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Unknown's avatar Jon Awbrey 10:17 am on December 27, 2025
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Sign Relations • Denotation

One aspect of a sign’s complete meaning concerns the reference a sign has to its objects, which objects are collectively known as the denotation of the sign.  In the pragmatic theory of sign relations, denotative references fall within the projection of the sign relation on the plane spanned by its object domain and its sign domain.

The dyadic relation making up the denotative, referent, or semantic aspect of a sign relation L is notated as \mathrm{Den}(L).  Information about the denotative aspect of meaning is obtained from L by taking its projection on the object‑sign plane.  The result may be visualized as the “shadow” L casts on the 2‑dimensional space whose axes are the object domain O and the sign domain S.  The denotative component of a sign relation L, variously written as \mathrm{proj}_{OS} L,  L_{OS},  \mathrm{proj}_{12} L,  or L_{12}, is defined as follows.

Display 3

Tables 3a and 3b show the denotative components of the sign relations associated with the interpreters \mathrm{A} and \mathrm{B}, respectively.  The rows of each Table list the ordered pairs (o, s) in the corresponding projections, \mathrm{Den}(L_\mathrm{A}), \mathrm{Den}(L_\mathrm{B}) \subseteq O \times S.

Denotative Components Den(L_A) and Den(L_B)

Looking to the denotative aspects of L_\mathrm{A} and L_\mathrm{B}, various rows of the Tables specify, for example, that \mathrm{A} uses ``\text{i}" to denote \mathrm{A} and ``\text{u}" to denote \mathrm{B}, while \mathrm{B} uses ``\text{i}" to denote \mathrm{B} and ``\text{u}" to denote \mathrm{A}.

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar Jon Awbrey 11:24 am on December 25, 2025
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Sign Relations • Dyadic Aspects

For an arbitrary triadic relation L \subseteq O \times S \times I, whether it happens to be a sign relation or not, there are six dyadic relations obtained by projecting L on one of the planes of the OSI‑space O \times S \times I.  The six dyadic projections of a triadic relation L are defined and notated as shown in Table 2.

\text{Table 2. Dyadic Aspects of Triadic Relations}

Dyadic Aspects of Triadic Relations

By way of unpacking the set‑theoretic notation, here is what the first definition says in ordinary language.

The dyadic relation resulting from the projection of L on the OS‑plane O \times S is written briefly as L_{OS} or written more fully as \mathrm{proj}_{OS}(L) and is defined as the set of all ordered pairs (o, s) in the cartesian product O \times S for which there exists an ordered triple (o, s, i) in L for some element i in the set I.

In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of L can be recognized as formalizing aspects of sign meaning which have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology.

Of course, traditions vary with respect to the precise formation and usage of such concepts and terms.  Other aspects of meaning have not received their fair share of attention and thus remain innominate in current anatomies of sign relations.

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar antlerboy - Benjamin P Taylor 4:07 am on December 22, 2025  

Top ten most read posts on the Systems Community of Inquiry in 2025 (number four will have you *shook*!)

Every now and again I look at the stats for this site. It’s a useful little reality check for what people actually look for when they land here.’ (The stats I think only pick up web visitors; my suspicion is that a bunch of people look just at the emails).

If you’re new: this site is a public commonplace book, or what used to be called a ‘weblog’ – ostensibly an attempt to share all the systems | complexity |cybernetics links I come across, partly an Electric Monk, resource-based, a compost heap towards a curriculum.

The top clicks tell a clear story. People keep coming for foundations, for sources, and for practical bridges between ‘systems’ as an idea and systems as work.

McLuhan consistently sits at the top. That always makes me smile, because his point is basically what this site is for. Tools are extensions, and therefore amputations. If you extend your memory into a notebook, you also stop rehearsing. If you extend your judgement into a dashboard, you also numb your situational sense. Pretending otherwise is how we end up surprised by our own inventions.

Then comes the pragmatic end of the field, if we squint: poka-yoke, homeostasis, STAMP, promise-based management. The appeal here is not ‘be cleverer’, it’s ‘design so normal humans can succeed without heroics’. A cybernetic idea: shift the work from willpower to feedback.

Reading lists feature heavily too, which is both flattering and slightly alarming. A reading list is an honest artefact: it admits you don’t have the map. It also changes you as you build it. You notice what you keep omitting. You start to see the field as much as being a set of disagreements as a set of answers. Which is why debates like ‘systems thinking and complexity’ keep drawing attention. We want a tidy resolution, rarely get one, but sometimes get better questions.

