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The division of individuals Morel, Richard 1980

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THE DIVISION OP INDIVIDUALS by RICHARD MOREL B.Math., The University of Waterloo, 197^ A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of Philosophy) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1980 (c) Richard Morel, 1980 In p resent ing t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Co lumbia , I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r re fe rence and s tudy . I f u r t h e r agree tha t permiss ion f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood tha t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed wi thout my w r i t t e n p e r m i s s i o n . Department of Philosophy The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P lace Vancouver, Canada V6T 1W5 D a t e May 2, 1980 i i ABSTRACT While Jones* old heart is f a i l i n g , s t r i c t copies of his brain are implanted into the brainless bodies of Smith and Brown. Soon two individuals awaken, each claiming to be Jones* Could each of these two persons be Jones? This is the puzzle John Perry tackles i n "Can the Self Divide?" and i t i s also the central problem of this thesis. Perry-develops three semantic theories, the branch language, the person-stage language, and the lifetime language, each grounded on a different concept of what a person consists of. Eventually he rejects the f i r s t two languages in favor of the third. In Chapter II I examine Perry's reasons for rejecting the branch language and contend that the branch concept of a person need not be blamed for the branch lan-guage's shortcomings. In Chapter III I inspect the person-stage language and uncover a fault much more severe than those Perry complained of» the person-stage language robs persons of properties we know them to have. Hence i t can-not account for normal cases of personal identity, l e t alone complex ones like Jones'. This crippling fault also a f f l i c t s Perry's f i n a l semantic theory, the lifetime lan-guage) the theory and i t s defects are described i n Chapter IV. In Chapter V David Lewis' contributions are reviewedi i i i there I maintain that various parts of his theory conflict, notably his analysis of personal identity and his theory of person counting. Finally, Chapter VI contains my own attempts at resolving the problems encountered by Perry and Lewis. The theory I present i s based on the branch con-cept of a person, as i s the branch language and Lewis*,the-ory! i t s analysis of personal identity, though, differs radically from either Lewis* or Perry's, being couched not in terms of s t r i c t identity but in terms of identity at a given time. As far as I can t e l l , the theory i s free from any of the defects plaguing i t s forerunnersi i t s philoso-phical foundation, however, needs much c l a r i f i c a t i o n . Dr. Howard Jackson Thesis Supervisor iv CONTENTS ABSTRACT i i CHAPTER I. INTRODUCTION 1 CHAPTER II. THE BRANCH LANGUAGE 4 A. The branch language's theory of persons . . 5 B. The branch language's theory of naming . . 7 C. The branch language's truth-conditions . . 8 D. The adequacy of the branch language . . . . 12 E. Perry's evaluation of the branch language . 18 F. Additional flaws in the branch language . . 22 G. Chapter summary 28 CHAPTER III. THE PERSON-STAGE LANGUAGE 30 A. The elements of the person-stage language . 30 B. Concept of a person versus the theory of personal identity 36 C. Perry's assessment of the person-stage language . . . . . 39 D. The seamy side of the person-stage language . . . . . . . . . . . 42 CHAPTER IV. THE LIFETIME LANGUAGE 47 A. The lifetime language's theory of persons . 47 B. The lifetims language's theory of naming. . 49 C. The lifetime language's truth-conditions. . 53 D. The lifetime language and the mentalist . . 56 E. The shortcomings of the lifetime language 58 F. The lifetime language's theory of person counting . . . . . . . . . . . . . . 61 G. Criticism of the lifetime language's theory of person counting 66 H. Chapter summary 70 CHAPTER V. DAVID LEWIS AND THE FISSION OF PERSONS 72 A. Lewis' concept of a person 74 B. Lewis' theory of person counting . . . . . 76 V C. Naming in Lewis' discussion of fis s i o n . . . . . 78 D. An evaluation of Lewis' theory of counting . . . 80 E. A criticism of Lewis' analysis of personal identity 84 F. Chapter summary . 88 CHAPTER VI. THE B LANGUAGE 90 A. Persons in the B language 90 B. The B language's theory of person counting . . . 91 C. The B language's theory of naming . . . . . . . 94 D. The B language's truth-conditions for sentences of the form 'N has F at t" 96 E. The B language's truth-conditions for sentences of the form 'N is the same person as M at time t' 100 F. Tensed identity and i t s relation to s t r i c t identity 104 G. Personal identity and person counting in the B language . I l l H. The B language's theory of person counting compared to Lewis' methos . . . . . . . . . . . 112 I. Extending the B language's theory of person counting 118 J. Chapter summary and conclusion . . . . . . . . . 121 BIBLIOGRAPHY 126 1 CHAPTER I INTRODUCTION Brown, Jones, and Smith enter the hospital for brain rejuvenations. (In a brain rejuvenation, one's brain is removed, i t s circuitry is analyzed by a fabulous machine, and a new brain i s put back in one's skull, just like the old one in a l l relevant respects, but built of healthier grey matter. After a brain rejuvenation one feels better, and may think and remember more clearly, but the memories and beliefs are not changed in content.) Their brains are removed and placed on the brain cart. The nurse accidentally overturns the cartt the brains of Brown and Smith are ruined. To conceal his tragic blun-der, the nurse puts Jones's brain through the fabulous machine three times, and delivers the duplicates back to the operating room. Two of these are put in the skulls that formerly belonged to Brown and Smith. Jones's old heart has failed and, for a time, he i s taken for dead. In a few hours, however, two individuals wake up, each claiming to be Jones, each happy to be f i n a l l y r i d of his headaches, bu± somewhat upset at the drastic changes that seem to have taken place in his body. We shall c a l l these persons 'Smith-Jones' and * Brown-Jones *. The question i s , who are they?