There are six choices:
The problem with choices 1 and 2 is that Lefty and Righty each seem to have an equally good claim to be identical to David. Why should one of them be identical to David, but not the other?
The problem with choice 3 is that personal identity is a transitive relation. What it means for a relation to be transitive is that, if the relation holds between A and B, and it also holds between B and C, then it must also hold between A and C.
So in this case, if Lefty is one and the same person as David, and David is one and the same person as Righty, then, since personal identity is transitive, it follows that Lefty must also be one and the same person as Righty. But Lefty and Righty are clearly not one and the same person. They are two different people, with their own experiences, beliefs, and bank accounts. So it cannot be the case that David is identical to Lefty and also is identical to Righty.
Choices 5 and 6 are interesting, but complicated. For present purposes let us merely remark that Lefty and Righty do not appear to make up a composite person, any more than you and I make up a composite person. (Lefty and Righty do have a common set of shared memories, it is true, but they have gone their separate ways since the fission. They cannot "read each other's mind," or anything like that. They may disagree about many issues.) Let us also remark that it does not appear as if, before the fission, two people are occupying David's body. So choices 5 and 6 both have some prima facie implausibility.
That leaves choice 4. When David undergoes fission, he ceases to exist. This is surprising. But it seems to be the most sensible, and least problematic, answer.
Here are some other possible fission cases:
What if you step into the teletransporter, and it decomposes your body and your brain and radios the signal to Mars. A perfect copy of you is created on Mars. At the same time, some hackers are "sniffing" the radio traffic to Mars, and they pick up your signal and create a perfect copy of you on Venus. Each of the copies looks like you and talks like you. They both seem to remember events from your past life. Neither seems to have a better claim to be identical to you than the other. This would be another case of fission.
Proposal #5: Stage A* and stage B* are parts of the same person iff they are parts of a chain, all of whose later stages quasi-remember (or are able to quasi-remember) "from the inside" events experienced by the immediately preceding stages.If the right thing to say about fission cases is that the original person is identical to neither of the resulting people, then Proposal #5 cannot be correct. For both Lefty and Righty are psychologically continuous with David. Hence, Proposal #5 would count them both as being identical to David. Yet we've just said that neither is identical to David.
(This is the objection Gretchen Weirob makes on pp. 32-33 of Perry's dialogue. Gretchen states the point in a very compressed way. I have tried to spell it out in more detail.)
Proposal #6: If A* and B* are parts of a chain of psychologically continuous person stages, and if the later stages in this chain do not co-exist with any other "competitor" stages, not part of the chain, which are also psychologically continuous with A*, then A* and B* are parts of the same person (p. 33).
One of my former students, Tom Kelly, offered the following analogy.
Take a piece of chalk, Chalky. Now suppose that as I write on the board with Chalky, it gradually gets worn down to a stub Stubby, half the size of the original piece of chalk. If I started the class holding Chalky in my hand, and end the class holding Stubby in my hand, it seems right to say that I've had the same piece of chalk in my hand for the course of the class. That is, it seems right to say that Chalky and Stubby are the same piece of chalk. (It's just that this piece of chalk has gotten worn down as the class progressed.) Contrast a second case, where I hold Chalky up at the start of class, and break it perfectly in half. In my right hand I have a stub S1, and in my left hand I have a stub S2. We can imagine that S1 is exactly the same size and shape as Stubby was, in the first case. We can even imagine that S1 and Stubby are made of the same molecules. However, although in the first case it seemed right to say that Stubby is the same piece of chalk as Chalky, here it does not seem right to say that S1 is the same piece of chalk as Chalky. S1 has a competitor, S2. S1 and S2 seem to have equally good claims to be identical to Chalky; hence, we're forced to say that neither is identical to Chalky. In the first case, though, where the stub in my right hand had no competitors, it did seem right to count that stub as the same piece of chalk as Chalky. So the presence or absence of competitors makes a difference to whether we count the stub as being the same piece of chalk as Chalky.
The defenders of proposals like Proposal #5 and Proposal #6 are often referred to as "psychological continuity theorists." There are some other refinements of Proposal #5 we could consider instead. I'll label them as follows:
Proposal #7: If A* and B* are parts of a chain of psychologically continuous person stages, and if the later stages in this chain do not co-exist with any other "at least as close competitor" stages, not part of the chain, which are also psychologically continuous with A*, then A* and B* are parts of the same person.That view is known as the "closest competitor theory".
Proposal #8: If A* and B* are parts of a chain of psychologically continuous person stages, and where that chain also includes most or all of the same persisting physical body, then A* and B* are parts of the same person.
Proposal #9: If A* and B* are parts of a chain of psychologically continuous person stages, and where that chain also includes most or all of the same persisting physical brain, then A* and B* are parts of the same person.Proposal #9 is discussed later in the Perry dialogue. Proposals #7 and #8 aren't discussed, though they are natural variations on the views that are discussed. I will postpone discussion of these alternatives to Proposal #6 until the lecture notes for Perry's Third Night.
We will note only the first of these objections here. This is that Proposal #6 makes the answer to the question "Does the chain connecting A* and B* compose a single person?" depend on matters extrinsic to that chain. Whether A* and B* count as parts of a single person will depend on whether B* has any competitors--that is, on whether there are any other person stages elsewhere in the universe which are also psychologically continuous with A*. But this seems wrong-headed. The facts about whether A* and B* are parts of the same person shouldn't turn on what other chains of person stages exist elsewhere in the universe. Personal identity should be an intrinsic matter. It should only depend or supervene on what the chain connecting A* and B* is like, intrinsically. Facts about other chains should not be relevant. (Think about whether this objection also applies to Proposals #7, #8, or #9.)