1 See Parfit Derek, Reasons and Persons (Oxford: Clarendon Press, 1984), p. 262.
2 See Lewis David, “Survival and Identity,” in The Identities of Persons, edited by Rorty A. O. (Berkeley, CA: University of California Press, 1976), pp. 17–40, esp. pp. 24–25.
3 For a rather confusing discussion of what counts as a sufficient number, see Parfit, Reasons and Persons, p. 206.
4 Parfit discusses three candidates for what counts as the right kind of cause: the normal cause, any reliable cause, and any cause (ibid., p. 207). On the latter two possibilities, a pre-beaming-up stage of Captain Kirk will be C-related to a post-beaming-up stage, as in a Parfitian Simple Teletransportation case. It is worth noting that some direct psychological connections between stages have causation “built into” them, such as memory connections.
5 In general, the ancestral of a relation is guaranteed to be transitive.
6 If x is psychologically continuous with y, then there is a chain of strong connectedness linking x to y through 0 or more stages. For example, it might be that xCz and zCy. Since C is symmetric, we have yCz and zCx. Thus, there is a C-chain linking y to x. Thus, y is R-related to x.
7 See Grice Paul's “Personal Identity,” in Personal Identity, edited by Perry J. (Berkeley, CA: University of California Press, 1975), pp. 73–95.
8 See Parfit, Reasons and Persons, p. 254.
9 Parfit would deny that BRC (see ibid., p. 302). But, as we have seen, any reasonable account of the R-relation must have R come out as symmetric, since, quite obviously, I is symmetric. Once it is made clear that R is symmetric, it will follow that BRC, just as in the famous Grice case discussed above in the text.
10 See Lewis, “Survival and Identity,” p. 27.
11 See Parfit, Reasons and Persons, p. 262.
12 For a discussion of a number of failed attempts to formulate a non-circular non-branching clause, see Brueckner Anthony's “Branching in the Psychological Approach to Personal Identity” (Analysis, 65 : 294–301).
13 For Formulation (5), see ibid., p. 298. Noonan Harold's article is “Nonbranching and Circularity—Reply to Brueckner” (Analysis, 66 : 163–77).
14 See Noonan, “Non-branching and Circularity—Reply to Brueckner,” p. 166.
16 See Parfit, Reasons and Persons, §87.
17 There are several other analyses of who is who during the disconnection that are even more implausible. We leave this to the reader to work through.
18 See Noonan, “Non-branching and Circularity—Reply to Brueckner,” p. 166.
19 According to (AX), it cannot be that two simultaneous person stages are stages of a single person. We saw earlier that, according to Lewis, one person stage can be a stage of two simultaneously existing persons.
20 If time travel is logically possible, then this leads to a further problem for (5). If President Bush were to travel backward in time and observe his fourth birthday party, then two co-personal stages of George W. Bush would exist simultaneously: a Presidential stage and a kiddy stage. Thanks here to an anonymous referee.
21 It is worth noting that Parfit's famous argument that the R-relation, not the I-relation, is what rationally ought to matter to us requires an account of the I-relation according to which ~(AIB) and ~(AIC) in fission cases, though we do have ARB and ARC. The argument is as follows. In a case in which the right hemisphere is damaged and never transplanted, A ought to be very pleased nevertheless at the prospect of the successful transplant of the left hemisphere. Call this case My Bungled Division (MBD). Since the relation between A and B in MBD is exactly similar to the relation between A and B in My Division, A ought to be equally pleased about the prospect of B's existence in My Division. We have ARB in My Division, but, given a violation of non-branching, we have ~(AIB). So R, not I, is what matters. Thus, Parfit's famous argument about what matters requires the availability of a successful formulation of a non-branching clause.