Claim: Asking whether God exists or not is like asking whether complex numbers or non-Euclidean geometries exist. The word “exists” of him doesn’t mean the same thing as asking whether dark matter or Santa Claus exists.
Objection: But God is supposed to act on the world: he moves things, causes things, performs miracles, responds to prayers, etc. If you make his existence as different as non-Euclidean geometries, then you cease to make his action continuous with the world at whatever point he is supposed to act.
Response: This muddles the difference between acting on the world and a physical action, which are as different as acting on a car and the action of a car. The objection assumes that to act on X requires that you use the sort of powers X uses to act – which would commit us to seeing a veterinarian as having a skill that was first possessed by dogs and horses.
The normal way of taking “act on” is to act from the outside, i.e. to take the action as not homogeneous or continuous with the thing on which it acts. If God exerted some force on the world or added new energy to it he wouldn’t be acting on it. It’s therefore precisely because God acts on the world that he cannot exist in the same way as the world, or act by the force, energy, momentum, etc. that perform the actions in a physical system.