antlerboy - Benjamin P Taylor 9:40 am on August 10, 2026

announcing The Necessary Tangle – a living evidence atlas of systems | cybernetics | complexity

I’ve been wanting for years to do a ‘better map’ of systems | complexity | cybernetics, having strongly criticised the Castellani ‘complexity map’ and seen some others – and been involved in the SCiO SysBoK where we tried to map key concepts, their necessary antecedents and dependent thingummies, people, meaning, and so on (- and always inspired by ‘rock family trees’ and the way it’s the constellation of influences and people around individual practitioners that actually makes the difference, as David Ing says).

So with the assistance of ChatGPT, and I’ve been building The Necessary Tangle – a living, evidence-backed atlas of systems | complexity | cybernetics.

It currently maps 411 public entries and 32 developed profiles from 93 registered sources.

The key difference from the usual family tree is that every line has to say what sort of relationship it represents: logical antecedent, historical precursor, documented influence, teaching, collaboration, practical use, and so on.

The eventual ambition to: trace the human as well as conceptual lineages; connect theory to practice; distinguish espoused intellectual genealogy from the clusters the evidence actually produces; and let categories emerge from the resulting network rather than deciding the schools in advance.

It’s very much a public alpha. Some areas are already quite deep; others are little more than markers saying ‘this belongs here’. I’m putting it out now precisely because corrections, missing connections, rival genealogies and ‘surely you can’t say that’ responses are part of building it.

AND I’m very happy to share, collaborate or whatever….

Have a look

https://antlerboy.github.io/the-necessary-tangle/

Benjamin
www.antlerboy.com

antlerboy - Benjamin P Taylor 9:21 am on August 14, 2026

Kyla Avis: Have you ever tried to work with a group of people to do system mapping?

Linkedin post from Kyla Avis: https://www.linkedin.com/posts/kylaavis_have-you-ever-tried-to-work-with-a-group-activity-7493696398811598848-MI6E?utm_source=share&utm_medium=member_desktop&rcm=ACoAAACuq-oBecVFDW6PCf3lkoG-peMeuLBeoho

Have you ever tried to work with a group of people to do system mapping? Maybe you tried it on Kumu or MIro or even on a whiteboard. It gets very messy, very fast. Even when the dialogue is powerful, the map can be useless at the end.

Gene Bellinger has created a really interesting tool with AI. His program will ask you/your team a series of questions to understand the problem and create a system map for you complete with highlighted feedback loops and system archetype descriptions. I’ve only started playing with it but it’s a very valuable tool if you like system thinking.

Here is a link to the tool: https://lnkd.in/gSTZ4SAB
Here is an explainer video: https://lnkd.in/gkuzvMaB

antlerboy - Benjamin P Taylor 7:56 am on August 14, 2026

Requisite Variety for safety – Jun 6, 2026 Todd Conklin’s PreAccident Podcast 601 – Rethinking Safety: AI, Pre-Jobs, and the Power of Listening Ron Gantt about the future of safety

I enjoy this podcast and – underprisingly perhaps – it’s quite systems | cybernetics | complexity – ish.
In this interview with Ron Gantt I was just thinking ‘hmm this is Requitie Variety for safety – that’s insightful/obvious’ and sure enough, Ron Gantt actually uses the phrase ‘the requisite variety necessary to manage a construction site’.
https://preaccidentpodcast.podbean.com/e/rethinking-safety-ai-pre-jobs-and-the-power-of-listening/

So I asked my chat j’ai pété to do a dive into RV as a concept in Safety. It said:

His argument has a recognisable lineage, but he gives it a particularly useful inter-organisational and political twist.

### The closest precedent: high reliability organising

The nearest match I have found is Karl Weick, Kathleen Sutcliffe and David Obstfeld’s 1999 paper, [‘Organizing for High Reliability: Processes of Collective Mindfulness’](https://www.theisrm.org/documents/Weick%20%281999%29%20Organizing%20for%20High%20Reliability%20-%20Processes%20of%20Collective%20Mindfulness.pdf).

They say that high-reliability organisations:

‘cultivate requisite variety and assume that it takes a complex system to sense a complex environment’.

