Nonbranching personal persistence
Abstract
Given reductionism about people, personal persistence must fundamentally consist in some kind of impersonal continuity relation. Typically, these continuity relations can hold from one to many. And, if they can, the analysis of personal persistence must include a nonbranching clause to avoid nontransitive identities or multiple occupancy. It is far from obvious, however, what form this clause should take. This paper argues that previous accounts are inadequate and develops a new proposal.
Keywords
Personal identity Nonbranching clause Fission Fusion PerduranceReductionism about people is the view that people exist but they’re not a fundamental part of the world. The view is perhaps best explained through David Hume’s analogy with reductionism about nations.^{1} Most of us are reductionists about nations: We believe that nations exist but also that their existing consists in more basic facts, such as the existence of citizens who organize themselves in certain ways on certain territories. So we could, in principle, provide a complete description of the world (and these more basic facts) without asserting that nations exist. In this manner, reductionism about people says that the world could, in principle, be completely described without asserting that people exist.^{2}
Given reductionism about people, personal persistence must fundamentally consist in an impersonal continuity relation holding over time. Some standard candidates for this impersonal continuity are different kinds of psychological, physical, and phenomenal continuity. Typically, these continuity relations can (at least in principle) branch by holding from one person at one time to two or more people at other times. And, if these relations can branch, the analysis of personal persistence must include a nonbranching clause in order to avoid either of two problems, namely, the problem of nontransitive identities and the problem of multiple occupancy.^{3} In this paper, I shall explore what form this nonbranching clause should take.^{4} I shall argue that previous accounts are implausible. But, with the help of some ideas from these accounts, I shall develop a new proposal.
Assuming a perdurance framework, we analyse personal persistence in terms of personstages at different times being Irelated, that is, being stages of the same continuant person.^{5} A person, on this framework, is a maximal aggregate of Irelated personstages, that is, an aggregate of personstages such that (i) each stage in the aggregate is Irelated to all stages in the aggregate and (ii) no personstage that isn’t in the aggregate is Irelated to all stages in the aggregate.^{6}
Personstages can (but need not) be extended in time, that is, they can be present not only at a single instant but also at each point in an interval of time.^{7} This opens up for some ambiguities about temporal order, which we should try to avoid. Let us say that a personstage x is simultaneous with a personstage y if and only if there is a time at which x and y are both present. Let us say that a personstage x is present before a personstage y if and only if there is a time at which x is present which is earlier than all times at which y is present. And let us say that a personstage x is present after a personstage y if and only if there is a time at which x is present which is later than all times at which y is present.^{8}

Temporally Ordered Connectedness

Personstage x is Crelated to personstage y (xCy) \(=_{\mathrm {df}}\) x and y are connected by the right kind of connection and x is either simultaneous with y or present earlier than y.

Temporally Unordered Connectedness

Personstage x is C′related to personstage y (\(xC'y\)) \(=_{\mathrm {df}}\) x and y are connected by the right kind of connection.
 (1)
Personstage x is Irelated to personstage y if and only if \(xC'y\).
That is, as an officer, a man remembers being a boy and, as a general, the man remembers being an officer but not being a boy.^{15} Suppose that The Boy, The Officer, and The General are personstages from the three periods of the man’s life. Then, if the relevant kind of connections are memories, The Officer is connected both to The Boy and to The General but The General isn’t connected to The Boy. The pattern of connections in this case can be represented diagrammatically as follows, where the doubleheaded arrows represent \(C'\)relations:Suppose a brave officer to have been flogged when a boy at school, for robbing an orchard, to have taken a standard from the enemy in his first campaign, and to have been made a general in advanced life: Suppose also, which must be admitted to be possible, that when he took the standard, he was conscious of his having been flogged at school, and that when made a general he was conscious of his taking the standard, but had absolutely lost the consciousness of his flogging.^{14}

The Brave Officer \((C'\)relations)


