Toward a Mythos of Meaning: 6 The Mythic Turn

In the preceding posts, we traced semiotic events, symbolic horizons, and the evolution of semiotic potential. We now arrive at the mythic turn: the emergence of highest-order construals, where meaning does not merely instantiate relational potential but orients further meaning-making itself.

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1. Myth as the Highest-Order Construal

Myth is not a story, a narrative, or a set of cultural fictions. In relational terms, myth is the semiotic event that structures the possibility of future events:

• It is first-order construal applied to semiotic horizons themselves.

• It orients meaning with respect to meaning, producing a recursive field where semiotic potential is actively shaped.

• It stabilises otherwise soft and indeterminate horizons, enabling cumulative and scalable symbolic alignment.

Where construal actualises local symbolic potential, myth scales across horizons, producing patterned stability in relational ecologies that would otherwise remain open and fluid.

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2. Myth as Horizon of Interpretability

Rather than treating myth as a “story,” we define it as a horizon of interpretability:

• It is the space within which semiotic events can be construed as meaningful.

• It defines what counts as coherent, salient, or legible in symbolic ecologies.

• It orients perception, construal, and subsequent semiotic events without prescribing their exact form.

In this sense, myth is structurally prior: it frames the semiotic landscape, creating soft boundaries that guide recursive meaning-making.

Myth is the ecology in which semiotic potential can propagate, diversify, and stabilise.

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3. The Relational Function of Myth in Stabilising Soft Infinities

Relational horizons, symbolic potentials, and semiotic ecologies are inherently soft and unbounded:

• Semiotic fields extend indefinitely, recursively modulating their own potential.

• Without higher-order structuring, this openness risks instability, incoherence, or drift into uninterpretability.

Myth stabilises this soft infinity by:

1. Aligning recursive semiotic events along patterned horizons.

2. Producing reference points for successive construals, enabling coherent propagation of symbolic potential.

3. Maintaining adaptive flexibility: myth does not rigidly fix meaning, but scaffolds it across scales.

Thus, myth is simultaneously structuring and generative: it stabilises relational infinity while enabling its recursive expansion.

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4. Implications for Semiotic Ecology

1. Myth transforms local semiotic events into system-wide interpretive patterns.

2. It is relational, not representational: meaning is produced in the field of symbolic potential, not imposed externally.

3. Myth enables human symbolic life to scale: from individual construals to cultural memory, shared norms, and generative symbolic traditions.

4. Myth is the engine by which soft horizons become robust yet extensible, permitting symbolic ecologies to flourish over time.

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5. Takeaway

The mythic turn shows that:

• Meaning can orient meaning—a recursive property unique to symbolic life.

• Myth is the highest-order construal, not a story, not a fixed narrative, but a horizon of interpretability.

• Myth stabilises relational potential while preserving the soft infinity of semiotic ecologies, allowing symbolic life to expand without collapse.

In the next post of this arc, we will examine metaphenomena and the ontology of story, connecting mythic horizons to the emergence of narrative structures, second-order semiotic effects, and the generative evolution of symbolic systems.

Toward a Mythos of Meaning: 5 The Semiotic Animal Revisited

Previous explorations have established semiotic events, symbolic horizons, and the evolution of semiotic potential. In this post, we examine the human as the apex constructor of semiotic ecologies—the semiotic animal, revisited in a clean, relationally coherent form.

Humans are not simply biological or social agents. They are niche constructors of relational horizons, capable of shaping and recursively reconfiguring symbolic landscapes.

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1. Meaning as the Human Niche

For humans, meaning is not incidental. Semiotic systems—language, culture, narrative, ritual—constitute the ecological niche in which human life unfolds.

• Unlike other animals, whose niches are defined primarily by metabolic and social constraints, humans generate symbolic affordances that actively reshape relational potentials.

• The human niche is semiotic at its core: every construal creates conditions for further construals, extending the horizon of possibility.

• Symbolic structures—words, concepts, stories—are not decorations of existence; they are the medium in which existence is made legible, generative, and extensible.

Thus, meaning is not a byproduct of human activity—it is the environment that humans actively construct.

