Copyright 2014 Graham Berrisford. Now a chapter in “the book” at Last updated 04/06/2021 12:00


The previous chapters summarized our description, type and communication theories. This chapter summarises some implications of those theories. It challenges other philosophical triangles, including those of Peirce and Popper. And questions whether what we think of as universal concepts, types and numbers, existed before life.


Correlating descriptions to described things. 1

Implications for system architecture. 2

Implications for the ISO/IEC 42010 standard. 4

Implications for semiotics. 5

Implications for philosophy. 7

Implications for mathematics. 8

Conclusions and remarks. 10


Correlating descriptions to described things

Famously, bishop Berkeley proposed things did not exist when not observed. Did he never hit his head on a low-lying beam he had not noticed? There is no doubt that in modern science that natural things (like the moon) exist before they are observed and described.


However, it also true that designed things (rockets) come into existence only after they have been envisaged and described.


And behaviors, including the laws of nature, only occur when and where things interact. (In quantum physics, the interaction is between observers and the observed.)


The position in this book is that everything in this table, left and right, exists in the sense that they occur in space and time.



Sensed/described phenomena



Your observation of a territory

The territory itself

Abstract systems

Physical entities that realize them.

Poker game rules

The playing of a poker game by a card school

Symphony scores

Performances of symphonies by orchestras

Your experience of some music

The performance of a musical piece

Numbers and formulae

The physical laws of nature they represent.


We can and do enjoy the physical sensation of music without understanding it. Musicians understand that reality by encoding the sound of music in some form (chords shapes, or a musical score) that can they can correlate well enough with the real-world phenomena.


More generally, we (describers) understand physical reality in so far as it is correlated with a sensation/description we can correlate well enough with real-world phenomena for practical use.


The epistemological triangle below should be read from left to right.


Epistemological triangle


<create and use>          <represent>

Describers <observe & envisage> Phenomena


Describers <create and use> Descriptions

There is an essential difference between our triangle and comparable triangles you can find in semiotics and philosophy. Most other triangles separate descriptions into two kinds: internal models (descriptions in the mind) and external models (descriptions in speech or writing).


By contrast, in our triangle, a description in the mind is at the apex, not the left. In the describer corner (to the left) are cognition processes: observing, envisaging, remembering, recalling, writing and reading. In the description corner (at the top) are all descriptions encoded and decoded by those processes, in the mind, in speech, on the page, wherever.


Descriptions <represent> Phenomena

A description typifies the described phenomenon. Suppose we describe a bird as an animal with feathers and a beak. The properties named “feathers” and “beak” appear in two forms. They appear in the description as generic property types, and in the phenomenon as particular properties that embody or exhibit those property types. (There is no third kind of property, neither encoded in a description nor exhibited in reality.)


A constructivist says there can be no construct without a constructor, no concept without a conceiver, no description without a describer, no type without a typifier.


Suppose you want to describe IBM. Don’t think there is a metaphysical concept of IBM out there, which you can find and express in a description. Think rather, your concept of IBM is your description of it – in mind, on paper, wherever. Destroy all copies of descriptions ever made of IBM (impossible to do of course), and there would be no longer be a concept of IBM.

Implications for system architecture

In the earlier discussion of systems thinking, an abstract system is a model (in mind or writing) that represents a physical system we observe or envisage as a phenomenon in reality.


System theory

Abstract systems

<create and use>              <represent>

System thinkers <observe and envisage> Physical systems


We have seen this view of description and reality can be found in other authors writings.


Russel Ackoff, a writer on management science, spoke of abstract and concrete systems. His abstract system is a description or model of how a concrete “organization” behaves, or should behave.


Ackoff’s system theory

Abstract systems

<create and use>            <represent>

System thinkers <observe and envisage> Concrete systems


W Ross Ashby, writing on cybernetics, distinguished entities in nature from the abstract systems they realise. His system is an abstraction, a theory or model of how “real machine” behaves, or should behave.


Ashby’s cybernetics

Abstract machines

<create and use>          <represent>

Observers    <observe and envisage>    Real machines


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 (resources or populations) that interact and affect each other by increasing or decreasing the amounts they contain.


System Dynamics

Stock and flow models

<create and animate>                     <represent>

Modellers <observe and envisage> Interacting quantities


Peter Checkland promoted a “soft systems methodology” for the design of business activity systems. He said different observers may perceive different systems, some in conflict, in any one human organization or other entity.


Checkland’s Soft systems methodology

Business activity models

<create and use>                <represent>

Observers <observe and envisage> Business activities

The fourth corner of the triangle

In addition to the three concepts in the triangles above, there is a fourth. That is, the physical entity that performs the activities. This table contains an example.


