Physics and formalism

You could tell the whole story of physics after Galileo and Descartes as one that took motion and extension as basic and simple. Until then, both were complex, whether they were divided into Aristotle’s active and passive sources or Plato’s idea that the sensible is an accident projected from a substance into an utterly featureless screen or receptacle.

Leaving aside the active and passive, motion and extension became indistinguishable from their mathematical abstraction. While the story is that this made all causality agent and material, it in fact redefined causality altogether so that precisely defined causes no longer had precisely defined effects, making physics purely formal. Physical processes just acted without needing anything to act in or act on.

Except not. Some subject of action has always proved indispensable. Newton could not understand the world of physical action except as set apart from a much truer, purely formal world of absolute space and time which is infinitely precise and exact, and in relation to which the actual world of physical events was less than formal; and we only cast this purely formal world out by two different systems that made the observer an integral part of the definition of the physical. On the Newtonian picture, physics required falling away from pure formalism since it could not be absolute; for us it falls away from it because some observer is required to concretize and individuate the formal elements of the system. And so physics has never succeeded in being purely formal, but has always demanded a duality of principles, one which is formal and another which individuates and is unintelligible of itself.

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