A philosophy of systems

A psycho-biological view of description and reality


Copyright Graham Berrisford 2014. Last updated 16/07/2020 12:38 One of a hundred papers on the System Theory page at http://avancier.website.


A philosophy of systems should help us to understand, identify and describe systems.

To do this, it must address questions debated by philosophers for millennia.

Notably, how do descriptions relate to realities?

You know a description is an abstraction from a reality, a map is not the territory it represents,




<create and use>     <represent>

Mappers      <observe>    Territories


But there is much more to be said.

This article does not say a great deal that is new.

It collates various views of description and reality, endorsing some and rejecting others.

But it does introduce and employ a new device – a triangle of the kind above – to relate describers, descriptions and realities.


The article uses the triangle to advance several arguments.

·       To show how abstraction underpins system theories (Bertalanffy, Ashby, Forrester, Checkland, Ackoff and others).

·       To reject some views expressed by Plato, Aristotle, Nietzsche and Wittgenstein.

·       To challenge the "semiotic triangle" and Peirce’s “triadic sign relation”.

And then to

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

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

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

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


PREFACE: some philosophy and some presumptions. 1

CHAPTER 1: Some psycho-biology. 1

A little psychology. 1

Information. 1

The message is not the meaning. 1

The ubiquity of coding and encoding. 1

Knowledge, truth and lies. 1

Description. 1

CHAPTER 2: The epistemological triangle. 1

Ways that describers describe realities. 1

What’s new? This epistemological triangle. 1

CHAPTER 3: Relating the triangle to other philosophies. 1

The criminalization of words. 1

Rebutting perceptivism and relativism.. 1

Other triangular philosophies. 1

Dissolving the problem of universals. 1

CHAPTER 4: What the triangle suggests about types, sets and numbers. 1

On descriptive types (REPEAT) 1

Types as biological phenomena. 1

The curious relationship of types to sets. 1

What the triangle suggests about type theory. 1

What the triangle suggests about numbers. 1

CHAPTER 5: Relating the triangle to system theory. 1

General system theory. 1

Particular system theories. 1

CHAPTER 6: More on philosophy. 1

A new tractacus logico philosophicus. 1

A table of philosophical dichotomies. 1


PREFACE: some philosophy and some presumptions


On describers, descriptions and realities

Philosophers debate the relationship of describers to descriptions and to realities.

“Systems thinkers”, who perceive and describe reality in terms of systems, run into the same questions.


"Internal cognitions do not reflect any external reality" one systems thinker.

Years after moving into our home, I noticed no pair of hot and cold taps is the same, and only one pair has red and blue dots on.

Surely, my cognition does reflect something of the reality out there?


“Each individual constructs his or her own reality” another systems thinker.

When I asked my wife if she had noticed all our taps are different, she replied “Yes, because I clean them.”

Surely, this shared perception is evidence that we can and do share some knowledge of reality?


The philosopher Neitzche argued no purely objective science can exist.

Because no concept or thought can exist outside the influences of an individual perception. 

In his “transcendental perspectivism”, each truth is the product of the perceiver.

However, he said, if two perceivers share a truth, then that truth transcends each individual perceiver.


Some distil Neitzche’s view by saying “shared perception is reality”.

The philosophy here rejects this: no description is the reality it represents.

A description, shared or not, is only a representation of a reality.

Sharing a description increases our confidence in its truth – meanings its degree of accuracy and usefulness.

But while descriptions are themselves real, no description, even a shared one, is the reality it represents.


On description and knowledge sharing as biological phenomena

Many philosophers have asked: What is reality? Does it exist or is it only imagined?

By contrast, a psycho-biologist asks: What is description, and what use is it?


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

Biologists describe how living things evolve and what they are made of; psychologists describe how they behave.

Psycho-biologists, who work at the intersection of those two sciences, naturally presume:

·       a reality is a thing (entity or event) we can observe and describe (or an assembly of such things).

·       there was no description of things before life.

·       description is a biological phenomenon that helps animals survive in the reality they perceive.


"… research highlights that the world we see is not the physical or the 'real' world.

Different animals have very different senses, depending on the environment the animals operate in,"

Professor Lars Chittka from Queen Mary's School of Biological and Chemical Sciences. https://www.bbc.co.uk/news/science-environment-11971274


For sure, how we see things is shaped by what species we belong to, and our personal experience of the world.

Does this mean we are all delusional? What we see as meaningful is only derived from our evolutionary and personal history?

No. Our neural systems evolved to enable us to perceive and remember something of what exists out there in the real world

Our survival depends being able to do this reasonably well, most of the time.

You and I share much by way of biology, psychology and experience.

And like all social animals, we can share descriptions of reality in messages.


That social animals do share knowledge is demonstrated whenever they cooperate successfully.

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

E.g. Honey bees share knowledge of where pollen can be found, using the form of a dance.

Humans also communicate using body language, postures and gestures.

More interestingly here, we describe things, in memories and messages, using verbal concepts, types and numbers.

On the presumption that our descriptions can represent realities well enough for practical use.



Descartes started his philosophy from the premise “I think therefore I am”.

In effect, psycho-biologists presume rather more than that.


·       Space and time exist in a physical sense.

·       Other physical phenomena - things and their effects - exist out there in space and time.

·       Things that exist include you, me and other people we can communicate with.

·       We can perceive things, remember things and recall things.

·       We can describe things in memories and in messages.

·       By exchanging messages, we can communicate and share knowledge of things that exist.


On descriptive types

Description is so fundamental to human existence that we have countless words for how we describe things.

We describe a thing using relevant descriptive types.

·       E.g. In general, a human body has height and shape property types.


We describe a particular thing as instantiating its descriptive types.

To instantiate a type is to embody, exhibit, exemplify, manifest or realize the type in a particular value.

·       E.g. In particular, one body’s height is 2 metres and its shape is humanoid.


Unfortunately, we are sloppy about distinguishing types from instances.

And confusingly, we refer to both general types and particular values as qualities, properties, concepts, characteristics, and attributes.


You may presume descriptive types are ethereal - they exist eternally, above and outside of time and space, as “Platonic ideals”.

How does that sit with the idea that knowledge is a biological phenomenon?

For most of this article, it makes no difference whether you believe types are eternal and ethereal or not.

However, you don’t need to presume any descriptive type exists outside of the physical world in a metaphysical way.

CHAPTER 1: Some psycho-biology

Presuming there is a reality out there, what does it mean to describe it?

There is no shortage of opinion on the matter.


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

·       “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).


We know animals of different species see the world somewhat differently. E.g. Birds and bees can see ultra-violet light

Demonstrably however, animals can perceive and remember things, and test those conceptualisations against reality.

