Other triangular philosophies

Copyright 2017 Graham Berrisford. One of about 300 papers at http://avancier.website. Last updated 24/11/2017 09:55


Enterprise architecture is about business system planning.

It can be seen as applying the principles of general system theory – which we’ll get to later.

This paper is one in a family of related papers – listed at the end of this paper.

The philosophy underpinning system theory is compatible with modern science.

This paper discusses other philosophies, and suggests revising the ISO 42010 standard.


The nub of our philosophy. 1

Cartesian dualism.. 2

Saussure’s dyadic sign relation. 2

Ogden and Richards’ semiotic triangle. 2

Peirce’s triadic sign relation. 3

Karl Popper’s three worlds view.. 4

ISO 42010 standard. 6

Conclusions and remarks. 8

Footnote: Terms and concepts in Peirce’s final account 8


The nub of our philosophy

Generally speaking, one description can be realised in many realities.

And one reality can be idealised in many descriptions.

But there is more to the relationship of description to reality than that.

Countless philosophers have proposed countless philosophies – both overlapping and contrary.


First, you should read these two pages on the philosophy expressed in this triangle.

Description theory

Descriptions (private & public)

<create and use>                   <idealise>

Describers     <observe & envisage>     Realities


The process of observing reality starts in perception and results in the creation of descriptive/mental models.

The process of envisaging reality starts in dream-like or consciously-directed brain activity and results in the creation of descriptive/mental models.

Describers translate descriptions from private to public forms, and back again.


By the way, although the universe is in reality a continuously unfolding process, there is a tendency to view the universe as a static entity.

Philosophers tend describe the universe in terms of structures rather than behaviors.

Cartesian dualism

Historically, theologians have drawn a division between what is mental and what is physical.

Cartesian dualism (after Descartes) is also based on the theory that the universe is composed of two essential substances:

·         Res Cogitans: the internal or mental world

·         Res Extensa: the external or physical world.


The two worlds are commonly called mind and matter.

Cartesian dualism

Minds   <perceive and manipulate>  Matter

bodily sensors and motors


Notice Cartesian dualism is really a triad - the third element being the sensors and motors of the body.

Descartes presumed mind and matter interact via the body.

And having decided the physical body cannot think, he was led to declare the mind can exist outside of the body.


Many people’s instinct is still to divide the universe into mental and physical worlds.

But the view taken today in cognitive science and psychology is that the mind has a physical biological basis.

And the two-way dichotomy of Cartesian dualism has long been rejected by philosophers.

Before we look at various three-cornered views of description and reality, a brief note on another dualism.

Saussure’s dyadic sign relation

Semiology or semiotics is the study the study of signs and symbols and their use or interpretation.

Saussure’s semiotics featured a two-way relation.

Saussure’s dyadic sign relation

Signified concepts <are signified by> Signifiers/symbols


Descartes might have expressed this as: mental models <are signified by> physical models/words.


Others found this view of semiotics too narrow, and developer richer triangular models.

Some retain a flavour of the mental/physical separation in Cartesian dualism.

Some start from linguistics, from thinking about verbal language.

Read on for notes on four triangular philosophies.

Ogden and Richards’ semiotic triangle

Ogden and Richards’s semiotic triangle (in “The Meaning of Meaning”) is usually represented along these lines

The Semiotic Triangle


<are symbolised by>          <stand for>

References             <refer to>               Referents


Descartes might have said: mental references <are symbolised by> physical symbols, which <stand for> physical things referred to.


Notice that the “refer to” relation hints at a process.

There must be intelligent actors who can not only perceive referents, and read symbols that stand for them, but also interpret those symbols.

Interpreting involves translating from one structure or behavior into another structure or behavior.


What is the meaning of meaning?

The semiotic triangle is usually read from the viewpoint of a linguist – the symbols are assumed to be verbal.

But meanings are found elsewhere - in non-verbal signs and in the after effects of behaviors.

In fact, meanings arise when and wherever an actor finds any usable information in any structure or behaviour.

The meaning of meaning is further addressed in this Information and Communication paper.


This is an attempt to align the semiotic triangle with our triangle.

The Semiotic Triangle - revised

Symbols (inc. references)

<create and use>          <stand for>

Referees             <refer to>               Referents


Peirce’s triadic sign relation

Charles Peirce developed a complex philosophy which is radically simplified in this triangle.

