Tuesday, 27 January 2026

After Totality: 2 Exhaustiveness Without Closure

How ontology can be complete locally without being total

If totality is refused, a predictable anxiety follows. Without the ambition to include everything, does ontology lose its claim to rigour? Does it collapse into partiality, relativism, or mere description?

This post argues that this anxiety rests on a confusion. Exhaustiveness does not require closure. Ontology can be disciplined, complete, and even exhaustive — provided that exhaustiveness is understood correctly.


1. The False Alternative

Ontology is often presented with a false choice:

  • either provide a complete account of reality as a whole,

  • or settle for fragmentary, local descriptions with no general force.

This framing assumes that completeness and totality are inseparable. They are not.

The task of ontology is not to say everything, but to say enough — enough to govern intelligibility without overstepping the conditions of actuality.


2. What Exhaustiveness Actually Means

To be exhaustive is not to leave nothing out in principle. It is to leave nothing out relative to a domain, a system, or a cut.

An exhaustive account specifies all that can matter given the constraints it has adopted. It does not claim to transcend those constraints.

Exhaustiveness is therefore always indexed. Closure pretends it is not.


3. Closure as a Category Error

Closure occurs when a description treats its own limits as irrelevant. It presents itself as final rather than situated.

But descriptions do not close reality; they only close themselves.

When ontology aspires to closure, it mistakes the internal completeness of a system for the completion of actuality. The result is not rigour, but overreach.


4. Local Completeness, Global Openness

Reality does not require global assembly in order to be fully present. What is given in any phenomenon is not partial reality, but reality under a perspective.

A perspective does not truncate actuality; it organises it.

Ontology can therefore be locally complete — fully adequate to what appears — while remaining globally open. What it cannot do is claim that openness as a defect.


5. Why Relativism Does Not Follow

Refusing closure is often mistaken for endorsing relativism. This is a mistake.

Relativism dissolves constraint. Non-closure preserves it.

An ontology without closure is still governed by:

  • systems that constrain possibility,

  • cuts that discipline instantiation,

  • and coherence conditions that distinguish sense from nonsense.

What is refused is not constraint, but the fantasy of finality.


6. Exhaustiveness and Systematicity

A system can be exhaustive with respect to what it makes possible. It cannot be exhaustive with respect to all that ever occurs.

This is not a weakness of systems, but their defining feature. A system that anticipated every possible instantiation would no longer be a system — it would be indistinguishable from totality.

Ontology must therefore be systematic without aspiring to closure.


7. The Second Discipline

If the first discipline of ontology is to refuse totality, the second is this:

Ontology may be exhaustive only relative to what it constrains, never relative to what is.

This discipline preserves rigour without importing completion. It allows ontology to remain general without becoming total.

In the next post, we will examine one of the most persistent evasions of this discipline: the claim that everything exists.

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