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2. Humans as Constructors of Relational Horizons

Humans instantiate relational horizons in two unique ways:

1. Horizons that can stabilise themselves:
   Human symbolic systems can organise semiotic events into coherent networks, producing patterned, scalable meaning structures.

2. Horizons that can reconstruct themselves:
   Humans can reflexively cut across existing symbolic ecologies, modulate their own semiotic horizons, and generate novel alignments.

This dual capacity—stabilisation and self-reconfiguration—is the hallmark of human semiotic ecology.

It enables:

• cultural accumulation,

• conceptual innovation,

• narrative complexity,

• recursive myth-making,

• the deliberate extension of semiotic potential across generations.

Humans are, in effect, meta-horizon engineers.

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3. Symbolic Life as Recursive Potential

Every semiotic action humans take—every construal, narrative, linguistic act—is recursive:

• A single semiotic event stabilises a horizon.

• That horizon enables further events, which themselves modulate prior horizons.

• Symbolic life becomes a self-propagating ecology of recursive potential, where every construal is both product and producer of the semiotic environment.

This recursive nature distinguishes human semiotic activity from the semiotic phenomena of other species:

• Other animals stabilise relational alignments locally and within immediate ecological constraints.

• Humans stabilise, modulate, and extend relational horizons across scales, generations, and cultural strata.

Symbolic life is therefore not merely lived experience, but living possibility.

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4. The Relational-Anthropic Implication

From a relational-ontological standpoint, the human semiotic niche demonstrates a key principle:

Humans are not meaning-bearing organisms.

Humans are meaning-generating ecologies.

• Meaning is not confined to internal representations.

• Symbolic systems are distributed, recursive, relational structures.

• Human agency is a modulation of semiotic potential, a set of recursive manipulations of relational horizons.

Every act of symbolic construction alters the horizon for subsequent acts, creating an expanding ecology of possibility.

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5. Takeaway

The semiotic animal, properly understood, is:

• Ecologically powerful: humans create niches defined by symbolic affordances.

• Horizontally expansive: humans extend relational potentials across social and cultural fields.

• Reflexively recursive: humans can restructure their own semiotic horizons.

Humans are the apex constructors and modulators of symbolic life, generating recursive semiotic potential that forms the backbone of culture, science, myth, and history.

Toward a Mythos of Meaning: 4 The Evolution of Semiotic Potential

Having traced the emergence of symbolic horizons, we now turn to how these horizons evolve. Semiotic systems are not static—they are dynamic ecologies of relational potential, where new symbolic affordances arise, drift, and occasionally collapse. Understanding this evolution clarifies why semiosis is generative yet non-teleological.

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1. Emergence of Symbolic Affordances

A symbolic affordance is a relational opportunity within a semiotic ecology: a potential construal that can be stabilised, transmitted, and aligned across horizons.

Affordances emerge when:

1. A relational cut produces a new distinction that is legible to future construals.

2. The distinction propagates across symbolic horizons, enabling recursive semiotic events.

3. The distinction reshapes local and cross-scale alignments, expanding the semiotic landscape.

Examples include:

• A new morpheme, gesture, or sign in language.

• A novel narrative trope in culture.

• A mythic archetype stabilising across generations.

Each affordance is not arbitrary; it arises from relational ecology but is not determined. Its emergence reflects possibility actualised, not preordained function.

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2. Semiotic Drift

Over time, symbolic affordances drift:

• Construals stabilised in one context may shift in meaning across horizons.

• The relational field modulates interpretations, creating gradual transformations in semiotic potential.

• Drift is not random; it is context-sensitive, guided by ecological alignment and horizon dynamics.

Semiotic drift demonstrates the flexibility of symbolic systems, allowing horizons to adapt without requiring teleological guidance or top-down control.

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3. Semiotic Innovation

Innovation occurs when:

1. A construal activates previously latent potentials, generating new symbolic affordances.

2. Cross-horizon interactions produce novel alignments not predictable from prior cuts.

3. The system self-extends, recursively increasing semiotic richness.

Innovation is a direct consequence of the openness of relational horizons: a semiotic ecology with many potential alignments can generate novelty purely through internal dynamics.

