Trikonic

Last updated
Figure 1.0: The Trikonic Symbol or 'trikon' represents three categorical elements and their relationship for the subject in consideration Trikonic - Figure 1.0 The Trikonic Symbol.jpg
Figure 1.0: The Trikonic Symbol or ‘trikon’ represents three categorical elements and their relationship for the subject in consideration

Trikonic, is a proposed method of philosophical analysis-synthesis. It is based on Charles Sanders Peirce's "trichotomic", which he described in 1888 as "the art of making three-fold divisions". Trikonic, or "diagrammatic trichotomic", was developed by Gary Richmond in 2005. [1]

Contents

Peircean Category Theory

A major part of trikonic analysis is the three Peircean categories; these consist of firstness, secondness and thirdness:

Figure 2.0 The Three Peircean Categories Trikonic - Figure 2.0 The Three Peircean Categories.jpg
Figure 2.0 The Three Peircean Categories

Another way of describing the basic understanding of these notions is from Sowa:

“First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction, with something else. Third is the conception of mediation, whereby a first and a second are brought into relation. (1891)”

Trikonically represented, the categories are (Figure 2.0):

There are many ways in which these notions can be interpreted.[ according to whom? ] These can be represented as:

Peirce's Three Universes of Experience (Figure 3.0):

Figure 3.0 Peirce's Three Universes of Experience: Trikonic - Figure 3.0 Peirce's Three Universes of Experience.jpg
Figure 3.0 Peirce's Three Universes of Experience:

These in turn represent Peirce's three Universal Categories (Figure 4.0 The Universal Categories):

Figure 4.0 The Universal Categories: Trikonic - Figure 4.0 The Universal Categories.jpg
Figure 4.0 The Universal Categories:

In addition to the universal categories, there are equivalent Existential Categories (Figure 5.0 The Existential Categories):

Figure 5.0 The Existential Categories: Trikonic - Figure 5.0 The Existential Categories.jpg
Figure 5.0 The Existential Categories:

We can also trikonically analyse thought, by identifying three Logical Modalities[ according to whom? ] (Figure 6.0 The Logical Modalities):

Figure 6.0 The Logical Modalities: Trikonic - Figure 6.0 The Logical Modalities.jpg
Figure 6.0 The Logical Modalities:

With these representations in mind, firstness, secondness and thirdness can be defined as the following[ according to whom? ]:

Vector Analysis

Figure 7.0 The Vectors Trikonic - Figure 7.0 The Vectors.jpg
Figure 7.0 The Vectors

There are six vectors[ according to whom? ] that can be used in trikonic vector analysis; these are shown in Figure 7.0.

These six vectors have also been referred to as “directions of movement through the trikon” (Richmond, 2005). They are permutations of the triad, i.e. they are different arrangements of the order of firstness, secondness and thirdness. They represent the relationships between firstness (1ns), secondness (2ns) and thirdness (3ns) for the object that is being analysed.

Figure 8.0 The Determination Vector Triknoic-Figure 8.0 The Determination Vector.jpg
Figure 8.0 The Determination Vector

Within trikonic are six directions, which are all permutations of logical paths of relations keeping the notion of 1ns, 2ns and 3ns throughout the object under consideration.

You can interpret these in many ways, for example, the Determination Vector and Representation Vector (Please refer to Figure 8.0 and Figure 9.0).[ according to whom? ]

Figure 9.0 The Representation Vector Trikonic - Figure 9.0 The Representation Vector.jpg
Figure 9.0 The Representation Vector

The reasoning behind the exploration of the six vectors within the triad aims at bringing a new view on analysis and a more systematic treatment to some of the difficult issues which arise especially in semiotic analysis, i.e. the vector process is a graphically logical analysis with aspects of dependence and constraint, and correlation, which tie in with the "living" reflection of the categories by the semiotic triad.[ according to whom? ]

The reasoning behind the vector analysis is to use the permutations within the triad for the theory and any actual semiosis, mostly the analysis of complex virtual communicative projects.[ according to whom? ] Semiosis is defined as:

"Semiosis is the making or production of meaning. The term was introduced by Charles Peirce (1839-1914) to describe the process of signification within the science of signs now termed semiology".

Trikonic analysis could lead to a kind of trikonic synthesis (the combination of separate elements or substances to form a coherent whole producing fundamental change in the further evolution of virtual community development.[ weasel words ]

Trikonic Analysis in HCI

Richmond suggests that “not all things can be trikonically analysed” (2005). However, there has been investigation into whether trikonic can be applied to HCI related issues.[ according to whom? ] Especially, those issues concerned with websites and culture, trikonic analysis using the Peircean Category Theory has been used to analyse how trust is invoked in a user when using websites.[ according to whom? ] It may be possible to use 1ns, 2ns and 3ns to categorise features of a website, for example the visual elements, colours or text used, layout, the content of the website, credibility, how the elements relate to the users actual purpose of using the website etc.[ weasel words ]

One of the purposes of trikonic is to explore whether it can help to identify what elements of a website actually influence the user to perceive it to be credible or not.[ according to whom? ]

Trikonic Analysis on the Interoperability of Conceptual Graph (CG) Tools

When approaching software problems like the interoperability of CG tools, it is often useful to look at a situation from a software engineering perspective to find a solution. However, with the use of trikonic it is possible to approach the software engineering problem in this way. Trikonic analysis is a very sophisticated method,[ weasel words ] and as shown in the examples above it can be used in many different ways and scenarios. Again, using the notions of 1ns, 2ns and 3ns it may be possible to see how certain elements of the CG tools relate to each other in this way and produce a good solution from this.[ weasel words ]

Examples of the three categories could be the programming language, the CG language and the architecture of the software. From this you could say, that:

“this CG language is a possibility” (1ns), “the programming language needs to be…” (2ns), “the architecture of the software is…” (3ns).