They could not find food to eat without objective-enough knowledge of the world.

A little psychology

The philosophy here is about things people can observe and envisage in space and time.

Especially, systems that contain actors (structures in space) that perform activities (behaviors over time).

Perception and sensation

Perception is the process that turns an input message into a sensation (model or image) we can respond to.

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 does nothing but focus the signal received; the retina may do more.

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

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

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


According to research discussed in this talk by Anil Seth, 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 - and 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 see is not purely fanciful; it is what a mix of what sensors detect, and inheritance and experience predict is likely to be true.

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


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 can be tested by using it.


How animals retain and recall memories is not important to the philosophy here.

This section is included to answer some readers’ questions.


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

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

Here it doesn’t matter how memory works.

All that matters is that we can observe the retrieval of meaningful information that was stored earlier.

E.g. As we see a honey bee communicate the location of pollen that it observed earlier.


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

McCullough, Pitts and others realized that a cyclic network of artificial neurons could act as a system with memory.

At first, some hoped they were identifying how the brain works, but by 1960 experiments suggested otherwise.

And by the way, other experiments have shown that most people find it difficult to apply the rules of logic.

It seems the human brain evolved, not to work logically, but to handle the complexities of human social interactions.


The brain does not store persistent data structures as a computer does, our mental images may be incomplete, fuzzy and malleable.

But it certainly does store information; how else could you describe a dollar bill to somebody?

So, while how human memory works is not understood, its presence can be inferred.

Evidently, the brain is not empty; it contains mental models that represent some features of entities and events perceived.

To remember and recall those features is to perform processes that create and use those mental models.

Knowledge acquisition

How animals learn is not important to the philosophy here.

This section is included to answer some readers’ questions.


Cognitive psychologists speak of procedural knowledge and declarative knowledge.

We learn both how to perform procedures:

·       physical procedures (e.g. to walk, to swim, to sing, to play the piano)

·       cultural procedures (e.g. to say please and thank you)

·       logical procedures (e.g. multiplication, algebra).

And learn descriptive types or facts:

·       physical facts (e.g. touching a hot plate is painful)

·       cultural facts (e.g. the colors of the rainbow)

·       logical facts (e.g. abstract patterns or types from observations, as in “machine learning”).


How knowledge is acquired is peripheral to this article, but for your interest, it might be acquired by:

·       inheritance (cats know to chase mouse tails, babies know not to crawl over a cliff edge).

·       practising a skill (to walk, to swim, to sing, to play the piano)

·       conditioning (after which we know not to touch a hot plate)

·       intentional trial and error (which key fits the lock?)

·       observing and copying another (how monkeys learn to use tools)

·       logical deduction (how Einstein found e = mc squared)

·       instruction or education (from a teacher of any kind).


Also peripheral to this article is the division that some make of knowledge into three kinds.

·       Explicit knowledge - expressed in a shareable description - like the colors of the rainbow.

·       Implicit knowledge – currently known in one or more minds, but not yet made explicit.

·       Tacit knowledge - cannot be articulated – like how to swim.


Polanyi said "in the end all knowledge is personal and tacit", but it is misleading to interpret this as meaning no knowledge is shareable 

Moreover, we do teach people to swim and to play music, so even tacit knowledge can partly be made explicit.


Here, how knowledge may be acquired or classified matters less than how it is communicated by encoding in memories and messages.


Ludwig von Bertalanffy said general system theory is much concerned with information.

Ashby’s cybernetics, which is a central pillar of general system theory, is also much about information.

So, what is information? And how does it differ from data?

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

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

This section distinguishes them using a simple ontology.


Several variants of a WKID hierarchy have been proposed and criticised. For example:


The WKID hierarchy below makes more sense than some.

Not especially the distinction between data, the physical signal, and information, the logical meaning encoded in and/or decoded from data.





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


Here “structure” may be read to embrace both data structures and process structures like the honey bee’s dance.

Humans can - with almost no effort - form countless structures in the form of 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

·       encode/create some meaning in a structure, and

·       decode/find some meaning in a structure.

So, information is meaning that only exists when and where actors encode or decode structures/signals.


A bacterium can encode information in DNA or RNA structure and pass it to another bacterium.

The second bacterium will process that data structure in the only way that the laws of chemistry dictate.


Human communication is far more flexible.

As Ashby might say, we cannot discuss the mysterious ways in which a brain works; we can discuss only what is observable of its abilities and actions.

We can observe that social animals succeed in conveying some of their ideas to other animals.

And human speakers encode meaningful information in words, and convey it to other humans.


Suppose you send out an SOS message, intending it to convey some meaningful information.

On receiving your message, I can only interpret it as you intended if I know the code you used.

Suppose I think SOS means Send Over Sausages, then I will extract one meaning from your message.

In reflection, after worrying about it, I might Google the meaning of “SOS” and decode your message second time, and so extract a second and different meaning.


In short, the association between message and meaning is not 1-1, since one message can convey several, potentially incompatible, meanings.

To encode an intended meaning in a message, or decode and interpret a meaning in a message, is a process.

Each meaning is inextricably associated 1-to-1 with a process that encodes or decodes the message.


Having said that, 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. when the knowledge of where to find some pollen is communicated by one honey bee to another.


Suppose a sender broadcasts an SOS message to any and every actor able to receive it.

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

Or else, it might be fake news, a lie, intended to waste the time of its receivers, in which case it conveys misinformation rather than knowledge.



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.

The message is not the meaning

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

One actor (sender) encodes some meaningful information in a message.

Another actor (receiver) decodes the same meaningful information from that message.

Successful communication requires the sent and received meanings to match - near enough.


An actor can use any kind matter/energy structure to convey a message

Consider a cave wall drawing, or honey bee’s wiggle dance.

And humankind has developed the astonishing phenomenon of verbal language.


Suppose somebody sends you a message saying: “I saw a man on a hill with a telescope”.

That sentence is a data structure or description that represents an observable reality.

Yet different receivers, might understand the message to mean:

·       There was a man on a hill, who I saw through a telescope.

·       There was man on a hill, who I saw has a telescope.

·       There was a hill that had on it both a man and a telescope.

·       I was on a hill, and from there saw a man using a telescope.

·       There’s a man on a hill, whom I’m sawing with a telescope.


So, where is the meaning of the message?

It does not exist in the sentence alone, or in the ether, regardless of any actor.

It exists only in the processes of encoding and decoding the message.


How to ensure meanings intended by speaker and interpreted by listeners are the same?

Given the fluidity of natural language (both vocabulary and grammar) one verbal message can be read many ways.

Verification tools include iteration, evidence and controlled languages.



If you cannot interpret a message, you can request a different message to convey the same meaning, and so on.