* So begins "Can the Self Divide?", John Perry's captivating paper on the division of individuals. Who indeed are Smith-Jones and Brown-Jones? Certain theories of personal identity seemingly confirm Smith-Jones' and Brown-Jones' assertions. These theories, briefly, analyze personal identity in terms of memory or i n terms of continuity of consciousness. Had only one body received a copy of Jones' brain these theories undoubtedly would imply that the resulting person i s Jones. *John Perry, "Can the Self Divide?", The Journal of  Philosophy 69 (September 9. 1972)« 463-88. 2 So one might well expect that applied to our present story, where not one body but two receive a copy of Jones' brain, these same theories would imply that each of the two resul-ting persons i s Jones. And apparently they do yield that result. Since SmithfeJones and Brown-Jones possess a l l of Jon&s' memories, beliefs, intentions, etc., their brains being exact duplicates of Jones', i t seemingly follows that 1) Smith-Jones i s the same person as Jones and 2) Brown-Jones i s the same person as Jones. But i f they are each the same person as Jones, then by the symmetry and transitivity of identity, i t further follows that 3*) Smith-Jones i s the same person as Brown-Jones. Quite plainly, however, Smith-Jones and Brown-Jones are not the same person. Even though they each received a s t r i c t copy of the same brain, Smith-Jones and Brown-Jones are as distinct from one another as are any two normal human beings. Sentence 3*» then, i s false, and the theories of personal identity which led to this falsehood must themselves be false. To an advocate of the theories under suspicion the choice i s clean deny that personal identity i s transitive and symmetric, or deny that the theories entail that Smith-Jones and Brown-Jones are each the same person as Jones. In essence Perry pursues the latter course. In point of fact, 3 however, his defense is quite elaborate. He develops a semantic theory, the lifetime language, which assigns truth-values to personal identity statements, and along with this theory, he provides a theory of how persons are counted, the lifetime theory of person-counting. But before presenting the lifetime language, Perry offers and investigates in his paper two other such theories, the branch language and the person-stage, both of which he eventually rejects. Just what these theories entail and how they differ w i l l become clear, I hope, as each i s examined in turn in the next three chap-ters. Then, in Chapter V, David Lewis* alternative to Perry's languages w i l l be scrutinized. Finally, Chapter VI w i l l intro-duce my own attempt at improving upon both Lewis' and Perry's solutions. CHAPTER II THE BRANCH LANGUAGE A l l three of Perry's languages present the same over-a l l design. First, they a l l build on the same foundation! they a l l take person-stages and the R relation as starting-points. Person-stages are the temporal parts of a personi they represent a person as he i s and the properties he has at a given time in his l i f e . Since, in a l l three languages, they act as building blocks from which persons are assembled, person-stages, as well as their properties, must be presumed to be readily identifiable. In Perry's f i c t i t i o u s example the person-stages are Jones' pre-operative stages, Smith-Jones' post-operative stages, and Brown-Jones' post-operative stages. The R relation is a relation which holds between person-stages. It expresses memory or continuity of cons-ciousness or any other psychological criterion used by the i theories of personal identity in question. If j i s an *Letting a single relation R stand for any such criterion may c a l l for a bi t of redefining, since not,all of these c r i t e r i a exhibit the same logical characteristics. For instance, memory i s usually antisymmetric, continuity of cons-ciousness i s not« i f a stage s i s available in memory to a stage r, r i s not available to s. To remove the discrepancy, 5 a r b i t r a r i l y chosen pre-operative stage of Jones and sj and bj are ar b i t r a r i l y chosen post-operative stages of Smith-Jones and Brown-Jones, respectively, then according to Perry's story, sj is R-related to j , bj i s R-related to j , but sj i s not R-related to bj. Second, a l l three languages exhibit the same struc-ture. Each consists of three elementst a theory or concept of what a person i s , a theory of naming, and a theory about the truth-conditions of sentences of certain types. The theory of persons t e l l s us which groups of person-stages form persons; the theory of naming says what name or names these persons have, i f they have any at a l l j and the theory about the truth-conditions of certain kinds of sentences gives us what properties these persons have, including which persons are the same and which are not. A. The branch language's  theory of persons To state clearly what a person i s in the branch language we need one definition. Call a set of person-stages le t R' be the relation expressing memory and l e t R be the relation holding between person-stages a and b just in case a has R' to b or b has R' to a. R so defined i s symmetric. Furthermore, R* w i l l be taken to be reflexive. In the pres-ent work as in Perry's, then, the relation R is taken to be symmetric and reflexive but not transitive. 6 a 'branch* i f and only i f a l l i t s members have the relation R to one another and no stage that has R to a l l the members is not i t s e l f a member. A branch, then, is just a set of a certain kind, one in which every member is R-related to every other and which is the largest such set; for short, a maximal R-interrelated set of person-stages. Applying this definition to the person-stages under scrutiny we find that they compose two branches. One is formed by a l l the pre-operative stages of Jones together with.iall the postoperative stages of Brown-Jones, the other by a l l the pre-operative stages of Jones together with a l l the post-operative stages of Smith-Jones. However, the set containing a l l the person-stages in both these branches, that i s , the set of a l l person-stages unties examination, is not i t s e l f a branch. The branch language makes this conjecturet persons 2 are branches. Every branch forms a person. According to the branch language, therefore, a l l of Jones' pre-operative stages taken with a l l the post-operative stages of Smith-Jones compose one person} and those same stages of Jones grouped with a l l the post-operative stages of Brown-Jones form another person. As illustrates the fact that these two 2 As Perry points out (Perry, p.4?2), the identifica-tion between persons and branches need not be made. A l l that matters i s that a one-to-one correspondence exist between bran ches and persons. S t i l l , the identification i s made for the sake of simplicity. 