two roles must be played.

·       One actor (a sender) must encode some information or meaning in a data structure or message.

·       Another actor (a receiver) must decode the same information or meaning from that data structure or message.


Consider how one bird (acting as a receiver) understands the alarm call made by another bird (acting as a sender).

Prior to exchanging that message, the sender and receiver may be entirely unknown to each other.

To communicate they must share the same language or code for encoding and decoding the message.


Alarm calls, body language, gestures and facial expressions are rarely ambiguous; because nature designed them to convey specific meanings

Words are so fluid and flexible that verbal communication is a continual search for mutual understanding.

In many social situations, we reduce ambiguity by testing understanding (“know what I mean?”) and repeating our message in different words.

In scientific endeavours, and in business, we strive to eliminate ambiguity by controlling how language is used.

People use controlled vocabularies in which words and phrases have universally agreed meanings (like SOS).


In short, the fact that social animals share knowledge is demonstrated whenever they cooperate successfully.

In a human social network, descriptions of the world are encoded both

·       Internally (and mysteriously) in the memories of individual actors, and

·       Externally in messages that actors exchange and in public memories/records that they share access to.

More about the epistemological triangle

Describers are realities

The realities of interest to us here include whatever is:

·       observed (including observed describers and descriptions) or

·       envisaged (including envisaged describers and descriptions).


A describer is an observable reality, such as a biological entity.

The more intelligent the entity, the more sophisticated the descriptions it can create and use.


Describers create descriptions by encoding them in some form of matter and/or energy.

Describers use descriptions by decoding them from those forms.

Communication between actors succeeds when they share descriptions, and encoded and decoded meanings are the same.

Or rather, near enough the same to be useful, because there can be degrees of truth.


Humans have transcended biological evolution by creating machines that can remember and communicate.

Computers can encode and decode memories that describe things in the world about them, and communicate via messaging.

Today, by applying “machine learning” to captured data, computers can even create and use new “types” to categorise things.

Types, correlations and patterns don't emerge from “big data” on their own.

They only appear when the processes of an intelligence (human or artificial) are applied to the data.

Descriptions are realities

A description is an observable reality, a physical matter/energy structure, created to represent some other reality.

Descriptions exist in the form of internal memories and external messages (using various kinds of representation).

Internal and external descriptions are different in many ways.

But they are similar in the most important way; they are created to be retrieved or read and used.


Many copies of a description can be created and used.

If all copies are deleted then the description disappears from the cosmos.

In other words, there is no ethereal description aside from what exists in one or more copies of it.

Descriptions as types

Animals do create and use signals that name or identify individual things, rather than describe them.

E.g. Every bottlenose dolphin has its own whistle, which tells the other dolphins that a particular individual is present.

But to describe a thing (rather than name it) is to typify it as being of one or more types.


“In describing a situation, one is not merely registering a [perception], one is classifying it in some way, and this means going beyond what is immediately given.”

Chapter 5 of “Language, truth and logic” A J Ayer.


Describers use types (classes, categories) to categorise and describe things.

The three essential relationships are:

·       Describers <observe and envisage > things.

·       Describers <create and use> types to help them recognize and deal with things.

·       Types <characterizes> things, be they entities or events, in terms of their structural and behavioral attributes.




<create and use>   <characterize>

Describers <observe and envisage > Things


The ability to describe things using words dramatically extended human descriptive/typification ability.

We can not only observe family resemblances between things, but also codify them.

Many have independently created and used the types we symbolise using the words “rock”, “plant” and “circle”.

That does not imply those types exist independently of their creation and use.


The premise here is that there were no concepts before conceivers, no descriptive types before life.

And just as descriptions are real rather than ethereal so, types are also real rather than ethereal.

Type are instruments that life forms developed as side effects of biological evolution.

There is no type outside of a description encoded in a matter and/or energy structure.

And when all descriptions in mind or record of “rock”, “plant” or “circle” have gone, that type will disappear from the cosmos.

The idea of an ethereal type is useless, redundant, and better cut out using Occam’s razor.

For more on ethereal types, see “The problem of universals” in the footnotes.


Our type theory begins with this relation: a thing can instantiate (realise, manifest, conform to) a type. 

To describe a thing (e.g. my pet) is to typify it (e.g. as a cat).

For more on type theory, see the footnotes on mathematics.

Testing the truth of a description

True means useful

Truth has no meaning in a world without description.

Truth is a measure we apply to our descriptions of the world.

The truth of a model = the degree to which the description proves accurate and useful.


Consider that physicists may describe light as a stream of particles or of waves.

They do not say either description is “true”, they say only that each model can be useful.


Consider Newton’s three laws of motion, which describe how objects move.

1.     Every object in a state of uniform motion will remain in that state of motion unless an external force acts on it.

2.     Force equals mass times acceleration (f = ma).

3.     For every action there is an equal and opposite reaction.


Engineers the world over regard these three laws as true.

Our lives depend on them applying the simple formula (f = ma) to physical situations.

Three centuries after Newton, Einstein showed this law fails when objects move closer to the speed of light.


In short, there is no absolute truth, only degrees of truth - or confidence - in the accuracy and usefulness of descriptions.


Accidental and deliberate lies

What a message sender considers true, a message receiver may consider false, and vice versa.

E.g. I feel the swimming pool is warm and tell you that; you take me at my word.

You dive in, but find the water is colder than you expected, and complain that I lied, if by accident.

This video illustrates that social animals do sometimes deliberately lie to each other.

However, biological evolution surely favours social animals that usually communicate what is empirically true.

Evaluating truth

Again, truth is a measure we apply to descriptions of the world.

How do we verify a description?


Social verification of descriptions

Biologists don’t need to draw a mind-body separation, but it is convenient here to speak here of mental models.

In one sense, a mental model is unique to the mind that holds it; our mental models are bio-chemically distinct and different.

Nevertheless, though your brain is unique to you, you can communicate some knowledge of the world to another.


E.g. You tell me there is an apple in the box behind the door; I open the door, open the box and eat the apple.

QED, you transferred some knowledge to me.

Demonstrably, we succeeded in sharing some “facts” that we abstracted from observing and envisaging a reality.


Other examples of knowledge sharing

You tell me a train is coming, and I then step off the railway track.


