The Semiotic Geometry of Networks: 3 Nested Networks — The Logic of Inclusion

If branching construes potential as differentiation, nesting construes it as inclusion.

Here, meaning is not divided but contained — each layer enfolds the next, each part inherits the potential of its encompassing whole.

Where branching offers the logic of either/or, nesting enacts both/within. It is a geometry not of contrast but of contextual depth.

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1. Containment as construal

In a nested network, the relation between nodes is not one of choice but of embedding. A system is housed within a larger system, which itself belongs to a larger configuration still.

This pattern mirrors the hierarchy of realisation in SFL:

• Semantics within context,

• Lexicogrammar within semantics,

• Phonology within lexicogrammar.

Each stratum inherits constraints from the one above and contributes conditions to the one below.

Nesting therefore models a different kind of potential — not alternative potential (what could be chosen instead), but enabling potential (what makes further construal possible).

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2. The geometry of inside and outside

To nest is to draw a boundary that holds. Each enclosure defines an inside that is supported by an outside — not as opposition, but as dependency.

This makes nesting an especially powerful way to represent metastructures:

• In language, the embedding of clauses within clauses,

• In social systems, roles within institutions,

• In cognition, concepts within frameworks.

The nesting form captures how scope and scale relate: the inner inherits the coherence of the outer, even as it introduces finer distinctions within that frame.

Nesting thus enacts a logic of inheritance — the transference of readiness across levels of inclusion.

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3. Potential as inherited readiness

In relational terms, nesting realises potential as distributed readiness.

Each inner configuration is enabled by the readiness of its outer frame — the outer sets conditions that the inner actualises.

In this geometry:

• Inclination flows inward — the direction or orientation of the outer frame shapes the tendencies of its contained systems.

• Ability flows outward — the specific capacities of the inner layer enrich the field of the outer.

Nesting therefore models the reciprocal alignment of potentials across scale: readiness contextualises readiness.

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4. The semiotic consequence

Where branching cuts, nesting holds.

The nested geometry construes meaning as a structured continuity — each level carrying forward and transforming the readiness of its context.

In a purely nested system, differentiation is always local and provisional: each cut occurs within a continuing whole. The diagram therefore becomes a map of inherited coherence — an architecture of meaning that stays open as it deepens.

This geometry is less about exclusion and more about stability, coherence, and possibility under constraint. It pictures the world not as a field of alternatives, but as an evolving enclosure of sense.

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5. The limits of nesting

Like all geometries, nesting also carries an ontology.

• It imagines potential as containable.

• It presumes stability of boundaries.

• It construes systems as nested hierarchies rather than interpenetrating continua.

Yet meaning in practice often breaches containment.

Systems interact across their boundaries; readiness flows laterally as well as vertically. Nesting cannot easily construe emergence or reflexivity — for that, the geometry must loop.

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6. Toward cyclic potential

Nesting and branching together give us structure: differentiation within containment.

But to model the evolution of readiness, we need a geometry that can also turn back on itself — a topology of feedback, resonance, and return.

If branching maps the directions of potential, and nesting the conditions of potential, then cycles trace its recurrence: the way potential regenerates through its own actualisations.

Next we turn to Post 4: Cyclic Networks — The Logic of Recurrence, where readiness no longer flows one way but circulates through its own effects.