Innovation demonstrates that meaning is not imposed but emergent.

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4. Semiotic Collapse

Not all affordances persist. Some distinctions fail to stabilise:

• Alignments may conflict, creating incoherence.

• Horizons may shrink, reducing relational potential.

• External pressures (ecological, social, cognitive) may render a construal irrelevant.

Collapse is not failure; it is a natural aspect of semiotic evolution:

• It prunes symbolic potentials that cannot sustain coherence.

• It redistributes energy and attention to viable affordances.

• It maintains the flexible, adaptive structure of semiotic ecologies.

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5. Semiosis Evolves Without Teleology

Across drift, innovation, and collapse, one principle is clear:

Semiotic evolution is inherently non-teleological.

• There is no end-goal, no optimal symbolic form, no preordained semiotic structure.

• Semiotic potentials are generated, stabilised, and modulated locally within relational fields.

• Recursive patterns emerge naturally, without invoking purpose.

The semiotic cosmos evolves like a living ecology, guided by alignment, coherence, and recursive interaction—not by design or intentionality.

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6. Takeaway

Semiotic ecologies are dynamic, open-ended, and generative:

• Affordances introduce new possibilities.

• Drift allows meaning to transform across contexts.

• Innovation extends the horizon of potential.

• Collapse prunes unsustainable pathways.

• No teleology directs the process; evolution is emergent from relational alignment.

In relational terms, this is simply the semiotic field performing its own recursive actualisation—meaning generating more meaning, unconstrained by external purpose.

Toward a Mythos of Meaning: 3 The Emergence of Symbolic Horizons

In Post 2, we identified construal as the semiotic event, the reflexive cut that transforms relational potential into symbolic value. Post 3 examines how individual cuts scale into horizons—structured networks of symbolic potential that can coordinate, constrain, and project meaning across a relational ecology.

This is the birth of symbolic horizons.

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1. From Relational Alignment to Symbolic Distinction

Semiotic events are local, perspectival, and contingent. A single construal stabilises a small horizon, but symbolic systems require coherent alignments across many events.

A symbolic horizon emerges when:

1. Relational alignments repeat and stabilise.

2. Construals become distinguishable from one another, forming patterns of differentiation.

3. These distinctions propagate across potential alignments, creating a semiotic field larger than any single instance.

In short: symbolic horizons are stabilised patterns of differentiable construals.

They are not properties of objects, nor of social groups, nor of individuals—they are patterns of relational potential actualised as semiotic possibility.

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2. Horizons as Semiotic Ecologies

Once semiotic events are aligned and patterned across space and time, they form semiotic ecologies:

• Nodes = stabilised construals

• Pathways = repeated alignments and potential modulations

• Boundaries = soft, dynamic, and perspectival, not rigid or pre-given

These horizons enable:

• cross-event coherence,

• the emergence of structured context,

• recursive potential for further semiotic growth.

They also create the scaffolding for complex meaning-making: narratives, argumentation, cultural conventions, and symbolic systems that extend far beyond any single construal.

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3. Takeaway

The emergence of symbolic horizons is the transition from local semiotic events to systemic semiotic structure:

• Semiotic events are first-order construals.

• Symbolic horizons are patterned alignments of these events, realised as potentials through semantic systems.

Horizons are soft, relational, and recursively extensible—the basis for all higher-order semiotic systems, from language to myth, culture, and eventually the evolution of possibility itself.

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In the next post, we will examine how symbolic affordances evolve, tracing the conditions under which semiotic potential expands, drifts, or collapses.

Toward a Mythos of Meaning: 2 The Cut That Interprets: Construal as Semiotic Event

If Post 1 established the relational ground of semiosis, Post 2 examines the moment of semiotic actualisation: the event in which relational potential becomes symbolic value. This is the semiotic event itself, the cut that interprets, the first-order instantiation of meaning in a relational ecology.

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1. Construal vs. Instantiation: The Perspectival Cut

Instantiations—what relational ontology has framed as “actualisations”—are not themselves semiotic. They are events of potential closure in the ecological field: a metabolic readout, a behavioural outcome, a coordinated alignment.

