Objection 1: We notice if it's the same person by seeing if they have the same body. The dualist view identifies our most central features completely independently of the body.
Response: Maybe the soul is always in the same body, so we use bodies to tell if it's the same person. Sameness of person happens to go along with sameness of body, but that doesn't mean it has to be that way.
Also, this isn't the only way we identify people. If we're on the phone, over email, or in chat rooms, how do we tell? We pay attention to mannerisms, personality, character, beliefs, memories no one else should know, etc.
Objection 2: Can I tell if I have the same soul I had yesterday? I usually think of the Simpsons episode where Bart sells his soul to Milhouse, and they show people's souls tagging along behind them, but Bart's (which looks like Bart) is tagging along behind Milhouse, along with Milhouse's own. Maybe our souls move from body to body, or maybe our souls die off and get replaced by new ones very quickly. It would be crazy to rule that out as a possibility without strong argumentation, and yet the dualist view seems to deny that.
Response: This assumes a certain dualist view according to which there's nothing distinctive about the soul. You can have a view according to which the same soul might go from one person to another, without all the mental characteristics continuing on with the soul in the new body. That's just not Descartes' dualist view, so it's unfair to say dualism doesn't allow life after death on these grounds. You can't object to one view by saying a different view has problems. In other words, Descartes accepts that the mind/soul and the mental properties of a particular mind go hand-in-hand. Thus he considers the soul to be an essential property, but he also thinks other properties will always go along with the soul.
If you lose all your memories and beliefs, what we take to be distinctive of you, are you a different person, even if you have the same soul? A radical version of this appears in Babylon 5 (see especially the third-season episode "Passing Through Gethsemane"), called death of personality. By the 23rd century, they'd replaced the death penalty with procedure that became colloquially referred to as a mind-wipe. The memory and personality characteristics of the convicted criminal get removed from the brain, and a new set of memories and personality replace them, with a desire to serve.
In the episode, a monk discovers that he was once a serial killer. At least that's how he describes it. Some will say he's a new person now. Are they right if they mean that literally? We say a man just out of prison totally changed is a new person - but not literally. It could be the same guy much changed. So this isn't much of an objection to dualist accounts.
We have no sure way to tell if it's the same soul, but does it need to be absolutely sure or just reliable? If dualism is true, the methods we do use to tell if it's the same person will be reliable until death, so what's the problem? Having the same soul would involve the same beliefs, character, memories, and those don't allow body-switching or soul replacement without the person knowing.
So I conclude that the original challenge Perry sets up at the beginning of the discussion is met. He has his Weirob character ask for an account of the possibility of her survival beyond her impending death from terminal illness. She says she'd be satisfied not with a full expectation of eternal life but with the mere possibility. Doesn't the dualist view provide that? Sure, there are dualist views that have problems as discussed above, but those aren't the standard dualist view, and objections to those don't show problems with the dualist view itself. Perry thinks he's removed the dualist view from his set of options for this reason, but that seems premature.
Now it's another matter entirely whether the dualist view is true. I haven't given any arguments for it yet. You might happen to think it's true because you're committed to dualism already and find it plausible that such a mind/soul just is you or is central to your being you. But the arguments for dualism, discussed earlier in this series, are not all that convincing to most philosophers today. I hope that by the end of this personal identity discussion we'll be much more inclined to consider dualism, because it seems to me to be the best way to handle all the problems that occur in personal identity discussions. But for now let's move on to other views to see their difficulties before returning to a view that has much less of an argument for it in the views of most philosophers today. The next post will look at psychological accounts of personal identity.