Relational Cuts: 5 Limits as Constitutive

Why incompleteness is not a failure

With system, instance, actualisation, and meaning established, we now confront limits. Physics made these limits visible: the impossibility of a fully detached observer, the inevitability of relational phenomena, and the structural constraints on what can be articulated. Relational ontology allows us to see these limits not as deficiencies, but as constitutive features of intelligibility.

Self-reference and paradox

Whenever a system attempts to describe itself fully, self-reference arises. A system contains potentialities, but these potentialities include the rules for their own actualisation. Attempting to capture the totality of the system from within it produces paradox — a limit that is structural, not accidental.

This is analogous to Gödel’s incompleteness: a system cannot fully articulate its own constraints without reference to something outside the articulation. But unlike metaphysical claims of insufficiency, this limit is a necessary condition of coherence. It is the price of intelligibility.

Limits as relational

Limits are relational because they depend on the configuration of systems, cuts, and instances. They are not errors, gaps, or failures. They define the boundary of what can be made intelligible from a given perspective. A phenomenon is only actualised within these boundaries; to exceed them would dissolve intelligibility itself.

Why incompleteness is constitutive

Every instance of actualisation respects relational constraints. Meaning itself is limited to these constraints. The boundaries that arise from self-reference and system-constraint are not obstacles to understanding; they are what make understanding possible. Intelligibility requires limits.

Physics revisited

Physics repeatedly encounters these boundaries:

• In quantum mechanics, no measurement reveals all potentialities simultaneously.

• In relativity, no frame can capture all events universally.

• In cosmology, observation depends on constrained cuts.

These are not technical problems; they are the conditions that make phenomena observable, measurable, and intelligible. Relational ontology clarifies why these limits appear and what role they play.

Structural payoff

Understanding limits as constitutive completes the relational framework:

• Systems define potential.

• Cuts define actualisation.

• Instances are perspectival manifestations.

• Meaning ensures intelligibility.

• Limits define the boundaries within which all of these operate.

Rather than signalling failure, incompleteness is the very mark of a coherent, relationally intelligible world. The next and final instalment will close the series by returning to physics itself, showing why this ontology was always required, and how it illuminates the patterns we observe without altering the practice of physics.