Construal, by contrast, is the perspectival cut:

• It is first-order meaning realised in a relational field.

• It is reflexive: the act simultaneously actualises a pathway and renders it legible within the horizon.

• It is not a representation of an external world; it is the appearance of relational potential as world-in-motion.

The perspectival cut distinguishes what is selected, stabilised, and made salient from the background of possibilities, without implying that there is a pre-given “thing” being represented.

In relational terms: construal is the relational event of turning readiness into semiotic actuality.

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2. Meaning as Reflexive Relational Modulation

Every construal is reflexive:

1. It modulates the relational field it emerges from.

2. It sets up conditions for further construals.

3. It creates a loop of semiotic feedback, where the horizon of potential is continuously reoriented.

Unlike simple instantiation, which leaves the background field largely unaltered, construal is recursive and generative. It does not merely act; it interprets the field of action as meaningful.

This reflexivity explains why semiotic systems—language, culture, myth—are not reducible to computation or signalling: they are self-reconfiguring ecologies of potential.

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3. From Relational Ecology to Semiotic Ecology

A relational ecology is a field of potential relations: a horizon of inclinations, readiness, and actualisable pathways. Construal converts this into a semiotic ecology:

• Nodes are no longer just positions in the field; they are meaningful sites, relationally poised for further construal.

• Pathways are no longer just actualisation routes; they are semiotic channels, carrying symbolic value across horizons.

• The field itself becomes semiotic terrain, structured by prior cuts and open to further recursive interpretations.

Semiotic ecology = relational ecology + reflexive construals that stabilise symbolic potential.

The shift is subtle but decisive: semiotics emerges when the relational field itself becomes interpretable.

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4. The Semiotic Event in Practice

A semiotic event is not merely an “instance of communication” or a “meaningful action.” It is:

1. A local cut in the relational horizon—a selection of potential actualisations.

2. A relational modulation—it reconfigures the surrounding field of inclinations.

3. A projection of symbolic value—it carries semiotic potential into future construals.

All three features occur simultaneously. There is no “internal representation” or “signal carrier” mediating between the event and the field: the event is the semiotic effect.

In Hallidayan terms, the semiotic event is where meaning construes meaning, prior to the imposition of field, tenor, or mode. Context is emergent from the cut, not imposed on it.

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5. The Philosophical Significance

Construal as semiotic event resolves several longstanding confusions:

• It dissolves the false duality between subject and object: meaning arises in the relational field, not inside a head.

• It removes the need for “codes” or “symbols” as prior ontological entities: symbols are stabilised relational potentials.

• It grounds semiotic recursion: each event produces conditions for subsequent construals, generating complex semiotic ecologies without reference to external systems of value.

Semiotic events are therefore first-order phenomena: not behaviours, not representations, not outputs, but actualisations of symbolic relationality.

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6. The Takeaway

The cut that interprets is the nexus of relational ecology and semiotic ecology.

• Relational ecology provides the field, the potentials, the horizons.

• Construal actualises a semiotic event, producing symbolic value.

• Semiotic ecology is the emergent network of reflexive cuts that stabilises, extends, and propagates meaning.

Every subsequent post in this series will examine how these cuts give rise to symbolic horizons, contexts, and higher-order semiotic structures, leading from individual events to fully-fledged systems of recursive meaning.

In short: construal is the event that turns possibility into symbolic reality.

Toward a Mythos of Meaning: 1 The Relational Ground of Semiosis

Semiosis begins not with signals, codes, or information, but with relation itself. The task of this post is to articulate the ontological foundation of meaning—what it is, how it arises, and why it cannot be reduced to the conventional scaffolds of computation or representation.

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1. Meaning as Symbolic Value, Not Biological or Social Value

In conventional discourses, meaning is often conflated with biological utility or social coordination. A neuron fires, a hormone shifts, a culture codifies a norm—and we call these “meaningful.” But in a Hallidayan, relational ontology, this is a category error.

Meaning is symbolic value, not value in the sense of:

• metabolic cost or readiness (biological), or

• social consequence or coordination (social).