Their mechanisms include diverse perspectives, overlapping checks, job rotation, adversarial review and what Schulman called ‘conceptual slack’: disagreement and alternative interpretations that prevent the organisation from collapsing complexity too soon.

Even closer to Gantt, they describe safety as depending on ‘negotiated complexity’: informal and continually renewed relationships between organisations. Those relationships are not peripheral niceties. They form part of the machinery through which safe operation is produced.

That is almost exactly Gantt’s construction-site problem. The expertise needed to regulate the work is dispersed among client, principal contractor, subcontractors, supervisors, trades and workers. No single organisation contains enough of the relevant variety.

### The direct safety literature

There is also a paper whose title answers your question almost comically directly:

Vanessa Becker Bertoni, Tarcisio Abreu Saurin and Flávio Sanson Fogliatto, [‘Law of requisite variety in practice: Assessing the match between risk and actors’ contribution to resilient performance’](https://doi.org/10.1016/j.ssci.2022.105895), published in *Safety Science* in 2022.

It applies Ashby’s law to the relationship between the variety of risks and the contribution of different actors to resilient performance, using social-network analysis in a healthcare setting. The practical proposition is that safety depends not just on possessing expertise somewhere in the organisation, but on whether the network makes the necessary people and capabilities available to one another.

A related paper by Hirose and colleagues, [‘Functional Analysis of Law of Requisite Variety’](https://doi.org/10.1016/j.ifacol.2022.10.231), links Ashby explicitly with resilience engineering and FRAM. Their modelling suggests that strategies with a greater repertoire of possible actions cope better with variability in working conditions.

So there is an identifiable, if still rather small, literature explicitly joining requisite variety and safety.

### Safety-II and resilience engineering

A much larger body of safety work makes essentially the same argument without always naming Ashby.

The early resilience-engineering formulation defines resilience as the capacity to adjust functioning before, during or after disturbances so that required operations continue under expected and unexpected conditions. The [EUROCONTROL resilience-engineering white paper](https://www.eurocontrol.int/archive_download/all/node/11591) says, in effect, that the less completely work can be specified in advance, the more performance variability is needed.

That is requisite variety translated into safety language:

Work generates more states and disturbances than procedures can enumerate.
People therefore have to notice differences, interpret them and adjust.
A safe system needs a sufficiently differentiated repertoire of responses.
Attempts to remove all variation from human performance can remove the very capacity that keeps the system safe.

Todd Conklin’s formulation that safety is ‘the presence of capacity’, rather than merely the absence of accidents, belongs in this family. Dekker and Tooma develop that idea more systematically in [‘A capacity index to replace flawed incident-based metrics for worker safety’](https://sidneydekker.com/wp-content/uploads/2024/12/ilr.12210.pdf). Among the capacities they identify are operational knowledge, resources, diversity of voices, local decision authority and the ability to respond to emerging risk.

### What Gantt is adding

Gantt’s point is not simply ‘we need more perspectives’. It is that the variety already present on a construction site is prevented from becoming usable regulatory variety.

This makes power a cybernetic variable. A worker or contractor may perceive a dangerous condition and know how to respond, but anticipated blame, contractual exposure or lack of authority can remove that response from the system’s effective repertoire.

In other words, nominal variety is not enough. It has to be:

perceptible;
communicable;
authorised;
resourced;
co-ordinated;
available quickly enough to matter.

Gantt’s suggestion that the more powerful client should accept some liability risk and actively earn trust is therefore not merely a cultural recommendation. It is an attempt to alter the control structure so that distributed knowledge can participate in regulation.

### One important qualification

Requisite variety is a necessary condition for regulation, not a complete theory of safety.

More variety is not automatically better. Unstructured diversity may produce noise, conflict or paralysis. Systems also achieve safety by attenuating disturbance variety: guarding machinery, separating traffic, simplifying interfaces, providing physical buffers and standardising genuinely repeatable work.

The useful question is therefore not simply ‘How do we increase variety?’ It is:

Which disturbances should we prevent or attenuate, and what remaining variety must the system be able to detect, interpret and respond to?

