After the Loss of the Picture
Quantum mechanics did more than revise physical theory; it shattered classical intuition about objects, motion, and measurement. Suddenly, the world could no longer be pictured in the familiar terms of everyday experience. The very sense of what it meant to have an object became elusive. In this vacuum, mathematics did not merely describe; it became the surrogate intuition of physics.
Mathematics provided a new way of seeing the world—without requiring direct experience. A successful formalism suggested structure where intuition could no longer operate, allowing theorists to navigate spaces of possibility that defied imagination.
This development, while ingenious, carried subtle but profound consequences for the discipline’s epistemic habits.
From Tool to Surrogate
In classical physics, mathematics was a tool. It served to formalise intuitions already grounded in experience, to model relationships among phenomena, and to generate predictions testable against the world. Theories were answerable to events; equations were instruments, not avatars of reality.
With the collapse of picturability in quantum mechanics, mathematics assumed a different role. It became a medium for construal itself:
It suggested entities, relations, and structures.
It mapped spaces of possible instances without requiring a phenomenal cut.
It provided a sense of coherence where intuition could no longer operate.
In short, mathematics began to function as intuitive authority, supplying guidance where empirical anchoring was absent or deferred.
The Subtle Drift from Possibility to Existence
Once mathematics assumed the role of surrogate intuition, a subtle shift occurred in the discourse of physics:
Possibility: internally coherent instances within a system were explored for their potential actualisation.
Expectation: certain possibilities were elevated rhetorically, described as likely or natural.
Existence: the rhetorical step was taken to treat these possibilities as ontologically real, even in the absence of phenomenal instantiation.
This drift is often unconscious, hidden under the twin banners of elegance and inevitability. It allows theory to claim ontological weight without cutting to phenomena.
A relational ontology exposes this without condemning it. Mathematics can remain a powerful tool, a source of insight, and even a guide to potentiality—so long as the distinction between possibility and actualisation is preserved.
Discipline Without Fear
The critical insight here is that the rise of mathematics as surrogate intuition need not trigger epistemic anxiety. Relational ontology provides a framework in which one can pursue highly abstract theoretical work while remaining disciplined about ontological claims:
System: the mathematical structure.
Possible instance: the configuration articulated within the system.
Phenomenal cut: the perspectival shift required to instantiate the system as first-order meaning.
Without this framework, the temptation to conflate internal coherence with reality grows almost inevitable. With it, the speculative ambition of physics can be preserved while the distinction between theory and phenomenon remains sharp.
Preparing for the Final Cut
Having traced the trajectory from quantum mechanics to modern theory-space, from disciplined cuts to mathematics as surrogate intuition, we are poised to confront the final consequence: the disappearance of the cut itself. When the distinction between possibility and actualisation is elided, realism floats free of actuality, and ontology becomes untethered from phenomena.
In the next post, we will examine the ultimate implications of this drift and demonstrate how relational ontology restores the discipline without curbing theoretical ambition.
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