Symbolic value arises in the relational interplay of horizons of potential, when construal actualises a cut that renders some possibilities salient while leaving others latent.

It is first-order meaning, not “what the organism or society gains.”

Symbolic value is recognisable by two properties:

1. Perspectival Actualisation — the moment when a relational potential is stabilised as experience or construal.

2. Cross-Horizon Legibility — the moment when this stabilisation can participate in further relational alignment, enabling recursive patterns of meaning to emerge.

Biological and social value are adjacent phenomena, but they are not meaning itself. Confusing the two collapses the semiotic into the instrumental—a trap relational ontology explicitly avoids.

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2. The Cosmology of Construal: How Meaning Actualises Worlds

Semiosis is cosmogenic. Each construal is a cut through relational potential that selects, stabilises, and projects certain possibilities. In other words:

To construe is to make a world present for action, thought, or reflection.

A single instance of meaning does not merely “represent” something. It entangles itself with the horizon in which it arises:

• The world is not a pre-given container of symbols.

• The world is actualised through construal.

• Horizons are not neutral; they are structured potentials that guide what counts as possible and relevant.

Meaning is thus world-generative. To construe is to bring forth a relational ecology in which some pathways are realised and others remain virtual.

In this sense, the cosmos of semiosis is open-ended: each act of meaning-making reshapes the horizon for future acts, recursively expanding the possibilities of the system.

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3. Why Semiosis Cannot Be Reduced to Computation, Information, or Representation

Modern theory often reduces meaning to:

• Computation: symbol manipulation according to formal rules, or

• Information: probabilistic or entropy-based measures, or

• Representation: internal models that “mirror” an external reality.

Relational ontology rejects all three:

1. Computation assumes discrete states and algorithmic determinacy.
   Semiosis is not deterministic; it is horizon-modulating and perspectival.

2. Information theory measures correlations, not construals.
   Shannon-style bits capture transmission potential, not symbolic actualisation.

3. Representation presupposes a pre-given world and a mirror-like internal mapping.
   Semiosis, by contrast, constitutes the world it engages, through relational cuts. There is no “unconstrued phenomenon” to map; there are only horizons in tension.

In short:

Meaning is not computation.

Meaning is not information.

Meaning is not representation.

Meaning is the active, perspectival actualisation of relational potential.

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4. The Takeaway

The relational ground of semiosis is therefore pre-symbolic, pre-representational, and ontologically primary. Meaning arises whenever relational potential is cut, stabilised, and projected into further potential alignments.

From this ground, symbolic systems—language, myth, culture, science—emerge not as overlays on reality, but as modes of relational actualisation: systems of recursively stabilised construals that extend the horizon of possibility.

Semiosis is not a tool; it is the cosmology of meaning itself.

In the next post, we will examine the cut itself: the semiotic event in which relational potential is made present as first-order construal.

Prelude to Semiosis — The Shift from Relation to Meaning

Semiosis begins where relationality starts doing something more than composing: it begins where relational potential orients itself toward value—not social value, but symbolic value.

Up to now, the focus has been on:

• relational potentials,

• perspectival cuts,

• structural alignments, and

• the open-ended ecologies of higher-order coherence.

But semiosis requires a new kind of cut—a relational re-entry in which meaning is not just construed within the relational field, but construes the field in return. Semiotic systems are not merely higher-order relational systems; they are reflexive relational systems, systems whose operations include the construal of their own horizon.

Three transitions mark the movement into the semiotic domain:

1. From Softness to Interpretability

Soft relational horizons become semiotic when their modulations count as symbolic distinctions—when a shift in alignment means something.

2. From Perspective to Metaperspective

Construal is not merely a viewpoint; it is a semiotic act that re-theorises the system even as it instantiates it. This opens the door to recursive meaning-making.

3. From Open Cosmos to Meaningful Cosmos

Meaning is not injected into the cosmos from above; it is a mode of living within relation—a way of stabilising, modulating, and extending cuts across horizons, across scales, across contexts.

This sets the stage for the next arc: a movement from relational ontology into the evolution of meaning itself, the emergence of symbolic life forms, and the mythic scaffoldings that allow them to flourish.