Temporally Ordered Continuity
 Personstage x is Rrelated to personstage y (xRy) \(=_{\mathrm {df}}\) either xCy or yCx, or there are personstages \(z_1\), \(z_2\), ..., \(z_n\) such that either
 (i)
\(xCz_1\), \(z_1Cz_2\), ..., \(z_{n1}Cz_n\), \(z_nCy\) or
 (ii)
\(yCz_1\), \(z_1Cz_2\), ..., \(z_{n1}Cz_n\), \(z_nCx\).
 (i)
 (2)
Personstage x is Irelated to personstage y if and only if xRy.^{16}
The pattern of connections in this case can be represented diagrammatically as follows, where Wholly is the personstage before the division and Lefty and Righty are the two resulting personstages afterwards:^{18}My body is fatally injured, as are the brains of my two brothers. My brain is divided, and each half is successfully transplanted into the body of one of my brothers. Each of the resulting people believes that he is me, seems to remember living my life, has my character, and is in every other way psychologically continuous with me. And he has a body that is very like mine.^{17}

My Division \((C'\) relations)

In terms of perdurance, we can state this suggestion as follows:^{21}The criterion might be sketched as follows. “X and Y are the same person if they are psychologically continuous and there is no person who is contemporary with either and psychologically continuous with the other.”^{20}
 (3)Personstage x is Irelated to personstage y if and only if xRy and there is no personstage z such that either
 (i)
xRz and y and z are distinct and simultaneous or
 (ii)
yRz and x and z are distinct and simultaneous.
 (i)

My Unbalanced Division \((C'\) relations)

In My Unbalanced Division, (3) yields that Wholly is Irelated to Old Lefty, since they are Rrelated and neither of them is simultaneous with any other personstage. Likewise, (3) yields that Old Lefty is Irelated to Lefty, since they are Rrelated and—even though Lefty is simultaneous with Righty—Old Lefty isn’t Rrelated to Righty. But, according to (3), Wholly isn’t Irelated to Lefty, since Wholly is Rrelated to Righty and Righty is simultaneous with Lefty. So (3) yields that Wholly is Irelated to Old Lefty, Old Lefty is Irelated to Lefty, and Wholly isn’t Irelated to Old Lefty. Hence, given (3), we have a nontransitive Relation I and thus multiple occupancy. Moreover, it’s implausible that Wholly is Irelated to Old Lefty, especially given that Wholly isn’t Irelated to Lefty.

The Senile General \((C'\) relations)


My Asynchronous Division \((C'\) relations; The Senile General pattern)


My Asynchronous Replication \((C'\) relations; The Senile General pattern)

In The Senile General, (3) yields that The Boy is Irelated both to The Officer and to The General, since The Boy is Rrelated to The Officer and to The General while there are no distinct and simultaneous personstages in that case—so the nonbranching clause in (3) doesn’t apply. And, given (3), The Officer isn’t Irelated to The General, since these stages are not Rrelated. So, like before, we have a nontransitive Relation I and hence multiple occupancy. This result is problematic, since the motivation for having a nonbranching clause is to retain the transitivity of Relation I and avoid multiple occupancy. If nontransitivity and multiple occupancy weren’t problematic, we could stick with (2), which is simpler than (3), or with (1), which is simpler still.
In terms of perdurance, this suggestion can be interpreted as follows:^{25}The Psychological Criterion: [i] There is psychological continuity if and only if there are overlapping chains of strong connectedness. X today is one and the same person as Y at some past time if and only if [ii] X is psychologically continuous with Y, [iii] this continuity has the right kind of cause, and [iv] there does not exist a different person who is also psychologically continuous with Y.^{24}
 (4)Personstage x is Irelated to personstage y if and only if xRy and there is no personstage z such that either
 (i)
xRz and not yIz or
 (ii)
yRz and not xIz.
 (i)

My Extended PreDivision \((C'\) relations)