7 persons have in common their i n i t i a l stages, the concept of a person embodied in the branch language allows the sharing of stages among persons, i t being possible for a person-stage to be a member of more than one branch. B. The branch language's  theory of naming The branch language supposes, f i r s t , that names are assigned to person-stages, that i s , that names are assigned by the picking out of a person-staget and second, that the name names the person—the branch—of which that person-stage is a member. If the person-stage to which a name is assigned is a member of more than one branch, the name f a i l s to refer; i t names no one. It is easy to see that the two branches obtained above are names 'Smith-Jones' and 'Brown-Jones'. The name •Smith-Jones' was assigned by isolating some stage s j , and i t i s a member of only one branch; so 'Smith-Jones' is the name of that branch. In like manner, 'Brown-Jones'was assigned by picking out a stage bj, which belongs to only one branch; so i t names that branch. What about the name •Jones'? Does i t name any of the two branches? To answer that question we must suppose that the name 'Jones' was assigned at baptism by someone's pointing to some j , a pre-operative stage of Jones, and saying 'Let us c a l l this person 8 'Jones'', just as 'Smith-Jones' and 'Brown-Jones' were assigned by Perry's pointing at post-operative stages of Smith-Jones and of Brown-Jones and declaring, "We shall c a l l these persons 'Smith-Jones' and*Brown-Jones'." Thus the theory of naming implies that the name 'Jones' f a i l s to refer, because the stage isolated at baptism belongs to more than one branch. Neither branch, therefore, i s named 'Jones'. C. The branch language's  truth-conditions In the branch language a sentence of the type N has F at t, where *N' is a personal name, F a property, and t a time, is true i f and only i f the branch referred to by 'N' contains a person-stage that occurs at t and has property F. If the branch contains no such person-stage or the name N does not refer, the sentence i s false. Here a qualification is in order. As just staged, the truth-conditions are patently wrong. Some properties that a person has at a given time depend not on the person's person-stage having the property at that time but on one of the person's future or earlier person-stages having a differ-ent property at that earlier or later time. As an i l l u s t r a -tion imagine Johnson, a normal patient, now in room 80 but about to be moved to room 90. He now has the property of being about to be in room 90. The sentence expressing that 9 fact, 'Johnson now has the property of being about to be in room 90', i s true i f and only i f Johnson has, at a later time, a person-stage that is then in room 90 and not, as the truth-conditions imply, i f and only i f he now has a person-stage which is about to be in room 90. Because the existence of a person-stage is more or less momentary, no person-stage can be about to be in room 90. It is the person who is about to be in room 90, not the person-stage. Consequently, i f we are to retain the truth-conditions expressed previously, we must restrict the properties that F can stand for to those that make the truth-conditions hold, properties such as 'being in room 80'. As far as I can t e l l , this restriction i s equivalent to Perry's stipulation that F represent a basic property of a person, a property a person has at a given time in virtue of events that occur only at that time(Perry, p.470). A person's non-basic properties at a time are those which he has wholly or partly in virtue of events that occur at other times. Like Perry, in order to simplify as much as possible the problem at hand, I w i l l assume that the non-basic properties a person has at a given time are a function of his basic properties at that and other times, and then I w i l l ignore non-basic properties altogether. What do the truth-conditions given so far imply about Jones, Smith-Jones, and Brown-Jones? For Jones the 10 implications are gloomy. The name 'Jones' being improper, any sentence of the form 'Jones has F at t', for any time t, is false. Thus even though we know, for example, that Jones entered hospital, the sentence stating that he did so i s f a l -se, i f we lend credence to the branch language. For Smith-Jones and Brown-Jones the consequences are brighter. Their names refer, so sentences containing them are not necessarily false. As we previously mentioned, Brown-Jones and SmithsJones share their pre-operative stages. It follows straight away that, for any time t prior to the opera-tion, Brown-Jones has F at t i f and only i f Smith-Jones has F at t, since the truth-value of 'BJ has F at t* and of 'SJ has F at t' depends on the properties of exaetly the same person-stage. Hence whatever Brown-Jones did, f e l t , or thought prior to the operation, Smith-Jones did, f e l t , or thdught, and at the same place and time as Brown-Jones; and vice-versa. A like generalization cannot be made for times following the operation, the stages of Smith-Jones and those of Brown-Jones being then distinct. Furthermore, the person-stages that Brown-Jones and Smith-Jones share are, we know, stages of Jones. Therefore anything we would say Jones experienced before the operation, the branch language would say Smith-Jones, and also Brown-Jones, experienced, at the same time and place and in the 11 same manner as did Jones. So Smith-Jones entered hospital. Brown-Jones entered hospital. They did a l l the things they remember doing. But are they Jones? Were they one another? These questions bring us to the branch language's thruth-cohditions for statements of personal identity. In the branch language a sentence o f the type N i s identical to M, where 'N* and 'M' represent personal names, i s true i f and only i f the branch referred to by 'N' and the branch referred to by 'M' are identical. If either *N' or 'M' i s improper, the sentence i s false. Accordingly, the sentences 4) SJ 3 i s identical to J and 5) BJ i s identical to J are false, since they both contain a name that f a i l s to refer, •Jones'. The sentence SJ is identical to BJ is also false. Though the two names in i t do refer, the branches they refer to are not identical. Therefore the sentence 6) SJ i s not identical to BJ is true. Wherever i t i s convenient to do so, the name 'Jones' w i l l be abbreviated to 'J', 'Smith-Jones' to 'SJ', and 'Brown-Jones' to 'BJ'. 