Category Theory Through the Lens of Relational Ontology: Concluding Summary Post: The Infinite Softness of Structure

Category theory was introduced as the mathematics of what happens between things, but the series has pushed one step further: from “between” to constitutive of. What matters is not the entities but the patterns of potential that make entities possible at all. The posts traced this shift—from the relational axiomatics of objects and arrows, through the perspectival actualisation encoded by morphisms, all the way to infinite ladders of higher-order relationality where the very horizon of the system becomes soft, revisable, and open.

Across this arc, four themes crystallised:

1. The primacy of relational potential – Nothing begins with objects; everything begins with the way potentials align, cut, and oscillate to yield instances.

2. Actualisation as morphic pathway – Arrows do not connect pre-given items; they are the act of carving instances from system-potential.

3. Cross-scale coherence – Functors and natural transformations articulate how relational horizons can translate, modulate, and re-align without collapsing into object-based metaphysics.

4. Soft hierarchies without closure – Bicategories, ∞-categories, and related structures expose a cosmos that never “bottoms out,” because relational potential is inexhaustible and no perspective can finalise it.

We end not with a system, but with a stance:

A willingness to treat every boundary as provisional, every instance as perspectival, and every coherence as something accomplished—never guaranteed.

This is the open relational cosmos: infinitely deep, endlessly soft, and always already meaning-bearing in its very mode of actualisation.

The next step is to ask how semiosis emerges from this cosmos—not as a layer added on top, but as a mode of relational orientation that discovers itself as both event and theory-in-practice.

Category Theory Through the Lens of Relational Ontology: 7 Higher Softness, Higher Ecology

When the Hierarchy Never Ends: Infinity-Categories and the Open Relational Cosmos

At every stage of this series, one lesson has repeated itself:

When relation is primary, horizons propagate.

Actualisation generates new potentials.

Construals yield further construals.

Alignments become horizons in their own right.

A category gave way to a functor category.

Functor categories gave way to 2-categories.

2-categories softened into bicategories.

And each shift was not an escalation of mathematical machinery,

but an ontological deepening:

• Real horizons are soft.

• Real relational systems do not stop at one level.

• Real meaning systems scale recursively.

• Real ecologies produce higher-order ecologies.

This final post examines the natural endpoint:

($\infty$, $n$)-categories and the open relational cosmos.

And we will see that this “endpoint” is really the abandonment of endpoints altogether.

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1. The Fundamental Realisation: There Is No Final Level of Relation

In a world built of objects, you can have:

• base level entities,

• relations between them,

• and perhaps some meta-level structure.

But in a relational ontology, this hierarchy does not close.

Relation does not bottom out.

Construal does not stop with a single cut.

Every construal opens new relational potentials.

Every horizon becomes the substrate for further horizons.

Thus the call for an infinite hierarchy is not mathematical indulgence.

It is ontological necessity.

Category theory recognises this necessity in the form of:

$(\infty, n)$-categories

structures where:

• there are morphisms of all orders,

• softness (weakness) pervades every level,

• coherence replaces equality all the way up,

• horizons never stop modulating.

This is the closest formal analogue to an open relational cosmos.

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2. Infinite Towers of Soft Construal

What does an $(\infty, n)$-category express, once translated into the relational idiom?

It expresses:

• horizons (objects),

• alignment pathways (1-morphisms),

• modulations of alignment (2-morphisms),

• modulations of modulations (3-morphisms),
  … infinitely upward.

But crucially:

At every level, coherence replaces identity.

Every layer is soft.

Every relation is perspectival.

No stratum is final.

This is not hierarchy for hierarchy’s sake.

It is the mathematical trace of recursive ecologies of construal.

A living system does not merely:

• perceive

• interpret

• act

It renegotiates:

• its horizons,

• its readiness,

• its attunement,

• its construal strategies,

• its meta-strategies for construal strategies.

Each of these is relational.

Each of these can be modulated.

Each modulation can itself be modulated.

The $(\infty, n)$-framework is simply the cleanest way to model that endless openness.