Peirce’s triadic sign relation


<understand objects from>                <represent>

Interpretants                       <refer to>              Objects


Like many philosophers, Peirce made life hard for his readers by changing his terms and their definitions, but here goes.



Objects are the reality out there, represented to interpretants by signs.



Peirce initially focused on symbols that represent objects in verbal language, but then widened his interest to include others kinds of sign.

His signs include icons (which imitate objects),  indicators (which reveal the effects of objects) and symbols (coded descriptions of objects).

Peirce treated interpretants as another kind of sign.



An interpretant is perhaps primarily the effect of a sign on a person, or a meaning or understanding reached on reading a sign.

However Peirce’s concept of an intepretant is wider, an ability of an interpreter, and a sign in itself.

Interpretant: the disposition or readiness of an interpreter to respond to a sign; a sign or set of signs that interprets another sign. (Merriam Webster)


Peirce’s signs can <suggest, direct or indicate meanings to> interpretants.

And interpreting involves translating from one structure or behavior into another structure or behavior.

 “[the interpretant] is perhaps more properly thought of as the translation or development of the original sign.

The idea is that the interpretant provides a translation of the sign, allowing us a more complex understanding of the sign's object.” https://plato.stanford.edu/entries/peirce-semiotics/


So, Peirce’s interpretant involves translating an external sign into an internal sign.

It seems to combine an interpreter’s performance of that process with the result of that process.

“In all cases [the Interpretant] includes feelings; for there must, at least, be a sense of comprehending the meaning of the sign.

If it includes more than mere feeling, it must evoke some kind of effort.

It may include something besides, which, for the present, may be vaguely called “thought”. https://plato.stanford.edu/entries/peirce-semiotics/


See the footnote on Peirce’s final account of his philosophy.

This is an attempt to align Peirce’s triadic model with our triangle.

Peirce’s triadic sign relation – revised

                   Signs (inc. interpretants)

<understand objects from>                <represent>

Interpreters            <observe and envisage>   Objects

Karl Popper’s three worlds view

In seeking to reject the “essentialism” of Cartesian dualism, Popper split the world into three worlds that interact with each other:

The definitions below are from “The Tanner Lecture on Human Values”, Delivered at The University of Michigan, April 7, 1978


“World 1: physical bodies

Stones, stars, plants, animals; also radiation and other forms of physical energy.

Non-living physical objects and biological objects.”


In other words, all physical matter and energy: the solar system, hurricanes, brains and all kinds of biological organism.

This must include all instantiations of world 3, such as aeroplanes and performances of the play “Hamlet”.

Does it include also the human thoughts, memories and mental models of world 2? If not, why not?


“World 2: mental or psychological world

Pain and pleasure, thoughts, decisions, perceptions, observations.

Mental states, processes, subjective experiences; conscious and subconscious experiences.”


This world seems to retain something of the internal/external Cartesian dualism Popper intended to shake off.

Let me record a thought I am about to have, in the very next sentence.

“Given a circle with a diameter of 2cm, its circumference is roughly 6.3cm.”

This objective thought started in world 2, why is my translation of that idea into writing part of world 3?


Similarly, composers (like Beethoven) can envisage and “hear” music in their heads.

Why is their translation of that mental musical sensation into a written musical score part of world 3? The one is a translation of the other.

We continually translate back and forth between internal and external, mental and documented, descriptions of world 1 and world 3


“World 3: products of the human mind

Languages, mathematical constructs, scientific conjectures and theories.

Fiction: tales, stories, myths. Art: songs, symphonies, paintings and sculptures. Engineering: aeroplanes, airports etc.”


This must include the designs of social institutions: choirs, churches, IBM, Google and the United States.

Why are products of the chimpanzee mind not included?

Or products of the honey bee mind, such as wiggle dances and honey comb?


Do Popper's worlds 2 and 3 reflect a subjective/objective distinction?

You might think so, but surely this cannot be the case.

World 2 contains thoughts (which may also be recorded as writing) that

·         are dreamlike, irrational, poetic or fantasies

·         were widely believed to be correct, but have since been falsified by testing

·         are derived by mathematical reasoning from agreed axioms

·         are supported by test cases, as well as we can measure them, so far.


The graphic seems a fair representation of Popper’s three worlds view.