You ask someone to call you at 11.00 hours; they call you at the appointed time.

Demonstrably, you share an understanding of the abstraction labelled “the time of day”.


Your fishmonger advertises cod steaks; you buy some and eat them.

Demonstrably, you share an understanding of what the abstraction labelled “cod steak” means.


A honey bee can encode their mental model of a pollen location in a dance.

Another bee can decode the dance into a mental model of where that pollen is.

To find the pollen, the second bee must share the mental model of the first.

This shows that both mental models represent the same facts – the distance and direction of the pollen source.

The facts recorded in these mental models are objective and accurate enough for us to call them “true”.

Suppose you see one honey bee finds the pollen described to it by another honey bee.

You (3rd party observer or experimenter) have evidence that they have shared an objective description of the world.

That is the very definition of objective (not limited to one intelligence - and confirmed by empirical evidence).

Moreover, in an example of cross-species communication, scientists can read the dance of a honey bee and find the pollen themselves!


We (you and I) can both read and remember this sentence.

Our two mental models of the sentence are different and yet the same.

They are different – our mental models are bio-chemically distinct and different.

They are the same - we can both recall and recite the sentence accurately.

The objectivity of our mental models is found not in their biochemistry.

It is found in communication showing we both recall and recite the sentence.

A 3rd party can test what we recite is objectively accurate.


Scientific verification of descriptions

Humankind brought many innovations to communication, notably:

·       Words: an infinitely flexible box of sounds for communicating, which cost almost nothing to create and use.

·       Speech: speaking and hearing words, using sound waves to symbolise meaning in messages.

·       Writing: recording words in persistent memory structures.

·       Science: proposing theories, testing them empirically, logically and socially


The scientific method formalises our natural approach to experience.

It is in our nature to observe the world, describe it to others and test what we are told against our experience of the world.




<create and use>          <represent>

Scientists <observe and envisage> Realities


How many subjective interpretations can different observers make of Newton's description of force: f = ma?

The accuracy of the description is revealed in its successful use, every day, all over the world.


Scientists are aware that our sensory tools, perceptions, memories and communications are subjective and imperfect.

That doesn’t mean science is unreliable and should be discarded; the reverse is the case.

The scientific method is the best tool we have to transcend limitations as individual observers.

It involves testing of results against predictions, logical analysis and peer group review.

That is how we incrementally improve our confidence that a model or theory is valid.

In short

There are three ways to test the truth of a theory, description or model.


It is empirically true - supported by evidence from test cases.

It can help you recognise and predict what exists and happens in reality.

E.g. If you stay on the railway track, your belief that the train will strike you will be confirmed.


It is logically true - can be deduced from other concepts within a body of knowledge.

It follows logically from axioms (presumed truths) that a body of knowledge is based on.

E.g. The force on a body struck by a moving train can be calculated from its mass and speed.


Last and least convincingly, it is socially true - widely believed in your social network.

Social animals who usually communicate what is true (rather than false) are better able to survive.

In the absence of empirical and logical evidence, we may retreat to the Nietzsche-like presumption that “shared perception is reality”.


Scientists put experimental evidence and logical analysis ahead of simply asking others to confirm a view.

Myths relating to general system theory and science

A general system theory was promoted by von Bertalanffy in his 1968 book.

He discussed many widely-used system concepts (encapsulation, input, output, information, process, system state etc.).

However, it seems several myths about system theory have grown out of misreading what von Bertalanffy wrote.

Even today, many sociological systems thinkers dismiss or put down a scientific and/or cybernetic approach to systems on spurious grounds. 


Myth 1: There can be a universal system theory or philosophy?

Fact: people who start from different metaphysical or ontological assumptions are likely to arrive at incommensurable positions.

Von Bertalanffy wrote: “One of the important aspects of the modern changes in scientific thought is that there is no unique and all-embracing "world system."

His general system theory is about general, rather than universal, features of systems (e.g. not all systems are open and hierarchical).


Myth 2: Science and/or cybernetics is "reductionist"?

Reductionists not only reduce a whole to its parts, but also describe those parts in isolation.

Fact: von Bertalanffy was deprecating some 19th century thinking, rather than modern scientific thought.

He wrote: “notions of interaction and of organization [of parts] were only space-fillers or did not appear at all.”

By contrast, modern science, cybernetics and engineering are very much about how parts interact to produce the "emergent properties" of a whole.


Myth 3: Science and/or cybernetics does not address goals, goal-directedness and adaptation?

Fact: Again, von Bertalanffy was deprecating some 19th century thinking, rather than modern scientific thought.

He wrote: “notions of teleology and directiveness appeared to be outside the scope of science”.

However, he went on to say:

"Cybernetics, proved its impact in basic sciences… bringing teleological phenomena (previously tabooed) into the range of scientifically legitimate problems." 1968 Page 23.

Teleological behavior directed towards a characteristic final state or goal is not off limits for natural science and [not] an anthropomorphic misconception of processes which are undirected and accidental. 

Rather it is a form of behavior which can well be defined in scientific terms and for which the necessary conditions and possible mechanisms can be indicated." 1968 Page 45.

Ashby’s cybernetics starts from the interest an observer has in a system; it addresses goals, goal-directedness and adaptation.


Myth 4: Science and/or cybernetics only address linear systems?

Fact: Cybernetics does address non-linear and chaotic systems.


Myth 5: Systems theory is relativist?

Some sociologists, management scientists and philosophers are extremist relativists.

They deny the concept of objective knowledge – and so deny the reality of concrete systems that are amenable to scientific analysis.

This is simply wrong, for reasons explained in the footnotes.

It is true that von Bertalanffy advocated what he called “perspectivism” over reductionism.

But first, since modern science and cybernetics are not reductionist, this is not an attack on them.

And second, his perspectivism does not deny objective knowledge.

It merely encourages systems thinkers describe systems from different viewpoints and levels of abstraction (physical, biological and social).

He wrote “All scientific constructs are models representing certain aspects or perspectives of reality.”

He did not deny the models represent something of reality, can be shared, and can be verified.


Myth 6: Every whole composed of parts is a system?

Any group of people who communicate can be bounded as a whole social network.

When and where the actors creatively invent how they interact, that network does not behave as a system.

