Axioms from Interactions of Actors Theory

Gordon Pask spent a lifetime interpreting concepts, exchanged by multiple participants in the manner of second order cybernetics, as the product of self-organisation. At the end of his life he enunciated his "Last Theorem". It states

Like concepts repel and unlike concepts attract

All circular, or more strictly organisationally closed, informationally open, self-referential processes that exert forces qualify as concepts to Pask. Conversation Theory (CT), initially seen as a theory of learning, has produced a theory of epistemology, self-organisation and evolution through consideration of the concurrent retention of stress in solids, liquids, gases and plasmas. Interacting Actors or Self-Organised systems retain a hard carapace which exerts a repulsive force protecting the concepts they embody.

While Pask was consulting commercially he stated a series of properties or axioms of Interaction which form the basis of the kinematic CT and its kinetic dual Interactions of Actors (IA) Theory. Definitions of the axioms are offered but exactly how to treat them is the subject of discussion. Condensation of several axioms into one or expansion of a single axiom into several is possible. Three concepts, each pair formally analogous and distinguished by the third, exist as a mutually stabilising Borromean link with residual odd either clockwise or anticlockwise parity. Concepts pack recursively "like wires in multi-core cable". We may thus look for linked counter-currents in vortices but the three closed processes have a tautomeric, resonant relation to each other filling the space around a void stochastically

Thanks to Paul Bourke at Swinburne U, Australia
Pask's Stable Concept Triple
linked as a Borromean Ring.
A putative model of Continuity,
the equilibrium of void &
not-void, around a void.
Context and Perspective

The local neighbourhood and the position of the participant observer or actor in it.

Respectability and Responsibility

Observability in both the classical and quantum sense. Excitation of a respectable actor is required if it is cold to make it responsible.


The availability of actors for interaction.

Agreement and Agreement-to-disagree

Produced when a concept is shared. In Agreement a stress is copied and a repulsion produced. In Agreement-to-disagree a stress is not copied and an attraction is produced.

Purpose and Unity that is not uniformity

Defines the difference that is feedback. Unity that is not uniformity defines a similarity defining a group. Purpose retains applicability in referring to convergent behavioural outcomes of the potentially equifinal kind. The goal of goals is to stay warm.


A property of a concept or assertion that persists until a contradictory counter example is found. The duration of an observation or experiment.

Beginnings and Ends (CT) and Eternally interacting (IA), Kinematic(CT) and Kinetic(IA)

Properties that distinguish CT and IA.

Similarity and Difference

Distinguishes concepts that attract and repel.

Adaptation, Evolution and Generation

The consequence of change and growth.

Conservation of Meaningful Information Transfer both Permissive (Ap) and Imperative Application (Im)

The equilibrium of imperative forces produces permissive application of concepts.

Informational Openness and Organisational Closure

The conventional requirements of second order cybernetic systems.

Void and Not-Void

The structure of the space supporting Actors which support M-Individuals in which P-Individuals interpret their concepts.

Some Expressions in Pask's Dynamic Lp to support the IA axioms


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