Descartes famously invokes a conceivability argument for substance dualism in his Meditaions. In this argument he proposes that he can conceive of his mind existing in a universe that consists of no material things. It certainly seems possible to concieve of a universe that consists of no material entities but Descartes proposes that he can conceive of his mind existing in this universe. Of course Descartes proves that his mind is not a material thing since it does not contain any essential properties of material things, namely extension. Descartes concludes that the mind is not identical to the body since the body is a material substance. Granting the fact that conceivability implies logical possibility, Descartes is able to deduce this while sitting in his armchair by the fire. Descartes does not need to go out and do any experimental science in order to come to this conclusion. This was certainly intended due to the circumstances he created with his skeptical arguments.
Descartes of course assumed that since the mind was immaterial it was outside of the realm of science since science exclusively dealt with material things. The appeal of the materialist position was the fact that if the mind could be reduced to a material entity it could be studied under the realm of science. This would solve our intuition that the mind has some mysterious causal effect on our body. The problem now is that immaterial entities are part of the content of science, namely physics. This is what initiated the evolution of materialism to physicalism. Since materialism could only account for extended things it could not account for photons and other entities that are not considered to be extended. Of course we want these entities to be considered part of the content of science so the 'scientific' view of mind evolved into physicalism.
Now since immaterial entities are actually considered within the realm of science, the body can consist of immaterial entities. So the mere fact that the mind is immaterial does not deliver the conclusion that the mind is not identical to the body.
There are some problems at this point that seem to put the mind/body argument on hold. First is that even the best physicists and physicalists cannot pin down an essential property of physical substance. This leads to problems with physicalism because there is no way a physicalist will ever want to concede that fundamental mental entities are within the realm of physics and have causal power. But since there is no essential physical property known at this point, physics has no determinate content (this is one horn of Hempel's Dilemma) and therefore the physicalist cannot rule out fundamental mental entities from being within the realm of physics.
Second, the substance dualist seems to be in a position where he can no longer use the Cartesian conceivability argument in his favor. In order to use this argument he must know an essential property of physical substance in order to demonstrate that the the mind and the body have incompatible properties. The dualist could always say 'Well I can imagine my mind existing in a universe with no physical things, therefore they are not identical.' But in order to do this wouldn't he need to know a priori that his mind is not physical? The way Descartes knew a priori that his mind was not material was because he could imagine material things and from his imagination determine an essential feature of all material things. Is it possible to discover an essential feature of the physical by using our imagination alone? It seems as if this issue is no longer an a priori issue.
Jessica Wilson of U of M presented a paper in which she addressed the problems of Hempel's dilemma and concluded that a physicalist must have a physics-based NFM (no fundamental mentality) account of the physical in spirit of the intentions of the physicalist's position as a solution to the mind-body problem. According to a physics-based NFM account, in order for an entity to be physical it must be within the realm of physics and it must be non-mental.
I just added in this last part as an interesting attempt to solve the problem on the physicalist's side...
I also may be creating a problem for dualists that may not exist. I was just thinking about this today and thought I'd throw it out there.