So my short answer is: yes, several traditions have done this. The strongest explicit precursor to Gantt is Weick, Sutcliffe and Obstfeld’s combination of requisite variety, collective mindfulness and ‘negotiated complexity’. What seems particularly sharp in Gantt’s version is the application to the client–contractor boundary: liability, hierarchy and mistrust can leave a construction system full of expertise while making that expertise cybernetically unavailable.

Jon Awbrey 7:40 am on August 12, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Comment 5

Let’s stay with Peirce’s example of abductive inference a little longer and try to clear up the more troublesome confusions tending to arise.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

$\text{Figure 1. Conjunctive Term}~ z, \text{Taken as Predicate}$

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

$\text{Figure 3. Conjunctive Predicate}~ z, \text{Abduction of Case}~ x \Rightarrow y$

One thing needs to be stressed at this point. It is important to recognize the conjunctive term itself — namely, the syntactic string “spherical bright fragrant juicy tropical fruit” — is not an icon but a symbol.‡ It has its place in a formal system of symbols, for example, a propositional calculus, where it would normally be interpreted as a logical conjunction of six elementary propositions, denoting anything in the universe of discourse with all six of the corresponding properties.

The symbol “spherical bright fragrant juicy tropical fruit” denotes objects which may be taken as icons of oranges by virtue of their bearing those six properties in common with oranges. But there are no objects denoted by the symbol which aren’t already oranges themselves. Thus we observe a natural reduction in the denotation of the symbol, consisting in the absence of cases outside of oranges which have all the properties indicated.

The above analysis provides another way to understand the abductive inference from the Fact $x \Rightarrow z$ and the Rule $y \Rightarrow z$ to the Case $x \Rightarrow y.$ The lack of any cases which are $z$ and not $y$ is expressed by the implication $z \Rightarrow y.$ Taking that in conjunction with the Rule $y \Rightarrow z$ gives the logical equivalence $y = z.$ But that reduces the Case $x \Rightarrow y$ to the Fact $x \Rightarrow z$ and so the Case is justified.

Viewed in the light of the above analysis, Peirce’s example of abductive reasoning exhibits an especially strong form of inference, almost deductive in character. Do all abductive arguments take that form, or may there be weaker styles of abductive reasoning which enjoy their own levels of plausibility? That must remain an open question at this point.

Remark

Readers will notice I have slipped at this point from using symbol in the precise technical sense Peirce introduced at the beginning of this discussion to the more ordinary sense all of us, Peirce included, tend to use on other occasions. Should it become a big problem we can always find a way to mark the distinction but so far it seems context has usually sufficed to resolve any likely confusion.

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.

Resources

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

#abduction, #c-s-peirce, #comprehension, #deduction, #extension, #hypothesis, #icon-index-symbol, #induction, #inference, #information-comprehension-x-extension, #inquiry, #intension, #logic, #peirces-categories, #pragmatic-semiotic-information, #pragmatism, #scientific-method, #semiotics, #sign-relations

antlerboy - Benjamin P Taylor 9:37 am on August 11, 2026

Loops all the way up: Recurrency as an implementation-first primitive for consciousness – ScienceDirect

https://www.sciencedirect.com/science/article/pii/S1571064526000606

antlerboy - Benjamin P Taylor 9:37 am on August 11, 2026

Strategic Foresight for Viable Futures

https://publicvitality.substack.com/p/strategic-foresight-for-viable-futures

antlerboy - Benjamin P Taylor 9:36 am on August 11, 2026

https://www.linkedin.com/posts/gandolfo-dominici-48206a9_bslab2027-systemsthinking-complexity-share-7491625601338863616-rsHN/?utm_source=share&utm_medium=member_desktop&rcm=ACoAAACuq-oBecVFDW6PCf3lkoG-peMeuLBeoho

antlerboy - Benjamin P Taylor 8:44 am on August 11, 2026

Teaching with the wrong ends of the constructivist stick – Christian Moore-Anderson

Teaching with the wrong ends of the constructivist stick

Jon Awbrey 2:06 pm on August 9, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Comment 4

Reflecting further on Comment 3, many things still puzzle me about Peirce’s account at this point. The question marks I added to the Figures of that post indicate the node labels I have remaining doubts about. For example, in Figure 3, is $z$ really an icon of object $y?$ Again, in Figure 4, is $u$ really an index of object $v?$ There is nothing for it but returning to Peirce’s text and trying once more to follow his reasoning.

