This article is a supplement to this description theory It reviews other philosophical triangles and revises them to match our epistemological triangle. This is not to say the existing triangles are “wrong”; all of them are mental models. It is to suggest that, revised as suggested here, the other triangles are simpler and clearer.

Contents

Philosophical and semiotic views of description and reality. 1

Four triangular views of description and reality – in short 2

Ogden and Richards’ semiotic triangle. 3

Peirce’s triadic sign relation. 4

Karl Popper’s three worlds view.. 6

Pierre Bordieu's three relations of knowledge. 8

Conclusions and remarks. 8

Philosophical and semiotic views of description and reality

Before we study triangular views, here are brief notes on two dualisms.

Cartesian dualism

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 – commonly called mind

· Res Extensa: the external or physical world – commonly called matter.

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

Cartesian dualism

Minds <conceptualize> Matter

And bodily sensors and motors?

Descartes saw the mind as separate from the body.

He 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 today, cognitive psychologists see the mind as an organ of body, the mind has a physical biological basis.

And philosophers and scientists see this two-way mental/physical dichotomy as naive.

Saussure’s dyadic sign relation

"Saussure proposed the new science semiology— later called semiotics, the science of signs.”

Saussure held that definitions of concepts cannot exist independently from a linguistic system defined by difference.

Or, to put it differently, that a concept of something cannot exist without being named."

"These various movements often lead to the notion that language 'constitutes' reality,

a position contrary to intuition and to most of the Western tradition of philosophy." https://en.wikipedia.org/wiki/Linguistic_turn

Descriptions, and symbols within them, are called “signs” in semiotics.

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

Where are the signifiers?

In other words: mental models <are signified by> physical models/words.

Others found this two-way view of semiotics too narrow, and developed richer triangular models.

Four triangular views of description and reality – in short

Semiotics emerged from a linguistic paradigm that differentiates

· organic/biological patterns (as in neural systems)

· inorganic/physical patterns (as in sound waves or gestures).

The four triangles below have been proposed; none are wholly satisfactory.

Some are not well explained. (On Peirce: "a baffling array of under-explained terminology." SEP)

Some put internal mental descriptions and external spoken or written descriptions in different corners of their triangle.

All four triangles look clearer (to me anyway) when revised to match ours.

Ogden and Richard’s Semiotic Triangle	Charles Peirce’s triadic sign relation	Karl Popper’s three worlds view	Pierre Bordieu’s three relations of knowledge
Symbols <are symbolised by> <stand for> References <refer to> Referents	Signs <understand objects from> <represent> Interpretants <refer to> Objects	3: Products of the mind <produces> <describes/predicts> 2: Mental world <observes and envisages> 1: Physical reality	Knowledge <social> <epistemic> Knower <objectify> Known
Issue: structures in the brain are symbols. Our version moves mental symbols to the apex.	Issue: structures in interpreters’ minds are signs. Our version moves mental signs to the apex.	Issue: structures in the mental world are products of the mind. Our version moves mental models to the apex.	Issue: knowledge is contained in both memories and messages.
Revised to match our triangle	Revised to match our triangle	Revised to match our triangle	Revised to match our triangle
Symbols (inc. references) <create and use> <stand for> Referees <refer to> Referents	Signs (inc. interpretants) <understand objects from> <represent> Interpreters <observe and envisage> Objects	Products of the mind <create and use> <represent> Minds <observe and envisage> Physical entity	Knowledge <create and use> <represent> Actors <observe> Known things

Our epistemological triangle moves from a sociological viewpoint to a psycho-biological one.

From the sociological: actors with a memory <express ideas using> messages to <represent> phenomena.

To the psycho-biological: actors with an intelligence <create and use> memories and messages to <represent> phenomena.

To us, all patterns (internal and external) created and used by organisms to represent things are at the apex of the triangle.

Read appendix 1 for a longer version of the analysis here.

Ogden and Richards’ semiotic triangle

Descartes’s view might be distilled as: mental references <are symbolised by> physical symbols, which <stand for> physical things referred to.

