1. And then there were three: John Perry multiplies fission victims
Can the Self Divide?
And then there were three: John Perry multiplies fission victims

2. And Then There Were Three
Jones
Brown-Jones
Smith-Jones
Persons’ names pick out lifetimes traced from stages that occur at different times.
A lifetime is the aggregate of stages we get tracing the whole path of the (intransitive!) R-relation from a given stage.

3. Another Defense of Neo-Lockeanism
Argument against ‘Mentalism’ (Neo-Lockeanianism): the Mentalist is committed to holding (1) to (3) which violate Transitivity of Identity (given Symmetry)
Smith-Jones is Jones
Brown-Jones is Jones
Smith-Jones is not Brown-Jones
Perry considers three accounts names, embodied in the Stage Language, the Branch Language, and the Lifetime Language that avoid this result.
Semantics saves the day! (but, under the hood…there are 3 people all along!)

4. Unity Relations
As with Locke, different sortals trace different spatio-temporal paths
The spatial unity relation for things of a kind, K, is the relation between spatial K- parts in virtue of which they are the same K.
The temporal unity relation for things of a kind, K, is the relation between temporal parts of a K’s history in virtue of which they are part of the history of the same K.
Perry warns us not to confuse the temporal unity relation (a.k.a. ‘genidentity’) with identity.

5. Spatial Unity Relation Not Be Transitive
Prima facie it looks as if unity relations inherit transitivity from the relation of identity and so show the Smith-Brown-Jones case to be logically cursed:
The K of which a is a part is identical to the K of which b is a part.
The K of which b is a part is identical to the K of which c is a part.
NOT-the K of which a is a part is identical to the K of which b is a part. BAD!
But where fission occurs and b is a shared stage (1) and (2) are not true since there is no the K of which b is a part: ‘the’ implies uniqueness.

6. Temporal Unity Relation Problem
Persons have their properties in virtue of their constituent stages having properties.
We need to be able to assign past and future properties to persons at times in virtue of the R-relatedness of their stages at those times to earlier and later stages, e.g.
[Before fission] Jones is going to be in Room 102
[After fission] Smith-Jones was in Room 100
Needed: an account of names that will allow us to avoid trouble with past and future tensed sentences.

7. Basic and Non-Basic Properties
Basic and Non-Basic Properties: A person's basic properties, at any time, are those properties which he has in virtue of events that occur at that time. His non- basic properties are those which he has wholly or partly in virtue of events that occur at other times.
A person-stage x, which occurs at time t has a basic property P iff every person of which x is a stage satisfies the conditions for having P at t.
Note: this doesn’t assume any account of personal identity.

8. Names: The Branch Language
Names are assigned to person-stages by ‘baptism’ (aka ‘dubbing’, ‘tagging’)
In the Branch Language a name names the branch of which that person-stage is a part: Lewis’s account--persons are branches.
N has F at t is true iff the branch named by N contains a person-stage that occurs at t and has property F.
N is identical with M is true iff the branch containing the person-stage to which N is assigned is identical with the branch containing the stage to which M is assigned.

9. Branch Language Problems
Semantic problem: before fission ‘Jones’ fails to refer since there is no unique branch named ‘Jones’.
Metaphysical problem: if fission occurs ‘Jones’ fails to refer--there is no Jones, but if Jones had died before fission, everything else being the same there would have been Jones.
Actual World: Fission occurs at t. Jones doesn’t, and never has existed.
Another Possible World: Jones dies before t, doesn’t fission. Otherwise everything up to t is exactly is it is at the Actual World. Here, Jones existed.

10. Semantic Circumvention
A sentence may have different truth value uttered at different times or within the scope of different temporal adverbs.
Two roles of temporal adverbs
In initial position they state that the sentence following is true at the time indicated
In predicate position they indicate the time the subject has the property expressed in the predicate
Temporal adverb in initial position determines to what, and if, a name in its scope refers.

11. Jones, Smith-Jones, and Brown-Jones
Where fission occurs, names refer to different people at different times--and at some times, when ‘improper’, fail to refer so that sentences in which they occur are not true.
Before fission ‘Jones’, ‘Smith-Jones’, and ‘Brown-Jones’ are proper, and name the same person so at that time
‘Smith-Jones is the same person as Brown-Jones’ is true.
After fission ‘Smith-Jones’ and ‘Brown-Jones’ name different people and ‘Jones’ is improper so
‘Smith-Jones is the same person as Brown-Jones’ is not true.