Let’s go back to Peirce’s example of abductive inference and try to get a clearer picture of why he connects it with conjunctive terms and iconic signs.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

$\text{Figure 1. Conjunctive Term}~ z, \text{Taken as Predicate}$

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

$\text{Figure 3. Conjunctive Predicate}~ z, \text{Abduction of Case}~ x \Rightarrow y$

The relationship between conjunctive terms and iconic signs may be understood along the following lines. If there is anything with all the properties described by the conjunctive term “spherical bright fragrant juicy tropical fruit” then sign users may use that thing as an icon of an orange, precisely because it shares those properties with an orange. But the only natural examples of things with all those properties are oranges themselves, so the only thing qualified to serve as a natural icon of an orange by virtue of those very properties is that orange itself or another orange.

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.

Resources

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

Jon Awbrey 6:40 am on August 9, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Comment 3

Peirce identifies inference with a process he describes as symbolization. Let us consider what that might imply.

I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of information. (467).

Even if it were only a rough analogy between inference and symbolization, a principle of logical continuity, what is known in physics as a correspondence principle, would suggest parallels between steps of reasoning in the neighborhood of exact inferences and signs in the vicinity of genuine symbols. This would lead us to expect a correspondence between degrees of inference and degrees of symbolization extending from exact to approximate (non‑demonstrative) inferences and from genuine to approximate (degenerate) symbols.

For this purpose, I must call your attention to the differences there are in the manner in which different representations stand for their objects.

In the first place there are likenesses or copies — such as statues, pictures, emblems, hieroglyphics, and the like. Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters. The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less; for they stand for whatever they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men or a decree of God. Such are tallies, proper names, &c. The peculiarity of these conventional signs is that they represent no character of their objects.

Likenesses denote nothing in particular; conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations. They connote attributes and so connote them as to determine what they denote. To this class belong all words and all conceptions. Most combinations of words are also symbols. A proposition, an argument, even a whole book may be, and should be, a single symbol. (467–468).

In addition to Aristotle, the influence of Kant on Peirce is very strongly marked in these earliest expositions. The invocations of “conceptions of the understanding”, the “use of concepts” and thus of symbols in reducing the manifold of extension, and the not so subtle hint of the synthetic à priori in Peirce’s discussion, not only of natural kinds but also of the kinds of signs leading up to genuine symbols, can all be recognized as pervasive Kantian themes.

In order to draw out those themes and see how Peirce was led to develop their leading ideas, let us bring together our previous Figures, abstracting from their concrete details, and see if we can figure out what is going on.

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

$\text{Figure 3. Conjunctive Predicate}~ z, \text{Abduction of Case}~ x \Rightarrow y$

Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.

$\text{Figure 4. Disjunctive Subject}~ u, \text{Induction of Rule}~ v \Rightarrow w$

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.

Resources

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

Jon Awbrey 10:46 am on August 7, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Comment 2

Let’s examine Peirce’s second example of a disjunctive term — neat, swine, sheep, deer — within the style of lattice framework we used before.

Hence if we find out that neat are herbivorous, swine are herbivorous, sheep are herbivorous, and deer are herbivorous; we may be sure that there is some class of animals which covers all these, all the members of which are herbivorous. (468–469).

Accordingly, if we are engaged in symbolizing and we come to such a proposition as “Neat, swine, sheep, and deer are herbivorous”, we know firstly that the disjunctive term may be replaced by a true symbol. But suppose we know of no symbol for neat, swine, sheep, and deer except cloven‑hoofed animals. (469).

This is apparently a stock example of inductive reasoning Peirce is borrowing from traditional discussions, so let us pass over the circumstance that modern taxonomies may classify swine as omnivores.

In view of the analogical symmetries the disjunctive term shares with the conjunctive case, we can run through this example in fairly short order. We have the following four terms.

