The soul and the indiscernibility of identicals
I love that phrase, "the indiscernibility of identicals." I sounds so fancy schmancy, that I feel smart every time I say it. It's actually more simple than it sounds, though. Basically it's just the banal observation that if some entity has every property in common with some other entity, then they're actually the same entity. If whatever is true of A is also true of B, and vice versa, then A and B are the same thing. If there's anything at all that is true of one but not true of the other, then they are not the same thing.
The mind and the brain are obviously not the same thing, because there are things that are true of one that are not true of the other. But when you look at some of the properties of a mind, you find that they aren't even reducible to the brain. For example, the mind can contain images. That's how you see things. Images are formed in the mind. You also have images in your mind when you dream. But you can look at the brain all day and never see any of these images. An image in your mind may have the property of greeness, but nothing in your brain is green.
We each have private access to our own minds that nobody else has, and that is problematic for the emergent property view. With every other example of an emergent property you can think of, those properties are open to public access. For example, wetness is an emergent property of H2O. An individual water molecule is not wet, but when you put a bunch of them together, the property of wetness emerges. But the property of wetness can be observed by anybody. If the mind is an emergent property of the brain, then the properties of the mind ought to be observable. But they are not. Only the person who owns the brain has access to thoughts, feelings, perceptions, etc. All of the properties of the mind are private in this way. A brain surgeon may know more about your brain than you do, but you know more about your thoughts than he does.
Imagine for a second that we're some strange form of life where brains don't look anything like they look in humans, so we really have no knowledge of what a brain is or how it works. Imagine we decide to look at human brains, not knowing what they are, and we're able to do it without killing the person in the process. No matter how much we observe the brain, not matter what instruments we use, we will never observe any thoughts, feelings, memories, perceptions, or anything remotely resembling the properties of a mind. We could never know from observation that there's some mysterious emergent property called a "mind" that these brains have.
But we know we have minds, because we experience first person subjectivity. We feel, think, remember, and perceive. It's true that a brain surgeon can look at an image of the brain that maps brain waves and brain activity and know something about what's going on in the mind. But the only reason he is able to know any correspondence between the mind and the brain is because of previous experiments where a person whose brain was being mapped gave input about his mental activity. The person being experimented on had to tell the experiment what was going on in his mind before the experimenter could then associate the brain state with the mental state.
The mind and all its properties are not observable by a third person, because the mind and all its properties are not part of the physical universe. They are nonphysical.
Again, people bring up computer analogies here. The inner workings of a computer produce images on a monitor, but you can look inside the computer all day and never see these images. Some argue the mind/body distinction is the same.
But the problem here is that what goes on in the computer is not observable until it is hooked up to a monitor. A monitor converts the signals into an image. Once it does, that image is open to public access. Anybody can see it. Not so with the mind. There's no monitor at all in the brain, and the only person who can see any image associated with the brain is the person who owns it.