There are plenty of reasons to believe in some sort of physicalist account of mind and reject the notion of dualism. Yet when I talk to dualists about it, they feel the same way about dualism. Of course this should be no surprise, as Catholics tend to feel that there are good reasons to be Catholic, and those who believe in psychic powers don't do so despite thinking there's a weak case for it.
Yet that we can justify what we already believe in doesn't mean that the case is very good. Perhaps the case for physicalism is really poor and the case for dualism overwhelming, from my perspective I try to understand where the case to the contrary is coming from and see whether that fits. At least in my head, I've got a list of certain things that dualism would have to account for in order to be considered a possibility. I've put these forward numerous times to dualists - yet I don't get any answers back at all.
Perhaps from their perspective, the problems are insignificant. Or perhaps I have fundamentally misunderstood the nature of the problems involved in the philosophy of mind. I don't know, all I can do is keep reading, listen to experts, and discuss the issues with others. Which brings me to the point of this post...
When it comes to intelligent design, most arguments for intelligent design fixate around the notion that there are certain patterns we can see in nature that are hallmarks of being designed. How a designer acts in order to design is a different question that a designer was involved - that a watch has a watchmaker can be inferred without knowing how the watch was made. So while evolutionary biologists will ask for a mechanism, the ID proponent doesn't claim to be able to show that - just to show that a designer was involved. This is done by trying to show that natural mechanisms cannot account for what we know designers can.
In a recent discussion with a dualist, I encountered the same such argument. That it didn't matter how mental phenomena worked, but that mental phenomena by definition could account for what physicalist models couldn't - and thus dualism. My objection to this is that labelling them mental stuff doesn't actually explain anything at all, but the goal of the argument isn't there to act as an explanation; it's there to demonstrate dualism - whatever that means. So me calling dualism incoherent and not actually explaining those things any better than a physical model would be missing the point.
Yet to what extent does this explanation carry? To my mind, such arguments are merely labelling our ignorance. What does mental causation mean, for example? To say that mental causation is part of the definition of dualism doesn't give any conception of possibility. A physicalist account involving neural networks and firing synapses is at least an attempt to make sense of mental causation. Dualism makes no such attempt, yet physicalism is judged on what is seen as a failure of explanation.
It's in that respect that explanations like Intelligent Design, God, pyramid-building aliens, or mental forces have a distinct advantage over any naturalistic explanation. The naturalistic explanations try to explain how something works, which for the most part are going to be imperfect and incomplete, yet the failure of such explanations is seen as evidence for explanations that don't even try to explain the evidence. In other words, just arguments are just taking our ignorance and giving it a label.
If such explanations were true, however, they would have empirical consequences. If dualism was true and there was mental causation outside the brain, then that would have empirical consequences. No matter how much personal introspection one does, if the brain is shown to be closed causally, then mental causation has no place in which to operate. This problem was not lost on Descartes, but it seems to be ignored some 400 years later by modern-day dualists. That we're living in an era of exploration of the brain should be all the more reason to be more empirical about it. It says a lot in the age of empirical inquiry that people are avoiding putting would could be scientifically-testable to the test.
Of course, all this might be a rationalisation on my part... but I really don't know why there's not even an attempt to turn dualism into an empirical model that can be tested and potentially falsified by scientific inquiry. Being "not even wrong" shouldn't be a selling point!