E.g. if an SOS message is not understood, the sender might send another message say Help!

That kind of iteration is very common in human discourse using natural language.

The receiver may stop the iteration when only one meaning is interpretable from the message, or a time-out of some kind is reached.


Empirical evidence

Having interpreted a message has having one meaning, you may still not be confident you have interpreted it as intended.

However, you (or an observer) may observe your interpretation is confirmed by the receipt of subsequent messages.

And as in all science, for as long as things turn out as predicted, a sufficient degree of confidence is established


Controlled languages

Another way to minimise misunderstandings is to use a more formal or controlled language.

The language used by mathematicians is the most controlled we have.

If one says the shape of a planet’s orbit is an ellipse, you can be sure another will get the meaning.

But even then, only because the two actors share the same language.


Remember, the message is not the meaning

It seems people tend to assume the meaning of a message or memory is found in its structure.

Yet after considering examples, on reflection, we must separate meanings and structures.

Given one message, meanings can be found in the intention of the message sender/encoder, and the interpretations of message receivers/decoders.

Given one memory, meanings can be found in the perception of the registrar/encoder, and the interpretations of readers/decoders.

If the message or memory structure is preserved perfectly, and decoding is a reversal of encoding, then it will have only one meaning.

Else, one message or memory can have many meanings.


Again, in short, the association between message and meaning is not 1-1, one message can convey several, potentially incompatible, meanings.

To encode an intended meaning in a message, or decode and interpret a meaning in a message, is a process.

Each meaning is inextricably associated 1-to-1 with a process that encodes or decodes the message.

The ubiquity of coding and encoding

We encode descriptions of the world internally in our memories

Nobody understands the mysterious processes by which conscious knowledge is encoded in and decoded from our biochemistry.

But we do understand those processes exist.


We also encode descriptions in messages to share them with others.

Messages can contain descriptions, decisions and directions, and questions and answers, relating to activity performed.


Communication involves a succession of coding and decoding steps – down and up a communication stack.

E.g. a speaker’s conscious thought is encoded in neural impulses, then vocal chord movements, then sound waves.

Then from sound waves to ear drum movements to neural impulses and conscious thought in the listener


Ashby wrote of “the ubiquity of coding” in the communication of information.

“Let us consider, in some detail, the comparatively simple sequence of events that occurs when a “Gale warning” is broad-cast.

It starts as some patterned process in the nerve cells of the meteorologist, and then becomes

·   a pattern of muscle-movements as she writes or types it, thereby making it

·    a pattern of ink marks on paper. From here it becomes

·    a pattern of light and dark on the announcer’s retina, then

·    a pattern of retinal excitation, then

·    a pattern of nerve impulses in the optic nerve, and so on through her nervous system. It emerges, while she is reading the warning, as

·    a pattern of lip and tongue movements, and then travels as

·    a pattern of waves in the air. Reaching the microphone it becomes

·    a pattern of variations of electrical potential, and then goes through further changes as it is amplified, modulated, and broadcast. Now it is

·    a pattern of waves in the ether, and next

·    a pattern in the receiving set. Back again to

·    a pattern of waves in the air, it then becomes

·    a pattern of vibrations traversing the listener’s ear-drums, ossicles, cochlea, and then becomes

·    a pattern of nerve-impulses moving up the auditory nerve.


… this very brief account mentions no less than sixteen major transformations

through all of which something [the intention] has been preserved,

though the superficial appearances have changed almost out of recognition.” (1956, 8/2)


After receiving and remembering a message, a listener can verify the accuracy of the Gale warning

Symbols used to encode meaning

Actors can describe a thing by imitating it. E.g draw a circle in the air, or describe an airplane by building a model airplane.

Our main interest here is in descriptions that symbolize things.


Fixed-meaning symbols

Consider that one bird (a receiver) can understand the alarm call made by another bird (a sender).

Prior to exchanging that message, the sender and receiver might have been entirely unknown to each other.

They can communicate because they both inherited the same language or code for encoding and decoding the message.


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

And another bee can decode that dance to create their own mental model of where that pollen is, and then find it.

This demonstrates the two bees succeeded in shared some knowledge of the world.

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


The languages of alarm calls, honey bee dances and facial expressions are rarely ambiguous.

Because those languages are inherited, and designed by nature to convey very specific meanings.


Flexible-meaning symbols

Humankind brought many innovations to communication.

We inherit the capability of speech – of speaking and hearing words - using sound waves to symbolise meaning in messages.

It cost us almost nothing to speak, and the set of sounds we can use for communicating is infinitely flexible.

The cost comes in the effort to learn to speak and write, and interpret what we hear and read.


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

We may reduce ambiguity by repeating our message in different words, or by testing understanding (asking, “know what I mean?”).

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

People use controlled vocabularies or domain-specific languages in which words and phrases (like SOS) have agreed meanings.

Knowledge, truth and lies

In this article, knowledge is information accurate or true enough to be useful.


Does truth have any meaning in a world without description?

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

And scientists are concerned to verify the accuracy or truth of descriptions.

The fuzziness of truth

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 rely on these laws being useful, and regard them as true.

Our lives depend on engineers having applied these laws to physical situations.

Yet three centuries after Newton, Einstein showed the second laws fails when objects move closer to the speed of light.


Even in such a hard science, there is no absolute truth, only degrees of truth - or confidence - in the accuracy and usefulness of a description.

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


The scientific method formalises our natural approach to experience.

Science is based on creating theories and testing that the real-world behaves as the theory predicts.




<create and use>      <represent>

Scientists    <observe and envisage>    Realities


The graphic above is the first appearance of the epistemological triangle to be explored in depth later.

The philosophy here allows there can be fuzziness in how closely realities conform to theories, or instances conform to types.

Three ways to evaluate truth

How to verify a description or the information we decode from it?


Suppose you see a honey bee finds some pollen where another honey bee has (by dancing) described it to be.

Evidently, the two bees have shared some knowledge - the distance and direction of the pollen source.

In other words, both of their mental models represent reality accurately enough for you to call them “true”.

And both mental models are “objective” in the sense that they are not limited to one intelligence – and are confirmed by empirical evidence.


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

The advance of science involves not only testing of results against predictions, but also logical analysis and peer group review.

Which is to say, a theory, model or description can be empirically, logically and socially true.


Empirically true - supported by evidence from test cases.

Information can help you predict what exists and happens in reality.

E.g. You buy a map and then find your way to a place via a route described on that map.

E.g. You hear a warning to step off a railway track, and then do so, thus avoiding on-coming train.


Logically true - can be deduced from other concepts within a body of knowledge.

Information may follow logically from axioms (presumed truths) that a domain 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.


