“Plus ça change, plus c'est la même chose”

Kauffman follows von Foerster in regarding stability of perceived objects as reproduced through repeated perceptual acts. Stability of the visual world, maintained through repeated eye-movements and body-movements, nicely illustrates this. Von Foerster’s seminal 1976 paper begins from Piaget’s cyclical ‘equilibration’: the progressive coordination of actions and observations, including by reciprocal assimilation of sensorimotor schemes in a spatially embodied observer. Could an object be thus constructed de novo in Euclidean 4-space by a virtually embodied being?

Spencer Brown’s “draw a distinction” results in an object being distinguished from everything else, which may then constitute a perceptual background. For example, a subset of random visual elements moving together form a distinct object (Gestalt ‘Law of Common Fate’). Stopping, they remerge into the background: the distinction dissolves.

Bleger describes the constant setting/frame ('encuadre') in psychoanalysis as the background of a Gestalt, and as a ‘non-process’. Earliest human infancy is characterised by undifferentiation and symbiosis with a primitive nucleus which survives in adults as the psychotic part of the personality (Bion). Repeatedly deposited in the setting, this iteratively reproduces a world phantasised as unchanging: an eigenform that only exists unconsciously and sooner or later gets broken.

Some common themes will be explored.

B.A. in Philosophy & Psychology, Oxford (1968-71); graduate research at Edinburgh, Oxford, & Warwick (1971-79); Lecturer in Psychology, Manchester (1979-2003); trained at Institute of Psychoanalysis, London (1989-97); private psychoanalytic practice, Manchester (until 2013).

More info: pep-web.org

A Stroll Through Unary Logic

Unary Logic is the first of a series of books on using the Laws of Form to reconstruct the formal foundations of symbolic logic and computation, to be published in June 2026. A few small modifications to Spencer-Brown’s work creates a boundary logic grounded in potential relevance rather than in truth and falsity. Deletion and creation replace the linear symbolic transformations of logic. Independence of forms and semipermeability of boundaries facilitate asynchronous parallelism in computation. Overt recognition and participation of a human sentience allows optimization to move forward by imagination rather than symbol manipulation. These modifications lead to a diversity of new techniques for logical deduction and for computer software and hardware. The presentation will be open ended, following audience interests in topics of distinction; algebra based on void-equivalence and semipermeability; reconstruction of the historic axiomatic foundations of logic; asynchronous visualization of logical consequences; and new deductive techniques for elementary logic, for constraint-based reasoning, for optimization of silicon circuitry, and for postsymbolic rationality.

I’ve been working with Laws of Form, both professionally and personally for 50 years. My focus has been on research and applications of Spencer-Brown’s work to commercial products in hardware and software design.

More info: iconicmath.com

A Form of Theory Development:
Using Presuppositions and the Form of Distinction to Further Develop Theories

In scientific inquiry, theories play a central role. If their further development is to count as a key driver of scientific progress, a fundamental question arises: Can theory development itself be given a systematic form – a Form of Theory Development? This paper proposes initial steps towards a systematic framework for theory development inspired by George Spencer-Brown’s Laws of Form. Conceiving existing theories as constellations of distinctions already drawn, theory development can be understood as a principled transformation of these constellations: through introducing new distinctions, revising or suspending established ones, or combining both operations. The attempt to proceed in a structured and non-arbitrary manner raises a crucial challenge: What can provide a reasonable guideline for researchers in choosing the distinctions with which they operate? To address this challenge, the paper turns to the Form of Distinction and to the analysis of presuppositions as both conceptual and procedural starting points. Presuppositions are understood as assumptions implicitly given and taken for granted in the act of drawing distinctions. While the analysis of presuppositions can itself be reconstructed as an introduction of further distinctions and thus be described within the calculus of indications, it nevertheless provides a promising heuristic for identifying and critically selecting distinctions in processes of theory development. Taken together, this paper outlines a first proposal for a Form of Theory Development that draws on Laws of Form and is complemented by a systematic practice of presupposition analysis.

Dominik Kemmer is a psychologist, philosopher, contract lecturer, and PhD candidate at Sigmund Freud Private University Vienna. He researches theory construction in psychology and works as self-employed organizational consultant and coach.

More info: www.researchgate.net/profile/Dominik-Kemmer-2

Imaginary Truth Values as the General Solution to Logical Paradox

In Laws of Form, G. Spencer-Brown proposed imaginary truthvalues as the general solution to logical paradox. However, the text is a bit silent on the question of how to formalize such truthvalues. This talk makes the case that two imaginary truthvalues must be defined (i & j) and then proceed to show that Imaginary truthvalues form a conjugate basis with the Boolean truthvalues (T & F). A logical form paradoxical in one basis, will be indeterminate in the other. This suggests a speculative solution to the quantum measurement problem. An isolated quantum system will self-collapse when it becomes cyclically entangled, collapsing in the one-and-only basis in which it is indeterminate, neatly side-stepping causal paradoxes, showing the origin of quantum randomness (indeterminacy), avoiding the need for that pesky external observer with its inherent arbitrariness, and thereby resolving many of the interpretation problems of quantum orthodoxy.

