I'm going a bit out on a limb and talking about stuff I haven't read too much about. But if blogs are for learning and fun discussion, I guess I don't need to be an expert! Also, this post is directed more toward people who are theists, substance dualists, and deniers of open theism.
Take Leibniz's theory of pre-established harmony (also called 'parallelism'), according to which the correlation between mental and physical states occurs by way of God's predestination. Suppose I am pricked by a needle at t5. God also determined from the beginning of time that I would feel a pain at t5 (or very shortly after t5). When I will to move my arm at t8, God also determined from the beginning of time that my arm move at t8. There is no direct causal relationship between the physical event and the mental event. Through parallelism, Leibniz has a complete story of how the mental states and physical states are well correlated; there is a pre-established harmony between the two realms. (We can see why the denier of open theism might not like parallelism; according to open theism, there are some acts of the will that God did not know would happen, and so God could not have predetermined which physical event should occur in certain instances of free mental acts.)
Take another view according to which God sets up some fundamental laws at the beginning of time which determine some mental states to follow from certain physical states and vice versa. Whenever certain brain states enter events of type A, then the soul feels pain. Whenever they are in type B, then the soul feels pleasure. Whenever a soul enters into a state of willing X, then certain brain states enter a certain state. There is genuine causal interaction on this view. Since I can't think of a better word, I'll call this view 'nomologism'.
I suspect that most theistic dualists would accept something like nomologism. (If not, then I'm curious what most theistic dualists would hold?)
But I wonder why nomologism is any better than parallelism, which is widely disregarded and even mocked? One downside of parallelism is the rejection of real causal relationships, but I'm not sure if that's so bad. The theories are still empirically identical. For the theistic dualist who rejects open theism, I can't see a compelling reason to hold to nomologism over parallelism.
For those who find intuitions about causal relationships to obviously set nomologism over parallelism, I wonder if there's any reason to accept nomologism over parallelism in addition to intuitions about causal relationships.
In fact, nomologism [edit: I should have said 'parallelism' here; thanks Clayton] seems to be the simpler theory in that God need not set up laws at the beginning of the universe, which would require determining what happens in nearby possible worlds, but simply what will happen in the future, which would only require determining what will happen in the actual world.
Anyway, for those who are more well-versed in this subject than me, I look forward to learning from you!