In standard quantum theory, probability is often taken to represent our uncertainty about measurement outcomes — a sign that nature is fundamentally indeterminate, or that some hidden structure remains beyond our grasp.
But this view carries assumptions drawn from substance metaphysics and classical statistics: that there is some underlying reality to be known, and probability reflects our incomplete access to it.
From a relational standpoint, probability has a different ontological status. It is not about uncertainty concerning actual states. It is about the distribution of potential across a constrained system — a topological measure of how coherence actualises under perspectival cuts.
1. The Classical Misreading: Probability as Epistemic Ignorance
Classical physics regards probability as an artefact of incomplete knowledge. For example:
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We don’t know the exact position or velocity of a particle, so we assign probabilities to its possible locations.
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Once more information is known, the probability collapses into certainty.
This presumes:
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That all properties have determinate values whether or not they are measured,
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That randomness is only apparent — a placeholder for missing data.
Quantum mechanics disrupted this view, but in many interpretations, the old assumptions persist in new form.
2. Quantum Probability: Born Rule and Beyond
In standard quantum mechanics:
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The Born rule gives the probability of a measurement outcome as the squared amplitude of the wavefunction component,
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This is often read as an objective probability: even if nothing is hidden, outcomes remain probabilistic by nature.
Yet even here, probability is typically conceived as a feature of the system — a property of the wavefunction, or a disposition of the particle.
Relational ontology reframes this again.
3. Probability as Measure over Potential
In relational terms:
Probability is not a property of a thing, nor a statement of ignorance.It is a measure of how relational potential is structured under constraint.
Specifically:
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A given cut on the system selects a constrained subspace of potential;
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The distribution of possible actualisations across that subspace reflects how coherence can resolve;
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Probability quantifies this structured distribution — it is the relational “shape” of possibility, not its concealment.
4. Why Probabilities Are Stable
The relational view explains why quantum probabilities are statistically reproducible, even though each event is singular:
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The underlying field of potential is structured by constraints that remain stable across trials;
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Each measurement enactment is a new perspectival cut, but the shape of constraint remains consistent;
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This yields consistent distributions — not because particles “choose” probabilistically, but because actualisation arises from the field’s coherent tensions.
In other words: it's not randomness, it's relational regularity in how potential resolves.
5. Probability and Construal
Probability also reflects the role of construal in making meaning:
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Each measurement is not just an encounter with nature but a systemic organisation of perspective,
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Different cuts yield different distributions — not because reality changes, but because construal organises potential differently,
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Probability thus becomes a function of perspective — of how the system constrains itself and resolves coherence under specific conditions.
This restores probability to its rightful place — not as a cloud of ignorance around reality, but as an expression of structured indeterminacy in a relational world.
Closing
Relational ontology does not deny probability — it redefines it.
Probability is not about hidden states or irreducible chaos.It is about the systemic articulation of potential under perspectival constraint.
In the next post, we’ll take up a closely related topic: entanglement. What does it mean, in relational terms, for distant events to exhibit coordinated behaviour? And why does this coordination not imply mysterious action at a distance — but rather, a deeper coherence of field and cut?
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