The network behaves as system only in so far as the actors interact in regular ways.

And that social network can realise more than one social system.

A philosophy for system theory       

Let us use the word “entity” to mean “an observable or conceivable part of the world”.

It could be a group of people, a planet, a hurricane, or a performance of a symphony.

We don’t usually confuse an entity with a description of it.

Yet equating entities with systems is the most common mistake in systems thinking discussion.


Von Bertalanffy introduced the idea of a cross-science general system theory in the 1940s.

In 1968, he wrote that “All scientific constructs are models representing certain aspects or perspectives of reality.”


General system theory

System Models

<create and use>          <represent>

Observers <observe and envisage> System Realities


Unfortunately, by referring to a biological entity as a system, he tended to conflate (at least in readers’ minds) the reality and the system. 

By contrast, other systems thinkers urged us to separate the model and the reality.


Russel Ackoff, a writer on management science, spoke of abstract and concrete systems.

An abstract system is a description or model of how an entity behaves, or should behave.

A concrete system is any entity that conforms well enough to an abstract system.


Ackoff’s system theory

Abstract systems

<create and use>                        <represent>

System thinkers <observe and envisage> Concrete systems


Consider these examples:


Systems thinker

Abstract system

Concrete system


a musical score

a performance of the score

Software engineer

 a program

a computer that executes the program


a social system model

a network of people playing roles in the system


An abstract system does not have to be a perfect model of an entity’s behavior; only accurate enough to be useful.

We can test that an entity realises an abstract system - to the degree of accuracy we need for practical use.


The relationship between physical entities and abstract systems is many-to-many.

One physical entity (e.g. a person) may realise countless abstract systems (e.g. body temperature maintenance, poetry recital).

One abstract system (e.g. the game of poker) may be realised by countless physical entities.


Peter Checkland promoted a “soft systems methodology”.

He regarded a system as an input-to-output transformation, a perspective of a reality, a world view or “Weltenshauung”.

Different observers may perceive different systems, some in conflict, in any one human organization or other entity.


Checkland’s Soft systems methodology

World views

<create and use>                        <represent>

Observers <observe and envisage> Human organizations


Jay Forrester (a professor at the MIT Sloan School of Management) was the founder of System Dynamics.

He defined a system as a set of stocks (or populations) that interact and affect each other.

Where one stock has an effect on another stock, that causal relationship is defined as an inter-stock flow.

·       A stock is a variable number representing the level of a quantity, or instances of a type.

·       A flow between two stocks represents how increasing or decreasing one stock increases or decreases another stock.

·       A causal loop connects two or more stock by flows that form a circular feedback loop.


The system’s behavior can be modelled in a causal loop diagram, supported by rules that modify quantitative variable values.

Generally, and mathematically, the system is seen as a set of coupled, nonlinear, first-order differential (or integral) equations.  

However, the system is commonly simulated in software by dividing time into discrete intervals and stepping the model through one interval at a time.

Which is to say, the system is animated as a discrete event-driven system (as many business systems are).


System Dynamics

Models of system dynamics

<create and animate>                          <represent>

System modellers <observe and envisage> Inter-related quantities of things

This site gives more detail http://systemdynamics.org/what-is-sd


W Ross Ashby, writing on cybernetics, distinguished entities from the abstract systems they realise. 

“At this point we must be clear about how a "system" is to be defined.

Our first impulse is to point at [some real-world entity] and to say "the system is that thing there".

This method, however, has a fundamental disadvantage: every material object contains no less than an infinity of variables and therefore of possible systems.

Any suggestion that we should study "all" the facts is unrealistic, and actually the attempt is never made.

What is necessary is that we should pick out and study the facts that are relevant to some main interest that is already given.” (Ashby 1956)


In cybernetics, a system is an abstraction, a theory of how an entity behaves, or should behave.

Ashby’s system is a model of some regular behavior; it represents any entity or “real machine” that performs as described in the model.


Ashby’s cybernetics


<create and use>                   <represent>

Observers <observe and envisage> Real machines


Ashby urged us not confuse an entity with an abstract system that the entity realises. 


In Ashby’s cybernetics

In this philosophy

An observer is

a describer

A system is

a description that abstracts from an observed or envisaged reality

A real machine

a reality that conforms (well enough) to a description


On testing and adapting systems

To apply systems theory should be to apply the general scientific method.

The conformance of real machines to described systems can and should be tested.




<create and use>          <represent>

Scientists <observe and envisage> Realities


The philosophy here allows for fuzziness in how closely realities conform to descriptions and types.

There can be fuzziness in how things conform to descriptions in memories and messages.

There can be fuzziness in how real machines conform to described systems.


System theory shares with biology that idea that a machine can change two ways.

It can change state over time.

It can change its nature from one generation to the next.


We can observe actual (current, baseline, as-is) systems; and envisage possible (required, target, to-be) systems.

And describe a process for analysing and designing a required system.

That process may be seen as a meta system to the required system.


For more high-level concepts related to systems, read An ontology for systems.

For more on how physics (e.g. thermodynamics) relates to system theory read The physics of systems.

FOOTNOTES on related and opposing views

This philosophy of systems takes the view that description and knowledge are instruments that evolved alongside life.

These footnotes:

·       challenge several other views, including the “semiotic triangle”.

·       challenge a postmodern trend in sociology and management science towards “relativism”.

·       promote a type theory that allows for fuzziness and transience in the conformance of things to types. 

·       compare and contrast this type theory with the more rigid set theory you may be familiar with.

·       question whether mathematical concepts “exist” in a real/physical or ethereal/metaphysical sense.

Other triangular philosophies

This philosophy of systems employs a particular epistemological triangle.

The two-way mental/physical dichotomy of Cartesian dualism (after Descartes) has long been rejected by philosophers and scientists.

Several have proposed three-cornered triangular views of description and reality.

Our epistemological triangle seems an improvement on those other triangles.

Read other triangular philosophies for comparisons with:

·       Saussure’s dyadic sign relation

·       Ogden and Richards semiotic triangle in “The Meaning of Meaning”

·       Peirce’s triadic sign relation

·       Karl Popper’s three worlds view

·       The ISO 42010 standard’s system-description-architecture triangle.

