Every network implies a logic. When that network branches, the logic is differentiation — the construal of potential as division into mutually exclusive paths. In a systemic network, each branch is a cut: one potential becomes many, and meaning emerges through contrast.
Branching is therefore not just a diagrammatic feature but an ontological stance. It pictures potential as choice, as a field that resolves into discrete alternatives.
1. Differentiation as construal
In the canonical system network, a node opens into alternatives — this or that. The branching form embodies a key assumption: that meaning develops through mutual exclusion. To choose one path is to foreclose the others.
This construal of potential underwrites much of linguistic theory:
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In lexicogrammar, systems like POLARITY or VOICE are modelled as binary or ternary differentiations.
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In semantics, options are realised by distinct structures.
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In ontology, instantiation is pictured as the selection of one realisation from a field of alternatives.
Yet this is not a universal geometry of meaning — it is one particular way of cutting potential.
2. The cut as event
In relational ontology, instantiation is not a temporal process but a perspectival cut — a construal of potential from within the event of its actualisation. The branching network materialises this cut spatially.
At each fork, potential is refracted into alternatives. The diagram performs the very operation it depicts: differentiation. Each line of the network is not a pathway through meaning but a boundary between construals — a topology of disjunction.
Thus the branching geometry enacts the logic of either/or — a world imagined as the sum of its distinctions.
3. Hierarchy and the deepening of choice
Because branches can themselves branch, differentiation becomes hierarchical. The network deepens as it divides. This is not simply greater delicacy but an unfolding of meta-differentiation — differentiation applied to its own outcomes.
At higher levels, choice concerns broad categories of meaning. As we descend, each branch becomes more specific, until potential is exhausted in a particular realisation.
The resulting structure construes meaning as progressive commitment — each choice constrains the next. It is a geometry of specialisation, of meaning’s movement from general potential to realised detail.
4. Limits of the branching logic
Branching carries within it a hidden ontology:
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Potential is imagined as divisible.
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Meaning is constructed through exclusion.
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Actualisation is the resolution of alternatives.
This works powerfully for modelling choice systems, but it struggles with continuity, overlap, or feedback. A purely branching geometry cannot easily construe re-entry, mutual influence, or self-reference — because it cuts potential apart rather than letting it fold back on itself.
Hence, the branching model is a semiotic commitment: it frames meaning as differentiation, not as emergence.
5. Toward a mixed geometry
Once we see this geometry as construal, its limits become generative. We can ask: what happens when branching meets other forms — when differentiation enters into nesting or cycles?
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When branching meets nesting, differentiation becomes contextualised: choices operate within containing frames.
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When branching meets cycling, differentiation becomes reflexive: earlier distinctions can be revisited or transformed.
Meaning systems in practice rarely remain purely branching — they hybridise geometries, allowing networks to fold, embed, and loop.
6. The conceptual move
To think relationally is to see that branching is not the shape of meaning but one mode of readiness — a way of organising potential for distinction.
Branching construes the world as differentiable: each act of construal divides the field of potential, shaping reality through contrast.
Next we turn to nested networks, where potential is not divided but contained — where meaning unfolds through layers of inclusion rather than exclusion.
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