Across mathematics, physics, and linguistics, a clear pattern emerges: science and theory often rely on strategies of closure that stabilise inquiry but exile relation.
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Mathematics: Platonic forms and formal necessity produce over-closure; infinities, singularities, and paradoxes signal where abstraction outruns accountability.
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Physics: Dualist separations and idealised formal systems isolate observer, context, and relational potential, producing anomalies and interpretive confusion.
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Linguistics: Chomsky’s Universal Grammar, combined with Cartesian dualism and anti-Darwinian assumptions, isolates syntax, exiling social, semantic, and emergent factors, generating the so-called “hard problems” of acquisition, variation, and use.
In each case, closure masquerades as ontology. The system appears self-contained; the anomalies appear in the world or the learner rather than in the cut that created the formal object.
1. The Pattern of Exile
The recurring structure is straightforward:
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Formal or conceptual closure stabilises a domain.
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Relation is bracketed or exiled, whether social, temporal, or environmental.
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Anomalies, paradoxes, or “hard problems” appear at the margins.
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These signals are misread as flaws of reality or intrinsic mystery.
This is the same structural habit across mathematics, physics, and linguistics. The domains differ, but the epistemic pattern repeats.
2. Relational Ontology as Consistent Remedy
Relational ontology restores coherence by re-inscribing what was exiled:
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Relation is ontologically primary: systems, substances, and forms are stabilised perspectives, not ultimate entities.
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Cuts are explicit: formalisation and abstraction are acknowledged as operations, not discoveries.
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Emergence and horizon matter: anomalies become intelligible as relational phenomena rather than irreducible mysteries.
Across domains, this shift dissolves paradoxes, repositions meaning, and recasts science as accountable construal rather than metaphysical assertion.
3. From Diagnosis to Constructive Practice
The lessons are general:
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Models are tools, not mirrors of being.
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Objectivity is disciplined engagement with relation, not horizon-erasure.
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Predictive success is valuable, but does not justify metaphysical extrapolation.
Where closure was once a necessity for tractability, relation now becomes a first-class conceptual feature, enabling coherent, rigorous, and flexible engagement with reality.
4. Forward
These series together form a unified insight: over-closure and exile are the hidden sources of paradox, anomaly, and confusion across domains.
Relational ontology does not reject mathematics, physics, or formal grammar. It re-situates them, allowing us to retain their predictive power while dissolving the metaphysical confusions that have historically accompanied them.
Where relation is accounted for, coherence returns. Where closure is held lightly, possibility survives. This is the recurring promise of relational thinking: science and theory finally remember their own conditions of possibility.
This coda explicitly links the three threads, showing a consistent pattern of over-closure → anomaly → relational restoration, and gestures forward to a generalised relational methodology across disciplines.
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