12 From the branch language, then, follow a number of implications about the persons i n Perry's f i c t i o n a l example. These implications, or predictions, as we w i l l c a l l them, can be used to evaluate the language. But before examining them in detail and comparing them to what we would say about the example, we should verify that the branch language i s adequate to Perry's purpose, D. The adequacy of the  branch language Perry's chief aim in constructing the branch language is to save from contradiction a dertain theory of personal identity, the theory that for any ar b i t r a r i l y chosen person-stages a and b, a and b belong to the same person i f and only i f the R relation holds between them. Applied to his f i c t i o n -a l example, where stage sj has R to stage j , stage bj has R to j , but sj does not have R to bj, the theory apparently implies that 1) SJ i s the same person as J 2) BJ i s the same person as J 3) SJ is not the same person as BJ, which are inconsistent unless the relation of being the same person as i s intransitive or not symmetric, a supposition Perry i s unwilling to make. In our evaluation of the branch language, therefore, 13 we should verify, f i r s t , that the theory of personal iden-t i t y under fi r e does bear upon the branch language, for i f i t does not, the enterprise of constructing that language was beside the point; second, that under the braneh language analysis of identity statements the relation of being the same person as does come out to be transitive, symmetric, and reflexive, as Perry wishes i t to be; and third, that sentences 1, 2, and 3 are not a l l implied by the branch language, for i f they are, the braneh language would indeed lead to contradiction. Fi r s t , then, how does the branch language bear upon the theory of personal identity i n question? In this wayt the concept of a person which i s incorporated in the branch language implies the theory in question but i s not implied by i t . The theory, since i t is a universally quantified biconditional, can be s p l i t into a conjunction of two con-ditional statements* for any person-stages x and y, chosen arbi t r a r i l y , A) i f a person contains both x and y, then x and y are R-related and B) i f x and y are R-related, then some per-son contains them both. Now statement A, which can be expressed i n logical notation by (x)(y)( 3z(Pz & xgz & yez)-»Rxy), Ik i s easily shown to be not merely implied by but actually equivalent to (z)(Pz-^(x)(y)((xfz &y£z)-»Rxy), which simply says that a l l a person's person-stages are R-related. (Here, x and y range over person-stages, z ranges over sets of person-stages, P stands for the property of being a person, and R stands for the R relation.) Since the branch language defines a person to be a set of R-inter-related person-stages which i s maximal, i t s concept of a person directly implies statement A. Statement B, which can be expressed in logical notation by (x)(y)(Rxy-* 3z(Pz&xfz&yfz)), says that for any person-stages x and y that are R-related there i s at least one person containing them both. That statement i s also implied by the branch language concept of a person. The proof i s as follows. Assume that persons are indeed maximal R-interrelated sets of person-stages, and assume also that Rab i s the case, that i s , that a is R-related to b, for some arb i t r a r i l y chosen person-stages a and b. The set consisting of these two person-stages either i s a person or i t i s not. If i t i s , fine? the proof i s complete, since a and b were chosen ar b i t r a r i l y . If the set i s not a person, then either the set i s not R-interrelated, or there i s another element, say c, which i s R-related to both a and b. This 15 set is R-related, however, since Rab (by assumption) and Raa and Rcc (R being reflexive)? so i t must be the case that there i s such an element c. Well, then, consider the set formed by a, b, and c; either i t i s a person or i t i s not. If i t i s , fine; the proof i s complete. If i t i s not, i t must be the case that there i s another element, say d, which is R-related to a, b, and c, since the set consisting of just those elements i s R-related. And so on, un t i l a set is formed which indeed i s a person. That this process w i l l not go on interminably is insured by the fact that no person is eter-nal. For any given pair of elements a and b that are R-related, therefore, we can always construct a person which w i l l include them both. Statement B, then, also follows from the definition of a branch. Hence, from the hypothesis that persons are branches, we can derive both A and B, and so the branch language implies the theory of personal identity Perry defends. His purpose is thus f u l l y served; for should the branch language prove to be consistent, so would the theory of personal identity. Whether the branch language i s in fact consistent is another matter, which remains to be proved. A l l we know so far i s that the theory of personal identity i s consistent i f the branch language i s . Second, we should check that the relation expressed by •is the same person as', the relation of personal identity, 16 generally believed to be transitive, symmetric, and reflex-ive, does turn ourt to have those properties under the anal-ysis provided by the branch language. A glance at that lang-uage, however, reveals no truth-conditions for personal iden-t i t y statements, statements of the form 'N is the same per-son as M*, but just those for sentences of the kind 'N i s identical to M'. The omission manifests Perry*s assumption that a sentence of the type *N is the same person as M* not only is equivalent to but is in fact synonymous with one of the form *N i s identical to M*, where 'identical' i s cons-trued as denoting s t r i c t or Leibnizian identity, the rela-tion everything bears to i t s e l f and only to i t s e l f . Perry is well aware of this assumption; proof i s found in his discussion of the other two languages. For example, he writes on p.486t Finally, the lifetime language, like the branch language but unlike the person-stage language, allows us to mean by our words what we think we mean, to wit, identity by •is the same person as' and so forth. In the branch language, then, statements of personal identity are presumed to be statements of s t r i c t identity between persons and hence are to be analyzed in terms of s t r i c t identity. Consequently the relation expressed by 'is the same person as' does turn out to be transitive, symmetric, and reflexive, since under the branch language analysis;, i t has a l l the properties of s t r i c t identity. 