Small Convergence Miracles
Merlin is bound to disappear at noon, taking with him all physical traces of his existence. Shortly before his magic disappearance, he casts a spell. As a result, at noon on the following day, the prince turns into a frog.1
In virtue of what does the spell cause the metamorphosis? For instance, it is not at all clear that by Lewis's standards of similarity, some world containing neither spell nor metamorphosis is more similar to actuality than any world not containing the spell but containing the metamorphosis. The problem is that the only trace left by the spell, after Merlin's magic disappearance, is the metamorphosis itself:
In a nearby world not containing the spell, a small miracle (with respect to the laws of the original world, which I call "actuality") occurs that prevents the spell. At noon, Merlin disappears both in actuality and in the nearby world, and for 12 hours the two worlds perfectly match. In actuality, the prince then turns into a frog. Wouldn't another small miracle suffice to make that also happen in the nearby world, thereby securing perfect match of futures? If so, there is no counterfactual dependence between the spell and the metamorphosis (on Lewis's standards).
Or consider a nearby world where Merlin casts a different spell. Again, wouldn't a small miracle suffice for breaking the spell and securing perfect match of futures? If so, there is no relation of influence between the spell and the metamorphosis.
Intuitions about what's true in the story aside, it seems very strange to think that by erasing all but one trace of an action, you could make it true that the remaining trace is not a trace of the action any more. If you shot somebody and could magically erase all traces of the shooting except for the death of the victim, would you thereby see to it that you didn't shoot the victim in the first place? That sounds quite unbelievable.
Is there a reductive account of causation that can handle such cases?
1) So yeah, Merlin leaves a physical trace: that the prince turns into a frog. He removes all other, ordinary, phyical traces on his disappearance.