See also

Related Research Articles

In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities according to Amie Thomasson. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction. Various systems of categories have been proposed, they often include categories for substances, properties, relations, states of affairs or events. A representative question within the theory of categories might articulate itself, for example, in a query like, "Are universals prior to particulars?"

<span class="mw-page-title-main">Charles Sanders Peirce</span> American thinker who founded pragmatism (1839–1914)

Charles Sanders Peirce was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss, Peirce was "the most original and versatile of America's philosophers and America's greatest logician". Bertrand Russell wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever".

Semiotics is the systematic study of sign processes and the communication of meaning. In semiotics, a sign is defined as anything that communicates intentional and unintentional meaning or feelings to the sign's interpreter.

<span class="mw-page-title-main">Abductive reasoning</span> Inference seeking the simplest and most likely explanation

Abductive reasoning is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher and logician Charles Sanders Peirce beginning in the latter half of the 19th century.

In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics which provide only for true and false.

In semiotics, a sign is anything that communicates a meaning that is not the sign itself to the interpreter of the sign. The meaning can be intentional, as when a word is uttered with a specific meaning, or unintentional, as when a symptom is taken as a sign of a particular medical condition. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste.

A pragmatic theory of truth is a theory of truth within the philosophies of pragmatism and pragmaticism. Pragmatic theories of truth were first posited by Charles Sanders Peirce, William James, and John Dewey. The common features of these theories are a reliance on the pragmatic maxim as a means of clarifying the meanings of difficult concepts such as truth; and an emphasis on the fact that belief, certainty, knowledge, or truth is the result of an inquiry.

The semiosphere is an idea in biosemiotic theory proposing that, contrary to ideas of nature determining sense and experience, the phenomenal world is a creative and logical structure of processes of semiosis where signs operate together to produce sense and experience.

<span class="mw-page-title-main">Existential graph</span> Type of diagrammatic or visual notation for logical expressions

An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.

<span class="mw-page-title-main">Representation (arts)</span> Signs that stand in for and take the place of something else

Representation is the use of signs that stand in for and take the place of something else. It is through representation that people organize the world and reality through the act of naming its elements. Signs are arranged in order to form semantic constructions and express relations.

<span class="mw-page-title-main">Set (music)</span>

A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.

A sign relation is the basic construct in the theory of signs, also known as semiotics, as developed by Charles Sanders Peirce.

<span class="mw-page-title-main">Inquiry</span> Any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem

An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.

<span class="mw-page-title-main">Charles Sanders Peirce bibliography</span>

This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and Nachlass. For an extensive chronological list of Peirce's works, see the Chronologische Übersicht on the Schriften (Writings) page for Charles Sanders Peirce.

<span class="mw-page-title-main">John Deely</span> American philosopher

John Deely was an American philosopher and semiotician. He was a professor of philosophy at Saint Vincent College and Seminary in Latrobe, Pennsylvania. Prior to this, he held the Rudman Chair of Graduate Philosophy at the Center for Thomistic Studies, located at the University of St. Thomas (Houston).

<span class="mw-page-title-main">Diagrammatic reasoning</span>

Diagrammatic reasoning is reasoning by means of visual representations. The study of diagrammatic reasoning is about the understanding of concepts and ideas, visualized with the use of diagrams and imagery instead of by linguistic or algebraic means.

<span class="mw-page-title-main">Semiotic theory of Charles Sanders Peirce</span>

Charles Sanders Peirce began writing on semiotics, which he also called semeiotics, meaning the philosophical study of signs, in the 1860s, around the time that he devised his system of three categories. During the 20th century, the term "semiotics" was adopted to cover all tendencies of sign researches, including Ferdinand de Saussure's semiology, which began in linguistics as a completely separate tradition.

<span class="mw-page-title-main">Categories (Peirce)</span>

On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory of predication involving three universal categories that Peirce continued to apply in philosophy and elsewhere for the rest of his life. The categories demonstrate and concentrate the pattern seen in "How to Make Our Ideas Clear", and other three-way distinctions in Peirce's work.

Earthscore is a notational system that enables collaborating videographers to produce a shared perception of environmental realities. The system optimizes the use of video and television in the context of the environmental movement by incorporating the cybernetic ideas of Gregory Bateson and the semiotics of Charles Sanders Peirce. The intent of the system is to generate human behaviors that comply with the self-correcting mechanisms of the Earth. Earthscore has been studied and utilized by university students and academics worldwide since 1992.

References

  1. Richmond, Gary (2005). "Outline of trikonic⊳*k: Diagrammatic Trichotomic". Conceptual Structures: Common Semantics for Sharing Knowledge. Lecture Notes in Computer Science. Vol. 3596. Springer. pp. 453–466. doi:10.1007/11524564_31. ISBN   978-3-540-27783-5 . Retrieved 12 June 2024.

Further reading