1? Third and last, we must verify that sentences 1, 2, and 3 cannot be obtained from the branch language. Since these sentences contain the predicate 'is the same person as', we must, in order to find their truth-value, again rely on the branch language's hypothesis that statements of person-a l identity are just statements of s t r i c t identity. Under that assumption, 1, 2, and 3 are synonymous to 4) SJ i s identical to J, 5) BJ is identical to J, and 6) SJ i s not identical to BJ. As we explained in section C» above, the f i r s t two of these sentences are false and the third i s true. Sentences 4 and 5 are false because they contain an improper name, 'Jones'; sentence 6 i s true because i t s denial, or rather the senten-ce of which i t i s the denial, i s false, the branch referred to by 'Smith-Jones* not being identical to the branch refer-red to by 'Brown-Jones*. Therefore, not a l l of 1, 2, and 3 are true, and so the reasoning purporting to show that the theory of personal identity in question is inconsistent just does not apply. The branch language, at least on this ac-count, appears to be consistent. A l l that remains to be checked, then, i s how well the branch language accords with what we would say about Perry's example. This we tackle in the remaining sections of this chapter. 18 E. Perry's evaluation of  the branch language Perry junks the branch language. He explains why in the following passage (Perry, pp.4?2-3)t What are the merits of this view? Is our concept of a person the concept embodied in the branch language? I think not. The mentalist £for Perry, any defender of theories of personal identity like the ones in ques-tion], in adopting this solution, would be leaving the ordinary man far behindt for the ordinary man is not willing to admit that there was not a single person, Jones, before the operation, doing a l l the things Smith-Jones and Brown-Jones seem to remember doing. . . . i t seems clear that we are reluctant to abandon the prin-ciple that each person-stage identifies a person, so that i f we assign a name to a person-stage, we cannot but have named a person. Perry rejects the branch language because i t s concept of a person implies, he believes, that the person we c a l l 'Jones' i s not really a single person before the operation. Stage j belongs to two branches and hence, Perry reasons, two persons exist at that time* the person we c a l l 'Jones* i s actually two persons before the operation. But that conclusion i s somewhat implausible, and therefore we must discard the concept of a person that gave rise to i t . That reasoning, however, presupposes in addition to the branch language concept of a person a certain theory of counting which i s not mentioned in the branch languagei that the number of persons alive at a given time corresponds to the number of branches having a person-stage at that time; more precisely, that the number of persons alive at a time, 19 corresponding to each person-;-stage existing then, i s equal to the number of branches having that person-stage as a member. Since i t i s only in conjunction with a theory of counting that the undesired conclusion i s derived from the branch language theory; of a person, that concept of a person should not be rejected on the basis of that conclusion alone» for i t may be the theory of counting which i s at fault and not the theory of persons. Alternative theories exist which give the correct count» whether such theories are viable w i l l be discussed in a later chapter (Chapter V). For now we w i l l only point out that Perry's rejection of the branch language's concept of a person depends on the correctness of the theory of counting presupposed. Though the branch language, by containing no theory of counting, leaves i t open whether there i s a single person before the operation or not, i t does commit i t s e l f on two points* no one i s named 'Jones', and a l l sentences of the form 'Jones has F at t' are false. No one is named 'Jones' because, according to the branch language theory of naming, the naming procedure misfires, no single branch containing stage j . Hence the name 'Jones' f a i l s to refer, and a l l sentences of the form 'Jones has F a.**' are false, according to the branch language's truth-conditions. Do these predictions of the language match what we would say about Jones? Clearly they do not. First, there 20 i s no doubt, somebody in the story is called 'Jones', even though we are not certain of what becomes of him after his brain i s triplicated. It is Jones who enters hospital along with Brown and Smith, for instance, and i t is Jones whose heart f a i l s after the operation. Evidently, then, there i s a Jones in the story, at least before the operation. For us the naming procedure does not malfunction as i t does in the branch language. Second, we would not say that a l l sentences of the form 'Jones has F at t' are false. Some we take to be true, for example, 'Jones entered hospital some time before the operation't that i s , 'Jones has at some time prior to the operation the property of entering hospital'. Moreover, others are false not because 'Jones' f a i l s to refer but because Jones just did not have the property ascribed to himj for instance, 'At no time did Jones enter hospital'. The branch language, then, makes two predictions that do not agree with the facts—what we would say about Jones—and so, on that aecount, is inadequate. This