## Sunday, October 11, 2015

### An Aristotelian argument for a causal principle

1. Laws of nature are grounded in the powers of things. (I.e., Aristotelian picture of laws.)
2. Space can be infinite.
3. Newtonian physics is metaphysically possible.
There is a somewhat handwaving argument that if (1)-(3) are true, then an object cannot come into existence ex nihilo for no cause at all, and hence we have a causal princople.

Here's why. Say that a gridpoint in a Newtonian three dimensional space is a point with coordinates (x,y,z) where x,y and z are integers (in some fixed unit system).

Given (1)-(3) and assuming that objects can pop into existence ex nihilo, it should possible to start with a universe of finite total mass and then for a Newtonian particle of equal non-zero mass to simultaneously pop into existence at all and only those gridpoints (x,y,z) where z is positive, with nothing popping into existence elsewhere. Here's why. At each gridpoint, the object should be able to pop into existence. But objects that pop into existence causelessly at one location in space would be doing so in complete oblivion of what happens at other gridpoints. There should be total logical independence between all the poppings into existence. If so, then any combination of poppings or non-poppings should be able to happen at the gridpoints, and in particular, it should possible to have particles of equal mass pop into existence at the gridpoints with positive z-coordinates but nowhere else. But if this happened, then each particle would experience an infinite force in the direction of the z-axis (this follows from Newton's shell theorem and some approximation work), which would result in an infinite acceleration, which is absurd.

A relativistic version of this argument would require that spacetime can be infinite, so we could arrange the particles popping into existence along a single backwards light-cone.

There is a more general point here. The above example will remind regular readers of an argument I recently gave for causal finitism. I think many paradox-based arguments for causal finitism can be turned into arguments for causal principles in something like the above way. If this is right, this is very cool, because we can get both premises of a Kalaam Cosmological Argument out of the paradoxes then.