12. Stage Language Names Names are assigned to person-stages (as before)
Stage Language names are systematically ambiguous
At any time, t, an SL name, N, refers to the stage at t that is R-related to the stage that was tagged ‘N’ if there is a unique stage at t so related.
At a time, t, when there is no unique stage R-related to the stage tagged ‘N’ the name ‘N’ is improper so fails to refer.
Sentences in which an SL name is improper are not true.

13. Fission: the Stage Language Account
Before fission the following are true:
(17) Jones will be i n room 102 after the operation. (18) Jones will be in room 104 after the operation. (19) Jones will not be in room 102 after the operation. (20) Jones will not be in room 104 after the operation. (21) Jones will be in room 102 after the operation and Jones will be in room after the operation. (this is not ‘Jones will be in room 102 and room 104’)
After fission no sentence in which ‘Jones’ occurs will be true because then ’Jones’ is improper and so fails to refer.

14. Stage Language Problem
Adverb analysis of sortals: a past or future-tensed sentence ascribing a property P to an object N of a kind K are understood to say that N had or will have P K-ly, i.e. in virtue bearing the sortal-specific temporal unity relation for K to an earlier or later stage that has K.
Perry rejects this account as mistaken--basically, because it ‘violates our semantic intuitions’.
[Comment: Hrumph. Consider, e.g. how nicely this takes care of the Statue and the Clay. On this account there’s just one thing around which, if squished will persist lumpishly but not statuesquely. ’Nuff editorializing.]

15. Lifetime Language Names
Names are assigned to stages (as for both Branch and Stage Languages).
As in the Branch Language they name 4-dimensional worms (or things whose histories are 4-dimensional worms) rather than instantaneous stages.
As in the Stage Language, names are systematically ambiguous and, in fission cases, name different things at different times or within the scope of temporal adverbs indicating different times, and at some times being improper fail to refer.
However, the things they name are lifetimes and in a case of fission, there are three of them around at every time!

16. Lifetimes
Each person-stage identifies a unique lifetime, viz. the worm consisting of all and only stages that are R-related to it.
A person-stage determines the lifetime it identifies but may be a member of lifetimes that it does not determine.
j determines the Y-shaped structure; s-j and b-j the left and right branches respectively. j is in the lifetimes determined by s-j and b-j but does not determine either of them.
A lifetime is determinable only at a time when a stage at that time determines it.
The Y-shaped lifetime is determinable before but not after fission; the two branch lifetimes are determinable after fission but not before fission.

17. People only count when determinable
Jones
Brown-Jones
Smith-Jones
At times when an individual’s lifetime is not determinable his name fails to refer.
Before fission, ‘Jones’ refers to Purple; Red and Blue are not determinable so ‘Smith-Jones’ and Brown-Jones fail to refer.
After fission, ‘Smith-Jones’ and ‘Brown-Jones’ refer to Red and Blue respectively; ‘Jones’ fails to refer

18. The Lifetime Language
The primary referent of a name N is the person-stage, u, to which N is assigned
The secondary referent of N at a time t is the lifetime identified by u at t, i.e. the lifetime identified by a unique stage at t if there is such--if there is no such then N is improper at t.
‘Jones’ has no secondary referent after fission since at any post-fission time there are two person-stages that are R-related to pre-fission stage u to which ‘Jones’ was assigned, e.g. s-j and b-j at one of those times.
At post-fission times therefore ‘Jones’ is improper so sentences in which it occurs are not true, i.e. we can’t talk about Jones.

19. Talking Lifetime: Ascribing Future Properties
At any time, t’, ‘N has F at t’ is true iff the secondary referent of N at t’ contains a person-stage that occurs at t and has F.
Before fission the following are true:
(5) After the operation, Smith-Jones will be in room 102.
(6) Not-(After the operation, Brown-Jones will be in room 102)
The temporal adverb ‘after the operation’ makes the names in its scope refer to post-fission secondary referents identified by, e.g. s-j and b-j, that is the left and right branch lifetimes respectively, which are in, and not in, room 102 respectively.