Socially true - widely shared by others in whatever social network you refer to.

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


Evolution must have favoured social animals that communicate what is empirically true, since that helps them to survive.

But humans are surely unique in the extent to which they spread and believe “fake news”.

Now the internet has become a tool people use to spread and confirm false prejudices, perhaps the teaching of science and logic is ever more important?


The term “description” might be used in two senses.

·       A physical form: a data structure in/from which meaningful information is encoded/decoded.

·       An intent, perception or interpretation: some meaningful information created or found in a data structure.


Here, a description is the first of the above.

And to recap (because it is counter intuitive) there is no meaning in a description on its own.

Meanings exist only when actors create and use descriptions.

Descriptions as types (IMPORTANT!)

“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.


IOW, every description is a class or type that may be realized in many physical instances.

·       Physicists, having described one universe, can posit the existence of infinite other universes.

·       One symphony score may be embodied or realized in many symphony performances – by orchestras.

·       One set of building architecture drawings may be embodied or realized in many concrete buildings – by builders

·       One business system architecture description may be embodied or realized in many physical systems – by actors.


In each case, the description is a type that may be embodied or realized in many instances - by real-world entities.

A type is an expression or description – whether in mental or documented form.

An expression or description of a type is the type – which is translatable from mental to documented form and back again.

A description can be a very large and complex type, composed of smaller complex types, all the way down to primitive simple types.


What does a system architecture description express? The types to be instantiated in a physical system.

What does a system embody or realize? The types expressed in an architecture description.

Who conceives the types and translates them from a fragile mental form into a documented form? The system architects.

Demonstrably, we can test realities match descriptions

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

We evolved to maintain descriptions in our memories and communicate descriptions.

We can create and use descriptions of many kinds, narratives, drawings, three-dimensional models and maps.




<create and use>     <represent>

Mappers       <observe>     Territories

Demonstrably, knowledge can be shared

We don’t know how the brain works, but it is reasonable to speak here of mental models.          

In one sense, a mental model is unique to the mind that holds it.

Your mental model of an apple is bio-chemically distinct and different from mine.

Nevertheless, though your brain is unique to you, I can communicate some knowledge of an apple to you.


Communication succeeds when the meaning encoded in and decoded from a message are (near enough) the same.

How to verify that?

Scientists are cautious about saying any statement is true.

However, it is easy to verify that some knowledge has been shared.

·       You find your way to a place on a map.

·       You find an apple where I tell you it was, and eat it.

·       You ask someone to call you at 11.00 hours, and they call you at the appointed time.


A third party can test a message receiver succeeds in interpreted the intended meaning in a message.

Observers can look for evidence that a message receiver succeeds in responding as intended by the message sender.

E.g. observers see a customer places an order with a supplier, who responds by invoicing the customer.

This demonstrates customers and supplies share some knowledge of how to conduct business.

Demonstrably, a communication may fail or deceive

Actors may misread a message.

They may hallucinate (perceive something where there is nothing).

They can miss-remember or forget a memory.


There are accidental lies.

Actors may read a message correctly, yet find it to be a poor representation.

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.


There are deliberate lies.

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.

CHAPTER 2: The epistemological triangle

Questions debated by philosophers for millennia include how do descriptions relate to realities?

You know a map is not the territory it represents, and a description is an abstraction from a reality.

But there is much more to be said about the relationship.

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

This part introduces a new triangular way of relating epistemological concepts, and relates to other ways of thinking.

Ways that describers describe realities

We evolved to maintain descriptions in our memories, and to communicate descriptions in verbal messages.


Description in the mind

Description in writing

 Mental models

<form and recall>         <represent>

Animals           <observe>        Realities


<write and read>         <represent>

Humans          <observe>        Realities


Bear in mind that since describers and descriptions are also real, we can describe them too.

And we can create and use descriptions of many kinds, narratives, drawings, three-dimensional models and maps.



A mapper is concerned with two things, a map and a real-world territory.

1.     A map is a description composed of abstract descriptive property types.

2.     A territory is a reality composed of concrete embodiments of those types in observable values.




<draw and read>         <represent>

Mappers       <observe>     Territories


Note that one territory can be described in many different maps, showing a different selection of features.

We can test how accurately - allowing some fuzziness - a territory is represented in a map.



Imagination is essential to scientific advance, but it builds on existing knowledge (useful information).

Imagination not based on knowledge may lead to nonsense or fantasy.

Einstein was a lot more knowledgeable than some might lead you to believe.

"The 12-year-old Einstein taught himself algebra and Euclidean geometry over a single summer, and discovered his own original proof of the Pythagorean theorem. 

Max Talmud says that after he had given the 12-year-old Einstein a geometry textbook, after a short time he “had worked through the whole book.

He thereupon devoted himself to higher mathematics... Soon the flight of his mathematical genius was so high I could not follow."

His passion for geometry and algebra led the 12-year-old to become convinced nature could be understood as a "mathematical structure".

Einstein started teaching himself calculus at 12, and as a 14-year-old he says he had mastered integral and differential calculus". Wikipedia



Mathematical structures

<create and use>           <represent>

Physicists   <observe and envisage>   Nature



Before life, light existed and was reflected from the surfaces of objects.

But no color existed in the world then, either as a sensation or a description.

Experiments show animal brains manufacture the sensation of color, from a mixture of the light they perceive and their experience.

In the first place, a color is a sensation in the neural system, which acts to describe some light radiation, modified by what our brain expects to see.

After that, a color can be a verbal description of that sensation – as in Isaac Newton’s rainbow, or a color chart, or a wave length range.


Colors in biology

Colors in Newton’s rainbow

 Visual sensations

<form and recall>     <represent>

Animals      <observe>    Light waves

Seven colors

<named>        <represent>

Newton    <observed> Visual sensations



The structure of a building in reality, independent of any observer, is infinitely complex and incomprehensible.

Given a building, the word architecture might be used for:

·       the visual sensation of building formed by an observer (as seen in reality or in a photograph)

·       one or more architectural drawings of the building (of which several different sets might exist).


Architectures as sensed

Archiectures as drawn

 Visual sensations

<form and recall>     <represent>

Humans       <observe>     Buildings


<create and use>     <represent>

Architects <observe and envisage> Buildings



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

Some focus attention of the use of verbal language to describe things, as in triangles of this kind.


A linguistic philosophy 1

A linguistic philosophy 2

Verbal symbols

<expressed in>     <represent>

Mental models  <conceputalise>  Realities


<express ideas in>     <represent>

Actors w memories <conceputaliseRealities


Read other triangular philosophies for a critique of triangular models such as.

·       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.

