Mathematical metaphysics beyond physics
Up to this point, the series has traced a single inclination as it migrates: from number to form, from form to law, from law to physics. In each case, the same structural error recurs — the elevation of formal closure into ontological authority.
It would be tempting to treat this as a problem confined to the physical sciences. It is not.
Physics is merely the most refined and technically sophisticated site at which the error becomes visible. The inclination itself has already escaped far beyond its original domain.
This post shows how over-closure now operates across contemporary symbolic systems — wherever mathematical form is mistaken for reality, and wherever models are allowed to speak as final authorities rather than situated construals.
1. From Explanation to Governance
In physics, mathematical closure claims explanatory authority. Outside physics, it increasingly claims governing authority.
The phrase “the model says” has acquired an extraordinary cultural force. It no longer introduces a hypothesis. It concludes a discussion.
Whether in policy, finance, logistics, or administration, mathematical models are treated as neutral arbiters — systems that simply reveal what must be done.
The inclination is familiar:
If the model is internally coherent,
if it optimises a clearly defined objective,
if it converges on a solution,
then its output is treated as inevitable.
Once again, closure masquerades as necessity.
2. Economics: Equilibrium as Destiny
Modern economics offers a paradigmatic example.
Economic models often assume:
rational agents,
stable preferences,
equilibrium-seeking systems,
and optimisation under constraint.
These assumptions are not discoveries about human life. They are closure conditions — ways of making an open, conflictual, historically contingent field mathematically tractable.
Yet the results of such models are routinely treated as revelations about what economies are and what policies must follow.
When equilibrium is reified, deviation becomes pathology. Crisis becomes anomaly. Alternative futures become irrational.
3. Algorithmic Governance and the Erasure of Horizon
Algorithmic systems extend this logic further.
Risk scores, predictive policing models, credit assessments, recommendation engines — all rely on mathematical structures that enforce closure:
discrete variables,
fixed objectives,
pre-defined outcome spaces.
Once deployed, these systems do not merely predict behaviour. They reshape it. Horizons are narrowed. Possibilities are foreclosed. Individuals are encountered not as relational beings but as vectors in a state space.
Crucially, accountability evaporates.
Decisions are no longer made; they are computed.
Responsibility dissolves into formal necessity: the system could not decide otherwise.
4. Optimisation Culture and the Moralisation of Efficiency
Beyond specific domains, over-closure now functions as a general cultural ethos.
Optimisation is treated as a moral good. To optimise is to be rational. To resist optimisation is to be wasteful, emotional, or ideological.
This moralisation mirrors the ancient elevation of harmony and proportion.
Efficiency, scalability, and convergence become virtues not because they serve human flourishing, but because they align with mathematically closed forms.
Once again, a methodological preference is mistaken for a claim about reality.
5. Closure Without Relation
Across these domains, the pathology is the same.
Models operate by suppressing relation:
historical contingency is flattened into parameters,
social meaning is reduced to metrics,
lived experience is abstracted into variables.
This suppression is not in itself an error. It is how modelling works.
The error arises when the suppression is forgotten — when the cut is treated as transparent rather than consequential.
Closure without relation produces systems that are internally impeccable and externally brittle.
They optimise brilliantly — and fail catastrophically.
6. The Authority Trap
Over-closure becomes most dangerous when it acquires moral immunity.
If outcomes follow necessarily from the model, then no one is responsible for them. Harm becomes unfortunate but unavoidable. Injustice becomes inefficiency. Protest becomes ignorance.
This is the same authority structure we saw emerge with laws of nature and physical equations — now redeployed in social space.
Formal necessity has become a tool of governance.
7. Why This Is Still the Same Problem
What unites physics, economics, algorithms, and optimisation culture is not mathematics itself, but a shared metaphysical mistake.
In each case:
a symbolic system enforces closure,
that closure is mistaken for reality,
and alternatives are excluded by appeal to inevitability.
The domain changes. The inclination does not.
8. Opening the Next Horizon
This post demonstrates the breadth of the problem without diluting its rigour.
Over-closure is not a technical flaw. It is an orientational error — one that arises whenever mathematical necessity is allowed to speak without acknowledging the relational ground from which it emerges.
In the final posts of the series, we will turn toward repair:
How inclination can be made explicit rather than denied.
How modelling can remain powerful without claiming authority over being.
How mathematics might be practised relationally rather than imperially.
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