Formalising the Formalism: 3 The Rhetoric of Non-Closure: How Claiming Incompleteness Becomes Binding

Minimal formalisms often carry a claim:

“Closure is impossible. Any attempt to totalise is futile.”

At first, this is descriptive, even liberating. It frees users from impossible demands. But description can harden into rhetoric, and rhetoric into obligation.

This post examines how the refusal of closure becomes a structural pressure in itself.

---

When Description Feels Like Requirement

Declaring incompleteness does not neutralise expectation.

Instead, it generates:

• vigilance: users monitor whether the formalism is respected

• obligation: failure to apply the calculus everywhere feels like negligence

• saturation: minimal distinctions are invoked preemptively, repeatedly, unnecessarily

In effect, non-closure becomes a compulsory stance.

---

The Semiotics of “Cannot Be Closed”

The statement “this system cannot be closed” carries operational force:

• It signals limits of what can be explained, but also

• Imposes boundaries of permissible engagement

• Acts as a modulation device, adjusting what users must consider

Even a statement about impossibility becomes a binding agent in the field.

---

Hardening Into Stance

Over time, non-closure becomes performative:

• It defines the posture of the field

• It regulates attention and effort

• It creates prestige for those who maintain vigilance

• It imposes subtle obligations on newcomers

This is no longer an observation; it is structural guidance — almost a role obligation.

---

Minimal Calculus Under Meta-Pressure

The very distinctions that make the calculus elegant — potential/actualisation, readiness/commitment, modulation/modalisation, perspective/field — are now asked to:

• mediate not only phenomena, but also the performance of non-closure

• maintain consistency across contexts

• absorb scrutiny and expectation without failure

Saturation emerges at the meta-level, long before contradictions appear.

---

Why This Is Not Paradoxical

Claiming incompleteness does not violate the formalism.

It is simply another form of actualisation:

• the calculus is enacted through attention, citation, and application

• users become part of the system they study

• minimal distinctions must now support a field as well as a domain

The tool is binding the field.

---

The Cost of Hardening

Hardening carries risks:

• overextension accelerates

• modulation and readiness are taxed

• perspectives collapse under meta-obligation

• saturation becomes inevitable

Yet the rhetoric is seductive: it feels correct, responsible, and necessary.

And that is precisely why it generates binding load.

---

Next

The next post will examine how this saturation manifests clearly, not in theory but in effect:

Saturation at the Meta-Level

When theory itself becomes exhausting, and minimal distinctions are overworked.