Relativism in systems thinking

Some sociologists, management scientists and philosophers are extremist relativists.

They deny the concept of objective knowledge – and so deny the objective reality of systems that are amenable to scientific analysis.

This is simply wrong, for reasons explained below.


Hermeneutics is a philosophy that defines human experience through the use of language; it grew out of studies and interpretations of the bible.

Some promote the principle that the meaning of a message is determined only by its receiver.

Also important to the philosophy here is the meaning encoded in the message by its sender.

Since successful communication requires the two meanings (one encoded, one decoded) to match - near enough.

(Sometimes, the meaning decoded by a receiver differs from the meaning encoded by the sender.

This is a challenge for Ogden and Richards’ "semiotic triangle", and Peirce’s “triadic sign relation”.)


There is stuff out there; the physical world is the touch stone of all our observations of it.

Sure, we cannot know – perfectly and completely - what a thing is; that is not even a meaningful suggestion.

“We cannot know the essences of things in themselves; all we can know is what we know as abstracting nervous systems.” Alfred Korzybski

We can only know a thing as it is represented in a description, model or theory.

But that does not mean all our knowledge of world is entirely subjective or personal.


Subjective does not mean wrong; it means personal, influenced by an individual’s feelings, tastes, or opinions.

Objective does not mean infallible; it means not restricted to one individual and/or verifiable in some way, at least to a degree.


Objectivity is distinguished from subjectivity by how we make observations.

In subjective observation we allow all our personal preconceptions and experience to bear upon our observations.

In objective observation we strip out what is personal to us, and instead use a standardised model of observing.

An objective observation is one made using strict, standardised, procedures of measurement, designed to eliminate as much as possible of the subjective content.


In short, to transcend our subjective experience, we use science, logic and domain-specific languages.

We turn the subjective into the objective by empirical, logical and social verification.

To deny that would be to deny the success of social animals and science.

Second order cybernetics

Heinz von Foerster (1911 to 2002) was an Austrian American scientist who combined physics with philosophy.

He is widely credited as the originator of “second-order cybernetics.”

Followers of this school often refer to the quotes below.

“All experience is subjective (Gregory Bateson).

“Each individual constructs his or her own reality" (von Foerster, 1973).

"The environment as we perceive it is our invention." (von Foerster, 2007).

"Objectivity is the delusion that observations could be made without an observer." (von Foerster).


Von Foerster’s aphorisms lead some to deny that knowledge can be shared.

This is misleading because it disregards the effort required by innately subjective observers to undertake a ‘standardised observation’.

It is not that ‘objectivity’ assumes ‘observations without observers’ but rather that ‘objectivity’ requires observers, being ‘subjective”, to take great pains to remove their personality from their observations.


People do see the world somewhat differently from how birds, bats and bees see it. E.g. Birds can see ultra-violet light

However, animals of one species perceive things using the same tools, and can test their conceptualisations against reality.

Surely no biologist would accept the view expressed by one systems thinker that "internal cognitions do not reflect any external reality".

How do we find food to eat if we have no objective-enough knowledge of the world?


For a systems thinker to say “no one shares the same knowledge of the world” is misleading, since it denies the success of social animal species.

Sometimes a message may be interpreted differently by different receivers (due to using different codes or rules, or being in different states).

However, social communication would never have evolved if senders did not manage to share knowledge with receivers often enough.

The evidence is that we can and do share a considerable amount of knowledge about the world.


Evidently, we do perceive and know some things with a sufficient degree of truth for practical uses

This was the motor for the evolution of animal memory, social communication and science.

To deny that would be to deny the survival and flourishing of life on earth.

And deny the success of science in developing the technologies and medicines we rely on.


The more we check a belief by testing and agreement with others, the more confidence we have in it.

Our survival as a species depends on that confidence being justifiable most of the time.

And the stunning success of hard science is ample proof that testing and peer review maximise the degree of truth.

Relativism or perspectivism (or “perception is reality”)

Relativism is the idea that knowledge and truth exist only relation to particular culture, society, or historical context.

Von Foerster’s aphorisms (quoted above) misdirect some towards an extreme kind of "relativism" that undermines science.


Other historical figures, including Protagoras and Nietzsche, have subscribed to a kind of relativism.

Friedrich Nietzsche (1844 to 1900) was a philosopher whose metaphysical ideas influenced many Western intellectuals.

“Nietzsche claimed the death of God would eventually lead to the loss of any universal perspective on things, along with any coherent sense of objective truth.

Nietzsche rejected the idea of objective reality, arguing that knowledge is contingent and conditional, relative to various fluid perspectives or interests.

This leads to constant reassessment of rules (i.e. those of philosophy, the scientific method, etc.) according to the circumstances of individual perspectives.

This view has acquired the name perspectivism.” Wikipedia December 2018


Protagoras, Nietzsche and von Foerster have a lot to answer for, as discussed in Postmodern Attacks on Science and Reality.

Some postmodernists interpret relativism as meaning all descriptions of the world are subjective, or even equally valid.

Some Marxists believe the “dialectic” about communist principles is more important than the evidence of attempts to apply them.

Some sociologists and managements subscribe to the view that “perception is reality”.

Many bloggers on the world-wide web seem to presume their personal opinion is as true as the facts the world’s best scientists agree.


“We cannot transcend ourselves as organisms that abstract” Alfred Korzybski

Contrarily, the evidence suggests we can and do transcend ourselves as individual organisms.

Even a single-celled organism has enough knowledge of its environment to find food.

Neural systems evolved to help animals represent things in their environment (food, friends and enemies) in bio-chemical memories.

Social animals evolved further to share knowledge of things in their world, by translating internal representations into external messages (like alarm calls).

They can share their perceptions of reality, and test information that has been shared.


This philosophy of system rejects that idea that every subjective, persuasively argued or widely-believed assertion carries the same weight as science.

In cybernetics, it is presumed that two systems can exchange some knowledge about the state of the world.

What perspectivism means in general system theory

It is true that von Bertalanffy advocated what he called “perspectivism”, but he did not deny objective knowledge.

Here merely encourages systems thinkers describe systems from different viewpoints and levels of abstraction (physical, biological and social).

“We come, then, to a conception which in contrast to reductionism, we may call “perspectivism.”

