What is a person?
A lot of people, when they hear this "continuity through change" argument will begin to see that there is definitely a distinction between mind and body, and that a person maintains identity through physical change. But to them, this doesn't necessarily entail substance dualism. It could be that the mind is an emergent property of the brain. It's the mind that constitutes a person's identity, not the brain. Since the mind remains continuous through physical changes, the person maintains identity. Although the body changes, the memories are the same.
Some people think of the mind/body distinction like the distinction between hardware and software. The body (specifically the brain) is the hardware, and the mind is the software. What constitutes a person is not so much the hardware, but the software.
A particular mind emerges because of a particular pattern in the brain, just as software has its properties because of the ones and zeros written on the hard drive and the structure of the computer. You can change our cells all you want, and it will still be the same mind with the same memories, personality, etc. as long as the structure is the same.
I don't think these objections work, though. Lemme use some thought experiments to explain why. If it's true that the mind emerges from the brain, then all you would have to do to create a mind is to create a brain. But suppose you created two identical brains with perfectly identical structure, just as you might make a copy of a program and run it on two different computers at the same time. The minds that emerged would both have the same personalities, memories, and everything. But they couldn't both be the same person, because one person can't be in two different places at the same time. If we could create a perfect replica of you, brain and all, the replica would have all of your mental attributes--personality, memories, etc. The replica would think that he was you. But he couldn't be, because then you'd be in two different places at the same time. From the time the replica was created, you'd be two distinct persons even if you had all the same mental goings on.
Steve made me think of another way of looking at this. Suppose you have a person who has a total case of amnesia. They've lost all memory of the past. Do they literally become a different person? Or suppose you have somebody with multiple personalities. Are they literally different people? Or suppose somebody has a brain injury which causes a complete change in their personality as well as total amnesia. Do they literally become a different person? Common sense seems to dictate that they would still be the same person. We often say, "So & so's a different person," or, "You are no longer the person I fell in love with," but we don't mean this literally.
The point I mean to make is that the emergent property view is not an adequate theory to account for personal identity. It leads to counter-intuitive results. A person is more than their mental make-up. Not only do we maintain identity through physical change, but we also maintain identity through mental change, which means the soul is not merely an immaterial mind.
There are other problems with the emergent property view, but I'll get to those in future blogs.