Mind-body dualists hold that mind and brain are two different things. Dualists admit that the two are connected because mind altering chemicals and surgeries appear work. However, they claim that there is some non-physical aspect to mind. The mind, they claim, must be partly magical, partly beyond scientific explanation.
One of the particularly poor ways they make this claim is by using a special definition of human thought. According to this definition, what we perceive as rational thought and decision-making are those things that alter the deterministic course of matter. For example, it is our rational thought that causes a dam to be built that deflects the natural course of a river. If there were no rational thought, the river's course would be determined only by the laws of physics.
Unfortunately, this definition begs the question. Begging the question is a kind of fallacy wherein the question beggar sets up the premises such that his conclusions are inevitable. This is done by assuming the desired conclusion in one's definitions.
In this case, the dualists have implicitly defined rational thought as being non-physical and non-deterministic. For, if rational thought were a physical process, one could not define it as that which alters the natural course of physical processes.
In begging the question this way, the dualists are losing sight of the goal. We are all familiar with the experience of decision-making. We are also familiar with the appearance of decision-making in others. The question at hand is whether or not natural laws can explain decision-making. We don't get to go back to the experimental data and re-define the class of phenomena we are trying to explain.
In my opinion, we have already established the material nature of mind. Every aspect of human thought can be altered physically or chemically. Not what you would expect from a mind that requires something more than a brain.
So, what can mind-body dualists do?
Well, the thesis of the dualists is that there can be no explanation of mind, i.e., that we will never explain thought in terms of chemistry, neuroscience or any other scientific discipline. But on what grounds could they make such a claim?
Well, scientific explanations require two things. They require natural laws and logical consistency. Thus, the dualist must sacrifice one or both of these principles.
If we assume that mind is governed by logical principles (note that this is not the same as saying that we think logically), then we can only lack explanation by there being no natural laws to govern some aspect of mind. Unfortunately, dualists are a bit hazy on what aspects of thought are physical versus magical. Obviously sleepiness, nervousness, pleasure and the like are largely physical, as pharmacists are well aware. So either the magic is subtly spread over all of mind, or else it is located in some yet to be understood phenomenon of mind like qualia (what it feels like to experience things).
This game of "hide the magic in the gaps" tries to make its case by process of elimination. They regard their claim as analogous to claiming that there's no Ace of Diamonds in a particular deck of cards. That Ace represents the explanation of mind, and, if we go through 99% of the deck without finding it, then we're 99% sure that the Ace not in there. Likewise, the dualists argue that since we understand 99% of science (99% of physics, chemistry, neuroscience and so on), the odds of there being a scientific explanation of mind are only 1%. Of course, this betrays a misunderstanding of science. The fact is that we don't understand 99% of science. We probably understand only 1% of it. I'm not even sure that science is a finite search space. Thus, the dualist cannot argue for magic on the grounds that, if mind weren't magic, we would have found the explanation by now.
That leaves consistency as the dualist's only remaining target for attack. To utilize this attack, the dualist must identify some observable aspect of human thought that leads to an inconsistency. Suppose we measure some aspect of mind, let's call this aspect "MindUnit". To measure MindUnits we use a hypothetical MindMeter. What would inconsistency imply? It would imply that two MindMeters would not agree on a measurement of MindUnits for the same individual at the same time. Yet, if this were the case, we would all consider MindMeters to be completely useless tools, like voltmeters that could never agree on a voltage. Indeed, MindUnits would never have been recognized as an observable aspect of mind in the first place. This thought experiment (no pun intended) demonstrates that inconsistencies in the universe are generally invisible because they look like random effects.
Hence, the mind-body dualist can only ever have arguments by elimination (magic in the gaps).