And people really do care about attribution. The Kurt Lewin quote post keeps getting read. Good. There is far too much ‘systems’ talk built on lines no-one can trace. A misattributed quote can still be helpful, but it’s a different kind of helpful – dodgy authority rather than lineage.

A few other regular visitors show up in the stats: Bateson, Menzies Lyth, Joanna Macy. That’s the moral and emotional dimension of systems work. Organisations are not just information processing. They are also anxiety processing. If you don’t deal with that, you get defences that pretend to be structure.

And there’s a pleasing concentration of systems practice in the mix – SysPrac25, the upcoming Hull conference, and the OR Society: events, newsletters, debates. Systems | complexity | cybernetics stays alive when people meet, argue, teach, and keep the conversation going in actual places, not just on platforms. And this is in a year where I have substantially failed the core task and lost track of brilliant events from ISSS, CybSoc, ASC, Metaphorum, even SCiO.  But I think that the field also stays alive when someone bothers to ask ‘who are our fellow travellers?’.

Anyway, for what it’s worth, here’s the current ‘most read’ list. If it looks like a slightly eccentric syllabus, well, there y’go!

Media, attention, and extensions

Cybernetics, quality, and the craft of organising

How we know, what we can cite, and what we should read next

People, communities, and places where the field stays alive

See also

Top ten most read posts on the Systems Community of Inquiry in 2024
Top ten most read posts on the Systems Community of Inquiry in 2023 (rather surprising!)
Unknown's avatar antlerboy - Benjamin P Taylor 4:03 am on December 22, 2025  

Harish’s Notebook – Throwing the Fish Back into the Water (Jose, 2025)

Throwing the Fish Back into the Water:
Unknown's avatar Jon Awbrey 6:00 pm on December 19, 2025
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Sign Relations • Examples

Soon after I made my third foray into grad school, this time in Systems Engineering, I was trying to explain sign relations to my advisor and he, being the very model of a modern systems engineer, asked me to give a concrete example of a sign relation, as simple as possible without being trivial.  After much cudgeling of the grey matter I came up with a pair of examples which had the added benefit of bearing instructive relationships to each other.  Despite their simplicity, the examples to follow have subtleties of their own and their careful treatment serves to illustrate important issues in the general theory of signs.

Imagine a discussion between two people, Ann and Bob, and attend only to the aspects of their interpretive practice involving the use of the following nouns and pronouns.

\{ ``\text{Ann}", ``\text{Bob}", ``\text{I}", ``\text{you}" \}

  • The object domain of their discussion is the set of two people \{ \text{Ann}, \text{Bob} \}.
  • The sign domain of their discussion is the set of four signs \{ ``\text{Ann}", ``\text{Bob}", ``\text{I}", ``\text{you}" \}.

Ann and Bob are not only the passive objects of linguistic references but also the active interpreters of the language they use.  The system of interpretation associated with each language user can be represented in the form of an individual three‑place relation known as the sign relation of that interpreter.

In terms of its set‑theoretic extension, a sign relation L is a subset of a cartesian product O \times S \times I.  The three sets O, S, I are known as the object domain, the sign domain, and the interpretant domain, respectively, of the sign relation L \subseteq O \times S \times I.

Broadly speaking, the three domains of a sign relation may be any sets at all but the types of sign relations contemplated in formal settings are usually constrained to having I \subseteq S.  In those cases it becomes convenient to lump signs and interpretants together in a single class called a sign system or syntactic domain.  In the forthcoming examples S and I are identical as sets, so the same elements manifest themselves in two different roles of the sign relations in question.

When it becomes necessary to refer to the whole set of objects and signs in the union of the domains O, S, I for a given sign relation L, we will call this set the World of L and write W = W_L = O \cup S \cup I.

To facilitate an interest in the formal structures of sign relations and to keep notations as simple as possible as the examples become more complicated, it serves to introduce the following general notations.

Display 1

Introducing a few abbreviations for use in the Example, we have the following data.

Display 2

In the present example, S = I = \text{Syntactic Domain}.

Tables 1a and 1b show the sign relations associated with the interpreters \mathrm{A} and \mathrm{B}, respectively.  In this arrangement the rows of each Table list the ordered triples of the form (o, s, i) belonging to the corresponding sign relations, L_\mathrm{A}, L_\mathrm{B} \subseteq O \times S \times I.

