Say you’re standing near the bottom of a hill and see a small rock rolling down. How should the motion of the rock be interpreted? It could be that the rock happened to brake loose and roll down the hill. Or it could be that someone took the rock and rolled it down the hill. The motion observed could be exactly the same in either case. The only difference is the interpretation.
One interpretation would be called “natural” or “mechanistic”. In it motion occurs because of happenstance and the laws of motion. So the rock just happened to roll for reasons which are intractable and therefore considered chance. But once the rock started to roll, its trajectory followed the laws of motion.
Another interpretation would be called “artificial” or “teleological”. In it motion occurs because it fulfills a purpose in a way that accords with the laws of motion. The rock purposely moved toward an intended target or along an intended trajectory. The rock itself need not have any conscious intention; either the intention is that of an external agent or of an internal predisposition.
In the mechanistic interpretation time is the independent variable. When and where the rock starts to roll is a matter of happenstance or whatever – one doesn’t know or doesn’t care. In the teleological interpretation space is the independent variable. The placement of the rock, its initial motion, and its intended target or trajectory are a matter of independent purpose – of some internal predisposition or some external agent.
The statement of the laws of motion are mathematically equivalent in either case but the interpretation of the variables differs symmetrically. To translate from one to the other interpretation interchange the following: 3D space ↔ 3D time, scalar time ↔ scalar space, object ↔ subject, and mass ↔ ethereance. The laws of motion are formally the same for both interpretations. Only the meaning of the symbols changes.
From this exercise we learn that science determines the form of physical laws but not their interpretation. It would introduce metaphysics to specify that only one interpretation is valid. Science is not metaphysics but it allows metaphysics. Instead of excluding metaphysics, science affirms all metaphysical interpretations consistent with its laws. Science is pluralistic.