A closing synthesis
This series has traced the long, recursive journey of mathematical inclination: from seductive formal necessity, to sacred number, to Platonic form, to law, to physics, and finally into social, economic, and technological systems. We have diagnosed the pathologies of over-closure, and we have reopened ontology to relation, horizon, and cut.
The final post asks: what does it mean to practise mathematics and modelling once the metaphysical pretence has been set aside?
1. Mathematics Without Metaphysics
Abandoning mathematical metaphysics does not mean abandoning mathematics.
Mathematics remains a powerful symbolic practice. Its structure, discipline, and internal consistency make it an extraordinary tool for construal, coordination, and exploration.
What changes is authority:
Mathematics no longer commands reality.
It no longer dictates inevitability.
It becomes a lens — a selective cut through relational potential, not a tribunal of being.
The power of mathematics is thus restored without the danger of over-closure.
2. Relation as the Richer Medium
The turn to relational ontology reveals that relation is richer than form.
Form imposes constraints; relation produces context, horizon, and co-actualisation. While forms stabilise, relations animate. They generate the very space in which possibility, meaning, and novelty can appear.
Mathematics now participates in this relational ecology rather than dictating it. Equations, proofs, and models become oriented tools — disciplined cuts that highlight structure without claiming the whole.
3. Possibility Survives Only Where Closure Is Resisted
The heart of this practice is resisting over-closure.
Singularities, infinities, and collapse in physics emerge when closure is uncritically assumed.
Optimisation, algorithmic governance, and the authority of “the model says” become oppressive when closure is treated as reality.
Possibility — the space for contingency, emergence, and relational novelty — survives only where these closures are acknowledged and negotiated.
Mathematical practice is thus ethical as well as epistemic: it is an engagement with potential, not a claim about inevitability.
4. Inclination as First-Class Concept
Practising mathematics relationally requires treating inclination as a first-class feature.
Every formal system has orientation: it privileges some possibilities and suppresses others.
Every derivation and model enforces closure to achieve clarity, but this must be explicit, not assumed.
Decisions about what to stabilise, what to suppress, and what horizon to respect become central to practice.
Inclination restores reflexivity: the modeller is responsible for the cuts they enact, aware of what is included and what is foreclosed.
5. Reclaiming Meaning
Mathematics, once reclaimed as construal rather than being, contributes to a broader project: restoring semiotic awareness across all domains.
In physics, this makes singularities intelligible rather than terrifying.
In economics, it allows models to guide rather than govern.
In governance, it situates algorithms as tools rather than arbiters.
Meaning itself is preserved: it is the relational potential actualised through cuts, now accompanied by awareness and responsibility.
6. Opening Forward
This series closes the arc from formal seduction to relational practice.
Mathematics is not abandoned. Possibility is not erased. Closure is not eliminated but made explicit, accountable, and responsive.
By recognising the semiotic ground, we can practise modelling — mathematical, scientific, social — without mistaking our cuts for reality itself.
Mathematics becomes a conversation, not a decree.
Meaning survives, not by collapsing into form, but by navigating the space between potential and actualisation.
The journey continues, not toward inevitability, but toward relational richness.
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