Stickleback mating ritual

Abstract system (roles, rules and variable types)

The type, a model of the ritual

Physical system (actors and activities, variable values)

One instance of the mating ritual

Physical entities

A pair of sticklebacks, nest and eggs


Our epistemological triangle glosses over the distinction between a physical activity system and the entity that realizes it, but to clarify the distinction, this table contains some more examples.




abstract type


physical instances


physical entities


A symphony score

symphony performances


Business architect

A set of roles and rules

businesses processes

business actors

Software engineer

A program

program executions


Game designer

The rules of “poker”

games of poker

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.


In writing, we can create a very large and complex type, composed of smaller simpler types. We can create an architectural model of a system far beyond any model we can hold in mind. The model may typify

·       actors (structures in space that perform activities) by defining roles,

·       activities (behaviors that advance the state of the system or its environment) by defining rules, and the

·       system’s state (structures changed by activities) by defining state variables.


System architecture

Logical Roles, Rules, Variables

<create and use>                            <represent>

System architects <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. some of which may be in conflict. Conversely, countless real-world entities or situations may realise the same abstract system type.


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).

Implications for the ISO/IEC 42010 standard

The ISO/IEC 42010 standard is for the architectural description of software-intensive systems. The concern here is the way the standard relates three concepts in 1-1 associations.


The ISO/IEC 42010 standard

1 Architecture Description

<is expressed in>                <identifies>

1 Architecture      <is exhibited in>         1 System


An Architecture Description represents (in an abstract form) any System that it describes. What is that third thing called “Architecture”? If it is neither a description nor a described things then when and where does it exist?


If an architecture is a documented description of a thing, then in ISO 42010 terms, it is an Architecture Description. If it is a described thing, then in ISO 42010 terms, it is a System observed in reality or envisaged in the mind. If it is neither one nor the other, then where is it?


ISO 42010 presumes architect collaborate on one documented description - the whole standard is written from that viewpoint. In practice any number of descriptions can exist – in different minds and documented forms. Any two of those descriptions may be the same or different. However similar they are, if they are different, then they are different, and so correspond to different systems.


To say “a weight describes the weight of a thing” is tautologous. To say “a type describes the type of a thing” is tautologous. To say “an architecture description describes the architecture of a system” is tautologous. It is really to say either “a description describes the description of a thing”, or else “a description describes the thing of a thing”.


More accurately: “An architecture description sets out concepts or properties that a system that will embody.” That is all we need to discuss. So better, revise the concept graph thus.


System architecture

1 Architecture Description

<create and use>               <represents>

N Architects    <observe and envisage>   N Systems


For longer and deeper analysis of ISO/IEC 42010, read the chapter on implication for system architecture.

Implications for semiotics

In thinking about descriptions of the world, you might be drawn to linguistics, studying the use of verbal language to describe things. Semiotics emerged from a linguistic paradigm that differentiates organic/biological patterns (as in neural systems) from inorganic/physical patterns (as in sound waves or gestures). Here, all patterns (internal and external) created and used by organisms to represent things are equivalent.


Remember: there is an essential difference between our triangle and comparable triangles you can find in semiotics and philosophy. Most other triangles separate descriptions into two kinds: internal models (descriptions in the mind) and external models (descriptions in speech or writing). By contrast, our triangle separates cognition processes (observing, envisaging, remembering, recalling, writing and reading) from all the descriptive structures those processes create and use (in the mind, in speech, on the page, wherever). So, a description in the mind is at the apex, not the left.


The four triangles below have been proposed; none are wholly satisfactory. Some are not well explained. All four triangles look clearer when revised to match ours.


Ogden and Richards appear to position internal descriptions and external descriptions in different corners of their triangle.


Ogden and Richards’ Semiotic Triangle


<are symbolised by>          <stand for>

References             <refer to>               Referents

Above, references include mental constructs?

Below, our version moves them to the apex.

Revised to match our triangle

Symbols (inc. references)

<create and use>              <stand for>

Referees               <refer to>               Referents


Charles Peirce’s philosophy is "a baffling array of under-explained terminology." (SEP). In his triadic relation, the interpretant is a mysterious entity.


Charles Peirce’s triadic sign relation


<understand objects from>         <represent>

Interpretants              <refer to>              Objects

Above, interpretants include mental constructs?

Below, our version moves them to the apex.

Revised to match our triangle

Signs (inc. interpretants)

<understand objects from>            <represent>

Interpreters      <observe and envisage>      Objects


Karle Popper’s three world view appears to deny that mental models are products of the mental processes.


Karl Popper’s three worlds view

3: Products of the mind

<produces>              <describes/predicts>

2: Mental world <observes and envisages> 1: Physical reality

Above, the mental world incudes mental constructs?

Below, our version moves them to the apex.

Revised to match our triangle

Products of the mind

<create and use>                      <represent>

Minds         <observe and envisage>     Physical reality


Pierre Bordieu’s knowledge appears to be limited that which is exchanged socially.


Pierre Bordieu’s three relations of knowledge


<social>             <epistemic>

Knower              <objectify>             Known

Above, the knower has private memories?.