$\begin{array}{lll} s_1 & = & \mathrm{neat} \\ s_2 & = & \mathrm{swine} \\ s_3 & = & \mathrm{sheep} \\ s_4 & = & \mathrm{deer} \end{array}$

Suppose $u$ is the logical disjunction of the above four terms.

$\begin{array}{lll} u & = & \texttt{((} s_1 \texttt{)(} s_2 \texttt{)(} s_3 \texttt{)(} s_4 \texttt{))} \end{array}$

Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram.

$\text{Figure 2. Disjunctive Term}~ u, \text{Taken as Subject}$

Here we have a situation which is dual to the structure of the conjunctive example. There is a gap between the logical disjunction $u,$ in lattice terminology, the least upper bound of the disjoined terms, $u = \mathrm{lub} \{ s_1, s_2, s_3, s_4 \},$ and what we might regard as the natural disjunction or natural lub of those terms, namely, $v,$ cloven‑hoofed.

Once again, the sheer implausibility of imagining the disjunctive term $u$ would ever be embedded exactly as such in a lattice of natural kinds leads to the evident naturalness of the induction to the implication $v \Rightarrow w,$ namely, the rule that cloven‑hoofed animals are herbivorous.

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.

Resources

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

antlerboy - Benjamin P Taylor 11:09 am on August 6, 2026

The SysPrac26 programme is taking shape – 21–22 September 2026 at Cranfield University, UK

Submissions are still coming in through our Call for Contributions, and we’re already getting a sense of what September will look like.

Confirmed speakers (at this early stage) include:

Janne Korhonen
Jan de Visch
Denis Fisbacher Smith
Kim Warren
Roelien Goede
Patrick Hoverstadt
Simon MacCormac
John Rogers
Gavin Roberts

What’s clear so far is that SysPrac26 stays true to its founding idea:

No keynotes, no lectures from a stage
Themed streams built around real practice – public service, health, organisational change and more
Workshops and talks where you bring the challenge and your experience

If you’ve got a case, challenge or experiment from your own practice, there’s still time to submit and be part of the programme.

We’ll be sharing more on streams, sessions and who you’ll be learning alongside over the coming weeks.

SysPrac26 is 21–22 September 2026 at Cranfield University. Early bird tickets are open until 17 August.

+++++++++++++++++

Contribute your practice by 10 August: https://tally.so/r/q4eWEk?source=sciolinkedin

Tickets at early bird prices available until 17 August: https://www.tickettailor.com/events/scio/2291367?r=sciolinkedin

#SysPrac26 #SystemsThinking #SystemsPractice

Jon Awbrey 9:10 am on August 5, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Comment 1

Selection 1 ends with Peirce drawing the following conclusion about the links between information, comprehension, inference, and symbolization.

Thus information measures the superfluous comprehension. And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.

(Peirce 1866, p. 467)

At this point in his inventory of scientific reasoning, Peirce is relating the nature of inference, information, and inquiry to the character of the signs mediating the process in question, a process he describes as symbolization.

In the interest of clarity let’s draw from Peirce’s account a couple of quick sketches, designed to show how the examples he gives of conjunctive terms and disjunctive terms might look if they were cast within a lattice‑theoretic framework.

Looking back on Selection 5, let’s first examine Peirce’s example of a conjunctive term — spherical, bright, fragrant, juicy, tropical fruit — within a lattice framework. We have the following six terms.

$\begin{array}{lll} t_1 & = & \mathrm{spherical} \\ t_2 & = & \mathrm{bright} \\ t_3 & = & \mathrm{fragrant} \\ t_4 & = & \mathrm{juicy} \\ t_5 & = & \mathrm{tropical} \\ t_6 & = & \mathrm{fruit} \end{array}$

Suppose $z$ is the logical conjunction of the above six terms.

$\begin{array}{lll} z & = & t_1 \cdot t_2 \cdot t_3 \cdot t_4 \cdot t_5 \cdot t_6 \end{array}$

What on earth could Peirce mean by saying that such a term is “not a true symbol” or that it is “of no use whatever”?

