Here is a simple indiscernibility argument for substance dualism, presented simply:
1. If two things are identical, then whatever is true of the one is true of the other, and vice versa.
2. It is true of me that I can (logically) exist disembodied.
3. It is not true of any body that it can (logically) exist disembodied.
Therefore
4. I am not identical with any body.
The argument is valid in point of logical form, and (1), the Indiscernibility of Identicals, cannot be reasonably disputed. (3) too is irreproachable: it is surely impossible that a physical body exist without its body. My coffee cup can survive the loss of its handle, but not the loss of its very self. Destroy all its parts and you destroy it. So the soundness of the argument rides on the truth of (2). If (2) is true, there is no escaping the truth of (4). For an argument to be probative, however, it is not enough that it be sound; the premises must either be known to be true or at least reasonably believed to be true.
Do I have good reason to think that it is logically possible that I exist without a body? If so, then it is not necessarily the case that if you destroy all my physical parts, you destroy me. Well, the following is true and known to be true:
5. It is conceivable that I exist without a body.
By 'conceivable,' I don't just mean thinkable — round squares are thinkable — I mean thinkable without logical contradiction. And surely it is thinkable without logical contradiction that I exist without a body. Read your Descartes. I had a student once, a hopeless materialist, albeit otherwise alert and intelligent, who just could not appreciate the point. He kept repeating, "But if I shoot you dead, then you cease to exist!" What I found bizarre was that his religious upbringing hadn't even softened him up for the conceivability of post-mortem existence. It was as if he was so sunk into his bodily existence that the mere thought of not being identical to his body was unavailable to him. So I branded him a Cave-dweller and gave up on him. And then some years later, I gave up on teaching entirely. Why spend your life among unteachable troglodytes?
But now comes the hard part. How do we move validly from conceivability to possibility, from (5) to (2)? (2) affirms the (broadly) logical possibility of disembodied existence. But it is not clear why being able to conceive a state of affairs should guarantee its logical possibility. Note that it would serve no purpose to stipulate that logical possibility just is conceivability. That would have all the advantages of theft over honest toil. Broadly logical possibility is a species of real possibility, and one cannot just assume that what one can conceive without contradiction is possible in reality. (On the other hand, one can be certain that a concept harboring a contradiction cannot have anything answering to it in reality.)
Consider the FBI, the floating bar of iron. If my thought about the FBI is sufficiently abstract and indeterminate, then it will seem that there is no 'bar' to the FBI's logical possibility. If I think of the FBI as an object that has the phenomenal properties of iron (e.g., hardness) but also floats, then those properties are combinable in my thought without contradiction. There seems to be no logical contradiction in the thought of a hard metal that floats.
But if I know more about iron, including its specific gravity, and I import this information into my concept of iron, then the concept of the FBI will harbor a contradiction. The specific gravity of iron is 7850 kg/cu.m, which implies that it is 7.85 times more dense than water, which in turn implies that it will sink in water. For someone with this richer understanding, the FBI is a bar of iron that both floats and does not float — which is a contradiction.
What this example seems to show is that my failing to find a contradiction in my concept of X does not entail that X is logically possible; for it may be that my concept of X is insufficiently determinate, and that if I had a sufficiently determinate concept of X, then I would see from the concept alone that X is logically impossible. Now let's apply this to our problem. My disembodied existence is conceivable. But it might well be that my identity with my body is hidden from my powers of conception in a way similar to, but more radical than, the way the logical impossibility of floating iron is hidden from someone whose concept of iron is inadequate. It may be that my belief in the possibility of disembodied existence feeds on ignorance. How can I rule out this possibility?
If the only way to rule it out is by assuming the truth of (4), then the modal argument begs the question. So I conclude that the above argument is not rationally compelling or rationally coercive: a consumer of the argument can reasonably resist it. But the argument is rationally defensible and does provide a good though not compelling argument for dualism.