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3. The Cosmos Is Weakly Structured, Not Strictly Ordered

The strict vision of reality is hierarchical and closed.

The relational vision is ecological and open.

In strict metaphysics:

• entities are primary,

• relations secondary,

• identity is absolute,

• structure is rigid,

• hierarchy bottoms out.

In relational metaphysics:

• relations are primary,

• entities are local stabilisations of relational practice,

• identity is coherence,

• structure is soft,

• hierarchy is unbounded.

Thus:

An 

$(\infty, n)$-category is not a mathematical universe —

it is a metaphysical stance.

A commitment to openness.

A refusal of finality.

It reflects the living cosmos more faithfully than any object-first ontology ever could.

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4. Softness as the Signature of Real Systems

As we ascend to higher dimensions of relation, strictness becomes impossible.

Not merely awkward — impossible.

Why?

Because in biological, cognitive, semiotic, and cosmological systems:

• perspectives shift,

• horizons deform,

• alignments vary,

• constraints emerge locally,

• and every actualisation reconfigures potentials.

There is no stable point at which one can declare:

“Here, at last, all further relational levels are unnecessary.”

This is as true for ecosystems as it is for mind, meaning, and spacetime.

The cosmos itself is a soft hierarchy.

$(\infty, n)$-categories are simply that insight rendered precise.

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5. Infinity as Openness, Not Size

When people encounter “infinity-categories,” they imagine:

• mathematical excess,

• unwieldy abstraction,

• technical overkill.

But the relevant sense of “infinity” is not magnitude but openness.

It means:

There is always another possible construal.

There is always another horizon of coupling.

There is always another modulation of meaning.

Infinity is not a number.

It is a commitment to never closing the relational ecology.

This is what makes $(\infty, n)$-categories the perfect capstone for a relational ontology:

• they reject closure,

• they embrace perspectival stratification,

• they encode coherence without reification,

• they preserve the generativity of relation itself.

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6. The Relational Cosmos: A World Made of Soft, Endless Construal

We can now articulate the capstone thesis:

Reality is an open, multi-scale ecology of relational potential,

coherent at every level,

soft in every alignment,

and unbounded in its capacity for further relational individuation.

This is the metaphysical consequence of our entire ontology:

• instantiation as perspectival cut,

• construal as meaning-making,

• horizons as relational potentials,

• readiness as ecological modulation,

• systems as theories of their instances,

• and no “unconstrued phenomenon” anywhere.

An open relational cosmos is the natural terminus of this worldview.

It is not infinite in any mathematical sense.

It is open in every ontological sense.

Category Theory Through the Lens of Relational Ontology: 6 Bicategories and the Softness of Systemic Horizons

Why Not All Horizons Are Rigid — and Why This Matters for Relation

In the previous post, we saw how higher-order relationality arises inevitably once construal itself acquires horizon-like structure.
But there is a subtlety—an ontological inflection point—hidden in the transition from categories to bicategories:

Not all horizons hold their boundaries with the same rigidity.
Some horizons flex.
Some bend.
Some maintain coherence without enforcing strict equalities.

Category theory formalises this as the shift from:

• strict identity laws
  

  to

• up-to-isomorphism coherence.

Relational ontology frames the same shift as:

• the softness of ecological horizons,

• the tolerance inherent in lived relationality,

• the non-crisp nature of multi-scale alignment,

• the fact that many relational structures persist without exactitude.

This post introduces bicategories not as mathematical oddities, but as natural expressions of soft relational ecology.

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1. The Problem: Strict Horizons Are Too Clean

In an ordinary (strict) category, identities and compositions must satisfy rigid equalities:

$$(f \circ g) \circ h = f \circ (g \circ h)$$

This is elegant from a formal standpoint—but ontologically brittle.
Real horizons, biological horizons, cognitive horizons—none of them operate on strict associativity.

Nature does not say:

“This pathway composed with that pathway is literally identical to the other grouping.”

Instead:

It maintains coherence up to equivalence.
Systems align “close enough” to function.

This is not sloppiness.
It is the structural condition of a relational world where no horizon is frozen.