What’s new? This epistemological triangle

Linguistics is not the starting point here, since even without words, animals can remember and communicate descriptive facts about the world.

The innovation in our epistemological triangle below might be generalised as moving:

·       From the sociological: Actors with a memory <express ideas using> Messages <represent> Realities.

·       To the psycho-biological: Actors with an intelligence <create and use> Memories and Messages <represent> Realities.




<create and use>    <represent>

Describers <observe and envisage> Realities


Describers are actors that create and use descriptions to remember or convey information about any conceivable part of reality.                             

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

Describers create and use descriptions

Look to the left-hand side of the triangular relation.

Describers are intelligent actors (natural or artificial) that can encode and decode descriptive models of realities.

Descriptions embrace all kinds mental and digital models, speech and writings, paintings and physical models.




<create and use>   <represent>

Describers <observe and envisage> Realities


Ashby observed that in the creation and use of descriptions “coding is ubiquitous”.

To create a description is to write or encode a model (mental, documented or other kind) that represents some feature(s) of reality.

To use a description is to read or decode a model, and use it in any way, perhaps to respond to or manipulate the reality that is described.

Describers observe and envisage realities

Look to the bottom side of the triangular relation.

Describers are intelligent actors (natural or artificial) that can encode and decode descriptive models of realities.

A reality is anything that can be observed or envisaged in time and space, including descriptions and describers.




<create and use>   <represent>

Describers <observe and envisage> Realities


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.

Neither of those exist in material reality today, but we can describe them, and infinite other possibilities.


Some portions or aspects of the cosmos that do exist may never be envisaged or observed by describers.

Conversely, some realities envisaged by describers (e.g. unicorns) may never actually be realized in the cosmos.

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

Descriptions represent realities

Look to the right-hand side of the triangular relation.

Descriptions embrace all kinds mental and digital models, speech and writings, paintings and physical models.

A reality is anything that can be observed or envisaged in time and space, including descriptions and describers.




<create and use>    <represent>

Describers <observe and envisage> Realities


This section looks at descriptive representation from the viewpoint of Darwinian biology.

The premise here is that there was no description of reality before life.

And description is a tool that emerged as a side effect of biological evolution.


In thinking about descriptions of the world, you might be drawn to a study of linguistics.

This philosophy rejects the idea that communication started with words.

Because animals recognized things for billions of years before they attempted to communicate more than mating intentions.

And social animals described things to each other for millennia before humankind could forms words.


How and why did processes for encoding and decoding memories and messages evolve in animals?

Consider some stages in the evolution of description.

1.     Molecular memory: organisms recognize molecular structures.

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

3.     Social 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.


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 thing in reality, an animal must have access to a description of it.

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

And there can be fuzziness in how accurately descriptions in memories and messages represent things.

A description does not have to be perfect, it need only represent a reality well enough to enable recognition.


·       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.


In short, a description does not have to be complete or perfect, it only has to be useful.

The question is: Does it help an animal to understand, predict and manipulate things in reality?

Recursion in the triangle

The triangle is recursive in the sense that realities include descriptions and describers.

Both describers and descriptions can be observed, envisaged and described.


Descriptions are realities

Descriptions embrace all kinds mental and digital models, speech and writings, paintings and physical models.

A description is a real-world entity, a physical matter/energy structure, which can be described.

Descriptions held in internal memories and external messages are different

Yet they are similar in the most important way; they are created to be 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.


Describers are realities

Describers are intelligent actors (natural or artificial) that can encode and decode descriptive models of realities.

A describer is a real-world entity, a physical matter/energy structure, which can be described.


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 are applied to the data.

CHAPTER 3: Relating the triangle to other philosophies

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

This section uses the epistemological triangle to challenges other views.

The criminalization of words

The philosophy here emphasises that successful communication requires two meanings (one encoded, one decoded) to match - near enough.

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

The hermeneutic principle is sometimes taken to mean that receivers alone determine the meanings of the words they hear/read.

And some sociologists promote the principle that the meaning of a message is determined only by its receiver.


This has led some into a poisonous kind of “identity politics” in which some words are criminalised for offending people..

Better, we neither assume nor grant the right never to be offended by words, but

·       take no offence at being accurately described

·       do not assume a word for a skin color means any more than that, and

·       accept with good grace that others may disagree with us.

Rebutting perceptivism and relativism

Some sociologists and philosophers (somehow related identity politics)  appear to deny the concept of objective knowledge.


·       “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).


Some are extremist relativists who say “perception is reality”.

Some go as far as to deny the objective reality of systems that are amenable to scientific analysis.

Objectivity is NOT a delusion

The distinction between subjective and objective views is far from simple.


A subjective view is more fallible because it is personal, and influenced by an individual’s feelings, tastes, or opinions.

We regard an observation as subjective if we believe it is shaped by a person’s preconceptions and experiences.


An objective view is not infallible; but it is verifiable empirically and/or logically, and probably shared by two or more observers.

Objectivity is distinguished from subjectivity by how we make observations.

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

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


True, in quantum physics, where observing something changes it, an observer-independent view of reality is impossible.

But at the level of classical physic, where we describe biological, social and technological systems, an observer-independent view is possible.


Given an observation made by only one observer, you may suspect it is subjective.

Given two observations, by two observers, which are the same, you more likely regard them as objective, pending supporting evidence.

The more observers and observations lead to the same description of reality, the more objective you will consider.

The objectivity of Newton's description of force (f = ma) is revealed in its successful use, every day, all over the world.


In short, to transcend our subjective experience, we use science, logic and peer review (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.

Perception is NOT 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.


For 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

Yes, 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.


Evidently, two honey bees can share some knowledge - the distance and direction of a pollen source.

Their mental models are objectively true in that they are a) not limited to one intelligence and b) demonstrably confirmed by empirical evidence.


Relevance to system theory?

This philosophy rejects that idea that every subjective or widely-believed assertion carries the same weight as science.

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

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

“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.”

However, von Bertalanffy did not deny objective knowledge.

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

Other triangular philosophies

Read other triangular philosophies for a critique of other triangular models.

·       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.


Dissolving the problem of universals

Philosophers draw a contrast between particulars and universals.

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

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




<create and use>       <typify>

Describers  <observe and envisage> Particulars


Universals are sometimes called types, qualities, properties, concepts, characteristics or attributes.

The “problem of universals” is the question of whether universals exist as real things or ethereal things (or else, what it means to “exist”).


You may presume descriptive types are ethereal.

In other words, they exist eternally, above and outside of time and space, as “Platonic ideals”.

How does that sit with the idea that knowledge is a biological phenomenon?


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

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

The question arises: do descriptive types exist in real and/or ethereal forms?         