Sign Relation Twin Tables LA & LB

The Tables codify a rudimentary level of interpretive practice for the agents \mathrm{A} and \mathrm{B} and provide a basis for formalizing the initial semantics appropriate to their common syntactic domain.  Each row of a Table lists an object and two co‑referent signs, together forming an ordered triple (o, s, i) called an elementary sign relation, in other words, one element of the relation’s set‑theoretic extension.

Already in this elementary context, there are several meanings which might attach to the project of a formal semiotics, or a formal theory of meaning for signs.  In the process of discussing the alternatives, it is useful to introduce a few terms occasionally used in the philosophy of language to point out the needed distinctions.  That is the task we’ll turn to next.

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar antlerboy - Benjamin P Taylor 7:04 pm on December 16, 2025  

An Interview with Eric Trist, Father of the Sociotechnical Systems Approach – Fox (1990)

Not available except behind paywall from main link, but fully readable if not downloadable on Scribd:

William M. Fox

The Journal of Applied Behavioral Science Volume 26, Issue 2

https://doi.org/10.1177/0021886390262014

Abstract

William M. Fox interviews Eric Trist, eminent scholar and social scientist, who was a founder and chairman of the Tavistock Institute in London. Trist recounts the foundation of the institute as an outpatient clinic and its evolution into a leading center of action research and applied behavioral science. He discusses his work in the British coal mining industry, from which he developed the concept of the sociotechnical system. Descriptions of his work and experiences with the British Army during World War II and of the various projects he undertook with multinational firms and smaller companies illustrate the resistance, suspicion, and other obstacles that he and his colleagues often encountered while working to implement new systems. Finally, Trist describes his sociotechnical systems work in the ailing industrial town of Jamestown, New York, and on the Ten recommendations.

https://journals.sagepub.com/doi/10.1177/0021886390262014

Unknown's avatar Jon Awbrey 12:56 pm on December 16, 2025
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Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.  In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject.  In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve.  In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation.  Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

  • Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA.  Reprinted (1991), Prometheus Books, Buffalo, NY.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online (doc) (pdf).

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar antlerboy - Benjamin P Taylor 2:10 am on December 16, 2025  

The IFSR Quarterly 4_2025 – a window into and mirror of the cybersystemic community. Brought to you by the IFSR.org

[Includes my short reflections on the SysPrac25 conference – longer version will be published here eventually, if I haven’t already done that!]

https://www.linkedin.com/pulse/ifsr-quarterly-42025-window-mirror-3vnff/

Louis Klein introduced it thusly:

#quarterly International Federation for Systems Research (IFSR) with musings by Ray Ison, a generated reflection on hashtag#sysprac25 by Benjamin P. Taylor, a link by Dr. Louis Klein, a (one more thing …) contribution by Philippe Vandenbroeck and the attention of Rika Preiser Pamela Buckle Dr. Nam Nguyen as well as in gratitude to the numerous contributors for a series of hashtag#calls Angela Espinosa Cathal Brugha Martin Reynolds Sven-Volker Rehm (…) into the cybersystemic community – enjoy reading, and sharing!

https://www.linkedin.com/pulse/ifsr-quarterly-42025-window-mirror-3vnff/

Unknown's avatar Jon Awbrey 12:00 pm on December 15, 2025
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Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.  Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places.  In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

  • Correspondence.  From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself.  In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.
  • Determination.  Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes.  First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms.  Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.
  • Non‑psychological.  Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism.  He was quite interested in matters of psychology and had much of import to say about them.  But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar Jon Awbrey 9:36 am on December 14, 2025
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Sign Relations • Anthesis

Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun.

— C.S. Peirce, Collected Papers, CP 2.274

In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or semiosis, Peirce uses the technical term representamen for his concept of a sign, but the shorter word is precise enough, so long as one recognizes its meaning in a particular theory of signs is given by a specific definition of what it means to be a sign.

Resources

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #connotation, #denotation, #inquiry, #logic, #logic-of-relatives, #mathematics, #relation-theory, #semiosis, #semiotic-equivalence-relations, #semiotics, #sign-relations, #triadic-relations

Unknown's avatar antlerboy - Benjamin P Taylor 12:59 pm on December 5, 2025  

@RedHotWorld on Twitter: thread on Limits to Growth

[Interesting to see how the story is told]

@RedHotWorld

It has been called “the most prophetic work of humanity”. In 1971, it told us why collapse is coming and how to avoid it. It was denounced by almost every leading economist – but it was right. This is the story of The Limits To Growth.

