Having established systems as structured possibility spaces and actualisation as perspectival selection among admissible cuts, we now turn to stability. Stability is the capacity of a system to persist in its structure of admissibility over sequences of actualisations, without invoking teleology or causation.
Stability Without Teleology
A system can persist not because it aims at a goal, but because its structure allows certain sequences of cuts to be coherently enacted. Stability is a relational property of admissible cuts: sequences that maintain internal coherence do not destabilise the system.
This reframing removes teleological assumptions. Stability is not the result of purposeful preservation; it is the endurance of admissibility under successive selections.
Local Coherence and Sequences of Cuts
Each actualisation is locally coherent within the system. When cuts are enacted in sequence, the system’s structure determines which sequences are admissible. Some sequences naturally support continued coherence; others would violate relational constraints and are inadmissible.
Persistence arises when successive cuts are mutually compatible within the system. This is a property of the system’s relational structure, not an external force or guiding principle.
Examples
Combinatorial Grid: Certain switch configurations can follow others without breaking structural constraints. Stability is the capacity to enact multiple sequences of admissible configurations without violating the system’s wiring.
Conceptual Network: Certain assertions or distinctions can be introduced successively without incoherence. The network persists as a coherent structure because admissible cuts are enacted in sequences that maintain its internal relations.
Ecosystem: Admissible species interactions sustain the system. Stability is achieved when sequences of interactions respect relational constraints of energy, resource, and habitat, without requiring that the system have a purpose or direction.
Structural Persistence
Stability is therefore a matter of structural persistence. The system continues to define what is admissible, even as cuts are actualised. Persistence is relational and contingent: it depends on which sequences of admissible cuts occur and how they interact.
There is no teleology, no causal necessity, only the ongoing coherence of admissibility.
Implications
By understanding stability in terms of admissibility rather than causation or purpose, we can analyse systems in terms of what they allow to persist rather than what they produce. This perspective prepares us to examine interacting systems and overlapping possibility spaces, which will be the focus of the next post.
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