How has the problem of universals been answered in philosophy?

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.


Since Plato and Aristotle, philosophers have developed a confusingly diverse and overlapping set of positions.

Today, simply put, I believe idealism may be contrasted with realism as follows.


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


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.


But it seems to me there something fundamentally wrong, or misleading, about the contrast drawn above.

On the one hand, pragmatic system theorists tend to see themselves as realists and empiricists; and some promote what us called scientific realism.

Yet at the same time, the Darwinian psycho-biological philosophy of systems in this article is compatible with idealism and solipsism.


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

And 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, whether in our biochemistry or 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 this article, which is largely what I read as said or implied by Darwin and Ashby alone.

For me, today’s, philosophical positions overlap in confusing ways; and some seem to turn the idealism/realism distinction on its head.

How is the problem of universals answered here?

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

You could say it is pragmatic, instrumentalist, materialist, empirical and epistemological.


Is the philosophy a kind of realism or idealism? You could say both.

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

As Maturana said, knowledge is a biological phenomenon.

It isn’t that concepts exist out there, sooner or later to be encoded somewhere in biological entities or their records.

It is that biological entities (and now their computing devices) abstract concepts (like “round” and “yellow”) from what exists and happens.

The descriptions that describers create can be located in space and time, in mental and documented models.

They exist in brains, in computers, on paper etc.


E.g. Consider the concept of an ellipse.

In truth, planets don’t orbit in ellipses, they only approximate to that model of their behavior.

The concept of an ellipse is an idealised description of a reality, encoded in countless mental and documented models

For sure, planets moved (approximately) in ellipses before the concept of an ellipse was thought of,

And they will probably still being doing it after all descriptions of an ellipse have been erased from the universe.

But by that time, the concept of an ellipse will no longer exist in any physical or material form.


Many believe or propose that every concept exists for eternity in a metaphysical sense, but this has no practical implication or use.

Using Occam’s razor, we can cut it out of our philosophy with no loss; and scientists are favour of discarding what is redundant.

CHAPTER 4: What the triangle suggests about types, sets and numbers

This philosophy is centred on the epistemological triangle.

It takes the view that description and knowledge are instruments that evolved alongside life.

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

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

On descriptive types (REPEAT)

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

To describe a thing (e.g. a drawing of the sun) is to typify it (e.g. as a “round” and “yellow”).


Description is so fundamental to human existence that we have countless words for how we describe things.

We describe a thing using relevant descriptive types.

·       E.g. In general, a human body has height and shape property types.


We describe a particular thing as instantiating its descriptive types.

To instantiate a type is to embody, exhibit, exemplify, manifest or realize the type in a particular value.

·       E.g. In particular, one body’s height is 2 metres and its shape is humanoid.


Unfortunately, we are sloppy about distinguishing types from instances.

And confusingly, we refer to both general types and particular values as qualities, properties, concepts, characteristics, and attributes.


You may presume descriptive types are ethereal - they exist eternally, above and outside of time and space, as “Platonic ideals”.

How does that sit with the idea that knowledge is a biological phenomenon?

For most of this article, it makes no difference whether you believe types are eternal and ethereal or not.

However, you don’t need to presume any descriptive type exists outside of the physical world in a metaphysical way.

Types as biological phenomena

Before life, light existed and was reflected from the surfaces of objects.

But no color existed in the world then, either as a sensation or a description.

Experiments show animal brains manufacture the sensation of color, from a mixture of the light they perceive and their experience.

They also show that we perceive the same light waves as different colors, depending on the situation.

For more on color perception, read https://www.bbc.co.uk/news/science-environment-14421303.


Surely the concept of an elephant did not exist before elephants evolved, before their kind came to be encoded in some DNA?

When we define the elephant type in words, we encode it in another kind of description.


For sure, the planet type did not exist before life, it is a construct of the human mind.

The truth of the statement “Pluto is a planet” depends on how that type is defined.
And what is true has changed, as astronomers define and redefine the planet type.


The things we describe (as elephants and planets) exist in time and space.

The descriptions we create (of “elephant” and “planet) also exist in time and space.


The orbits of real planets (being pulled by gravity in many directions) are never perfect ellipses.

Where does the general concept or type called ellipse exist?

Plato believed the concept or type exists in an ideal or ethereal sense.

It makes no practical difference here whether you agree with Plato or not.

Because the only types we can discuss are ones encoded in our minds and other descriptive forms.


In short, this philosophy presumes that types 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.

The curious relationship of types to sets

For millions of years, social animals have described things using symbolic gestures or sounds – as an alarm call symbolise dangers.

Over many thousands of years, people have described things by typifying them verbally – as an elephant, a planet, or round and yellow.

Some words represent mathematical concepts – a triangle, an ellipse, and of course, a number.


Many animals can recognise the difference between there being one, two or three things of a type.

Ancient peoples quantified the items in a collection using words to represent numbers.

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.

Wittgenstein use the example of “game”, which I have tried to define below, with no confidence of convincing you.


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.

What the triangle suggests about type theory

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


This philosophy is centred on the epistemological triangle.

And takes the view that description and knowledge are instruments that evolved alongside life.

This part:

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

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

From family resemblances to quantification and numbers

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.


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.


Given different intelligent species on different planets live in the same universe, they will recognize the same patterns.

They will evolve and learn to:

1)     detect much the same family resemblances between similar things.

2)     formalize those into similarly defined types (e.g. “star”, “planet”, “plant”, “parent” and “river”).

3)     judge whether a thing is an instance of type or not (lead to the logical concepts of true and false).

4)     count the instances of a type, then add to and subtract from that total (numbers).

5)     recognize when subtraction exhausts the instances of a type (leaving zero instances), and so on to mathematics

6)     typify when an instance of one type leads inevitably to an instance of another type, and so on to logic.


Of course, the base for mathematics might be 12 rather than 10.

But the existence of numbers and logic in the discourse of different species follows from their typifying things - in the same universe.

So, there is no reason to think that their mathematics or logic would evolve along significantly different lines.


People do plausibly argue the laws of logic must have existed before any intelligent entities thought of them, recorded them or used them

But it is not necessary or useful for them to have existed then, it could never be proved, and it requires you to posit the existence of ethereal things.

You can use Occam’s razor to eliminate them from your philosophy, with no loss to its credibility or usefulness.

That seems an equally consistent philosophical position, and without ethereality, it is more economical.


In this philosophy, there were no concepts before conceivers, no descriptions before describers.

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

There is no ethereal type outside of a description encoded in a physical form by an intelligent entity.

And when all descriptive concepts (e.g. “star”, “planet”, “plant”, parent” and “river”) have gone from the cosmos, types too will disappear.