In “The Meaning of Meaning” (Odgen & Richards, 1923) the authors drew what might look like similar triangular structure.

However, the semiotic triangle below is rather different from Descartes.

A reference appears to be a thought or concept, as symbolised in the mind.

Ogden and Richard’s Semiotic Triangle

Symbols

References <refer to> Referents

Issue: structures in the brain are symbols. Our version moves mental symbols to the apex.

Revised to match our triangle

Symbols (inc. references)

Referees <refer to> Referents

A referent is something to which a symbol can refer.

A symbol is a sign (word or other representation) of something – to a creator or user of that symbol, and in a language they use.

A reference is said to be a thought or concept (as symbolised in the mind?).

On the need for language

When reading the semiotic triangle, a linguist may assume the symbols are verbal.

Of course, we and other animals can remember and communicate meaningful information without words.

The meaning of both verbal and non-verbal symbols is language dependent.

The referent/object referred to by a symbol/word depends on the language used.

Conversely, the symbol/word used to symbolise a referent/object depends on the language used.

On the need for language users

If a reference is a thought or concept, where in the triangle is the thinker of the thought, the conceiver of the concept?

The “refer to” and “symbolised by” relations hint at processes performed by intelligent actors.

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

Peirce’s triadic sign relation

Charles Peirce (1931-1958) had similar notion to the semiotic triangle.

Sometimes it seems he conflate a describer, their intelligence, thoughts and memories into “interpretant”.

Other times it seems as though the interpretant is only a thought, concept or mental sign.

Charles Peirce’s triadic sign relation

Signs

Interpretants <refer to> Objects

Issue: structures in interpreters’ minds are signs. Our version moves mental signs to the apex.

Revised to match our triangle

Signs (inc. interpretants)

Interpreters <observe and envisage> Objects

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

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

Signs were originally symbols that represent objects in verbal language, but then widened to include others kinds of sign.

Peirce’s 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.

Interpretants are hard to understand, they are not simply people.

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

However, the concept of an intepretant seems wider, it can be 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/

More detail from Peirce’s final account of his theory

This section is edited from https://plato.stanford.edu/entries/peirce-semiotics/

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.

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

“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/

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.

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:

Karl Popper’s three worlds view

3: Products of the mind

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

Issue: structures in the mental world are products of the mind. Our version moves mental models to the apex.

Revised to match our triangle

Products of the mind

Minds <observe and envisage> Physical entity

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?

And aren’t biochemical memories also products of the mind.

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 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.

Before life, there were only 1) mindless 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 things 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.

Pierre Bordieu's three relations of knowledge

The closest triangle to ours is probably a relatively new one, Pierre Bordieu's three relations of knowledge.

https://www.researchgate.net/figure/Three-relations-of-knowledge-claims_fig1_237337613.

Pierre Bordieu’s three relations of knowledge

Knowledge

Knower <objectify> Known

Issue: knowledge is found in both memories and messages.

Revised to match our triangle

Knowledge

Actors <observe> Known things

Bordieu's three entities look similar to ours, but are not the same,

It seems his knowers are not envisagers, and it is unclear whether a knower can create knowledge on their own.

Does his knowledge include both memories and messages?

The meanings of social and epistemic are unclear.

Bordieu doesn’t connect his triangle to psycho-biology, system theory and philosophy as we do.

Conclusions and remarks

This article is a supplement to this description theory.

Where this general triangle is used to relate describers and descriptions to what is described.

Episteomology

Descriptions

Describers <observe and envisage> Phenomena

This article reviews other philosophical triangles and revises them to match our epistemological triangle.

E.g. it revises the classic semiotic triangle, and Peirce’s triadic sign relation, to match the new triangle.

This is not to say the existing triangles are “wrong”; all of them are mental models.

It is to suggest that, revised as suggested here, the other triangles are simpler and clearer (or perhaps, they should be turned into squares).

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

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 – too human-centric.

· Heraclitus and Kant – close to my philosophy

· Charles Darwin and W Ross Ashby - my touchstones.

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