i s probably part of Perry's meaning when he says, " . . . for the ordinary man is not willing to admit that there was not a single person, Jones, before the operation, doing a l l the things Smith-Jones and Brown-Jones seem to remember doing" (Perry, pp. 472-3). That i s , not only would the ordinary man say that there was a single person doing:all the things 21 they remember , or seem to remember, doings he would also say that that person was named 'Jones*. But that these two predictions do not match the facts does not mean, or does not necessarily mean, that the concept of a person which is at the base of the branch lang-uage is i t s e l f faulty. Other elements of the branch language enter into the derivation of the predictions at odds with the facts, and those elements may be the ones to blame, not the concept of a person. For instance, the prediction that no one in the story i s named 'Jones' stems not just from -the branch language's concept of a person but also from i t s theory of naming. Similarly, the prediction that a l l senten-ces of the type 'Jones has F a.t* t' are false involves the theory of naming and part of the branch language truth-con-ditions as well as i t s concept of a person. How does one decide which part of the language is faulty and which i s not, especially when the entire language may be faulty? Well, perhaps the surest way of exonerating the branch language's concept of a person is to offer an alternative branch language, a language based on the same concept of a person as the branch language but containing a different theory of naming and different truth-conditions, and then to show that this alternative language i s viable, with a l l or at least most of the virtues of the branch language but none of i t s vices. That avenue w i l l be explored in: the last chapter of 22 the present work. David Lewis, in his paper "Survival and Identity," follows a similar route; his contribution w i l l be reviewed in Chapter V. Perry, for his part, takes a wholly different approach. He discards the branch language's concept of a person and devises a language based on a dif-ferent concept of a person. Perry's alternative language and the alternative to i t w i l l be examined in Chapters III and IV, respectively. But for now, we continue our inves-tigation of the branch language. F. Additional flaws in the branch language Up until now in our evaluation we have compared the branch language's predictions with what we have called the "facts," what we know with certainty, or almost with cer-tainty, about Perry's example, such as that someone in the story i s called 'Jones', that he entered hospital, and that he was one person before the operation, not two. These "facts" are not totally beyond doubt; one might question, for instance, whether baptism can be effected by someone's pointing to a person-stage and saying, "I hereby name you •Jones'." But this procedure i s so similar to actual bap-tism ceremonies, i f not identical,that there i s l i t t l e room h David Lewis, "Survival and Identity," The Identities of Persons, ed. Amelie Oksenberg Rorty (Berkeleyi University of California Press, 1976), pp.17-40. 23 to doubt that persons can indeed be named in this way. Or one might wonder whether Jones, before the operation, even though he has only one body and one mind and is normal in practically every respect, is not actually two persons because he w i l l later be divided into two persons, each of whom was him (supposing, of course, that he does divide in this way). Again, the supposition that he was two persons before the operation i s not absurd, but i t is one we would resist, because we do not, when counting the number of persons, say, in a room, consider what w i l l happen to them once they w i l l have l e f t the roomi we just count them without paying attention to their future. These facts, then, though not positively beyond suspicion, nonetheless are quite cer-tain, certain enough for us to expect the branch language (and other languages as well) to agree with most of them, or at least not to contradict them. There is another realm of considerations, however, that are often flimsy, which usually go by the name of 'intuitions'! these we dare hope a language w i l l c l a r i f y or perhaps even corroborate. It is to those considerations that we now turn. Since we have already declared the branch language inadequate, our discussion w i l l be academic in one respect. S t i l l , i t w i l l be profitable, as i t w i l l serve to introduce a few cardinal issues. In section D above we saw how the fact that sentences 1 and 2 are false and sentence 3 true renders the theory of 2k personal identity Perry defends immune to the charge of in-consistency. But with this immunity come a few problems for the branch language. We remarked in our examination of the branch language's truth-conditions ?(in section C above) that the following equivalence holds for any time t prior to the operationi SJ has F at t i f and only i f BJ has F at t. Whatever property SJ has before the operation, BJ has, and vice-versa. Before the operation, SJ and BJ have exactly the same properties, and moreover, each has them at the same time and place as the other. This remarkable coinci-dence i s easily explained* SJ and BJ share stages before the operation. At any time prior to the operation, SJ's stage at that time is precisely BJ's stage, and vice-versa. In other words, i f BJ stands before me sometime prior to the opera-tion, so does SJ? and i f I point to SJ, I point to BJ. That their stages are identical before the operation, then, strong-l y suggests that at that time, SJ and BJ are the very same person. The one i s the other, at least before the operation. The fact that they are the same person at that time would explain why, prior to the operation, the above equivalence holds. Yet, concerning the sameness of BJ. and SJ, the branch language makes only one statement * BJ and SJ.are not the same person. While i t seems that, before the operation, BJ and SJ 25 are the same person, but after the operation, different per-sons, the branch language concludes only that BJ and SJ are different persons. What appears to be a relation that varies with time—before the operation BJ and SJ are the same, after the operation they are not—the branch language treats as unvarying. A similar argument