What the triangle suggests about numbers

I hear that physicists are increasingly confident their latest mathematical models are true to the reality of the universe.

That implies earlier models are approximations, and doesn’t imply those mathematical models existed before life.

This section explores the idea that, like natural language, mathematics is an instrument for description and prediction - useful in so far as it works.

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


Where do numbers and other mathematical types and concepts come from?

The argument is that logic and mathematics cannot exist until intelligences have crystallized family resemblances into types.

You can’t say a statement is true or false, until you know the type(s) referred to.

You can’t say “This man is my brother” is true or false, until you know the properties of a brother.

You can’t count the things of a type until you know the type.

You can’t count your siblings until you know the properties of a sibling.

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.


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.

Where do numbers come from?

Earlier, physics was represented thus.



Mathematical structures

<create and use>           <represent>

Physicists <observe and envisage> Nature


At an even more basic level, where do numbers come from?

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.

CHAPTER 5: Relating the triangle to system theory

System theory is concerned with activity systems in which actors perform activities.

General system theory

The systems of interest here are activity systems in which actors perform activities to advance the state of the system.



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 food, nutrients and waste

A church


people who

play roles in the church’s organization and services.

many and various attributes of roles and services


Here, a system is orderly, active and an abstraction from the real world.


Every observable entity or situation can be divided into parts or elements, but that does not make it a system.

To be a system of interest, the parts must be organized – there must be some order or regularity in how they are related.


The term system is sometimes applied to passive structures like the Linnean classification of species, the Dewey decimal system or the periodic table in Chemistry.

Those structures are highly organized, but they are passive.

The systems of interest here are dynamic, meaning they display behavior and change state over time.

E.g. Consider a tennis match, whose current state is displayed on the score board.


In short, a system is definable as a particular set of orderly (regular or repeatable) interactions.

The systems of interest here feature actors (or components) that interact in the performance of activities.

Actors are structures that exist in space and perform activities; and in social systems thinking they are almost always human.

Activities are behaviors that happen over time, and change the state of the system or something in its environment.


System theory distinguishes abstract system types and physical instances of them.

Think of Beethoven’s 5th Symphony as an activity system.

1.     The system architect, Beethoven, conceived and organised the musical notes he wanted an orchestra to play in the symphony.

2.     His symphony score is a model - an abstract system type – a record/expression of the notes he conceived and how they relate to each other.

3.     Symphony performances are physical system instances, which each exhibit the selected notes as sounds in a real-world venue.

4.     Orchestras are social entities that employ musicians to play given roles in physical system instances.


Think of any particular business activity system:

1.     The system architects conceive and organise some activities they want business actors to perform, to meet some aims of system sponsors.

2.     Their system architecture definition is a model - an abstract system type – a record/expression of the activity types architects conceived and how they relate to each other.

3.     Business systems in operation are physical system instances, which each exhibit the selected types as activity instances in the real world.

4.     Enterprises are social entities that employ actors to play given roles in physical system instances.


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.”

System design is based on creating abstract system descriptions or models, then testing that physical systems perform as described.

Again, there can be fuzziness in how well real-world systems conform to system models


General system theory

Abstract systems (types)

<create and use>     <represent>

Observers <observe and envisage> Physical systems


Unfortunately, by referring to a biological entity as a system, Bertalanffy 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.

Bertalanffy, Ashby, Forrester, Checkland and others all defined a system as a model, an abstraction, a perspective of a discrete entity.


Ashby noted that people use the term “system” in at least two ways.

·       An entity = a real-world thing (e.g. all the people, processes, materials and equipment used in a tennis match) regardless of which observer looks at it.

·       A system = an observer’s view of some regular or repeatable activities that advance some variables/quantities.


Ashby noted that the second is the practical view.

"Though the first sounds more imposing… the practical worker inevitably finds second more important."

"Since different systems may be abstracted from the same real thing, a statement true of one may be false of another."

“There can be no such thing as the unique behavior of a [real-world entity], apart from a given observer.”

"There can be as many systems as observers... some so different as to be incompatible.”

“[Therefore] studying real-world entities] by studying only carefully selected aspects of them is simply what is always done in practice.” (Ashby 1956).


In his introduction to cybernetics, Ashby wrote:

“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).


Ashby’s student Krippendorff wrote:

"Ashby defined a system not as something that exists in nature.

A system consisted of a set of variables chosen for attention and relationships between these variables, established by observation, experimentation, or design."


In other words, a real-world entity is only a "physical system" when, where and in so far as it realises what Russell Ackoff called an "abstract system".

The abstract system is a model (mental or documented) that represents the particular features that the entity displays when realizing the system that is modelled.


A physical entity or situation is describable as a system when, where and in so far as it realises an abstract 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


Systems as types

You can think of an abstract system description as a type, and a physical system as an instance of that type.

Having observed or envisaged a physical system in operation, 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

Logical Roles, Rules, Variables

<create and use>              <represent>

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


Ashby pointed out that countless system descriptions (mental or documented models) may be abstracted from one substantial real-world entity or situation. 

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

Conversely, countless real-world entities or situations may realise the same abstract type, such as “a commercial business”.


In short, 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).


An abstract system does not have to be a perfect model of a physical 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.

Particular system theories


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

In cybernetics, a system is an abstraction, a theory or model of how an entity or “real machine” behaves, or should behave.


Ashby’s cybernetics


<create and use>          <represent>

Observers <observe and envisage> Real machines


Ashby’s system theory shares with biology that idea that a machine can change two ways.

·       It can change state over time (by the regular processes of the system)

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

System dynamics

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.


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

Soft systems

Peter Checkland promoted a “soft systems methodology” for the design of business activity systems.

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

Management science

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

His 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

Enterprise architecture

Clearly, the triangle fits the world of enterprise architecture


Enterprise architecture

Architecture Definitions

<create and use>            <represent>

Enterprise architects <observe and envisage> Business systems


Sadly, enterprise architects do share a controlled vocabulary.

However, it is possible to relate terms in an ontology and give examples.


"A service is a discrete behavior that delivers a result of value to its user(s).

E.g. Apply for Loan. Replace Tyre.

"A system or component is a ‘black box’ that exposes services.

·       E.g. any software system encapsulated by an API. Or any business whose services are defined by an SLA.

"A layer is a collection of systems or components in a client-server hierarchy.

·       E.g. UI layer, application layer, data layer.

"A platform is a layer or system that sits below the layer or system of interest.

E.g. The technology layer is the platform for the application layer.

The application layer is the platform for business operations. Our ERP system is the platform for business operations."

Second order cybernetics

Heinz von Foerster was an Austrian American scientist who combined physics with philosophy.

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

A basic idea was to include the system describer in the system that is described.

