Thursday, October 1, 2015

Two ways of violating causal finitism

Causal finitism holds that the causal history of anything is finite. On purely formal grounds (and assuming the Axiom of Choice--or at least Dependent Choice), it turns out that there are exactly two ways that a world could violate causal finitism:

  1. The world contains an infinite regress.
  2. Some effect is caused by infinitely many causes.
Historically, a lot of attention has been paid to the first option, with arguments back and forth on whether this is possible. Not much attention has been paid to the second. But notice that in an infinite universe with Newtonian physics, we do have a type (2) violation of causal finitism, in that the motion of each object is instantaneously gravitationally caused by the pull of infinitely many objects. I suppose that insofar as that sort of a world seems logically possible, that's an argument against causal finitism, though not a decisive one.

But perhaps the last observation can be turned into an argument for causal finitism. For if it is possible to have infinitely many objects working together causally, it should be possible to haven an infinite Newtonian universe. But it would be strange to suppose that some but not all infinite arrangements of physical objects are compossible with the Newtonian laws. After all, we can imagine asking: "What would happen if angels shuffled stuff?" So it should be possible to suppose a universe that has nothing in the half to the left of me, but in the half of the universe to my right is an infinite number of objects arranged in a uniform density in space. If that happened, I would experience an infinite force to the right (think of the gravitational force of a solid ball of uniform density at the surface: the Newtonian law makes the force be proportional to the ball's radius as the cube-dependence of the mass beats out the inverse-square-dependence), and accelerate infinitely to the right. That's impossible.

1 comment:

Anonymous said...

Sure you can suppose that angels shuffle stuff, but in your example you suppose that they shuffled an infinite amount of stuff. That is enough to explain the impossibility without saying that the Newtonian universe is impossible.