The major difficulty with substance dualism is the interaction problem. This is the problem of accounting for how something physical and something non-physical could interact with each other. This problem is characterized in various different ways. If substance dualism is true, then the mind/soul has causal influence over the brain (which is how you are able to will your arm to move or act on any of your desires), and the brain has causal interaction with your mind/soul (which is how you are able to perceive through your sensory organs).
I came up with a solution one time that I have since then abandoned, but let me tell you about it. My solution was to say that maybe the mind has the unique ability to create energy ex-nihilo. Let me explain how I thought this could solve the interaction problem.
Imagine you've got some particle at rest, and you want it to move. Well, if that same object began to move, then it would have to have kinetic energy that it didn't have before, and that energy would have to come from somewhere. In the case of physical causation, energy is transferred to the particle by something else that has energy. Maybe something collided with it, or maybe it was pushed. But something that is non-physical doesn't have energy because energy is a physical thing. So it would appear to have no way to move the particle unless it had the ability to create energy ex-nihilo. So imagine that it could create another particle. All it would have to do is create the particle in proximity to the other particle, and the forces of nature could take over from there. If both particles were electrons, then there would be a force of repulsion between them. The direction of motion could be determined by the location of the created particle in relation to the already existing particle.
The causal interactions in the brain could be so subtle as to be unobservable or indistinguishable from random quantum events. One new electron could be sufficient to set of an avalanche of chemical reactions in the brain resulting in behavior. It might only require the release of potential energy through the pulling of a trigger.
I liked this solution when I first came up with it because it had a second use. In the Kalam cosmological argument, you get an immaterial cause of the universe, but then you need additional arguments to show that it's a person. William Lane Craig has two arguments for the personhood of the cause of the universe, and I don't think either one is all that persuasive.l But if it turned out that minds had the unique ability to create ex-nihilo, then we could argue for the personhood of the cause of the universe by saying something like this: Since minds are the only things we know of capable of creating ex-nihilo, it follows that a mind is the best candidate for an explanation for the beginning of the universe.
The only problem is that this solution only works when the direction of causation goes one way. It doesn't work as well when causation goes in the other direction. It explains how a mind could have causal interaction in the brain, but not how a brain could have causal interaction over the mind.
One possible solution was to imagine that the reverse happens. When the brain causes something in the mind, it does so by annihilation rather than creation. I don't think this works, though. It would require that matter has the ability to annihilate itself, but only when interacting with the mind. That just seems unlikely. You can't attribute the ability to the mind since that would require that the mind was doing the causing. We are trying to explain how the brain can do the causing, so it's the material of the brain that has to bring about the annihilation. Maybe somebody else can toy with that idea and make it work, but I don't see how it would work. It is for this reason that I've pretty much abandoned this whole solution to the interaction problem.
Currently, I have no good solution to the interaction problem. But the interaction problem isn't a major obstacle to my belief in substance dualism for a few reasons.
One reason is because in spite of the difficulty of solving the interaction problem, the arguments for substance dualism seem sound to me. If I were to give up substance dualism, I'd be trading one problem for even more problems. I think physicalism and idealism are even more problematic than substance dualism.
Another reason is because we don't have to know how something happens to know that it happens. There are mysteries in the physical world that we don't deny in spite of how strange they are. I'm thinking particularly about quantum entanglement. If two particles are entangled, then no matter how far apart they become, measuring the properties of one appears to determine the properties of the other. There appears to be instantaneous causation over large distances, or what Einstein called "spooky action at a distance." We know that it happens, and it's very strange, but we have no idea how it happens. If the world is strange enough to contain phenomena like this, then the interaction problem shouldn't bother us.
Lastly, it isn't as clear to me as it is to others why the interaction problem is a problem in the first place. I mean I do see that there's a problem. I just don't think the problem is as formiddable as some people think it is. That may be due to my own lack of understanding, but I can't help that.
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