can be advanced about the rela-tionship between SJ and Jones, and BJ and Jones. The proper-ties that SJ and BJ have in common before the operation are, we know, properties of Jones, though the branch language does not ascribe them to him, the name 'Jones' being improper in that language. We know the properties are Jones' because the stages BJ and SJ share are, as we would say, stages of Jones. So i t seems that before the operation SJ and Jones are the same person and BJ and Jones are also the same per-son. Again the branch language does not reflect the s i t -uation before the operation; 1) SJ is the same person as J and 2) BJ is the same person as J are both false, with no reference to time. The branch language's truth-conditions for personal identity statements, then, though they make no mention of time, describe only the situation as i t stands after the operation. In fact the truths-values they give are the only ones possible which w i l l correctly describe the situation 26 as i t stands after the operation, i f the relation of same-ness is to retain i t s usual properties and the argument against the theory of personal identity is to be defeated. Sentence 3 3) SJ i s not the same person as BJ appears to be clearly true after the operation; therefore i f the argument against the theory Perry supports i s to be neutralized, one of sentences 1 and 2 must be false; and hence both must be false, there being between SJ's relation to Jones and BJ's relation to Jones no difference that would warrant only one of 1 and 2 being false and the other true. The truth-values the branch language gives to 1, 2, and 3» then, are just the ones we would expect for after the oper-ation? but unfortunately, they are the opposite of what we would expect for before the operation. In short, the branch language's truth-conditions for personal identity statements lack a temporal perspective. Perry would agree with this assessment. His intui-tion also i s that, before the operation, SJ, BJ, and Jones are a l l the same person. Proof i s that he presents two alternatives to the branch language; the f i r s t , he says, "allows the mentalist to say just what he wants to say about the example"(Perry, p.479); the second he accepts as definitive; and both imply that before the operation, BJ, SJ, and Jones are a l l the same person. 27 But here Perry faces a grave problem, as does anyone wanting to claim both that statements of personal identity are statements of s t r i c t identity and that BJ and SJ are the same person before the operation but not after. If sen-tence 7 7) BJ i s the same person as SJ before the operation i s analyzed as the referent of 'BJ* and the referent of 'SJ' have a l l properties in common, past, present (i.e. before the operation), and future and sentence 8 8) BJ is not the same person as SJ after the operation i s analyzed as the referent of 'BJ' and the referent of 'SJ' do not have a l l their properties in common, past, present (i.e. after the operation), and future, then the two statements are contradictory, since their anal-yses are contradictory, the sum of an object's properties over time being the same regardless of which instant or period of time is taken as present; at least there i s no in-dication that Perry thinks otherwise, that the sum total over time of an object's properties varies with time. In other 28 words, sentence 7 reduces simply to BJ 3 SJ and sentence 8 to BJ f SJ. But these are contradictory. If both these statements are to be true, therefore, i t must be the case that some of the prop-er names in the statements, i f not a l l , are ambiguous. And we w i l l find that, in both of Perry's alternative languages, one of which he considers f i n a l , the reference of proper names does indeed shift from one time to another, so that both sentences 7 and 8 come out true. How this shifting occurs w i l l be explained in the next chapter. G. Chapter summary The braneh language f u l f i l s a l l prerequisites for defending the theory of personal identity Perry supports* i t entails the theory in question yet does not imply a l l three seemingly inconsistent sentences 1, 2, and 3$ and i t endows personal identity with transitivity, symmetry, and reflexivity, properties we would expect i t to possess. Perry rejeets the branch languange because he believes that i t s concept of a person implies that Jones was actually two persons before the operation and that no one was named "Jones' in the story, implications which are almost certainly false. Perry therefore devises a new language, one based on a differ-ent concept of a person. 29 Though the branch language, I contend, does not entail that Jones was actually two persons before the op-eration, i t does imply that no one was named 'Jones', and hence i t ought to be rejected. Moreover, i t s truth-con-ditions for personal identity statements lack a temporal perspective, a defect which results in i t s f a i l i n g to des-cribe the relationship holding between Jones, Smith-Jones, and Brown-Jones before the operation. However, none of these shortcomings, I maintain, decisively inculpates the branch concept of a person. 30 CHAPTER III THE PERSON-STAGE LANGUAGE A. The elements of the  person-stage language The person-stage language i s Perry's f i r s t alter-native to the branch language, one he eventually rejects in favor of the lifetime language. Like the other languages i t derives i t s name from i t s concept of a persont in the person-stage language persons are assumed to be person-stages. Each person-stage constitutes a person. That hypothesis seems very odd. Persons are usually thought to be continuant entities, things that last through time, and not possibly momentary objects like person-stages, entities that might exist no longer than an instant. How could the hypothesis that persons are person-stages be an improvement over the branch language's concept of a person, which at least can correspond to objects enduring through time? Perry abandoned the notion that persons are branches because i t led, he believed, to the unacceptable conclusion that Jones, at any time before the operation, was really two persons, each of his stages then occurring being shared by the two branches alike. The person-stage language's con-31 cept of a person certainly obviates that difficulty? each person-stage constituting