There are alternative models of neural networks which do not depend on threshold neurons and endlessly fiddling with weights.
Incidental Reflection 2
The series of three blog posts linked below present a case study comparing two ways of handling a classic example from the Parallel Distributed Processing paradigm, namely, the “Jets and Sharks” database problem, first taking up the original treatment by McClelland and Rumelhart and then proceeding according to a program I developed for propositional logic modeling. The latter method makes use of ideas from Grossberg’s competition‑cooperation and winner‑take‑all dynamics, but is purely propositional‑logic based, involving no extraneous weights.
Theme One Program • Jets and Sharks • (1) • (2) • (3)
John A Challoner on facebook https://www.facebook.com/groups/ISARC51Sociocybernetics/?multi_permalinks=10167637583268709¬if_id=1787904672000000¬if_t=group_activity&ref=notif
New paper and course modules: Foundational Causality
Causality is fundamental to systems thinking, explanation, diagnosis and intervention. Yet causal relationships are often represented in highly compressed form: A → B.
My latest General Systems Theory paper, Foundational Causality, asks what lies behind that arrow.
Beginning with processes and physical transfers of matter, energy and embodied information, the paper progressively examines multiple causal contributions, causal chains and networks, PTP and TPT perspectives, recurring causal structures, persistent causal organisation, conditions and constraints, systems and emergence, causal leverage, and the development of causal knowledge.
A central idea is causal decompression: progressively exposing the processes, transfers, conditions and constraints concealed within apparently simple causal relationships.
The paper is accompanied by eleven free course modules (GST 81–91). These take the learner from elementary cause-and-effect reasoning through causal networks and systems to leverage, causal knowledge and the interaction between hypotheses, explanations and theories.
A single flooding example develops throughout the modules so that learners can see a simple causal representation progressively become a systems-level causal analysis.
Recent research in science education has highlighted the importance of mechanistic reasoning, while other recent work has explicitly explored its relationship with systems thinking. The paper approaches that territory from a General Systems Theory perspective.
I would particularly welcome comments, criticisms and suggestions from systems thinkers, educators and researchers.
Alongside the paper I have also published a new set of General Systems Theory course modules featuring plain-English explanations, diagrams, examples, and practical exercises.
Both the paper and the course modules are open access. The paper is available at:
Open access (self-paced): https://rational-understanding.com/gst-course/
Supported learning: via Google Classroom through the ISSS Student SIG
Those in full-time or part-time education are especially encouraged to join the Student SIG, where they can benefit from guidance by experienced systems scientists, discussion with fellow learners, and access to a wider international community. To join go to:
As Senior Systems Thinking Manager, you’ll be one of the leading Systems Thinking practitioners within the organisation, helping shape how the railway approaches complex operational, strategic and organisational challenges. – Full Time Hours – Salary: £85,395 – £104,160 – Location: London Puddle Dock, Blackfriars – Closing Date: 30/08/2026
Encounters with the Other How we continue to misunderstand, dehumanize, scorn, humiliate, oppress − and even kill − others. And how we can stop. Barry Oshry
Let’s stay with Peirce’s example of inductive inference a little longer and try to clear up the more troublesome confusions tending to arise.
Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram.
Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.
One final point needs to be stressed. It is important to recognize the disjunctive term itself — the syntactic formula “neat, swine, sheep, deer” or any logically equivalent formula — is not an index but a symbol.‡ It has the character of an artificial symbol which is constructed to fill a place in a formal system of symbols, for example, a propositional calculus. In that setting it would normally be interpreted as a logical disjunction of four elementary propositions, denoting anything in the universe of discourse which has any of the four corresponding properties.
The artificial symbol “neat, swine, sheep, deer” denotes objects which serve as indices of the genus herbivore by virtue of their belonging to one of the four named species of herbivore. But there is in addition a natural symbol which serves to unify the manifold of given species, namely, the concept of a cloven‑hoofed animal.
As a symbol or general representation, the concept of a cloven‑hoofed animal connotes an attribute and connotes it in such a way as to determine what it denotes. Thus we observe a natural expansion in the connotation of the symbol, amounting to what Peirce calls the “superfluous comprehension”, the information added by an “ampliative” or synthetic inference.
In sum we have sufficient information to motivate an inductive inference, from the Fact and the Case to the Rule
Remark
Here, once again, I have departed from using symbol in the precise technical sense Peirce introduced at the beginning of this discussion, reverting to the more ordinary sense all of us, Peirce included, tend to use on other occasions. Perhaps the best way to smooth the wrinkle in usage is to mark a distinction among symbols, singling out the natural, normal, canonical, or simple symbols within the more general run of artificial, compound, or complex types. Taking that tack has the beneficial side‑effect of aligning the work of abduction and induction, at least, in a pre‑established universe of discourse, with the mainstream of work in computation which takes us from dubious terms to clear signs for the objects of our interest.
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.
Open access (self-paced): https://rational-understanding.com/gst-course/
and the Case 
to the Rule 
Systems Community of Inquiry 
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