Dualism is the belief that the mind and body are separate things, but the specifics of this belief means different things to different people. One of the more common forms of dualism is called "substance dualism," which argues that the mind can exist (and persist) outside of the brain. I do not accept substance dualism. I believe that the mind is an emergent property of the brain that only exists when the brain is functioning, kind of like software running on a computer. And, just like software ceases to run when the computer is turned off, the mind ceases to function when the brain is shut down from death.
A common argument is to think of the mind-body problem like a piano player being the mind and the piano being the body. Even if the piano is damaged causing the music to sound out of tune, or even destroyed entirely, the piano player persists. However, this argument, like all others I've heard in favor of substance dualism, is ad hoc. Our current understanding of neurology shows that the mind is a product of the brain. We see no evidence of non-corporeal minds and a change in the brain, will create a predictable change in the mind. This analogy presents the evidence backwards, probably because of their belief that souls exist.
Another argument I've heard in favor of substance dualism is that, since the mind can be thought of as something different than the brain, it therefore is different from the brain, and can therefore exist outside of a brain. I agree with the first part of this argument, that the mind can be thought of as being different from the brain. I also agree that, if a suitable analog were created, we might somehow be able to transplant a mind from one brain to another (evidence shows that the target brain would have to have a near-identical structure to the original to prevent the thought process from being horribly disrupted). However, the conclusion, that a mind can continue to function if it is removed from any brain, not only ignores the evidence that the mind is a product of the brain, but ignores reality in general. Using the hardware and software analogy above, this conclusion is similar to saying that you can turn off a computer, and the software will continue to run.
- en.wikipedia.org/wiki/Mind%E2%80%93body_dualism - Wikipedia.