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

We can, however, find constructs and possibly laws within the individual levels.

The world is, as Aldous Huxley once put it, like a Neapolitan ice cream cake where the levels (the physical, the biological, the social and the moral universe) represent the chocolate, strawberry, and vanilla layers.

We cannot reduce strawberry to chocolate; the most we can say is that possibly in the last resort, all is vanilla, all mind or spirit.

The unifying principle is that we find organisation at all levels.

The mechanistic world view, taking the play of physical particles as ultimate reality, found its expression in a civilization which glorifies physical technology that has led eventually to the catastrophes of our time.

Possibly the model of the world as a great organization can help to reinforce the sense of reverence for the living which we have almost lost in the last sanguinary decades of human history.” Von Bertalanffy

The problem of universals

Today, there is little debate about the existence of material things; we all presume there is physical stuff out there.

And surely, most accept that memories and records of them also exist in physical forms

Still, philosophers ask: do descriptive qualities, properties, concepts, or types also exist?


Philosophers draw a contrast between particulars and universals.

Particulars are discrete things (entities and events) we observe and envisage.

Universals are types like “tall”, “circular” and “dangerous”.

We describe a particular thing by typifying it in terms of general properties, qualities, characteristics or attributes.

We may go on to attach a measure or degree to the property, like 2 metres tall, or roughly circular.




<create and use>             <typify>

Describers   <observe and envisage>  Particulars


The “problem of universals” is the question of whether universals exist (or what it means to “exist”).

Three possible philosophical positions are:

·       Platonic realism: a descriptive type exists in a metaphysical form independently of life and record of it.

·       Aristotelian realism: a descriptive type exists only when things of that type exist.

·       Idealism: a descriptive type is a property constructed in the mind, so exists only in descriptions of things.


Over several millennia, philosophers have developed a confusingly diverse and overlapping set of positions.

Simply put, idealism may be contrasted with realism as follows.


Idealism is the view that reality as we know it is a construction of the mind.

Solipsism is the view that we cannot logically prove that things (we think we know) exist in reality.

Also, that the past is an illusion we construct to account for our present state of mind.

These views may lead people to conclude all ideas about the world are equally valid.

And since abstract systems are constructs of the mind, all systems are equally valid.

This is a kind of "relativism" that devalues science and system theory.


Realism is the view that things exists in reality, independently of our perception of them and conceptual schema.

Empiricism is the view that our knowledge of entities in the world comes from our perception of them.

Most scientists would probably describe themselves as realists and empiricists.

They test how well some entity behaves according to what a theory predicts.

Just as systems theorist tests that some entity behaves as a system predicts


You may assume that pragmatic system theorists are realists and empiricists.

And some promote what is called Scientific Realism.

But there is something misleading about the contrast drawn above, because system theory is compatible with epistemological idealism.

Epistemological idealism is the view that reality can only be known through ideas, that only psychological experience can be apprehended by the mind.

This kind of idealism (even solipsism) is compatible with a Darwinian analysis of how animal intelligence evolved.


To instrumentalists, the existence of universals is a question for biology, psychology and epistemology.

Their view is that descriptions are encoded in real-world forms and functions, both in our biochemistry and in records and machines we make.


Aside: Ian Glossop tells me the view above is compatible with many philosophers.

Including Searle, Dennett, Dretske, Fodor, Kim, Davidson, McGinn, Putnam, Popper and Russell.

But I don't promise they would endorse all of what follows, which is largely what I read as said or implied by Darwin and Ashby alone.


Today, philosophical positions overlap in confusing ways; some seem to turn the idealism/realism distinction on its head.

We don’t need to take sides; we can jump over the philosophical word play, with reference to biology, classical cybernetics and the scientific method.


The "the problem of universals” not so much resolved as dissolved by the philosophy here.

The viewpoint is pragmatic, instrumentalised materialist, empirical and epistemological, drawing on biology and psychology.

The pragmatic, instrumentalist view is description and knowledge are tools that evolved alongside life.


This philosophy of systems promotes a type theory that allows for fuzziness and transience in the conformance of things to types. 

The premise here is that there were no concepts before conceivers, no descriptive types before life.

Type are instruments that life forms developed as side effects of biological evolution.

There is no type outside of a description encoded in a matter and/or energy structure.

And when all descriptions of a “rock”, “plant” or “circle” destroyed, that type will disappear from the cosmos.

The idea of an ethereal type is useless, redundant, and better cut out using Occam’s razor.

Mathematical concepts as realities

According to our philosophy of systems, where do numbers and other mathematical types and concepts come from?

Just as natural language is an instrument for description and prediction - useful in so far as it works.

So, mathematics is also an instrument for description and prediction - useful in so far as it works.

Like words, numbers are side effects of biological evolution, have evolved over time, and only exist in material forms.

This section explores this idea.

Recognizing and sharing quantitative knowledge

Primitive animals probably don’t classify things into rigid “types”.

But they can recognize “family resemblances” between similar things (e.g. food items, friends and cliff edges).

And learn to respond to similar things in appropriate ways.


Every earthworm knows enough to recognize another worm of the same type – for mating purposes.

Certainly, a worm can recognize other members of the worm family, but surely does count those it encounters.


Scientists have studied how far honey bees, dolphins and babies can understand a "quantity" of similar things.

We know many animals can recognize when a smallish family of similar things gains or loses a member

Experiments show dolphins can recognize which of two boards has, say, five dots rather than six.

And babies (before they have words) can recognize when a small group of things gains or loses a member.


The survival of a social group depends on its members sharing ideas, like where food can be found.

Social animals evolved to share quantitative knowledge using gestures and/or noises.

Honey bees can communicate the direction and distance of a pollen source.

Astonishingly, experiments suggest honey bees can count up to four and communicate that amount to other bees.

Numbers as quantitative types

Sentient animals evolved to recognize family resemblances.

Humans go further; they formalise the description of a family member into a “type”.

The proposal here is that all types and mathematical concepts emerged out of:

1.     the animal brain's ability to recognize "family members"

2.     the particularly human ability to more formally describe/symbolise a family member using words.


Numbers emerge from enumerating things – the members of a family - that resemble each other.

