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 your 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.