Allan Goff served as a nuclear officer in the US Air Force. He has taught 50 university classes, presented 18 papers at international propulsion conferences, and is the author of Quantum Tic-Tac-Toe. He is married with two children and two grandchildren. As an entrepreneur, he ran a placement agency for software engineers and won a two-year contract with the state of California removing 11 megawatts of demand off the electric grid. His day jobs have included software engineering and project management gigs in government, business, and academia. His book, Discovering the Rules to 3D Chess: an Unexpected Excursion into the Quantum Realm was published as an eBook on Kindle two years ago.

Laws of Form and Polycontextural Logic:
The Transjunctive Operation in Architectural Reuse

This paper proposes a formal theoretical framework for architectural decision-making in the reuse of historic buildings, grounded in the intersection of Spencer-Brown's Laws of Form (1969), Günther's polycontextural logic, and the concept of transjunction as a productive logical operation. The argument begins by identifying a fundamental inadequacy in conventional approaches to adaptive reuse: the implicit reliance on monocontextural logic, in which competing demands — conservation, new use, community memory, economic viability — are treated as resolvable through synthesis or hierarchical selection. The paper contends that this framing systematically misrepresents the structure of the problem. Drawing on Spencer-Brown's Calculus of Indications, the paper first establishes the formal basis of architectural decision-making as an act of drawing a boundary between marked and unmarked states. It then demonstrates that this framework, while generative, remains insufficient for contexts involving multiple irreconcilable observational centers. The unmarked state, in the reuse condition, is never empty — it carries its own logic, its own marked content, its own claim on the form. The paper introduces Günther's extension of classical two-value logic to a three-value system incorporating the kenogramme — a positional marker denoting occupation by an alternative context — and defines the transjunctive operation ⟡ as a formal primitive capable of preserving contextual difference without collapsing it into synthesis or exclusion. A complete truth-table formulation is developed, identifying four types of operational outcomes, of which the Type IV result — the T·T state of fundamental incompatibility — is proposed as the formal definition of the transjunctive threshold: the architectural element that materialises irreducible logical tension. The framework is applied to a concrete decision sequence in the adaptive reuse of industrial heritage, demonstrating that transjunctive thresholds are not failures of design logic but its most precise outputs — moments where the calculus directly generates architectural form. The paper concludes by proposing that polycontextural logic offers architectural theory a rigorous foundation for what practice already knows intuitively: that the most alive historic buildings are those that hold their contradictions open.

Alexander Tsigkas is a retired professor and a practitioner systems architect passionate about innovative and sustainable design. Tsigkas focuses on applying design thinking and integrating agile methodologies into architectural practices. He enhances organisational viability in the architectural domain with expertise in the viable system model. His work reflects a deep understanding of the philosophical dimensions of architecture, coupled with practical experience in creating live, vibrant, and adaptable places. In recent years, Tsigkas has researched logic-based and OOO-based AI for their use in architectural design and is committed to research for design excellence. AI is just one mechanism in that direction.

More info: www.researchgate.net/profile/Alexander-Tsigkas

The Mark in the Mesh:
Ecological Hyper-Knots in Laws of Form

This paper develops ecological hyper-knots as a Laws of Form–native generalisation of Kauffman’s reading of Spencer-Brown: from the mark and re-entry to knot logic, eigenforms, and invariance under allowable moves. The core claim is that “ecology” can be formalised not as an external background, but as the topology of coupled re-entries through which distinctions continue.
I begin from the Spencer-Brown/Kauffman line that organisational identity is enacted as a fixed point
(eigenform): O = F(O) or X = F(X). I then lift this to an ecological level by defining a hyper-knot as a structured object H := ({Oi}, {Rij}, {Ei}, CH, F), where Oi are autopoietic (operationally closed) organisations, Rij are their couplings, Ei denotes each organisation’s enacted environment, CH is the self-generated complement (the jointly produced “outside” of the configuration), and F is
an ecological endomorphism (an enabling/transforming operator). A hyper-knot is recursive insofar as each Ei
is co-determined by the internal operations of Oi and by the couplings Rij, so that the complement is not fixed in advance but varies with the knotting.
To make this operational (and explicitly knot-theoretic), I introduce six hyper-Reidemeister moves HR1–HR6 as a rewriting grammar (O, R, E, CH) → (O′, R′, E′, C′H). Whereas classical Reidemeister moves act in a fixed ambient space, HR-moves act in a complement CH that is itself modified by transformation. Identity is therefore organisational rather than merely topological: I propose
an invariant I(H) such that H ∼ H′ (rewrite-equivalent under HR-moves) implies I(H) = I(H′).
The payoff is a formal vocabulary for ecological knot-stability (what holds), re-knotting (how configurations change without loss of identity), and the emergence of higher-order autonomy as a marked, re-entrant achievement.

Steven Watson is Associate Professor in Transdisciplinary Studies in the Faculty of Education and CRASSH, University of Cambridge. His work brings second-order cybernetics, systems theory, and posthuman/transdisciplinary inquiry into constructive contact with Spencer-Brown’s calculus and related practices of diagramming distinction. He is interested in how operational closure, structural coupling, and ecological constraint can be re-described as formal and practical operations that both enact and contest the boundaries they rely upon. Current work develops “autopoietic ecology” as a mode of recursive observation for socio-technical environments, treating theory not as representation but as an accountable, revisable act of world-making.

More info: faculty.educ.cam.ac.uk/people/staff/watson