As soon as we have a family in mind, we can count the members of that family.

As soon as we can count the members of a family, we find some families have something in common.

That is, they share the number that enumerates how many members belong to the family.




<create and use>      <represent quantities of>

Mathematicians   <observe and envisage>  Families of things


Thus, a number acquires the status of a type (quality or concept) that can be instantiated many times.

Numbers are types that represent what families of the same size have in common:

·        “oneness” is the property shared by all families with one member

·       “twoness” is the property shared by any one-thing family to which we have added one.

·       “empty (zeroness)” is the property of any family (observed or envisaged) that currently has no  members.


It appears the Sumerians were the first people to develop a counting system.

And the number zero was invented later, perhaps independently by the Babylonians, Mayans and Indians

But surely the concept of an empty family was understood eons before that.


Quantifiable variables, such as “speed” or “height” can be regarded as types


Type name

Type qualities or attributes


The distance from bottom to top of a standing object


One thing that instantiates the type “height” is me.

My instantiation of the type is measurable as 1.84 metres, or 6 feet and 0.5 inches.

What does it mean say a number “exists”?

A type does not exist in a thing that instantiates it.

So where is it? To answer that question, we must decide what “exist” means.


Some mathematicians and take the view that a type is eternal, it exists outside of space and time.

They think of a type like “even number” as a “universal” or “Platonic ideal” that has existed since the cosmos began.

The alternative view here is that a type is a tool created to describe a thing.

It only exists when encoded in some mind (mysteriously) or record (using a known symbology).


For example, the current “largest known prime” is a number that exists in current records.

The next one exists only as a concept or type in current minds, as an envisaged possibility.

The next number (N) is not yet known, does not yet exist as instantiating the “largest known prime” type.


Suppose an instance of N already appears in a list of “odd” numbers, where its primeness goes unrecognized.

A mathematician may say that this N already exists in the three eternal, ethereal sets of “odds”, “primes”, and “largest known primes”.

But that is to use the word “exist” in a different way.


By this logic, everything that exists already instantiates infinite as yet undefined types, and is a member of infinite possible sets.

So, do all types and sets (all possibly-conceivable ones) exist eternally and ethereally?

This view of what it means to “exist” is an untestable and useless assertion, surely better removed using Occam’s razor.


Now suppose the “largest known prime” algorithm runs further and generates a second copy of N.

The new actor (the second N) plays the role labelled “largest known prime”.

The old actor (the first N) still plays the role called “odd number”, where its primeness goes unrecognized


But at any moment you can read any number (a discrete thing) and prove by testing it instantiates any number of type(s).

Because the type does not exist in the thing itself; the match of a thing to a type is an encoding or decoding process.

Mathematical entities as instruments

Many or most mathematicians are reluctant to believe that there were no numbers before mankind, or life.

But surely, you cannot have numbers until you have types, of which instances can be counted?

And you cannot typify things until there is some kind of intelligence?


There were always things that an intelligent observer will regard as similar.

In the history of the cosmos, this was first true at the level of atomic particles, then stars and planets.

So, there were always numerous similar things – which we can now regard instances of a type.

But numbers only existed the form of types when people started to create, remember and communicate types.


This instrumentalist and materialistic view of mathematics may seem radical or strange to many – especially mathematicians

But it seems enough for the purpose of describing “real machines” as “systems”.

The collection of things that instantiate a type

A type describes one thing, of which there is a collection.

That collection may contain any number of things (zero, one or many).

That number is the cardinality or quantity or extension of the collection.


Is a collection universal and eternal, or limited in space and time?

We could speak of all things that instantiate a type across the cosmos.

But our practical interest is more usually in things within our sphere of influence on planet earth.


We could speak of all things that instantiate a type over all time (past, now and future).

But our practical interest is more usually in things that instantiate a type right now.

Or things that instantiate the type for a period of time we are interested in.


Mathematicians usually think of a type as defining instances across all space and time.

However, you can limit the collection by extensional definition, or by including space and time constraints on the intensional definition of a set member.

Or by making set membership a decision, signified by assigning an identifier to a thing.


Type name

Type qualities or attributes

Registered vehicle

A vehicle with a registration number (regardless of its other attributes).


E.g. the designers of a vehicle registration system create types like “vehicle owner” and “vehicle”.

They don’t mean to an express an interest in every instantiation of those types in the lifetime of the cosmos.

They mean to classify only things observed or envisaged in the system of interest.

Can a collection be infinite?

It is perfectly legitimate to discuss infinite abstract mathematical objects and sets.

But the practical interest here is in modelling “real machines” in societies and businesses that are finite in reality.


Things have life times; and (because types are things we create and use) types have life times too.

We model things that exist in time and space (for a while), using descriptive types that also exist in time and space (for while).


E.g. consider modelling some regular behavior of a “real machine” as a “system”.

Having described a system, we can imagine it being instantiated by infinite real machines.

But in finite time and space, the number of real machines that can instantiate one system description is finite.


E.g. consider modelling the size of a collection of things using a number.

Given a number (say 8), we can imagine infinite collections that contain 8 things.

But in finite time and space, the number of real-world collections is finite.


E.g. consider types of number.

Given a type of number (such as “even number”) we can imagine an infinitely extendable collection of such numbers.

But in finite time and space, the number of numbers that can exist in minds, records and computers is finite.


For sure, we can posit the infinite extension of the set of prime numbers.

But our main concern is with things and types that demonstrably exist, or can be made to exist, in time and space.

And in the processes by which new instances of a type can be generated when needed.


The largest known prime number exists in material reality

The prime number beyond the highest calculated so far does not exist yet.

However, we can describe the process for generating the next largest known number.

Type theory as separable from set theory

This philosophy of systems is based on type theory that differs from the more rigid set theory you may be familiar with.

It promotes a type theory that allows for fuzziness and transience in the conformance of things to types. 

Types evolved before set theory

Animals have described things using types for millions of years.

Much more recently, types have been created and used by mathematicians.

Ancient peoples created and used the general concept of “number” to quantify the items in a collection.

About 5 thousand years ago, mathematicians introduced the type “zero”, to describe the emptiness of a collection that has no items.

About 2 thousand years ago, mathematicians created the decimal number system.