Popper’s three worlds view

3: Products of the human mind

<produces>              <describes/predicts>

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


However you look at, Popper’s three-way division seems odd.

And like Peirce, Popper seems conflate describers’ intelligences and their mental models in world 2.


The position taken here is neither Cartesian nor monist, it is that of a biologist or psychologist.

The view taken today in cognitive science and psychology is that the mind has a physical biological basis

Minds and all their thoughts are products of Darwinian evolution.

Yesterday, there were only 1) things in a mindless universe.

Today, there are also 2) life forms and 3) the descriptive products of life forms.

Tomorrow, life forms will be extinct, any descriptive products that remain will become meaningless, but the mindless universe will persist.


So, the philosophy here modifies Popper’s three worlds view thus.

·         World 1 The universe: all physical matter and energy (including worlds 2 and 3).

·         World 2 Descriptions: models of the universe as perceived and described in terms of discrete things.

·         World 3 Objective knowledge: descriptions that, when tested, match the universe well enough.

·         Describers: Organisms and AI machines capable of forming and using descriptions in world 2.


This is an attempt to align Popper’s worlds with our triangle.

Popper’s three worlds  view - revised

Worlds 2 and 3

<create and use>                      <idealise>

Humans            <observe and envisage>         World 1


This is more distant from Cartesian dualism than Popper.

It seems to me a more productive way of looking at description and reality.

The ISO 42010 standard on system architecture

Beside system describers, there are two things of importance here: abstract system descriptions and concrete system realisations.

A system’s architecture (aka high-level design or specification) exists in both abstract and concrete forms:

·         property types or variables in an abstract system description.

·         instantiations or values in a concrete system realisation.


The web site of the ISO 42010 standard on architecture description says.

"The premise of the Standard is, For a system of interest to you, the Standard provides guidance for documenting an architecture for that system."

The standard oddly posits not two but three things, related in 1-1 associations.

ISO 42010 triangle

 1Architecture Description

<is expressed in>                <identifies>

1 Architecture         <is exhibited in>               1 System


Analysis of the three concepts

There is description D and described reality R.

D is composed of abstract descriptive property types.

R is composed of concrete embodiments of those types in observable values.

Yet the standard names three things.


The “system” is surely R.

“The standard takes no position on the question, what is a system?”

It is any conceivable reality, which eviscerates the “system” concept.


The “Architecture Description” is clearly D.

It is a “work product used to express an architecture".


So what is the “Architecture”?

This is a “<system> fundamental concepts or properties of a system in its environment embodied in its elements, relationships, and in the principles of its design and evolution"

The definition starts off referring to D, the abstract descriptive property types.

Then shifts to R, the embodiment of those types in observable values.

And then throws in some constraints on the design activity.

This definition adds no meaning to D and R; it is redundant.

If there is a third corner to the triangle it is the architect, or architecting.


Analysis of the triangular relationship

Remember that:

One description can be exhibited in many realities; one reality can be idealised in many descriptions.

One type can be exhibited in many things; one thing can be idealised in many types.

One system description can be exhibited by many entities; one entity can be idealised in many system descriptions.


Consider this two-way relation.

·         1 Architecture Description <identifies> 1 System.


Surely one Architecture Description can be realised in many real-world Systems?

Else, what is the one System?

·         Is it to be found in somebody’s head? If so, whose head?

·         Is it the ethereal and eternal Platonic ideal of the System?


Now consider the other relations.

·         1 System < exhibits the property types in> 1 Architecture which <is expressed in> 1 Architecture Description.


Where else could the property types be, other than in an Architecture Description - be it mental, documented or other?

Else, what is the one Architecture?

·         Is it to be found in somebody’s head? If so, whose head?

·         Is it the ethereal and eternal Platonic ideal of the Architecture Description?


The ISO 42010 editor suggested to me that both "System" and "Architecture" could be ethereal and eternal Platonic ideals

Which is to add redundancy to redundancy.


Revising the ISO 42010 triangle so it makes sense

Suppose we agree the System is a concrete system realisation.

But take the ISO 42010 view that all is defined from the perspective of 1 and only 1 Architecture Description

Then the relations in the standard could well be expressed as:

·         1 Architecture Description <can describe> N Similar Systems

·         1 System <can exhibit the property types in> 1 Architecture Description.


