If a system network models potential as structured coherence, and if choice is the perspectival construal of that coherence, then the next question is one of topology:
What is the shape of potential?
To speak of topology is to treat potential not as a set of discrete possibilities, but as a relational field whose internal structure conditions how actualisation can occur. Different systems may share the same ontological logic — potential actualised through construal — yet exhibit distinct geometries of differentiation.
Language, matter, and life each instantiate potential in their own topological idiom.
1. The semiotic field: potential as paradigmatic weave
In the linguistic case, the topology of potential is paradigmatic. The system network maps a field of possible meanings structured by contrast — this rather than that — where every choice gains sense from its relation to the alternatives it excludes.
The network’s geometry is therefore weblike:
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Each node is a locus of internal tension;
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Each pathway traces a line of differentiation;
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The overall structure forms a manifold of meaning potential.
What construal “cuts” through is not an empty space but a densely woven fabric of relational interdependence. The network is the topology of that weave: a map of how meaning can unfurl without ever leaving the relational field that makes it possible.
This paradigmatic topology gives language its peculiar stability and fluidity — its ability to evolve indefinitely without losing systemic coherence. The semiotic field is both bound and generative because its potential is relationally taut: meaning arises through tension, not enumeration.
2. The physical field: potential as phase space
In physics, the topology of potential takes a different form. The quantum field or phase space defines a region of possible states, each related to others by lawful transformations.
Here, the field’s structure is not paradigmatic contrast but dynamical continuity. Potential is represented as a smooth manifold: a continuous set of relational configurations from which discrete events can be actualised.
A measurement, in this sense, is a perspectival construal of the field’s coherence — a cut through the manifold that yields a local actualisation (a “particle,” a “value,” a “state”). The event does not destroy the field; it realigns perspective within it.
The topology of physical potential is therefore metric and continuous, rather than categorical and contrastive. Where language differentiates through contrast, matter differentiates through curvature: construal in physics is an alignment of amplitude and phase, not a selection among alternatives.
3. The biological field: potential as morphogenetic attractor
Between the linguistic and the physical lies the biological — a domain where potential is organised not as contrast or curvature, but as morphogenetic directionality.
In developmental biology, the morphogenetic field or epigenetic landscape defines the set of possible forms an organism can actualise. These potentials are not distributed randomly; they cluster around attractors — stable configurations that constrain development.
The topology of potential here is multistable. Each attractor represents a basin of coherence: a relational configuration toward which the system is drawn. Actualisation occurs not by external cause but by self-alignment within the field.
Biological potential thus exhibits both linguistic and physical traits:
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Like the physical field, it is continuous and dynamical;
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Like the semiotic field, it is discretely differentiated by relational tension.
It bridges the paradigmatic and the phase-space logics, translating potential into form.
4. Three geometries of construal
| Domain | Topology of Potential | Mode of Construal | Actualisation as |
|---|---|---|---|
| Language | Paradigmatic network (contrastive) | Choice (categorical cut) | Meaning |
| Physics | Phase space (continuous manifold) | Measurement (amplitude alignment) | Event |
| Biology | Morphogenetic field (multistable attractors) | Differentiation (self-alignment) | Form |
Each domain construes the same ontological relation — potential actualised through perspective — but does so through a distinct geometry of coherence.
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Language differentiates horizontally, through contrast.
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Physics differentiates vertically, through collapse or alignment.
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Biology differentiates diagonally, through self-organisation.
These are not competing metaphors but complementary projections of the same relational topology. Each represents a different phase of construal: semiotic, energetic, and morphogenetic.
5. The system network as a general schema
The power of the system network, seen in this light, lies in its transposability. It is not tied to lexicogrammar; it expresses a general architecture of potential:
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Nodes model relational coherence (stable regions of potential).
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Pathways model lines of differentiation (possible cuts through coherence).
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Entry conditions model the context of construal (the point of perspectival alignment).
Nothing prevents such a network from being redrawn to model quantum fields, ecological dynamics, or social formations — provided we interpret the nodes not as “features” but as regions of relational stability within potential.
The system network could thus serve as a general diagrammatic formalism for structured potential — a way of rendering relational topology visible across disciplines.
6. Toward a general geometry of being
If the system network models meaning as structured potential, and if other fields model energy and form through analogous structures, then we might glimpse a deeper synthesis:
Being itself may be the topology of potential —a coherence that differentiates itself through construal.
Each domain — physical, biological, semiotic — enacts a distinct geometry of that differentiation. To understand them together is not to collapse them into one ontology, but to see them as phases of the same relational process: the continual articulation of potential through perspective.
In this sense, the system network, far from being a local linguistic device, prefigures a general semiotics of being — a way of diagramming how possibility becomes actual across the strata of existence.
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