And allow the system to be self-organizing, in the sense of creatively self-describing.


Ashby and Maturana rejected self-improvement as undermining the concept of a system.

Ashby said: “No machine can be self-organizing in this sense.”

And that to re-organize a system, it must be coupled to another “higher” system

In effect, Ashby argued that second order cybernetics (yet to be defined) confuses:

·       the acts of actors in an activity system with

·       the acts of actors in a social entity that can define or change the activity system.


The epistemological triangle, being recursive, presents us with an alternative view to second order cybernetics.

To change a system (S) from one generation to the next you need a higher-level process or meta system (M).

A human actor can play a role in both systems.


Followers of von Foerster’s “second-order cybernetics” often quote him as below.

·       “Each individual constructs his or her own reality"

·       "The environment as we perceive it is our invention."

·       "Objectivity is the delusion that observations could be made without an observer."


These aphorisms lead some to deny that knowledge can be shared, which is misleading.

It disregards the effort required by innately subjective observers to undertake a ‘standardised observation’.

It is not that ‘objectivity’ assumes ‘observations without observers’.

Rather, ‘objectivity’ requires observers, being naturally ‘subjective”, to take great pains to remove their personality from their observations.


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.

CHAPTER 6: More on philosophy

A new tractacus logico philosophicus

This section of the article is an attempt to distill some presumptions and consequences of what is discussed above.


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, Wittgenstein developed an entirely different linguistics.

He turned from seeing language as precise to seeing language as fluid.

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


Some classical and linguistic philosophes seem to have been overtaken by biological and software sciences.

This philosophy sees language as only one tool for describing things.

Its starts from this general epistemology in which descriptions can take any form, including paintings for example




<create and use>   <represent>

Describers <observe and envisage> Realities


This philosophy 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”.


There follows an informal “tractacus” about description and reality.

It written from the perspective of a psycho-biologist rather than a linguist or mathematician.



·       Space and time exist as physical phenomena.

·       Other physical phenomena - things and their effects - exist out there in space and time.

·       Things that exist include you, me and other people we can communicate with.

·       We can perceive things, remember things and recall things.

·       We can describe things in memories and in messages.

·       By exchanging messages, we can communicate and share knowledge of things that exist


We don’t “know” space and time in some ideal or perfect sense.

We do have concepts (three dimensions of distance, and units of time) for describing them.

There is no need to presume those concepts existed before life.



-1- Describers are intelligent actors (natural or artificial) that can encode and decode descriptive models of realities.


-2- A reality is anything that can be observed or envisaged in time and space.

Realities include descriptions and describers.


-3- A description is created by a describer to represent a reality that is observed or envisaged.

Descriptions can be formed in mental and digital models, speech and writings, paintings and physical models.


-4- A description has a degree of truth to its creator and any user.

True means true enough, and false means not true enough.

The judgement of “enough” may be made differently by different observers on different occasions.


-5- A description is fanciful to an actor who believes it represents an imagined reality (e.g. a unicorn).

However, on discovering a reality that matches the description (e.g. on the discovery of unicorns) the description becomes true.


-6- Types are descriptions, and descriptions are types.

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

However large and complex a description is, it can be seen as a compound type.


-7- Describers formalise resemblances between realities into generic types.

To this, they codify types using the symbols/words of a symbolic/verbal vocabulary.

In natural language, the meanings of words are fluid and fuzzy.

In a controlled vocabulary the meanings of words are fixed.


-8- A controlled vocabulary must start from some (ideally very few) basic axiomatic types.

Since words are defined in a circular fashion using other words.

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


-9- Communication is a process that can creates and conveys a description from a creator to a user.

It succeeds when the meaning/information in descriptive types are near enough the same when encoded and decoded.


-10- Communication requires speakers and listeners to share the same vocabulary for encoding and decoding a description.

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


-11- To communicate verbally, human speakers and listeners must share a great deal.

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


Answering a reader’s questions

Q1) Does the meaning or concept of “ellipse” exist in a description of it?

A1) No, it exists only in a process that creates or uses the description.


Q2) Is a description of the concept “ellipse” the same as the concept?

A2) It corresponds to the concept only in those moments when actors decode the intended meaning from the description.


Q3) If I write down the mathematical formula for ellipses, is that a description of an ellipse?

A3) Yes, but to find your intended meaning in that description, an actor must decode it using the code you used to write it.


Q4) If we send that formula into space, it is still a description that somehow ‘equals’ the concept of ellipse?

A4) The description is less than the concept, since that requires also an intelligent actor able to decode the description.


Q5) If I give the formula to you, will you have approximately the same understanding of the concept ‘ellipse’?

A5) Only if and when I decode the formula using the code you used to write it.


Q6) If an alien receives the formula, can they form a mental image equivalent to our understanding of ellipses?

A6) Only if and when the alien decodes the formula using the code you used to write it.


Q7) If humans are extinct but aliens haven’t evolved yet, will the formula still describe the concept of ‘ellipse’?

A7) The formula can represent an ellipse, but only to an actor able to decode it.


Q8) So, is the concept encode in the description independent from any ‘mind’ or ‘brain’ that interprets it?

A8) No, the concept existed also in the mind of the describer – you, when you encoded it in the formula.


Q9) According to quantum physics, elementary particles ‘exist’ as a probabilistic wave form

There is no sharp boundary between existence and non-existence.

In what appears to be vacuum, there is a finite, non-zero, probability that a particle will pop into existence.

(See https://en.wikipedia.org/wiki/Vacuum_state.)

Surely that implies there is a non-zero (admittedly tiny) probability that several such particles form into the shape of an ellipse.

Would that shape itself be a description of an ellipse, i.e. embody the ellipse concept, in your philosophy?


A9) That shape will be an ellipse (an instance),

But will only describe an ellipse to an actor who interprets that shape an instance of the generic type.


Q10) What is the difference between a deliberate description of ellipses, and a randomly occurring ellipse shape?

A10) The first is an intentionally encoded concept - a type, which an actor might interpret as typifying all ellipses.

The second is an instance of that type, which might or might not be interpreted by an actor as exemplifying the general type.


Intelligent actors who communicate about “ellipses” must remember the concept, however vaguely, in some mysterious biological form.

But the meaning of that concept to the actors exists only in the processes of creating/encoding and decoding/using that memory.

An actor might arrange a set of golf balls in an ellipse shape with the intent to describe what all ellipses look like.

The intent is in the thought processes of the actor who forms the shape.

An actor who already knows the ellipse type, or is told the shape embodies the ellipse type, may perceive the shape as exemplifying that type.

The interpretation is in the thought processes of the actor who observes the shape.

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

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)


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.