A thinking triad

This article addresses the ontology of epistemology, the study of how we describe the world using signs, symbols and signals.

• "Signs, symbols, and signals are basic to our existence on many organizational levels, from the biological to the psychological to the social. The ‘semiosphere’… envelopes and incorporates us at every turn. Semiotic concepts, properly developed, are critical for a deep understanding of the organization of life, the functioning of the brain, and the functional organization of the observer." P. Cariani

For over 100 years, semioticicans and or epistemologists have tried to relate thinkers, thoughts, words and things in a triangular concept graph. Notable triads include:

• Ogden and Richards: Semiotic Triangle
• Charles Peirce: Triadic sign relation
• Karl Popper: Three worlds view
• The OMG model for Business Vocabulary and Rules
• Pierre Bourdieu: three relations

This article compares the five older triads above with the newer triadic form introdiced in the preface below.

Contents: Five older semiotic/epistemological triads. A better triadic model. More about systems thinking. Remarks on a tetrahedric model. Further reading.

Preface (recap)

The triadic concept graphs in these articles illuminate how we describe reality.

In verbal thinking, we continually abstract from the detail of things we observe in reality to descriptions of them. We generalise from particulars to universals, from instances to types. We create types like "pentagon" and "smile" and use them in memories and messages to describe both what we observe, and fantasies we envisage.

The triadic models help to illuminate the text here. but I should mention also sets and tokens.

1. Type: a description, definition or model of an individual, a set member.
2. Set: a collection of 0, 1 or many set members.
3. Token: a name or other kind of symbol for a type.
4. Instance: a manifestation of a type in an observable phenomenon.
5. Thing: an object or a process that may manifest a variety of types.

Discussions of philosophy and systems thinking can become confused or confusing when we blur the difference between 1 and 2, or 3 and 4, or 4 and 5.

Below are four more graphics that may help you to understand what this article is about.

Five older semiotic/epistemological triads

The article on Description and reality explores how knowledge is found in the acts of creating and using a description, in the moments it is paired with things or acts in reality (or fantasy).

For example, the meaning of a bird's alarm call is not in the symbol alone, it is in the pairing, in a bird's mind, of the symbol with its meaning, a direction to fly away from danger.

How people describe things that they observe and envisage, using signs and symbols, is the subject matter of epistemology and semiotics. There is a tradition of drawing triadic models that relate thinkers, thoughts, things and words. This section outines five triadic models/

Ogden and Richards: Semiotic Triangle

Ogden and Richards might have been the first (1923) to try to express how thoughts, things and words are related, in a triadic concept graph.

The triad says words stand for things. One might also plausibly say words stand for thoughts, or thoughts stand for things.

Aside: The relationships in a such a concept graph can be named in either direction. I usually favor the direction in which the statement contains an active verb rather than a passive one.

Charles Peirce: Triadic sign relation

Charles Peirce offered a variation of the triad above.

What Peirce meant by the three concepts is not straightforward, and evolved over time. From what I have read and been told, I believe the following is a fair summary.

An object is either a thing that exists regardless an interpreter, or else, just those features of a thing that manifest signs - a phenomenon as it is observed or envisaged.

A sign is a thing that represents an object. It can be iconic, symbolic (a name or token, a description or type) or indicative of an object. In other words, it can be a simulation, a symbol or symptom.

An interpretant is "something like a mind, a mental act, a mental state, or a feature or quality of mind" (Stanford Encyclopedia of Philosophy). Is it an interpeter, an interpretation, or both? A correspondent tells me it is the effect of a sign on a mind, which can be immediate, dynamic or final.

To my mind, there is much ambiguity here. Peirce's triad is confusing because in each corner there are two meanings:

• "Interpretant" conflates interpreters and interpretations
• "Object" conflates things (unobserved) and their manifestations of signs
• "Sign" conflates indicative symptoms and representative symbols.

Moreover, the triad separates signs or symbolic representations between:

• organic or neural symbols in memory (referred to as interpretants)
• verbal symbols in messages (referred to as signs).

We continally and instantly translate between these two kinds of sign, even as we speak or type a message. Our thinking brains hold both organic or neural senses of things, and verbal descriptions of them. Our thoughts may be both the effects of signs detected, and the triggers of signs created.

Karl Popper: Three worlds view

Popper’s triad is also open to interpretation. Is it a mental world a thinker or a thought? And surely products of fhe mind include mental models as well as spoken words?

Popper's triad appears to separate private and public models of the world. But as Ashby pointed out, thinkers translate between them, in either direction, with amazing speed and dexterity.

The OMG model for Business Vocabulary and Rules

The Object Management Group (OMG)'s SBVR standard formalizes the use of natural language for modeling concepts and sharing meanings. It presumes a triad of the kind below.

