If inclination is first-class, modelling becomes an art of relational positioning.
Physics has long treated mathematical formalisms as neutral containers—transparent vessels through which the structure of nature simply appears. Once we recognise this as a myth (Post 7), the way forward becomes clear: modelling is not about discovering the right container; it is about choosing, analysing, and iterating the inclinations through which phenomena can be construed.
This post sketches how physics might look if it embraced this shift.
1. Formalism as orientation, not ontology
A relational practice begins by naming the act physics has always performed implicitly:
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To choose a formalism is to take a stance.
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To take a stance is to incline the space of possible construals.
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To incline construal is to shape what counts as a phenomenon.
Nothing about a mathematical model is ontologically neutral. A Riemannian manifold, a Hilbert space, a category of processes—each imposes a topology of salience and suppression. In a relational practice, these inclinations are not hidden behind the rhetoric of “fundamentality.” They become first-class objects of analysis.
Instead of asking:
“What is the correct model of spacetime?”
we ask:
“What inclinations does this formalism impose, and what phenomena does it actualise or foreclose?”
The shift is subtle but transformative. It turns modelling into a reflexive, relational craft.
2. The triad of relational modelling
A systematic articulation.
A relational practice treats every modelling choice as involving three separable but interdependent components:
(a) Phenomenal orientation
This acknowledges that “the phenomenon” is not a raw given but an already construed experience (first-order meaning).
(b) Semiotic inclination
What formal system is being selected, and what inclinations does it impose?
This includes:
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its topology of allowable distinctions
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its commitments about continuity, smoothness, or discreteness
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its architectures of symmetry, invariance, or composition
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its constraints on what can count as a lawful trajectory or event
This is the heart of the relational turn: treating inclination explicitly as a second-order meaning system.
(c) Interpretive actualisation
How does the chosen formalism stage, frame, or generate a construal of the phenomenon?
This is where the model actualises meaning—where potential is carved into event by the perspectival cut.
The triad replaces the old representational fantasy (“model ↔ world”) with a systematic, stratified, relational understanding of modelling.
3. Modelling becomes iterative co-individuation
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adjusting the phenomenal orientation
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adjusting the mathematical inclination
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adjusting the construal produced through their encounter
Each round is a co-individuation of meaning: phenomenon, form, and interpretation mutually refine one another. Inquiry becomes a dance of relational adjustments—not a search for the one formalism that magically captures reality.
This reframes scientific progress as the evolution of possibility (picking up the parallel thread in our mythos series): the systematic widening, sharpening, or recontouring of what kinds of construal can actualise.
4. The methodological payoff: new clarity about singularities
When inclination is first-class, pathological phenomena cease to be “cosmic breakdowns” and become:
points where the inclinations of the chosen formalism conflict with the way the phenomenon resists being carved.
In a relational practice, this is not a failure—it is diagnostic feedback. A cue to reinterpret the phenomenon or change the formal inclination.
5. The practical payoff: plural modelling without metaphysical panic
Physics currently experiences theoretical plurality (GR, QFT, string theory, causal sets, loop models, amplituhedra, categorical formalisms) as a crisis: too many incompatible pictures of “the universe.”
Instead of demanding unification at the level of ontology, we seek relational coherence among inclinations:
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What does each cut illuminate?
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What does each suppress?
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Where do inclinations conflict?
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How can they be coordinated, composed, or layered?
This opens a path toward a genuinely post-representational physics.
6. The theoretical payoff: modelling as relational design
Once we abandon transparency, we can design new mathematical formalisms for their inclinations rather than their ability to mimic older ones.
For example:
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A category-theoretic formalism might be chosen for its inclination toward compositional process rather than state-based ontology.
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A topos-structured formalism might be chosen for its inclination toward context-dependent logic.
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A relational metric theory might be chosen for its inclination toward distributed coherence without forcing global smoothness.
Formal design becomes semiotic design.
7. A new ethos of modelling
A relational practice of mathematical modelling is governed by three principles:
(1) Reflexivity
(2) Multiplicity without metaphysics
(3) Evaluation by relational adequacy
Models are judged not by their metaphysical fidelity but by how well their inclinations enable coherent construal of the domain.
8. Closing trajectory: from modelling to mythos
If physics embraces inclination as first-class, its practice becomes more honest and its models more flexible. But more importantly, the universe stops being a fixed object to describe and becomes a moving horizon of possible construals—a relational field whose intelligibility evolves through the practices that engage it.
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