Parfit presents three spectra.
One involves a series of psychological changes, another involves a series of bodily changes, and the third involves a series of both kinds of changes.
The first two lead people to think that neither psychological nor bodily continuity is necessary for personal identity. That is, considering the changes on a spectrum leads people to think that the person on the left side would be identical with the person on the right side.
But this is not the case with the final spectrum. If both my entire body and my entire mind were replaced, well, I wouldn’t be around.
The final spectrum is aimed at Williams’s claim that questions about personal identity must have determinate answers. The idea is that there is a range of cases in the middle of the spectrum for which there is no way of saying whether the person would be me or not. By contrast, the cases at the edges do seem to have determinate answers. It will still be me even if they change a few of my cells and memories. And it will definitely not be me even if the Garbo-like person has a few of my cells and memories. But what about the person that is 50% me in mind and body and 50% like Garbo? 45-55? 40-60? 35-65? 30-70? And so on.
Where we all stand
Brittany, Gloria, and I are all a bit stuck. We agree with Williams that we can’t imagine indeterminate cases of personal identity. But Parfit has us stumped since he seems to have shown us that this can happen, even though we can’t imagine it.
Tom is feeling pretty comfortable with saying that questions about personal identity can have indeterminate answers or, at least, that they are what Parfit calls “empty” questions. My example of the altered table involves an empty question. The question “is it the original table?” is empty. All I can say is that it has some of the original parts and quite a few replacements. There’s nothing more to say about the table and what there is to say doesn’t prove that it is or that it isn’t the original.
There is one way that B, G, and I can go. We can give up on our belief that the only thing there is to being a person is mind and body. (That is what Parfit calls “Reductionism”; it involves ‘reducing’ the person to its constituent parts, either body, mind, or both). A person, we might say, has something special that explains why questions about its identity must have determinate answers. It has an indivisible soul.
In other words, someone might take Williams’s argument against the possibility of indeterminacy and Parfit’s argument that seems to show the opposite to show that there must be something more to human life than just body and mind.
In fact, someone has argued in exactly this way. See: Swinburne, Richard. “Personal Identity.” Proceedings of the Aristotelian Society 74 (1974): 231-47.