In My Extended PreDivision, it seems that Young Wholly should be Irelated to Wholly. But this is ruled out by (4). For proof by contradiction, assume that Young Wholly is Irelated to Wholly. Since the nonbranching clause in (4) then cannot rule out that Young Wholly is Irelated to Wholly, it is not the case that Young Wholly is Rrelated to Lefty while Wholly isn’t Irelated to Lefty. Therefore, since Young Wholly is Rrelated to Lefty, we have that Wholly is Irelated to Lefty. According to (4), Lefty isn’t Irelated to Righty, since Lefty isn’t Rrelated to Righty. Therefore, since Wholly is Rrelated to Righty while Lefty isn’t Irelated to Righty, the nonbranching clause in (4) rules out that Wholly is Irelated to Lefty. We then have the contradiction that Wholly both is and is not Irelated to Lefty.
 (5)Personstage x is Irelated to personstage y if and only if xRy and there is no personstage z such that either
 (i)
xRz and not yRz or
 (ii)
yRz and not xRz.
 (i)

My Temporary Division \((C'\) relations)


My Forgetful Temporary Division \((C'\)relations)

 (6)Personstage x is Irelated to personstage y if and only if xRy and there is no personstage z such that
 (i)
z is not present before each of x and y is present,
 (ii)
z is not present after each of x and y is present,
 (iii)
zRx,
 (iv)
zRy, and
 (v)
there are two distinct and simultaneous personstages u and v such that \(zC'u\) and \(zC'v\).
 (i)
In My Extended PreDivision, (6) yields—just like (4)—the implausible result that Young Wholly isn’t Irelated to Wholly. Young Wholly’s being Irelated to Wholly is ruled out by the nonbranching clause in (6), since Young Wholly is Rrelated to Wholly while Wholly is Rrelated to itself and is \(C'\)related both to Lefty and to Righty.
In The Senile General, the nonbranching clause in (6) doesn’t apply, because there are no distinct and simultaneous personstages in that case. So (6) yields that The Boy is Irelated both to The Officer and to The General (since The Boy is Rrelated to them) and that The Officer isn’t Irelated to The General (since they’re not Rrelated). Hence we get a nontransitive Relation I and thus multipleoccupancy, which defeats the purpose of having a nonbranching clause.

My Forgetful Division \((C'\)relations)

In My Forgetful Division, (6) yields that Young Wholly is Irelated both to Lefty and to Righty, even though there is clearly branching here given that Lefty and Righty are distinct and simultaneous personstages.^{29} Clause (v) in (6) doesn’t hold in this case, because no personstage is \(C'\)related to each of two simultaneous personstages.

Temporally Unordered Continuity

Personstage x is \(R'\)related to personstage y (\(xR'y\)) \(=_{\mathrm {df}}\) \(xC'y\) or there are personstages \(z_1\), \(z_2\), ..., \(z_n\) such that \(xC'z_1\), \(z_1C'z_2\), ..., \(z_{n1}C'z_n\), \(z_nC'y\).
 (7)Personstage x is Irelated to personstage y if and only if \(xR'y\) and there is no personstage z such that either
 (i)
\(xR'z\) and not \(yR'z\) or
 (ii)
\(yR'z\) and not \(xR'z\).
 (i)
 (8)Personstage x is Irelated to personstage y if and only if \(xR'y\) and there is no personstage z such that either
 (i)
\(xR'z\) and y and z are distinct and simultaneous or
 (ii)
\(yR'z\) and x and z are distinct and simultaneous.
 (i)
 (9)Personstage x is Irelated to personstage y if and only if \(xR'y\) and there are no distinct and simultaneous personstages u and v such that either
 (i)
\(uR'x\), \(uR'y\), and \(vR'x\) or
 (ii)
\(uR'x\), \(uR'y\), and \(vR'y\).
 (i)

My Unbalanced Division \((C'\)relations)


My Unbalanced Division \((R'\)relations)

