Sunday, 14 December 2025

How Mathematical Inclination Colonised Ontology: Overview: Mathematical Critique and Relational Reorientation

This overview maps the eight-post series from the seduction of formal necessity to a relationally-grounded practice of mathematics and modelling. It highlights the internal logic, key relational moves, and two overarching threads: the critique of mathematical metaphysics and the reassertion of semiotic awareness.


Thread 1: The Mathematical Critique

This thread traces the historical and structural migration of mathematical closure into ontological and social authority.

  1. Post 1 — The Seduction of Formal Necessity

    • Introduces the core problem: formal coherence masquerading as reality.

    • Key relational move: highlighting how internal consistency of systems leads to perceived inevitability.

    • Sets the analytic spine: formal closure → metaphysical inevitability.

  2. Post 2 — Pythagoras: Number as Sacred Closure

    • Examines the first major export of mathematical inclination into ontology.

    • Key move: number as cosmic principle rather than tool; moralisation of proportion and harmony.

  3. Post 3 — Plato: Form Without Horizon

    • Shows how over-stabilisation of formal cuts leads to the removal of horizon and perspectival construal.

    • Key move: mathematics becomes the privileged access to “what truly is,” over-closure becomes metaphysics.

  4. Post 4 — From Form to Law: The Birth of Ontological Necessity

    • Demonstrates the migration from metaphysical form to law-like governance.

    • Key move: law treated as explanation and compulsion; derivation equated with inevitability.

  5. Post 5 — Physics as the Apotheosis of Mathematical Ontology

    • Integrates the previous physics critique into the historical arc.

    • Key move: singularities, infinities, collapse, and renormalisation as symptoms of over-closure; mathematics forgotten as semiotic practice.

  6. Post 6 — Over-Closure Everywhere

    • Extends the critique beyond physics to economics, algorithmic governance, and optimisation culture.

    • Key move: the phrase “the model says” demonstrates closure without relation as systemic pathology.


Thread 2: The Semiotic Reorientation

This thread foregrounds relational ontology and the restoration of mathematics as construal rather than being.

  1. Post 7 — Re-Opening Ontology

    • Reclaims horizon, relation, and cut.

    • Key move: form as orientation, not essence; mathematics as disciplined construal; ontology re-grounded relationally.

  2. Post 8 — Meaning After Number

    • Synthesises the series and outlines the forward-looking implications.

    • Key move: mathematics retains power without authority; possibility survives only where closure is resisted; inclination treated as first-class concept for modelling practice.


Internal Logic and Progression

  • Diagnosis: Posts 1–6 trace how mathematical inclination migrates and hardens into metaphysical and social authority.

  • Re-grounding: Posts 7–8 restore the semiotic cut, horizon, and relational orientation, enabling mathematics and modelling to be powerful without claiming inevitability.

  • Structural Consistency: Each post identifies closure, over-closure, and the forgetting of relation, then progressively widens the scope from metaphysics to physics to society.


Key Relational Moves Across the Series

  1. Identification of over-closure: recognising when formal systems suppress horizon.

  2. Tracing migration of authority: showing how closure becomes treated as ontological necessity.

  3. Integration of semiotic awareness: restoring cuts, construal, and perspectival orientation.

  4. Reclaiming mathematics as practice: separating symbolic power from metaphysical pretension.

  5. Extension beyond domain: demonstrating that over-closure occurs wherever models forget their relational roots.


Series Takeaways

  • Mathematical closure has historically been misread as metaphysical or social necessity.

  • Over-closure manifests across physics, economics, algorithmic governance, and optimisation culture.

  • Relational ontology restores semiotic awareness, acknowledging horizon, cut, and inclination.

  • Mathematics is powerful when treated as disciplined construal, not as reality itself.

  • Possibility survives only when closure is explicit, accountable, and responsive.

The series thus provides both a diagnostic framework and a constructive pathway, showing how to retain the effectiveness of mathematical and symbolic systems while avoiding the pathologies of over-closure.

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