In particular, consider the following statement.

If it occurs in the predicate and something is said to be a spherical bright fragrant juicy tropical fruit, since there is nothing which is all this which is not an orange, we may say that this is an orange at once. (Peirce 1866, p. 470).

In other words, if something $x$ is said to be $z$ then we may guess fairly surely $x$ is really an orange, in short, $x$ has all the additional features otherwise summed up quite succinctly in the much more constrained term $y,$ where $y$ means an orange.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

$\text{Figure 1. Conjunctive Term}~ z, \text{Taken as Predicate}$

What Peirce is saying about $z$ not being a genuinely useful symbol can be explained in terms of the gap between the logical conjunction $z,$ in lattice terms, the greatest lower bound of the conjoined terms, $z = \mathrm{glb} \{ t_1, t_2, t_3, t_4, t_5, t_6 \},$ and what we might regard as the natural conjunction or natural glb of those terms, namely, $y,$ an orange.

In sum there is an extra measure of constraint which goes into forming the natural kinds lattice from the free lattice which logic and set theory would otherwise impose as a default background. The local manifestations of that global information are meted out over the structure of the natural lattice by just such abductive gaps as the one we observe between $z$ and $y.$

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.

Resources

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

antlerboy - Benjamin P Taylor 1:41 am on July 31, 2026

Jesuit Cybernetics Culture Research Unit (JCCRU) – call for abstracts

Jesuit Cybernetics Culture Research Unit (JCCRU)

CALL FOR ABSTRACTS

Patristics, Medieval, and Renaissance Conference
Villanova University (Online & In-Person)
October 9–11, 2026 (panel schedule, date, and time TBA)

This panel of the 2026 Patristics, Medieval, and Renaissance Conference seeks to explore and develop a new Jesuit Cybernetic critique of the Cybernetic Culture Research Unit (CCRU) (c. 1995–2000) for the purpose of renewing the hidden theological tradition of cybernetic theory in light of Trinitarian Ontology.
JCCRU

https://methexisinstitute.com/jccru

Jon Awbrey 10:10 am on July 30, 2026
Tags: Abduction ( 16 ), C.S. Peirce ( 67 ), Comprehension ( 13 ), Deduction ( 18 ), Extension ( 13 ), Hypothesis ( 12 ), Icon Index Symbol ( 18 ), Induction ( 20 ), Inference ( 13 ), Information = Comprehension × Extension ( 15 ), inquiry ( 34 ), Intension ( 12 ), logic ( 69 ), Peirce's Categories ( 12 ), Pragmatic Semiotic Information ( 12 ), Pragmatism ( 13 ), Scientific Method ( 16 ), Semiotics ( 44 ), Sign Relations ( 40 )

Information = Comprehension × Extension • Selection 6

Selection 1 opens with Peirce proposing, “The information of a term is the measure of its superfluous comprehension”, and it closes with his offering the following promise.

Summing up his account to this point, Peirce appears confident he’s kept his promise. Promising on our own account to give it another pass, we’ll let him have the last word — for now.

We have now seen how the mind is forced by the very nature of inference itself to make use of induction and hypothesis.

But the question arises how these conclusions come to receive their justification by the event. Why are most inductions and hypotheses true? I reply that they are not true. On the contrary, experience shows that of the most rigid and careful inductions and hypotheses only an infinitesimal proportion are never found to be in any respect false.

And yet it is a fact that all careful inductions are nearly true and all well‑grounded hypotheses resemble the truth; why is that? If we put our hand in a bag of beans the sample we take out has perhaps not quite but about the same proportion of the different colours as the whole bag. Why is that?

The answer is that which I gave a week ago. Namely, that there is a certain vague tendency for the whole to be like any of its parts taken at random because it is composed of its parts. And, therefore, there must be some slight preponderance of true over false scientific inferences. Now the falsity in conclusions is eliminated and neutralized by opposing falsity while the slight tendency to the truth is always one way and is accumulated by experience. The same principle of balancing of errors holds alike in observation and in reasoning.

(Peirce 1866, pp. 470–471)

References

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432. Archive. Online.