 (10)Personstage x is Irelated to personstage y if and only if xRy and there are no distinct and simultaneous personstages u and v such that either
 (i)
uRx, uRy, and vRx or
 (ii)
uRx, uRy, and vRy.
 (i)
Even so, (10) yields the wrong result in My Extended PreDivision. The nonbranching clause in (10) rules out that Young Wholly is Irelated to Wholly. This is because Lefty and Righty are distinct and simultaneous and Lefty is Rrelated both to Young Wholly and to Wholly while Righty is Rrelated to Wholly. And (10) yields that Young Wholly and Wholly are not Irelated to themselves, because they are Rrelated to the distinct and simultaneous Lefty and Righty. Hence (10) violates the reflexivity of Relation I.
Moreover, in The Senile General, (10) yields that The Boy is Irelated both to The Officer and to The General while The Officer is not Irelated to The General. This is because there are no distinct and simultaneous personstages in that case; so all personstages are Irelated except The Officer and The General. The Officer and The General are not Irelated, since they’re not Rrelated. Hence, as with (3) and (6), we get a nontransitive Relation I and thus multiple occupancy.
 (11)Personstage x is Irelated to personstage y if and only if xRy and there are no personstages u and v such that
 (i)
neither u nor v is present before each of x and y is present,
 (ii)
neither u nor v is present after each of x and y is present,
 (iii)
uRx,
 (iv)
vRy, and
 (v)
there is a personstage z such that either (a) uRz and not vRz or (b) vRz and not uRz.
 (i)
The idea behind the nonbranching clause in (11) is to characterize the intuitive idea of there being two personstages u and v in different branches in the continuity between x and y. Clauses (i) and (ii) make sure that the relevant branching doesn’t occur before or after both x and y; so we avoid the problem (4), (6), and (10) had with ruling out that, in My Extended PreDivision, Young Wholly and Wholly are Irelated. Clauses (iii) and (iv) make sure that u and v are part of the relevant continuities to or from x and y respectively. Finally, clause (v) makes sure that u and v belong to different branches in the sense that there is a personstage that is continuous with one of them but not with the other. Clause (v) is similar to the nonbranching clause in (5), but, unlike the nonbranching clause in (5), it doesn’t require that u and v are identical with x and y respectively; so it rules out, in My Temporary Division or My Forgetful Temporary Division, that Wholly is Irelated to Old Wholly.
Note also that, (11) doesn’t rely on the identity or distinctness of personstages, which (3), (4), (6), (8), (9), and (10) all rely on. This lets (11) sidestep any worries about the alleged circularity in relying on Relation I, identity, or distinctness between personstages in an account of Relation I.^{36} And (11)—unlike (1), (2), and (7)—yields the desired result in My Division, namely, that all personstages are Iunrelated to each other. It also yields acceptable results in the other cases. In these cases, (11) yields the following: In The Brave Officer, all personstages are Irelated. In The Senile General, My Temporary Division, and My Forgetful Temporary Division, all personstages are Iunrelated to each other. In My Unbalanced Division, the only Irelated personstages are Lefty and Old Lefty. In My Extended PreDivision, the only Irelated personstages are Young Wholly and Wholly. And, in My Forgetful Division, the only Irelated personstages are Wholly and Lefty.
One might be worried about the result in The Senile General.
First, one might think that The Officer should be Irelated to The General.^{37} If so, one might be tempted to rely on Relation \(R'\) rather than Relation R; but, as I argued earlier, relying on temporally unordered continuity doesn’t fit with some plausible ideas about branching in cases like My Unbalanced Division. If there is a possible case structured like The Senile General such that it seems that the stage corresponding to The Officer should be Irelated to the stage corresponding to The General, then a more promising approach is to revise the criteria for what counts as the relevant kind of connectedness so that these stages will be connected.^{38}
Second, one might think that The Boy should be Irelated to The Officer. And one might think that whether The Boy at \(t_1\) is Irelated to The Officer at \(t_2\) shouldn’t depend on what personstages The General at \(t_3\) (after both \(t_1\) and \(t_2\)) is connected to. If The General had a connection to The Officer like in The Brave Officer, then The Boy would be Irelated to The Officer. For similar reasons, one might think that, in My Forgetful Division, Young Wholly should be Irelated to Wholly.^{39} As long as the connections between personstages are structured like they are in these cases and we rely on temporally ordered continuity, it is hard to deny that the continuity branches between \(t_1\) and \(t_2\). If this dependence on the future is implausible, there is a more promising way to avoid such dependence than to rely on temporally unordered continuity, namely, to restrict the relevant kinds of connectedness so that it only holds between personstages without any temporal gaps between them.^{40} Given this restriction, the connection in The Senile General between The Boy and The General would be invalidated, and then (11) would yield that The Boy is Irelated to The Officer. Similarly, in My Forgetful Division, this restriction would invalidate the connection between Young Wholly and Righty, and then (11) would yield that Young Wholly is Irelated to Wholly.
