Can questions about personal identity have indeterminate answers?
What the question is
Can it ever be indeterminate whether I am the same person as person P?
This has a corollary: supposing that person P is feeling an intense pain, can it ever be indeterminate whether I am feeling that very pain? The assumption behind the corollary is that if it's indeterminate whether I'm P, then it's indeterminate whether I'm feeling what P is feeling.
Indeterminacy is not supposed to be a question about knowledge: given that our knowledge of the facts is typically limited, we may well not know whether P is the same person as me. If P exists way off in the future, and we know very little about him, we may not know whether he's me or not.
This is different.
Indeterminacy here concerns a matter of fact. If you knew all the facts there are to know about me and person P, could it be indeterminate whether I am P or not?
But how could I know all the facts and not know that?
But if I know all the facts about something, then I know what it is identical with? That's a fact about the thing, after all, right?
Wrong. I can know all the facts about this collection of sand and still not know whether it is a heap of sand. It may be one of those indeterminate cases: there's a lot of sand, but not so much that it's clearly a heap. Whether the collected grains of sand are a heap or not is an indeterminate issue. In the indeterminate zone, there is no fact about whether a given collection of sand molecules constitutes a heap of sand. Consquently, it's indeterminate whether the collection is the same heap that I saw in the same place just a minute ago (for example).
We learn something from this. The thesis that questions of personal identity can be indeterminate is the thesis that it's possible that there is no fact of the matter as to whether person A is the same person as person B. Person A is the same person as B in a sense, but not the same in another sense.
It seems perfectly possible that I would still exist after undergoing a process like teletransportation: I'd wake up on Mars and feel what it's like to be there: dry area, weird light, etc.
It's odd, but still very compelling, to imagine that something like this would be true if I were "reduplicated" as a part of such a process. Say the teletransporter puts one version of me on Mars and the other on the Moon. It's very tempting to say that everything important about me would survive in both places. Perhaps we couldn't say that I'm identical with either person, but that seems like a logical problem more than a problem about persons
But is that really as compelling as it seems?
Suppose the guy on Mars will feel very hot, the guy on the Moon will feel chilly. Will I feel hot?
There's no straightforward, yes or no answer.
On the one hand, we have to say 'no.' After all, I'm not identical with either of them. (see the reduplication argument).
On the other hand, we are drawn to say 'yes.' I seem to survive, in some sense, both on the Moon and on Mars. After all, I would have gladly used the Teletransporter to get to Mars. Why should the addition of another guy on the Moon make a difference to whether I live or die on Mars?
But how can that be? There is a person who will be hot. Will it be me? There's no determinate answer, there's only "partly yes, partly no." But that's crazy. How can it partly be the case that I feel hot and partly not be the case that I feel hot?
Williams and Parfit
Williams: that answer shows you can't survive any process that is subject to reduplication
Parfit: the intuition that you can survive in one of these reduplication cases is correct. What has to go is the thought that in order to survive into the future, someone in the future must be identical with me.
Parfit's koan: I can survive into the future even if no one in the future is me.
Repeat that until it seems both obvious and contradictory at the same time. Then you're ready to read Parfit.
Mark's version of indeterminacy
Mark is ready to defend the possibility of indeterminate answers. Excellent! But he does so in a different way: he thinks a person is a combination of a mind and a body and so it's no surprise that indeterminate cases pop up when you start pulling these things apart. His argument is more like Parfit's "Combined Spectrum" than it is like teletransportation. But we can worry about that later.
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