We can’t say there is an interaction problem between an immaterial and material thing without assuming that the action of one on another must be an interaction. But why assume this? We could just stipulate that we are using the terms as perfect synonyms, but this only explains the problem away. If all we meant was “action”, then why did we gravitate towards the term “interaction”? A closer look at actions and interactions reveals important differences between them which illumine how one thing might act upon another without needing to interact with it. In fact, a closer look at (even natural) actions shows that the higher the action is, the less it interacts.
It’s safe enough to say that one physical thing can’t act on another without some interaction, that is, without the other reacting upon the one that acts upon it. If the bowling ball hits the pins, the pins hit the bowling ball. This is just Newton’s third law. As clear as it is, there are at least some fuzzy edges: light can act on empty space by illuminating it, but the empty space doesn’t act on the light (N.B. we’re considering the empty space as really empty, and not so far as it might have some body other than the light in it). Again, it’s hard to see how this interaction hypothesis is of much value in describing the actions of bodies and fields. The action of a body on space does not have an equal and opposite reaction of the space on the body; and similar things might be said about magnetic fields and the bodies they affect. Closer to our common experience, there are many other actions to which the third law does not apply: if I persuade you to vote for Jones, I’ve done an action that has no equal and opposite reaction. Even setting aside human interactions, not every action of one thing on another is an interaction. For every bound of a ball there will be a rebound, but not every painting has a repainting (an antipainting?) nor does every burning have an antiburning. In other words, it’s not at all hard to understand what we mean when we speak of some actions not being interactions.
But here we have one of the simpler responses to an interaction problem: not every action is an interaction. If we take all the things we call actions, the ones that involve actual interactions are comparatively rare. It is true that every action of one physical thing on another will involve an interaction so far as we consider the action in certain ways (i.e. if we consider the sculptor’s action a “pushing” or “an action of one body on another” then there will be the reaction of resistance, but if we consider it as “sculpting” then there is not the reaction of anti- sculpting). But if this is what we mean by interaction, it is utterly irrelevant to considering a stipulated action of a non-physical thing on a physical one. Such a definition isn’t universally true anyway, since empty space as empty doesn’t act on light, and the definition is a poor fit to describe the actions of bodies and fields; but even if we admitted its universality arguendo it only applies to physical actions if we consider them in a certain ways and not others.
But I’m less interested in refuting an argument than illuminating an important difference among actions that allows us to articulate an action without a reaction, which renders intelligible what the action of the non-physical on the physical would be. What we are doing when we speak of “intereaction” is visualizing an action such that there is a causal arrow not only from A to B, but also from B to A. “Interaction” is the name we give to a multitude of causal lines. But we only understand this multitude through the individual or the one, and this one causal arrow, in all of its simplicity and intelligibility, is the best way to understand the action of the immaterial on the material. In fact, the closer we get to understanding what is most causal in nature, the closer we get to understanding the sorts of entities having causal arrows pointing in only one direction. I might lift up a pencil and release it, and so “change its potential energy to kinetic energy”, but such an action is action on a pencil, not an action upon energy. What we say about energy is pretty much what the Medievals said about the celestial bodies. We both might be wrong, but we won’t be wrong about the highest sort of causes having uni-directional causal arrows upon their effects; and this is a case where nature shows us what must be true of actions transcending the natural realm.