The SBVR standard says representations such as records in information systems exist as real world things. But representations in speech, writing, drawings, and neural networks also exist as real world things.

Also, however fuzzy, fragile and forgettable the concepts we conceive are, they too exist when and where we conceive or communicate them .

Moreover, the SVBR triad appears to separate private representations of things from public representations of things. But both are symbolic of what they represent, and thinkers translate between private and public representaions, in either direction, with amazing speed and dexterity.

Pierre Bourdieu: three relations

This triad is different. As I read it, the knowledge corner can be information held in the mind, spoken or written, its makes no difference what form it takes

Bordieu's triad helps us to see concepts in mind, speech and writing as interchangable forms of knowledge.

A better triadic model

The table below compares the five older triadic models of semotics (above) with triads to follow in this article.

The older five triads above don't distinguish the instantiation or manifestation of a description from the thing that is described - which is so much more than any desription of it.

The instantiation or manifestation of a type (by a thing) is observable as phenomenon that is distinct from both the type and the thing. (Data modelers will understand this as resolving a many-to-many relationship between descriptive types and things.)

The map is not the territory

• "The map is not the territory it represents, but if correct, it has a similar structure to the territory, which accounts for its usefulness." Alfred Korzybski, a Polish-American philosopher and engineer.

The graph to the right below separates an instantiation (mapped features) from the descriptive type they instantiate (map) and the thing (territory) that manifests the mapped features.

To say “The map is not the territory” is to say a represention of reality (in mind, speech or writing) is distinct from the reality.  And as Korzybski said, to be correct (true, useful), the mapped features must correspond to those in the territory.

Aside: in Neurolinguistic Programming (NLP), the phrase means how we see the world is subjective and based on our own life experiences, perspectives, and beliefs. Some misinterpret that to mean "my truth" is as true as any other, which is misleading, since to be correct, the features in "my truth" must correspond to those in reality.

A thinking triad

Axiomatic here is the idea that thinkers <create and use> models to <represent> phenomena they <observe and envisage> in real world things. And the model is true to the extent it accurately represents the phenomenon it is related to.

The terms above are defined below.

Phenomenon: one or more things as they are perceived or envisaged to be. It may be an instance, example, or manifestation in reality of a model.

Thinker: an entity able to observe and envisage, create and use models of, phenomena. And perhaps also share models in a communicable form.

What is the difference between observing things such as horses, and envsaging things such as unicorns?

Observe: consume information from a phenomena. Observing is a process (organic or inorganic) by which sensors detect phenomena (perceptible in reality) and create models, memories or descriptions of them.

Envisage: create information about a possible phenomena, create a model of it. Envisaging is a process (natural or artificial) that creates models, memories or descriptions of phenomena not directly observed - typically, by manipulating past models, memories or descriptions.

The processes of observing and envisaging things in reality create descriptions in memories we may call mental models.

Model: something created or used to represent or symbolize selected features of something else, be it observed or envisaged. You might replace model by type, theory or description

We're not talking here of iconic models (such as statues); we're talking of symbolic models, which may be neural or verbal.

A model is both abstract and real. It is only a model in relation to whatever phenomenon it is created or used to model. And it only plays the role of being a model in the process of being created or used in that way by some actor.

The systems thinking triad to the right below is a variant of the more general triad to the left.

The two examples below separate instantiations (card games and symphony performances) from the descriptive types they instantiate and the things that instantiate them.

For more on these systems thinking triads, read this article.

Remarks on a tetrahedric model

You may have seen a tetrahedron in which the fours corners are Objects in the world, Concepts in the brain, Designators (terms) used in communication, and Definitions of those designators. Below, I've turned the tetrahedron into a concept graph, and added some verb phrases to link the four corners.

Verbal models (in memories and messages) typify what they represent. A concept is defined by pairing of a type token/designator ("circle") with a type definition (a line drawn around and equidistant from a point) defines a concept.

Whether a concept is real or imaginary, like "unicorn", the concept has a physical form. It may be encoded in any or all of a sensation in the nervous system, vibrations in the air (speech), graphical symbols (writing), electronic recordings, and patterns on computer memory cards.

Yes, a neural model is inside a person, a verbal model may be used to communicate between people, and an electronic record may be used to communicate between computers. However, much of our conceptualisation is an internal narrative conducted using the same verbal designators and definitions we use for external communication.

My version of the tetrahedric model is this.

Further reading

The triadic model in this article features in the related articles below.

• The nominalist’s viewpoint
• Description and reality
• A thinking triad
• A theory of types
• Knowledge structures
• A systems thinking triad.