Less than 2 hundred years ago, the mathematician Cantor introduced the concept of a set - a collection of things.


Set theory is a branch of mathematical logic, and most often applied to mathematical concepts.

Traditionally, set theory begins with this relation: a thing can be a member of a set. 

A set is a collection of members; change the members and you change the set; or rather, you a create a new set.                                                                                                                                          


A set can be described:

·       by extension, by listing its members. E.g. The rainbow colours set is {red, orange, yellow, green, blue, indigo, violet}. 

·       by intension, by a type that lists one or more attributes of a member. E.g. A vehicle in the vehicle set has wheels, a weight and a fuel type.


So, to speak of a set, you need one or other way to define a member.

You need either a list of members (an extensional definition), or at least one type (an intensional definition).


Mathematicians usually think of a set as a collection of members across all space and time.

However, you can limit the set in two ways, first by extensional definition.

Or second, by including space and time limits on the intensional definition of a set member.


One type expressed in different ways

What at first sight appear to be two sets, with two different types, can turn out to be equal and the same set.


Type name

Type qualities or attributes

Doubled number:

A number exactly divisible by two.

Even number

A number greater than an odd number by one.


Since everything conforming to one type must conform to the other, there is only one set.


Two types that relate to the same or different sets

A set is identified with its members.


Type name

Type qualities or attributes

Your friend

A person whose personal number is in your phone right now.

My friend

A person whose personal number is in my phone right now.


Today, we have the same friends, and there is one set.

Tomorrow, when one of us adds or removes a friend from our phone list, there are two different sets.

Over two days, there have been three sets, but the two types have not changed.


Three types associated with overlapping sets

Where one set overlaps with another set, or is a subset of another set, there are different sets.


Type name

Type qualities or attributes


A homo sapiens who has lived, is living, or will live in the cosmos.

Person of interest

Extends “Person” with the constraint that the Person must recorded in our database

Person alive now

Extends “Person” with the constraint that the current time is after birth and before death


Clearly, we can associate sets with types.

But people created and used types eons before any set theory was established.

You may assume that once set theory was established, it embraced type theory.

But today, there several set theories and several type theories.


Although a type can be associated with a set, we can define and use types with no knowledge of sets.

And while a set is identified with a fixed number of members, there is no need to presume a type has a fixed number of instances.


All we need for our system theory is a simple theory of types as tools for describing things.

To change a type within a system is to change the system.

Replacing one set by another (with more or fewer members) doesn’t affect the design of a system or require system testing.

But replacing one type by another is more significant, since it does affect the design of a system and requires system testing.

Types can be fuzzy

Some mathematicians presume a type is monothetic, meaning every set member embodies every attribute included in the type.

Types in softer sciences, in social and business systems, are polythetic, meaning a thing may embody only some of its attributes.

And sometimes, no particular attribute is needed for membership of the typified collection of things.


Type name

Type qualities or attributes


An activity performed for enjoyment, or to practice some skill, or to win some prize, or to gain some advantage


Basic set theory doesn’t embrace polythetic types - in which the attributes of a type are optional.

Also, it doesn’t allow the conformance of a thing to a type to be fuzzy, or a matter of degree. E.g. the people who conform to the type “your friend”

Given such a fuzzy type, the extent of an associated set is debatable – two observers may associate different sets with the same type.

A new tractacus logico philosophicus

This philosophy of systems addresses questions debated by philosophers for millennia.

Ludwig Wittgenstein (1889-1951) influenced the “Vienna circle” of logical empiricists (aka logical positivists).

He argued philosophical disagreements and confusions can be resolved by analysing the use and abuse of language.

In his “Tractatus Logico-Philosophicus” he set out seven propositions.

The propositions are famous for being a tough read, and have been interpreted in various ways.

That doesn’t matter here, because Wittgenstein later realised his tractatus was self-contradictory.

In “Philosophical Investigations”, published after his death, he developed an entirely different linguistics.

He turned his focus from the precision of language to the fluidity of language.

He dropped the metaphor of language “picturing” reality and replaced it with language as a tool.


Here, we see language as only one tool for describing things, and start from this more general epistemology.




<create and use>     <represent>

Describers <observe and envisage> Realities


In so far as philosophy is about language, knowledge and truth, it seems to have been overtaken by biological and software sciences.

This philosophy of systems looks at description from the viewpoint of Darwinian biology.

It promotes the modern view of "knowledge" and "truth" as instruments that evolved alongside life.

It promotes a type theory that allows for fuzziness and transience in the conformance of things to types. 

It compares and contrasts this type theory with the more rigid set theory you may be familiar with.

And questions what it means for mathematical concepts to “exist”.


This new attempt at a “tractacus” is written from the perspective of a psycho-biologist rather than a linguist or mathematician.


1 A reality is something that exists in matter and energy, in space and time.

What we describe as reality is some part or aspect of the cosmos.


2 A description is created by an actor to represent a reality that is observed or envisaged.

A description is a model of a reality that is observed or envisaged.


3 A description is itself a reality

Descriptions are not ethereal; they are real and can be described.


4 A description (on its creation and in its use) has a degree of truth.

The words “true” and “false” may be read as judged to be “true enough” and “not true enough”.

Those judgements may be made differently by different observers on different occasions.

The scientific method is the best tool we have to determine how true an assertion is.


5 A description is fanciful to an actor who believes it represents an imaginary reality

However, it might later turn out to be true (we may yet discover unicorns).


6 Communication succeeds when the meanings/information in a description are near enough the same when encoded and decoded.

Communication is a process that creates and conveys a description (and/or other information) from a creator to a user.

The processes are performed by actors that may be animals or machines.


7 Communication requires speakers and listeners to share the same language for encoding and decoding a description.

A language contains a set of symbols used in the process of creating and using descriptions.

(Mostly, we talk about languages with verbal or graphical symbols, but symbols can also be gestures or even smells.)


8 To communicate, human speakers and listeners must share a great deal

They must largely share same language, psychology, biology, and experience of the world.

9 A description typifies what is described; it attributes general properties or qualities to particular things.

Every description could, potentially, be realised in several realities.


10 Natural language types are loose, fuzzy and flexible (as Wittgenstein observed).

However, the process of forming a system description involves formalising descriptive types.