Footnotes
 1.
 2.
Parfit (1984, pp. 210, 212).
 3.
A relation over a set is transitive if and only if—for all x, y, and z in the set—if x is related to y and y is related to z, then x is related to z. And a relation over a set is nontransitive if and only if it isn’t transitive.
 4.
I won’t, however, defend the use of nonbranching clauses from more general objections, for example, that these clauses conflict with the onlyxandy principle—see Wiggins (1980, p. 96) and Noonan (1989, pp. 233–254)—or that they are ad hoc—see Oderberg (1993, p. 58), Schechtman (1996, p. 43), Olson (1997, p. 49), and Hawley (2005); yet compare Demarest (2016, pp. 577–578).
 5.
Lewis (1976b, p. 21). On perdurance, persons persist by having stages present at different times, with no stage being wholly present at more than one time. The assumption of perdurance won’t be crucial for the argument of this paper. An alternative to perdurance is endurance. On endurance, persons persist by being fully present at different times; see Lewis (1986, p. 202) for the endurance/perdurance distinction. While we shall assume a perdurance framework for our discussion, we could translate the proposals from this framework to an endurance framework, replacing personstages by people and Relation I by personal identity (see Appendix D for an endurance translation of each proposal). This translation would mainly strengthen the arguments for my proposal in so far as they rely on transitivity, because it is more obvious that identity is transitive than that Relation I is transitive. For another advantage, see note 36.
 6.
Lewis (1976b, p. 22).
 7.
Lewis (1983, p. 76).
 8.
To distinguish cases of fission or fusion from cases where someone time travels to a time where a younger or older stage of them is also present, we can rely on some kind of personal time rather than external time; see Lewis (1976a, p. 146). We can then treat the continuities in fission and fusion cases as branching without thereby treating the continuities in timetravel cases as branching (unless they also feature fission or fusion).
 9.
 10.
 11.
 12.
A relation over a set is reflexive if and only if, for all x in the set, x is related to x. And a relation over a set is symmetric if and only if, for all x and y in the set, if x is related to y, then y is related to x.
 13.
That view is often attributed to John Locke. See, however, Gustafsson (2010) for a rebuttal of that interpretation.
 14.
 15.
We follow Locke’s (Essay II.xxvii.8–9; 1975, p. 335) distinction between man and person. A man or a woman in Locke’s sense is a human animal rather than a person.
 16.
Perry (1972, pp. 471–472) and Lewis (1976b, pp. 18–24). Lewis (1976b, p. 30) allows, however, that Relation R might have some restrictions on the maximal duration between two Rrelated personstages, which can come into play in cases of extreme longevity. Lewis is also indecisive regarding whether to emphasize Relation \(C'\) as in (1) or Relation R as in (2). If the sole objection to (1) is that it allows multiple occupancy, (1) should be acceptable to Lewis, since he accepts multiple occupancy.
 17.
 18.
The ‘Lefty’/‘Righty’ terminology is due to Strawson (1970, p. 186).
 19.
The idea of analysing personal identity in terms of a onemany relation in combination with a nonbranching clause dates back to Shoemaker (1970, pp. 278–279).
 20.
Parfit (1971, p. 13). Against Parfit, Demarest (2016, p. 578) argues that it would be better to just analyse personal persistence in terms of nonbranching continuity. The trouble, however, is that it is far from clear when a continuity relation has a nonbranching form. Parfit’s proposal is a first attempt to clarify the notion of a nonbranching form, on which we shall try to improve.
 21.
Brueckner (2005, p. 295) interprets Parfit as relying on a temporally unordered continuity. Parfit (1984, p. 206) doesn’t mention a temporalorder requirement in his main definition of psychological continuity, which is the continuity his (1984, p. 207) psychological criterion relies on. But Parfit (1971, p. 21n, 1984, p. 302; 1993, pp. 23–24) makes clear elsewhere that the chain of psychological connections needs to be temporally ordered. One might object that a difference between our definition of Relation R and Parfit’s definition of psychological continuity is that he (1971, p. 20, 1976, p. 106n23) at times seems to take psychological continuity to be transitive. Parfit (1971, p. 20n29, 1984, p. 302, 1993, pp. 23–24) makes clear, however, that psychological continuity is only supposed to be transitive when considered in one direction in time. Note, however, that, in Parfit’s terminology, ‘Relation R’ isn’t psychological continuity. In his (1984, p. 206) terminology, psychological continuity consists in overlapping chains of strong psychological connectedness, whereas his (1984, p. 215) ‘Relation R’ is ‘psychological connectedness and/or continuity with the right kind of cause.’ As defined by Parfit, ‘Relation R’ differs from psychological continuity, because two personstages can be psychologically connected without being strongly psychologically connected. Unlike psychological continuity and Relation R as we define it, Parfit’s ‘Relation R’ isn’t transitive when considered in one direction in time. To see this, consider a variant of The Brave Officer with the same pattern of connections except that the connections aren’t strong. Parfit’s relation then holds from The Boy to The Officer and from The Officer to The General but not from The Boy to The General (because The Boy and The General are neither psychologically connected nor related by overlapping chains of strong connectedness).
 22.
 23.
 24.
Parfit (1984, p. 207). In the 1987 reprinting, the fourth clause was changed to “it has not taken a ‘branching’ form.” Nevertheless, in that reprinting, Parfit (1984, p. 267) still claims that, ‘On what I call the Psychological Criterion, a future person will be me if he will be Rrelated to me as I am now, and no different person will be Rrelated to me.’ It is hard to make sense of this claim given Parfit’s terminology. In his (1984, p. 215) terminology, ‘Relation R’ isn’t psychological continuity but ‘psychological connectedness and/or continuity with the right kind of cause.’ There can be psychological connectedness without psychological continuity, since psychological continuity requires overlapping chains of strong psychological connectedness and there can be psychological connectedness that isn’t strong; see note 21. Consider a case with two personstages, \(s_1\) at \(t_1\) and \(s_2\) at \(t_2\), where these stages are psychologically connected but not strongly psychologically connected. Suppose that these stages aren’t psychologically connected to any other personstages. Then, at \(t_1\), there is only one future personstage that will be related to \(s_1\) in terms of Parfit’s ‘Relation R’, namely, \(s_2\). But, according to Parfit’s psychological criterion, \(s_1\) and \(s_2\) cannot be Irelated, because they’re not psychologically continuous (as they’re not related by overlapping chains of strong connectedness).
 25.
Parfit’s criterion only rules out branching in cases of fission and not in cases of fusion. My interpretation, however, treats fission and fusion in the same way. But this difference won’t matter for my objections to (4), because they only rely on cases of fission.
 26.
Rather than (4), Brueckner (1993, p. 22n21, 2005, p. 298) actually criticizes a temporally unordered variant of (4), that is, a proposal just like (4) except that Relation R has been replaced by Relation \(R'\) (temporally unordered psychological continuity, defined later). In the same way as (4), this variant is open to the problem with incompleteness in The Brave Officer—presented later. Moreover, in My Extended PreDivision (presented later), this variant implausibly rules out that Young Wholly is Irelated to Wholly unless Lefty is Irelated to Righty. For proof by contradiction, assume that Young Wholly is Irelated to Wholly and that Lefty isn’t Irelated to Righty. Since the nonbranching clause in this variant of (4) then cannot rule out that Young Wholly is Irelated to Wholly, it’s not the case that Young Wholly is \(R'\)related to Lefty while Wholly isn’t Irelated to Lefty. Therefore, since Young Wholly is \(R'\)related to Lefty, we have that Wholly is Irelated to Lefty. But, given this variant of (4), Wholly isn’t Irelated to Lefty, since Wholly is \(R'\)related to Righty and we assumed that Lefty isn’t Irelated to Righty.
 27.
 28.
 29.
Lefty and Righty are distinct and simultaneous not only in external time but also in personal time; see note 8.
 30.
 31.
 32.
Noonan (2006, p. 167n5).
 33.
Noonan (2006, p. 167n5).
 34.
Yi (2010, p. 195).
 35.Yi (2010, pp. 196–210) explores a series of analyses of xIy as \(xR'y\) in conjunction with a nonbranching clause that isn’t expressible in terms of Relation \(R'\). His three preferred proposals all have the following form:First of all, requirement (i) is superfluous given (ii). But the main problem is that proposals of this form do not preserve the transitivity of Relation I. To see this, consider The Senile General. In The Senile General, (iii) cannot fail to hold, since there are no distinct and simultaneous personstages in that case. Since The Officer is Rrelated (and thus \(R'\)related) to The Boy, we have that The Officer is Irelated to The Boy. And, since The Boy is Rrelated (and thus \(R'\)related) to The General, we have that The Boy is Irelated to The General. But, since The Officer is not Rrelated to The General, (ii) rules out that The Officer is Irelated to The General. Hence Relation I is nontransitive given proposals of this form.
 Personstage x is Irelated to personstage y if and only if
 (i)
\(xR'y\) (‘xRy’ in Yi’s notation),
 (ii)
xRy (‘\(xC^*y\) or \(yC^*x\)’ in Yi’s notation), and
 (iii)
there are no distinct and simultaneous personstages u and v such that ...
 (i)

