Readiness as Categorial Grammar: Inclination, Ability, and the Architecture of Potential: 4 Ability as Exogenous Coherence: External Constraints on Morphisms

If inclination is the endogenous topology of potential—internal morphism pressure—then ability is its necessary counterweight:

the exogenous coherence conditions that determine which transitions can stably compose with the surrounding system.

Where inclination answers the question “What does this structure tend toward internally?”

ability answers “Which of these tendencies can remain coherent when extended into the larger system?”

Ability is not skill.

Not capacity in the biological or psychological sense.

Not competence.

Not power.

Not even possibility in a general modal sense.

Ability is the compatibility between a local potential and the global structure it must compose with.

This post formalises ability as external coherence, giving readiness its outer contour.

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1. What “Exogenous” Means in a Relational Ontology

Again, we avoid spatial metaphors.

There is no “inside” and “outside” in a container sense.

Exogenous = arising from the relational environment that conditions the actor’s potential.

It is the system’s global pattern of morphisms—the broader topology of potential—within which the actor is positioned.

Ability is not owned by the actor.

It is granted by the relational field.

A transition is “able” only when:

• the resulting state sits coherently in the environment

• the transition composes with the surrounding morphisms

• the system’s broader constraints accept the extension

• the actor’s internal trajectory aligns with external topology

Thus:

Ability is the compatibility of a local morphic pattern with the global morphic architecture.

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2. Morphism Compatibility: The Essence of Ability

In categorical terms, a morphism is only meaningful if it composes.

If a transition cannot be integrated into the system’s broader morphic structure, it is not a valid part of the category.

This is exactly what ability construes:

• the actor may have many internally coherent pathways (inclination)

• but only some of these will compose into the system’s larger pattern

• those that do are the actor’s abilities

• those that do not simply are not abilities, regardless of inclination

Thus, ability = the external compositional admissibility of a transition.

In a more refined statement:

Ability is the set of transitions that remain globally coherent given the constraints of the system’s environment.

This is the categorical meaning of “can.”

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3. Ability Is Not Permission, Not Authority, Not Opportunity

This is crucial.

In interpersonal semantics, “ability” is often entangled with:

• opportunity

• authority

• social permission

• contextual affordances

We strip away all of these.

Ability is not:

• what the actor is allowed to do

• what they have resources for

• what others sanction

• what conditions afford

All of those belong to the social value system, not the semantic system, and absolutely not the ontological system.

Here, ability is ontological coherence.

A morphism is “able” if and only if:

• it can be extended

• it fits

• it composes

• it doesn’t violate global constraints

Ability = fit within the relational whole.

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4. Ability as a Constraint Map

Where inclination is a gradient, ability is a filter.

Inclination says:

“These transitions cohere internally.”

Ability says:

“These internally coherent transitions remain coherent when lifted into the environment.”

In categorical terms:

• inclination corresponds to internal morphism density

• ability corresponds to morphism compatibility across interfaces

This means ability can be seen as a kind of constraint map:

• mapping internal potential to the set of externally admissible morphisms

• excluding morphisms that fail global coherence

• retaining those that align with the system’s relational structure

This map is not psychological; it is structural.

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5. Where Ability Lives: At the Boundary of Local and Global Potential

Inclination is purely local.

Ability exists at the boundary—the relational membrane where local structure meets global topology.

This boundary is not a border in space.

It is the interface of compositional systems.

Ability is the structure of this interface.

To put it succinctly:

• inclination organises transitions within a potential

• ability organises transitions between potentials

Together, they partition readiness into:

• endogenous morphism pressure (inclination)

• exogenous morphism compatibility (ability)

This is readiness in full systemic form.

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6. A Categorical Picture of Ability

Category theory gives us three interlocking insights:

(1) Not all morphisms compose

Ability marks which compositions are admissible.

(2) Composition is determined globally

A morphism’s coherence depends on the system’s entire topology, not just the actor’s.

(3) Identity morphisms stabilise potential

Ability presupposes the identity: the actor’s structure must be preserved across the transition.

Thus:

Ability is the global coherence condition that governs compositional admissibility.

It is a property of the relational system, not of the actor.

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7. Where This Leaves Us

We now have a complete cut across readiness:

• Inclination: internal morphism pressure (endogenous topology)

• Ability: external coherence (exogenous compatibility)

These two meet, overlap, restrict, and amplify one another.

The next post will synthesise them into a single structure:

readiness as a functorial organisation of potential.

Post 5 will show how inclination and ability interlock as structure-preserving mappings, giving readiness the stability, generality, and relational depth that category theory is uniquely suited to express.