According to Perry, the best interpretation of our beliefs about persons is that we use what he calls the "lifetime language." Here's the relevant machinery for this view.
Start with the four-dimensional person-stage idea.
Definition of lifetime: there is some member in the set of person-stages such that all and only members of the set have relation-R (a psychological relation, like Parfit's) to that person-stage. e.g. the Y-shape made by A, B, and C is a lifetime.
What it means to determine a lifetime. Each person stage determines one and only one lifetime (although each may be a member of several). (e.g. A determines the Y that includes A, B, and C; B determines one branch of the Y).
Lifetimes are determinable only at certain times; after fission occurs, the lifetime that A determines is no longer determinable, though the two branches (B and C) are.
Here's a parallel case: "the Senator from California" can be proper name (one that refers to only one person), if, e.g. the other Senator resigns and a replacement hasn't yet been appointed. But then "the Senator from California" can be proper on Monday (before appointment) but not on Wednesday (after a new one has been appointed). So, "The Senator from California will be in Washington on Wednesday" can be true on Monday, but "Wednesday, the Senator from California will be in Washington" would be false. There is just one Senator from California on Monday, but on Wednesday there will be more than one.
Definition of a branch: a set of person-stages is a branch iff all the members of the set have R to one another, and no stage that has R to all the members of the set is not a member.
With all this in hand, here's how the lifetime language handles fission cases.
Before the operation if you ask "Will A be in the sunny room after the operation?" the answer is yes.
What you're asking, according to Perry, is whether the lifetime determined by the person stage A will be in the sunny room and the answer is yes. It will also be true that the lifetime determined by the person stage A will be in the dark room.
However, if you ask "after the operation, will A be in the sunny room?" the answer is no.
After the operation, the name "A" no longer refers to a determinable lifetime. The names "B" and "C" do refer to determinable lifetimes. Moreover, each of those determinable lifetimes includes A's stage on the single stem of the Y.
So how many people are there before the operation (A's room = room 100)?
"Before the operation, how many persons were in room 100?"
Answer: one (A)
"After the operation, how many persons were in room 100 before the operation?"
Answer: two (B and C)
John Perry "Can the Self Divide?" Journal of Philosophy 69 (1972): 463-488.
According to Mills, Lewis and Perry get into trouble by holding that there is only one stream of consciousness before fission. Assuming that there could be only one person associated with a body if there was only one stream of consciousness associated with that body, Mills concludes that Lewis and Perry are stuck saying that B and C were one person prior to fission and thus that they don't solve the problem.
Instead, Mills holds that there are two streams of consciousness prior to fission: B's and C's. Each has his own thoughts, etc. Thus, there are two persons prior to fission and each is identical with one of the resulting fission successors.
So, what is A? A never exists. Only B and C do.
Does that make any sense? Mills considers many objections. Here's one. When I say that I'm hungry, who is hungry, B or C? Here's what he says (it's an inventive argument).
"B's use of "I" before fission does refer uniquely (to B) and so does C's (to C). When the A-body utters, say, the words "I am hungry", each person associated with the body is hungry (assuming sincerity), and each utters the sentence intending the use of "I" to refer to himself. If mental events cause physical ones--a question on which I take no stand--then we have here a case of causal overdetermination: the intention (or volition, or whatever) of either person is sufficient to produce the utterance, but all of them do produce it. (This could be true on either a dualist or monist reading.) In any case, we have here multiple uses of a single sentence token, each of which results in a distinct referent for the word "I" and the expression of a distinct proposition.(8)
There is nothing mysterious about this possibility. On many airplanes, each row of seats has a single call-light for a flight attendant, and each seat in the row is equipped with a button which activates the light. Suppose the light is a sign saying "I want attention" and that all parties concerned know these and other relevant facts. Now, if two passengers in the same row happen to hit their buttons simultaneously, their actions overdetermine the sign's going on. Each has used the same token at the same time to express that he wants attention; each has used the same token of "I" to refer to himself; and each may well be ignorant of the other's action."
Eugene Mills "Dividing without reducing: bodily fission and personal identity." Mind 102 (Jan 1993): 37-51.
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