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….
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 really an icon of object Again, in Figure 4, is really an index of object 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.
Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.
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.
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.
Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.
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.
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.
Suppose is the logical disjunction of the above four terms.
Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram.
Here we have a situation which is dual to the structure of the conjunctive example. There is a gap between the logical disjunction in lattice terminology, the least upper bound of the disjoined terms, and what we might regard as the natural disjunction or natural lub of those terms, namely, cloven‑hoofed.
Once again, the sheer implausibility of imagining the disjunctive term would ever be embedded exactly as such in a lattice of natural kinds leads to the evident naturalness of the induction to the implication 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.
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.
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.
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.
(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.
Suppose is the logical conjunction of the above six terms.
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 is said to be then we may guess fairly surely is really an orange, in short, has all the additional features otherwise summed up quite succinctly in the much more constrained term where means an orange.
Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.
What Peirce is saying about not being a genuinely useful symbol can be explained in terms of the gap between the logical conjunction in lattice terms, the greatest lower bound of the conjoined terms, and what we might regard as the natural conjunction or natural glb of those terms, namely, 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 and
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.
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.
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.
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.
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.
Such a term, formed by the sum of the comprehensions of several terms, is called a conjunctive term. A conjunctive term has no extension adequate to its comprehension. Thus the only spherical bright fragrant juicy tropical fruit we know is the orange and that has many other characters besides these. Hence, such a term is of no use whatever. 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. On the other hand, if the conjunctive term is subject and we know that every spherical bright fragrant juicy tropical fruit necessarily has certain properties, it must be that we know more than that and can simplify the subject. Thus a conjunctive term may always be replaced by a simple one.
So if we find that light is capable of producing certain phenomena which could only be enumerated by a long conjunction of terms, we may be sure that this compound predicate may be replaced by a simple one. And if only one simple one is known in which the conjunctive term is contained, this must be provisionally adopted.
(Peirce 1866, p. 470)
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.
Selection 3 showed how it was possible to combine symbols in such a way as to end up with species of representation outside the class of genuine symbols and introduced the concepts of conjunctive terms and disjunctive terms to describe two ways of doing that. The essence of wit being quickly grasping the middle term, Peirce’s wit fastens on those terms to highlight the links between manners of representation and modes of inference.
Selection 4 finds Peirce in the middle of articulating the connection between indexical reference and inductive inference, using examples of disjunctive terms as pivotal cases.
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. There is but one objection to substituting this for the disjunctive term; it is that we should, then, say more than we have observed. In short, it has a superfluous information.
But we have already seen that this is an objection which must always stand in the way of taking symbols. If therefore we are to use symbols at all we must use them notwithstanding that. Now all thinking is a process of symbolization, for the conceptions of the understanding are symbols in the strict sense. Unless, therefore, we are to give up thinking altogether we must admit the validity of induction. But even to doubt is to think. So we cannot give up thinking and the validity of induction must be admitted.
(Peirce 1866, p. 469)
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.
So much to unpack from the Re-braiding Sympoisum#1:”The Split”, held on 25 March 2026, but I’ll jump-in with some explorations on Artorga as a good place to build on?
From Symposium #1 – Thank you to fellow attendee Anthony Weiss for making the connection to ARTORGA as being relevant to Re-braiding, and to Bernard Scott’s direct insights on the organisation.
I’ve dug into Artorga a bit, and I found it fascinating and rich with leads to Re-braiding, and historic cybernetics in general.
In terms of Hugh and Paul’s Re-braiding timeline (available on the Re-braiding repository), Artorga seems to have been active from 1958 to ~1970, right at the overlap of Cybernetics and Symbolic AI:
Artorga stood for the endeavour of Artificial Organisms, and broadly speaking, ARTORGA was a…
(a) Laboratory/ series of experiments …
(b) that “… sought to revise cybernetics’ disciplinary history, claiming its origins in biology rather than information theory and operations research.” (Cartelli, 2023)
(c) running from 1958 – ~1970
(d) Steered by: Oliver Wells; and an Advisory Group involving: Stafford Beer, Gordon Pask, Heinz von Foerster.
(e) Producing:
A network of interested people.
A mainly monthly Newsletter, called ‘Communications’
Pamphlets
Books
Conferences
Products (the Drogulus)
An ‘Investment group’
The most comprehensive review on Artorga I’ve found so far on is this reference:
Machines, Fabrics, and Models: ARTORGA and Biology’s Cybernetic Utopia, by Gregory Elias Cartelli, 2023, 29 pages. I attach a copy that someone has extracted (available online here) (also of interest to CMU’s Architecture Code Lab?)
which really made alive for me, the Drogulus mentioned frequently in the Penrose papers and Oliver Wells communications from Artorga, and the whole pursuit of self-reproduction pursued by that early Cybernetic period.
I think this Penrose machine also speaks to Jill’s point of Cybernetics seeking general, self-reproducing behaviours, as a Cybernetic paradigm, in tension with AI’s different paradigm.
If anyone else is looking at Artorga, and or can help fill in the missing copies of the Communication newsletter, then I have compiled (,what I call, ) a ‘finding-aid’ on Artorga resources: (available here: Artorga-Collections). I also attach a latest copy to this email.
There are a lot of references to other foundational archival aspects. For instance, lots of mentions to the Namur meetings that Mike mentioned; and to meetings on self-organization, which also ties in to Mike’s foundational s-o theme that he presented on.
Many copies of the Artorga Newsletter are missing – so if anybody can help with that, please do get in contact.
There is a lot more emerging from this Artorga lens, including some tensions between Cybernetics and AI from that time. It strikes me that, unless we investigate (and mitigate somehow) these tensions from the past, then we may be ‘doomed’ to repeat them? That may be for future discussions, but for now, I am enjoying the hopes and aspirations that Artorga endeavoured, as Cartelli writes: “ARTORGA was a series of experiments that sought to revise cybernetics’ disciplinary history, claiming its origins in biology rather than information theory and operations research” (Cartelli, 2023, page 213).
Thanks to Paul Pangaro and the team for organising this Re-braiding Project.
You must be logged in to post a comment.