11 A description may be a singular type (e.g. tasty) or a compound type (hot, tasty, liquid).

A system description, however large and complex, can be seen as a compound type.


12 Most descriptions/types are defined in a circular fashion in terms of other descriptive types.

E.g. A “rock” might be described/typified as “dry”, “perceptibly discrete entity”, “solid body” and “mineral material”.


13 To create a consistent and coherent domain-specific language we must start from some basic axiomatic types.

To describe a system, we must create a domain-specific language.


For more, read an ontology for system theory.

A table of philosophical dichotomies

The table below is an attempt to help me and readers compare and contrast the terms and concepts therein.

The second and third columns were edited from the three sources below.

·       The philosophy book. ISBN 978-1-4053-5329-8

·       http://digitalcommons.colby.edu/cgi/viewcontent.cgi?article=2829&context=cq

·       http://www.hbcse.tifr.res.in/jrmcont/notespart1/node9.html (this may be a dead link)


The first column contains my view, distilled from history of life on earth in The science of system theory.

Since posting the table in 2014 I’ve had many reservations about it.

Some terms are defined differently in other sources and/or have multiple meanings.

Some terms presented as “different” are arguably not opposites.

Some definitions depend on other terms, such as “existence”, whose meaning is debatable.

And some philosophical positions seem like meaningless babble to me.

In so far as philosophy is about language, knowledge and truth, it seems to have been overtaken by biological and software sciences.


My view

Some philosophical positions

Some different philosophical positions

On “existence

Matter and energy exist, but are mysterious, beyond our full comprehension.

All our perceptions, descriptions and mental models of matter and energy also exist in the form of matter and energy.

Idealism: existence is mental or spiritual.

Foerster’s Constructivist Postulate:

"Experience is the cause, the world is the consequence."

Materialism: existence is material.

Foerster’s Realist Postulate:

"The World is the cause, experience is the consequence."

The modern view is “cognitive embodiment”.

The mind is part of the body rather than separable from it.

Cognitive embodiment: mental states and activities are bodily states; the mind is inseparable from the body.

Cartesian Dualism: views the mind as standing apart from the body; the mind controls, interacts with and reacts to the body. (After Descartes)

Wisdom is the ability to respond effectively to knowledge in new situations

Knowledge is information that is accurate or true enough to be useful.

Knowledge represents what exists – to help us manipulate it or predict its behavior.



Information is meaning created or found in a structure or behavior by an actor.

Communication requires speakers and hearers to share a language for encoding and decoding the structure of behavior.

The Hermeneutic Principle: "The hearer, not the speaker determines the meaning of an utterance."

The communication principle: Speakers create meanings in utterances; hearers find meanings in utterances; communication succeeds when the created and found meanings are the same.

Data is a structure of matter/energy in which information has been created or found.

Facts are encoded in the data structure by a sender and can be decoded from it by a receiver.



Knowledge acquisition

The members of a social species necessarily see the world similarly.

They evolved the ability to perceive and communicate about the world.

They do this well enough to survive.

We humans learn from a mix of

1.      empirical experience of real-world entities and events

2.      logical deduction

3.      social interaction


Each kind of learning has helped our species to understand reality and manipulate it.

Perspectivism, radical constructivism and post-modernism are dangerous ideas that people use to undermine science and its importance to society.

Empiricism: knowledge is acquired from information obtained from the senses rather from reasoning.

Interpretative: we understand things by perceiving them.

Functionalism: we build mental structures through maturation and interaction with the world.

Cognitive constructivism: knowledge is acquired by creating mental structures in response to experiences. (Piaget)


Social constructivism: knowledge is acquired from social interaction and language usage, and is a shared rather than individual (Prawatt & Floden).

Epistemological Postulate: "He who organises his experience organises the world". The world is unique to each individual.

Radical constructivism: knowledge is acquired from experience, but is not, in any discernible way, an accurate representation of the external world or reality (von Glasersfeld).

Perspectivism: There is no objective truth; knowledge is conditional upon personal perspectives or interests. (Nietzsche)

Rationalism: knowledge is acquired by reason and logical analysis.

Formalism: we understand things by manipulating symbols. E.g. Mathematics does not require the existence of objects or properties.

On language

Whether there is some truth in structuralism or not, the human mind is plastic and language is infinitely flexible.

To describe a testable system, an artificial domain-specific language is needed.

Structuralism: we are born with structures that determine how perceptions (phenomena) of concrete things (noumena or a priori objects) are brought together and organised in the mind.

Structuralism in linguistics: language consists of rules that enable speakers to produce an infinite number of sentences. (Wilhelm Wundt (1832-1920) and Chomsky).

On determinism

At a micro level, the world as we experience it is deterministic.

We can predict the next discernible event - at least in theory.


At a macro level, the world we experience appears indeterminate.

The long-term outcomes of events are unpredictable (aka chaotic).


At a psychological and sociological level we have no reasonable or acceptable option but to treat people of sound mind as having free will.

Deterministic: every state and event is the consequence of antecedent states and events. This implies that prediction is possible in theory.

Deterministic automaton: a machine in state Si,

when it receives input Ij,

will go into state Sk and

produce output Ol

(for a finite number of states, inputs and outputs).

Self-determination: choices arise from reasons or desires (regardless of how the processes of choice work).

Indeterministic: a state or event is not wholly the consequence of antecedent states or events. This seems to imply some kind of randomness in state transitions.

Random: haphazard, not-predetermined. In maths it is a measure of how unpredictable a future state or event is.

Chaotic: disorderly. In maths it means behavior in which small differences in an initial state or event yield widely diverging outcomes (even though the system is deterministic, with no random elements). This makes long-term prediction impossible.

Both holist and reductionist views of a system are important and helpful different times. Enterprise architecture is deprecated by some “systems thinkers” as being reductionist.

The implication is that other kinds of “systems thinking” are better for being purely holistic.  In practice, both enterprise architects and systems thinkers take both views of systems.

Holism: treats a system’s parts as inseparable. The properties of the whole system are not the properties of any part. These “emergent properties” emerge only from the interaction between parts

Reductionism: explains the properties of one thing by the properties of another (lower level) thing. Or else, ignores the higher thing in favour of discussing the lower thing(s).