Below, all memories and messages are at the top.

Revised to match our triangle


<create and use>         <represent>

Knowers         <observe>      Known things


For longer and deeper analysis, read the chapter on implication for semiotics.

Implications for philosophy

In short, the principles of description introduced above are.

·       Knowledge and description evolved in biological organisms

·       A good regulator has a description of the target regulates

·       Consciousness is a process that enables us to compare the past, present and future.

·       To describe a thing is to typify it in terms of types already understood

·       Every type is a description

·       Every description is a type

·       A description is meaningful to an actor only in the process of creating or using it

·       Coding is ubiquitous in the creation, use and sharing of symbolic descriptions

·       We share knowledge by verifying descriptions we share


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.


Is objectivity possible? Yes.

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, since it denies the success of social animal species. 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.


Being objective doesn’t mean an observation can be made without observers; rather it requires us (each being naturally ‘subjective”) to take great pains to remove our individual personalities from the observation we agree. 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.


Do types exist outside of descriptions we construct? No.

We presume reality exists out there; and we can observe and describe it to useful ends. We distinguish and discuss

·       types – descriptions, intensional definition of concepts or properties, created in mind, writing or other form.

·       instances – embodiment of concepts or properties in things we observe or envisage


Do types exist outside of descriptions we construct? Consider the example of a symphony. A score of Beethoven’s fifth symphony is abstract system, type or pattern. A performance of that symphony is physical system that instantiates or embodies that abstract system.


Where is the abstract system? The one used for a performance of a symphony is found in the score that is used. Every other other copy of that score contains the same abstract system. Suppose all memories, scores and recordings of the symphony and variations of it were destroyed. Then that symphony “type” would disappear from the universe.


In reality, Beethoven drafted several versions of his fifth symphony. His “autograph score” encodes the third movement in the form ABABA′. But most modern printed editions score it as ABA′ (scherzo, trio, modified scherzo). Which is the right version? Is there an abstract generalization that accommodates all known symphony variations? No. And until somebody specifies one, that concept is metaphysical and redundant.


For most of this book it makes no difference whether you believe types are real or ethereal. However, you don’t need to presume any descriptive type exists outside of the physical world in a metaphysical way. For more on philosophy, read the chapter on implication for philosophy.

Implications for mathematics

Is Mathematics Invented or Discovered?


Roger Penrose says there are different realities. The reality of the physical world. The reality of our mental experience (represented in sensations, memories and messages). And the reality of mathematical facts (like there are infinite prime numbers). He says mathematics is out there to be discovered, has a reality independent of physical reality. Physicists formulated the laws of nature ahead of observation and proof. It turns out that Newton’s laws have proved accurate to one part in ten million (10 to the power of 7). And Einstein’s laws have proved accurate the one part in 10 to the power 14.


Surely, things in the physical world and the laws of nature did exist before we discovered them. Where for things and forces to exist means they occur in space and time. Moreover, our mental experience is a biological phenomenon in physical world, along with all the types we define and share. The numbers and mathematical formulae we use to represent things and forces in nature were invented by us, and exist only in the memories and messages we create and use.


If an animal can remember a general pattern or type, then a startling new idea emerges. It becomes possible to count things of that type, and communicate the total number to others.


Abstraction of quantities from sets


<create and use>      <represent totals of>

Counters    <observe and envisage>  Things of a type


The argument here 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 types referred to. You can’t say “This man is my brother” is true, until you know the properties of the brother type. You can’t count your brothers until you know the properties of the brother type. You can’t count any things until you know the type they must conform to – well enough.


Primitive animals surely 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.


Scientists have studied how far honey bees, dolphins and babies can understand quantities. 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.


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

Honeybees are clever little creatures. They can form abstract concepts, such as symmetry versus asymmetry. And they use symbolic language — the celebrated waggle dance — to direct their hivemates to flower patches.  New reports suggest that they can also communicate across species, and can count — up to a point.”


A number is a description made by a describer who can do three things.

1.     observe or envisage several discrete things

2.     either aggregate them (e.g. items in basket) or match them to a given type

3.     count the things in the aggregate or matching the type


Types enable counting; numbers imply types. And types can be organised in type hierarchies.


Did numbers and types exist before life in an ethereal/metaphysical sense? Or do they exist only in a real/physical sense, in the models we create? People do plausibly argue numbers 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 before life. 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, and suffer no loss to the credibility or usefulness of mathematics. That is a consistent philosophical position. And by requiring no recourse to ethereal metaphysics, it is more economical.


For longer and deeper analysis, read the chapter on implication for mathematics.

Conclusions and remarks

This chapter summarizes some implications of our information, description and type theories. It challenges other philosophical triangles, including those of Peirce and Popper. And whether what we think of as universal concepts, types and numbers, existed before life.


Other chapters expand on arguments advanced in this one.