The doctrine of causal closure

Let us take a pair of electrons, Eric and Ed. Eric the electron is an electron in the body of Richard Dawkins. Ed is an electron inside the body of the Archbishop of Canterbury. Knowing this, we might know that Ed is far more likely to be inside of an Anglican Church this Sunday morning than is Eric. But if the physical is causally closed, then where Eric and Ed will be on Sunday morning is either fully determined by the present state of the world at the physical level plus the laws of physics (assuming determinism), or else where Eric and Ed are also affect by quantum-mechanical indeterminism. But this indeterminism, given causal closure, is brute chance and nothing more. It is not a “window” for intentional states to affect the physical. Imagine a being omniscient with respect to the state of the physical world. That physically omniscient being could learn nothing useful about where Eric and Ed will be if it learns that Eric is in the body of an atheist, while Ed is in the body of a Christian. The electrons will go where the laws say they must go, or where chance places them. To say otherwise would be to deny the causal closure of the physical world.