 36.
Brueckner (2005, pp. 298–299) rejects (8) due to this worry about circularity. Others, such as Noonan (2006, pp. 165–166), do not share Bruckner’s worry. See, however, Brueckner and Buford (2008, pp. 383–384) for a reply. This kind of reliance on the identity or distinctness of personstages is also a problem for Yi’s (2010, pp. 196–210) proposals; see note 35. If we replace our perdurance framework with an endurance framework, these claims about personstages being distinct become claims about persons being distinct—which raises the worry about circularity when they appear in an account of personal identity. See the endurance translations (3*), (4*), (6*), (8*), (9*), and (10*) in Appendix D.
 37.
Brueckner (2005, p. 296).
 38.
This is the approach I defend in Gustafsson (2011). I defend the view that the relevant kind of connectedness is phenomenal connectedness and, accordingly, that the relevant kind of continuity is phenomenal continuity, that is, the relation of sharing the same stream of consciousness. In addition, I defend the view that phenomenal connections can hold over temporal gaps such as periods of dreamless sleep. Regarding The Senile General, it seems to me that nothing in the standard memoryloss story for this case rules out that there is temporally ordered phenomenal continuity holding between The Officer and The General. In the rare cases where phenomenal connections really are structured in The Senile General pattern, it seems, I think, that the result of (11) is plausible (that is, the result that The Boy, The Officer, and The General are all Iunrelated to each other), for in that case the stream of consciousness of The Boy would split into two: one stream including the experiences of The Officer but not those of The General and one stream including the experiences of The General but not those of The Officer.
 39.
Yi (2010, p. 200, 2013, pp. 176–182). Yi discusses a case similar to My Forgetful Fission with a psychological kind of connectedness (it’s unclear whether Young Wholly is \(C'\)related to Lefty in his case) where Young Wholly is scanned at \(t_1\) and Righty is a replica created from this scan at \(t_3\). Yi’s complaint is that, if Young Wholly isn’t Irelated to Wholly, then a mere scan terminates the person of which Young Wholly is a stage. But it’s not the mere scan that is to blame; it’s the scan combined with the creation of Righty from this scan that rules out Young Wholly being Irelated to Wholly.
 40.
As mentioned in note 38, this is not the approach I favour.
Notes
Acknowledgements
I wish to thank David Efird, Lisa Forsberg, Tom Stoneham, Robert Trueman, and an anonymous referee for valuable comments.
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