Unknown's avatar antlerboy - Benjamin P Taylor 3:31 am on December 5, 2025  

The Structure of Wholes – Angyal (1939)

[I don’t usually share papers you can’t download without a paywall but you can get this – or a version of it, or the thinking behind it – in this book by the same author

https://ia902902.us.archive.org/13/items/foundationsforascienceofpersonality/Foundations%20For%20A%20Science%20Of%20Personality_text.pdf

…shared here obviously as early thinking on wholism, connection to gestalt, precursor to systems thinking etc. See also https://en.wikipedia.org/wiki/Andras_Angyal ]

Andras Angyal

Get accessShareCite

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Extract

In attempting to clarify the problem of personality integration the writer gained the impression that the difficulty of such a task does does not lie alone in the paucity of usable factual data but it is due, even to a greater extent, to the inadequacy of our logical tools. Such a handicap is felt not only in the study of personality, but in the study of wholes in general. Here the attempt will be made to develop some concepts which may be useful for the understanding of the structure of wholes.

You can see the beautiful classic type here

https://www.jstor.org/stable/184329

Another link if you have academic access:

https://resolve.cambridge.org/core/journals/philosophy-of-science/article/abs/structure-of-wholes/D9C306F0D4B2D2AA9A2CF6BD70DFB88D

Unknown's avatar antlerboy - Benjamin P Taylor 3:25 am on December 5, 2025  

Katarxis Nº 3 – NEW SCIENCE, NEW URBANISM, NEW ARCHITECTURE? with a forward by Christopher Alexander (2004)

‘People used to say that just as the twentieth century had been the century of physics, the twenty-first century would be the century of biology…  We would gradually move into a world whose prevailing paradigm was one of complexity, and whose techniques sought the co-adapted harmony of hundreds or thousands of variables.  This would, inevitably, involve new technique, new vision, new models of thought, and new models of action.  I believe that such a transformation is starting to occur…. To be well, we must set our sights on such a future.’

  –  Christopher Alexander, The Nature of Order

http://www.katarxis3.com/Introduction.htm

Unknown's avatar antlerboy - Benjamin P Taylor 3:55 pm on December 2, 2025  

Complex Systems Toolkit from the Enginering Professors Council – the voice of engineering academics

Find the right tool

Use the search to find the tools you need.

The EPC’s Complex Systems Toolkit provides accessible, practical resources for embedding complex systems concepts into engineering education. The Complex Systems Toolkit is supported by Quanser.
Complex Systems Toolkit
Unknown's avatar antlerboy - Benjamin P Taylor 9:39 am on December 2, 2025  

WæverConflictualization: A theory of how relations, societies and issues become formed by the logic of conflict – Bramsen and Wæver (2025)

Isabel Bramsen*, Ole Wæver

This article presents a Luhmann-inspired theory of conflictualization, that is, how objects, relations, and societies come to be defined by the logic of conflict. This article presents a Galtung- and Luhmann-inspired theory of conflictualization, that is, how objects, relations, and societies come to be defined by the logic of conflict. The article conceptualizes conflictualization as a threefold process of (1) forming social relationships, (2) displacing the focus toward “winning” the conflict, and (3) making an increasing number of issues into objects of contestation. It positions the concept of conflictualization in relation to contemporary (Nordic) peace research, securitization, politicization, and polarization, showing the added value of the theory in terms of teasing out how conflict “does something” and should therefore not be reduced to its causes or effects, but understood distinctly as conflict. To illustrate this, the article discusses three examples of how a society, a relationship, and an issue, respectively, are conflictualized: (1) how the Danish-Greenlandic relationship has been conflictualized, (2) how the war in Gaza has shaped social relations and conflictualized other issues like climate activism and LGBTQ+ rights across the Nordic countries, and (3) conflictualization of the Colombian society post-accord. Moreover, we discuss how conflictualization relates to agency and change, that is, the degree to which conflictualization can be seen as a deliberate process and calls for strategies of conflictualizing and de-conflictualizing issues.

https://journals.sagepub.com/doi/full/10.1177/00108367251382794