The Logic of Gradience: Differentiation as Ontological Form: 4 The Gradient and the Cut

Actualisation as perspectival inflection within continuous differentiation.

Gradients articulate the field of becoming, but actualisation — the emergence of events, acts, or expressions — requires a cut. Yet this cut should not be understood as a rupture imposed from outside; it is a local steepening of the gradient, a perspectival inflection within continuous differentiation. Every instantiation is a slice through the topology of readiness, but the continuity of the gradient remains, extending beyond any single event.

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1. The Cut is Not a Rupture

Traditional accounts of actuality often presume a binary: potential versus realised, pre-event versus post-event. In a gradient ontology, this binary collapses:

• The cut does not sever the field; it accentuates a slope locally.

• Potential and actual coexist along the same continuum; actuality is a temporarily intensified gradient, not a discrete unit imposed on a flat background.

• Every event is thus both an expression of readiness and a modulation of further potential.

In other words, the world does not “jump” into existence. It folds, inflects, and accentuates what is already inclining toward becoming.

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2. Instantiation as Gradient Intensification

Actualisation can be understood as a local amplification of the gradient:

• A steepened slope attracts relational activity, producing what we perceive as an event.

• This intensification does not flatten or eliminate adjacent gradients; it redistributes readiness in the surrounding field.

• Each instantiation is therefore context-sensitive, shaped by both local capacity (ability) and global disposition (inclination).

Through this lens, the distinction between “potential” and “actual” becomes a matter of degree rather than kind. Instantiation is a topological phenomenon, not a metaphysical leap.

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3. The Perspectival Cut

Every cut is perspectival: it reflects the relational vantage of the system observing or enacting it.

• In physics, a photon’s “choice” of path is a perspectival selection along energy gradients.

• In biology, a cell’s binding event is a local actualisation within a molecular field of readiness.

• In semiotics, a construal — a meaning, interpretation, or act of communication — is the field’s self-inflected gradient at a given moment.

The cut is thus the interface between global continuity and local actualisation: the moment where the slope is steep enough to produce a recognisable event, without violating the continuity of the underlying gradient.

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4. Re-entrant Gradience

Each cut feeds back into the field that produced it:

• Local intensification temporarily reshapes surrounding gradients.

• These modifications alter the landscape for future instantiations.

• The field of becoming is therefore self-modulating — its cuts generate new inclinations while preserving continuity.

Becoming is thus a reflexive process: gradients produce cuts, cuts reshape gradients, and the interplay sustains ongoing differentiation. Actuality is never a final state; it is always a re-entrant modulation of potential.

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Next: Gradience and Reflexive Coherence

The final part of this series will examine how coherence itself depends on maintaining gradience. We will see that reflexive tuning — the field’s ongoing adjustment of its own slopes — preserves both stability and openness, allowing the world to remain continuously differentiating without collapsing into either rigidity or chaos.