And the standard could reasonably use our triangle thus.

ISO 42010 standard triangle revised

1 Architecture Description

<create and use>              <idealises>

Architects     <observe and envisage>  1-N Similar Systems


Is the standard about systems at all?

The standard has nothing particular to do with a "system" as defined by anybody - even by other ISO standards. 

It can be applied equally to documenting different views of any thing that different stakeholders have concerns about.

And ensuring the documented description meets certain quality criteria.


Is the standard about architecture at all?

The standard has nothing particular to do with "architecture".

You can change all to "architecture" to "design" (or similar) without changing its intent or potential application.

Conclusions and remarks

Today, most consider we cannot fully understand any physical object - cannot know more than selected features of it.

And even that knowledge may be fuzzy or arguable (as is discussed in other papers).

Another complication is that objects are not static, they change over time.

Philosophers tend to model the universe by classifying structural elements; they find it difficult to model behaviors and state changes.


This paper has reviewed and revised four philosophical triangles in the light of our description theory.

This paper is one in a family of related papers.

1.      The nub of our philosophy

2.      Description theory >> How the brain works

3.      A communication theory

4.      A language theory

5.      A description and type theory >> Realism or Idealism?

6.      A philosophy >> Other triangular philosophies

7.      Knowledge and truth


Finally, people ask about my personal view of other philosophers.

I am not at all expert in other philosophers.

It doesn’t matter here, but at the risk of upsetting people, here are some glib thoughts.

·         Plato, Aristotle and Descarte – superseded.

·         Metaphysical and theological philosophy (e.g. Kierkgaard) - on a different planet.

·         Political philosophy (e.g. Engels and de Beauvoir) - tendentious.

·         Linguistic-based philosophy (e.g. Wittgenstein’s Tracticus) – too human-centric.

·         Heraclitus and Kant – say some things of interest.

·         Charles Darwin and W Ross Ashby - my touchstones. 

Footnote: Terms and concepts in Peirce’s final account

Peirce divided signs into:

·         Potisigns - signs that mimic the qualities of referred-to objects (e.g. a statue, or a colour chart)

·         Actisigns - signs that indicate objects by representing the effects of those objects (e.g. a molehill, or the smoke of a fire)

·         Famisigns - sign that encode descriptions of objects in symbols (e.g. a speech, or a symphony score).


Peirce recognised that signs convey partial, possibly inaccurate, information about objects.

He eventually addressed this by dividing objects and interpretants into immediate and dynamic kinds.

·         The immediate is the object or initial understanding of it, when a sign is first perceived.

·         The dynamic is the object or understanding of it at the end of a process of enquiry.

·         A final interpretant, which is the ultimate, complete, agreed, perfectly true, but possibly unattainable, understanding of an object.


This table (again from https://plato.stanford.edu/entries/peirce-semiotics/) is part of Peirce’s final account of his theory.


Peirce's 1908 letters to Lady Welby included the following ten elements and their respective sign types.

In respect of the

a sign may be either

Sign [See our Type, Type signifier  and Type token]

(i) Potisign (ii) Actisign or (iii) a Famisign.

Immediate Object

(i) Descriptive (ii) Designative or (iii) a Copulant.

Dynamic Object

(i) Abstractive (ii) Concretive or (iii) Collective.

relation between the Sign and the Dynamic Object,

(i) an Icon (ii) an Index or (iii) a Symbol.

Immediate Interpretant

(i) Ejaculative, (ii) Imperative or (iii) Significative.

Dynamic Interpretant

(i) Sympathetic (ii) Shocking or (iii) Usual.

the relation between the Sign and Dynamic Interpretant,

(i) Suggestive (ii) Imperative or (iii) Indicative.

Final Interpretant

(i) Gratiffic (ii) Action Producing or iii) Self-Control Producing.

the relation between the Sign and the Final Interpretant,

(i) Seme (ii) Pheme or (iii) a Delome.

the relation between the Sign, Dynamic Object and Final Interpretant,

(i) an Assurance of Instinct (ii) an Assurance of Experience or (iii) an Assurance of Form.


“Unfortunately, these ten divisions and their classes represent a baffling array of under-explained terminology,

and there is little to indicate precisely how we should set about the task of combining them.” https://plato.stanford.edu/entries/peirce-semiotics/



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