20. Talking Lifetime: Identity Statements
At any time, t’, ‘N is identical with M’ iff the secondary referent of N at t’ is identical with the secondary referent of N at t’
Before fission the following is true:
(4) Smith-Jones is the same person as Brown-Jones
Suppose ‘Smith-Jones’ and ‘Brown-Jones’ are assigned to s-j and b-j respectively. At any pre-fission time there is a unique stage to which each is R-related, e.g. j, that determines the Y-shaped life time. So before fission ‘Smith-Jones’ and ‘Brown-Jones’ both refer to that same lifetime, hence (4) is true. Afterwards they refer to different lifetimes, the left and right branches respectively.

21. Talking Lifetime: Counting
Just as we can only identify lifetimes relative to times, we can only count people relative to times where fission occurs because Lifetime Language names in such cases refer to different lifetimes at different times so there are 3 counting questions--but just 2 answers.
How many people were around before fission? One because then only one lifetime is determinable and all three names refer to it.
How many people were around after fission? Two because the two branches are then determinable but not the Y-shaped lifetime.
How many people were around all along? No answer.

22. Which language do we speak?
The Branch Language (Lewis): there are two persons all along
Before fission names are ambiguous
Before fission future-tense statements are neither true nor false
The Lifetime Language (Perry): there are three persons all along
Before fission we can only talk about one of them
After fission we can only talk about the other two

23. Lewis’s Response
Perry’s Treatment of Fission

24. For Perry, the R-Relation isn’t the I-Relation
At any time, t, the Rt and It subrelations of the R and I relations coincide but
The R and I relations in toto, which are viewed timelessly, don’t
s-j and b-j are not R-related but they are I-related since Perry identifies continuant persons with lifetimes and there is a lifetime, viz. the Y-shaped structure that includes both.
Lewis identifies continuant persons with branches so theY-shaped structure is not a continuant person, therefore s-j and b-j are not I-Related
On Lewis account, therefore, the R-relation is the I-relation.

25. Timeless Identification and Counting
In the Lifetime Language identifying persons and counting them is temporally perspectival, and in fission cases the time at which we identify and count makes a difference.
Lifetime Language names identify different people at different times, viz. those then determinable
At any time, only determinable people count
Before fission, Perry counts by identity, but only counts determinable people
Before fission, Lewis counts everyone, but doesn’t count by identity

26. Lewis’s Branches or Perry’s Lifetimes?
The Branch Language
The Lifetime Language
Synchronic counting isn’t by identity
Cohabitation: many people may count as one.
Timeless counting possible within the language
In fission cases, there are two people all along
But is this the correct answer? Why privilege the post-fission perspective- -or time at which there are the most people?
Synchronic counting is by identity but
Not everyone around counts (only people then ‘determinable’
Timeless counting not possible within the language
In fission cases, no answer to the question of how many people there are all along.
But maybe this is the result we want.
Do we want to count the maximal number at any time?

27. Another alternative
worm
A stage is a “temporal slice” of a worm
stage
Both Lewis’ account and Perry’s assume that continuant persons are space-time worms rather than stages

28. The Stage Language On the stage account individuals are just stages.
Jones
Jones
On the stage account individuals are just stages.
Names are systematically ambiguous (like indexicals)
They pick out different stages at different times

29. The Stage Language
Smith-Jones
Jones
Brown-Jones
Jones
Jones
Future tense statements about a person really say that the stage which he is, is R- related to another stage that is whatever.
[Before fission] Jones will be in room 102 after fission because the pre-fission stage ‘Jones’ picks out is R-related to a post-fission stage in room 102.

30. Bad, Bad, and Bad
All three accounts assume (or are compatible with) a four-dimensionalist ontology but chop it up differently, i.e. have different accounts of what persons and other ordinary objects are, and all are bad in their own way.
Ordinary objects are branches (Lewis): ’Cohabitation’ is fission cases--two or (possibly many!) more indistinguishible objects around before fission.
Ordinary objects are instantaneous stages: gets synchronic counting right counting by identity, but in diachronic counting, for ordinary as well as fission cases there are infinitely many objects.
Ordinary objects are lifetimes: cannot count timelessly at all.

31. Worms or Stages?
Worm-talk captures our intuition that future (and past) tense statements are true of us and not just other beings to whom we’re R-related.
Stage-talks capture our intuition that even in exotic branching cases, before fission there’s just one person.
Arguably, our decision can only be a matter of convenience: we choose the most cost-effective account--whatever that may be
Philosophy is a negotiation between our interest in making commonsense talk come out right and the demands of logic.
With enough fiddling we can make (most) commonsense talk come out right.

32. Philosophy is…fiddling.
Here endeth the lesson.