Mathematics is often treated as the language of nature — a precise, abstract mirror of physical reality. From Newton’s laws to quantum field theory, the success of mathematics in physics has led many to conclude that the universe itself is written in mathematical terms. Some even suggest that reality is a mathematical structure.
Yet this view presumes a kind of metaphysical realism: mathematics describes what is, independently of our modelling. The math is “out there,” waiting to be discovered.
A relational ontology takes a different approach. Mathematics is not the mirror of nature, nor the code of the cosmos. It is a grammar for constraining construal — a system for structuring potential so that coherent articulation becomes possible within a network of interdependence.
1. Mathematics as a Semiotic Resource
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Mathematics is not a separate realm of truth; it is a symbolic system,
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It allows us to model structured transformation, express dependency, and formalise constraint,
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Like any semiotic system, it makes sense only within a context of use — it is intelligible within a framework of relational meaning-making.
2. Formal Systems and Relational Potential
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Mathematical structures (groups, manifolds, Hilbert spaces) are not containers for reality,
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They are ways of mapping and managing potential — methods for constraining the space of coherent transformations,
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For example, group theory expresses how systems can transform while remaining intelligible — a grammar of symmetry and change.
3. Equations as Construal Rules
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A physical equation does not describe an external fact; it constrains how we articulate configurations within a theory,
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For example, Schrödinger’s equation does not describe a thing evolving; it models how constrained potential propagates across a system,
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The equation is part of a modelling practice: a way of managing interdependencies so that phenomena can be made sense of.
4. The Power and Limits of Formalism
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Mathematics is powerful precisely because it is internally consistent and externally extensible,
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But it does not determine reality — it constrains the space of viable descriptions,
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Many paradoxes (e.g. infinities, singularities, divergences) arise not because nature is broken, but because our formal constraints misalign with the relational field we are trying to model.
5. Mathematics and Ontology
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A relational ontology does not deny mathematics; it reframes it,
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Mathematics is not ontologically prior, but ontologically generative — it helps articulate reality, not because it is “true,” but because it shapes how potential can be constrained,
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It is not the language of the world, but a toolkit for coherent construal within structured systems.
Closing
Mathematics is not an oracle but an organiser. It constrains how relational systems can be interpreted and reconfigured, providing formal grammars for potential rather than mirrors of fact. Its power lies not in its proximity to truth, but in its ability to manage coherence under constraint.
In the next post, we will explore the meaning of quantisation itself — not as the discreteness of nature, but as a feature of how systems resolve under boundary conditions within constrained potential.
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