Possibility is often treated as a static landscape: a pre-existing set of potentialities from which actualities are drawn. But relational ontology compels a deeper reading. Possibility itself evolves, shaped by actualisations, constraints, and the relational horizons in which it is embedded.
This post inaugurates After Gödel (Revisited) by asking a subtle, recursive question: what happens when possibility observes, structures, and modifies itself?
First-Order vs. Second-Order Possibility
To make sense of self-observation, we must distinguish two levels:
-
First-order possibility:
-
Emerges in semiotic, physical, or mathematical systems.
-
Governed by constraints and horizons.
-
Actualisation selects among potential outcomes, generating novel configurations.
-
-
Second-order possibility:
-
Applies when the space of possibilities itself is subject to relational cuts.
-
Frameworks, theories, and conceptual horizons become active participants in shaping what can be actualised.
-
Here, possibility is meta-reflexive: it observes itself, constrains itself, and evolves in response to its own actualisations.
-
The distinction clarifies a recurring problem in philosophy and science: frameworks are often treated as static lenses, when they are themselves embedded in and evolving with the very phenomena they construe.
Horizons Observing Horizons
Relational horizons can be nested:
-
A horizon defines what distinctions can stabilise.
-
When horizons themselves are treated as relational systems, their constraints evolve based on actualisations at the first-order level.
-
This produces a dynamic meta-structure: possibility reshapes itself through iterative cuts.
Think of it as a field of possibility observing its own boundaries, adjusting them in response to successive actualisations, and thereby generating new potentialities that were previously unimaginable.
Implications for Theory
-
Frameworks are contingent: No theory or model can claim to be absolute; each is an actualised cut within a meta-horizon of possibilities.
-
Recursion is unavoidable: As theories evolve, they generate new relational constraints, producing emergent patterns that feed back into subsequent actualisations.
-
Novelty is structural: Unexpected possibilities arise not from randomness alone, but from the iterative, self-modifying architecture of horizons.
Even our attempts to formalise or codify possibility are themselves events in the evolving landscape of potentiality.
Connections to Previous Series
-
Category Cuts taught us that actualisation occurs through relational structures and functorial mappings.
-
The Semiotics of Emergence showed how meaning emerges in constrained horizons, producing novelty without pre-given objects.
-
Perspectival Physics demonstrated that physical laws and phenomena are relational cuts, actualising possibility across domains.
After Gödel (Revisited) generalises these insights: possibility itself is subject to the same relational dynamics, evolving recursively as frameworks, constraints, and horizons interact.
The Recursive Horizon
Consider a simple analogy:
-
A horizon of possibility is like a landscape.
-
First-order actualisations are like footprints; they alter paths, open some routes, and close others.
-
Second-order observation is the horizon perceiving the footprints, adjusting paths, and creating new terrain for subsequent steps.
Possibility is both terrain and traveller, both observer and observed. This recursive interplay produces the evolution of potential itself.
Conclusion
Possibility is not static. It observes, constrains, and actualises itself, giving rise to a dynamic, self-reflexive field in which theories, frameworks, and phenomena co-evolve.
The next post, “Constraints That Shape Themselves”, will explore how actualised possibilities iteratively modify the relational structures that govern them, showing the mechanisms by which possibility evolves over time and across levels of abstraction.
No comments:
Post a Comment