Formalising the Cut: 1 A Minimal Calculus: Formalising the Cut Without Closing the System

To formalise is often taken to mean to complete.

To give a calculus is assumed to be to specify rules, exhaust possibilities, or guarantee coherence. In many traditions, formalisation functions as closure: once the form is given, everything else follows.

That is not what is being attempted here.

This series proposes a minimal calculus of meaning — not to secure foundations, but to clarify what must remain distinguishable for meaning to function at all, even under strain, collapse, or breakdown.

And it could only come now.

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Why Formalisation Was Previously Premature

Earlier in this project, a calculus would have been dishonest.

Before examining:

• obligation without subjects

• power without agents

• persistence without closure

• breakdown of perspectival differentiation

any formal schema would have appeared totalising, or worse, aspirational.

It would have described meaning at its best.

We now have something better: meaning at its limits.

Formalisation can now proceed from failure, not ideality.

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What Survived the Collapse

The previous series showed that even when perspectives collapse:

• obligation persists

• coordination continues

• differentiation degrades but does not vanish

• minimal responsiveness remains

This tells us something crucial.

There are distinctions that continue to operate even when systems are overloaded, exhausted, or incoherent.

Those distinctions are not optional.

They are structural minima.

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What a Minimal Calculus Is (and Is Not)

This calculus will not:

• derive all meaning

• predict behaviour

• enforce coherence

• eliminate ambiguity

It will:

• name the smallest set of distinctions without which meaning cannot operate

• show how these distinctions relate

• track where each one fails

• remain open to incompleteness

The calculus is descriptive, not prescriptive.

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The Cut as the Primitive Operation

At the heart of this ontology is a single operation: the cut.

A cut is not a separation in space or time.

It is the differentiation of potential into a determinate configuration.

Every instance of meaning depends on such a cut:

• between possible and actual

• between readiness and commitment

• between modulation and modalisation

• between perspective and field

The calculus does not invent these distinctions.

It makes explicit what has already been doing the work.

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Why Minimal Matters

Maximal formalisms fail at precisely the point where meaning becomes most interesting.

They break under:

• ethical asymmetry

• power stabilisation

• perspectival collapse

• burnout and overload

A minimal calculus does the opposite.

It asks:

• what cannot be removed

• what continues to function under degradation

• what remains operative when everything else fails

Minimality is not elegance.

It is survivability.

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Formalisation Without Closure

Gödel taught us that closure is impossible.

This project has shown that systems nevertheless continue.

A minimal calculus respects this by:

• refusing totalisation

• marking its own limits

• remaining incomplete by design

The aim is not to finish the theory, but to keep it honest.

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What This Series Will Do

The next posts will examine each primitive distinction in turn:

• potential / actualisation

• readiness / commitment

• modulation / modalisation

• perspective / field

For each, we will ask:

• why it is irreducible

• how it enables meaning

• how it degrades

• where it fails

This is not a return to foundations.

It is a clarification of the machinery that remains when foundations give way.

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Next

The next post will take up the first and most basic distinction:

Potential and Actualisation

Why meaning requires a cut that cannot be undone.

That is where the calculus begins.