Thus the strict category is too rigid to model relational ontology in full fidelity.

Something more supple is needed.

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2. Bicategories: Coherence Instead of Equality

A bicategory relaxes the rigid equalities but preserves coherence via isomorphisms rather than equations.

Instead of demanding:

$$(f \circ g) \circ h = f \circ (g \circ h)$$

we require only that there exists a coherent associator:

$$\alpha_{f,g,h} : (f \circ g) \circ h \Rightarrow f \circ (g \circ h)$$

a natural, invertible 2-morphism that witnesses the alignment between the two composites.

Similarly, identity morphisms are replaced by unitors—coherent isomorphisms that align self-relations with larger pathways.

From a relational perspective, this expresses a simple truth:

Horizons do not produce identical pathways;
they produce coherent families of pathways.

A bicategory is thus a mathematics of soft horizons.

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3. Soft Horizons: The Relational Interpretation

In relational ontology, horizons are not static.
They dynamically shift with:

• metabolic readiness

• ecological coupling

• multi-scale attunement

• changes of perspective

• construal-level integration

Therefore:

Alignment across horizons is rarely exact.
It is negotiated, modulated, and “good enough” for action.

This is exactly what bicategories capture.

Strict categories

model rigid representational universes.

Bicategories

model ecologies of relational potential where:

• boundaries deform,

• mappings flex,

• and coherence is preserved without requiring identity.

They are mathematically dignified versions of biological and cognitive adaptability.

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4. Associators as Modulations of Flexibility

The associator $\alpha_{f,g,h}$ is not an algebraic leftover.

Ontologically, it expresses:

The modulation needed to transport relational structure across different perspectives on the same composite pathway.

Whenever we chain processes in a living or cognitive system—perception → construal → action—there is:

• a soft negotiation of relevance,

• a reconfiguration of readiness,

• a reselection of gradient sensitivity.

The associator is the formal trace of that modulation.

It is what ensures that even though the horizon flexes, the system’s coherence is not lost.

This is exactly how cognition maintains stability without rigidity.

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5. Bicategories as Models of Meaningful Practice

Every complex semiotic system—language, culture, mind—operates more like a bicategory than a strict one.

Why?

Because meaning is never:

• fixed,

• rigidly compositional,

• or exact in its pathways.

Meaning is:

• systemic but deformable,

• coherent but perspectival,

• stable enough to coordinate action,

• flexible enough to accommodate context and stratification.

A bicategory is the cleanest formal analogue of this.

This is the point where category theory starts to explicitly mirror the Hallidayan insight that meaning systems are:

• patterned,

• systemic,

• relational,
  but also

• inherently soft,

• inherently social,

• inherently contextually modulated.

The mathematics finally meets the semiotics without collapsing into representation.

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6. The Philosophical Consequence: Strict Systems Are the Exception, Not the Rule

Most of mathematics prefers strict categories because they are easier.
But ontologically:

Strictness is a degenerate case of relational ecology.
Soft coherence is the norm.

This flips the typical metaphysical orientation:

• Instead of thinking bicategories “generalise” categories,
  we see categories as artificially rigid caricatures of a richer relational field.

• Instead of thinking associators compensate for failure of equality,
  we see equalities as suppressions of relational nuance.

• Instead of thinking bicategories are complicated,
  we see them as minimal realism.

This is a philosophical realignment:
the world is bicategorical; strictness is the abstraction.

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7. Toward Post 7: Higher Softness, Higher Ecology

Once we accept that:

• horizons are soft,

• alignments are up-to-isomorphism,

• coherence replaces equality,

we arrive naturally at the final question:

What does a fully relational ontology look like when the entire multi-scale hierarchy is soft, perspectival, coherent, and endlessly open to further construal?

Category theory answers with:

• tricategories,

• $(\infty, n)$-categories,

• fully weak higher structures.

Relational ontology answers with:

• a vision of reality as an ecology of actualisations,

• coherence rather than identity,

• alignment rather than representation,

• and meaning as cross-scale relational attunement.

This is Post 7, the capstone:
When the Hierarchy Never Ends: Infinity-Categories and the Open Relational Cosmos.