an entire person, no person-stage is shared and so, according to Perry's theory of counting persons at a time, only one person exists at any instant prior to the operation. There is no risk, then, of Jones' being simultaneously two persons. The next conponent of the person-stage language, the theory of naming, is nore complicated than i t s branch langua-ge counterpart. Like the branch language the person-stage language presupposes that each name i s assigned by the picking out of a person-stage. But unlike the branch language i t supposes that the name nemes, not only the person—in this case the person-stage— that contains the person-stage, but every person-stage that has relation R to the stage picked out. In this language, then, proper names are ambiguous. We mentioned earlier (in section II-F) that i f the sentence •SJ i s the same person as BJ' i s to be true before but false after the operation, and the relation of personal identity is to be analyzed in terms of s t r i c t identity, then at least one of the proper names 'Smith-Jones* and 'Brown-Jones* must be ambiguous. That required ambiguity is built into the per-son-stage language's theory of naming. But the ambiguity i s systematic? at different times proper names name different persons. The device that guides the reference of proper 32 names i n a sentence is that of temporal adverbs i n i n i t i a l position, phrases like 'before the operation', 'after the operation', placed at the beginning of a sentence. In that position temporal adverbs function as temporal markers which indicate, among other things, which person-stage or person-stages a name names. As besfore, adverbs like 'before the operation' are assumed to refer to a specific instant within a period of time and not to the entire period. When within the scope of such an adverb a name names only the person-stages which occur at the time indicated by the temporal ad-verb and have R to rthe stage picked out during the assigning of that name. When no i n i t i a l temporal i s present a name names just the person-stages which occur at the time of utter-ance of the sentence and have R to the stage picked out i n the assigning of that name. And, fi n a l l y , just in case there is exactly one such person-stage at a given time is the name proper at that time. As an il l u s t r a t i o n consider the name 'Jones'. It i s assigned by isolating stage j , which occurs before the opera-tion. 'Jones', then, names at different times* a l l the per? son-stages that have R to j , namely, a l l the person-stages *0r so Perry claims. It seems odd, though, to say that the person-stages are named at different times when in fact one can by means of suitable temporal adverbs name at any time person-stages that occur at any particular time. Why not just say that a l l the stages in question are named 'Jones' and let the referential apparatus of the sentence do the choosing? 33 that occur in the story. In the sentence 9) Jones w i l l be i n room 102 after the operation, i f voiced at some time before the operation, the name 'Jones' names only the one stage which occurs at that time and has R tojthe stage j , and so the name 'Jones' i s proper at that time. But in the sentence 10) After the operation, Jones i s in room 102, uttered at any time, and the sentence 11) Jones is now in room 102, spoken after the operation, the name 'Jones' names the two stages that occur at that time after the operation and have R to stage j , and hence i t i s improper at that time, naming more than one person-stage at that time. In one respect, then, the person-stage language's theory of naming is an improvement over i t s predecessor. Someone now bears the name 'Jones', at least some of the time, whereas i n the branch language no one was ever named 'Jones'. The last component of the person-stage language, i t s theory of truth-conditions, also pertains to temporal ad-verbs placed at the beginning of a sentence. In that posi-tion temporal adverbs play two roles. One has already been explained, to dictate which person-stages, i f any, a proper name names and to f i x i t s referent, i f i t has one. The sec-ond function of a temporal adverb i n i n i t i a l position is to signal at which time the sentence following the adverb is to 34 be understood as being true. If no adverb occurs at the be-ginning of the sentence the sentence i s taken to be true at the time of i t s utterance. The second role of temporal adverbs in i n i t i a l posi-tion i s made very plain in the person-stage language's truth-conditions, which Perry characterizes as follows (Perry, pp. 477-8)i A sentence of the form N has F at t uttered at time t', i s true i f and only i f the person-stage named by N at t' has R to some person-stage that occurs at t and has F. A sentence of the form N i s identical to M i s true at t' i f and only i f the person-stage named by N at t* i s identical with the person-stage named by M at t*. A sentence with an i n i t i a l temporal adverb At f , N has F at t or At f , N is identical to M is true i f and only i f the sentence following the adverb is true when uttered at the time indicated by the adverb. For example suppose that, after the operation, SJ i s wheeled to room lo2 and BJ i s carted to room 104. Then, spoken at some time t' before the operation, the sentence 9) Jones w i l l be in room 102 after the operation (i.e., Jones has the property of being in room 102 at some time t after the operation), i s true, since there i s at time t a person-stage which is in room 102 and has R to the person-stage named by 'Jones* at time t'. For the same reason the sentence 9') Jones w i l l be in room 104 after the operation is true as well i f voiced also at some time t' prior to the 35 operation. However, sentence 10 and i t s parallel 12) After the operation, Jones i s i n room 104 are both false regardless of the time they were stated, be-cause the name 'Jones' is improper after the operation, two stages then being named by i t . The person-stage language's truth-conditions, at least in some respects, surpass their branch language coun-terpart. They allow us to ascribe to Jones properties we know him to have. The sentence 13) Jones entered hospital before the operation, which i s false in the branch language because 'Jones' does not refer, is true in the person-stage language provided i t is pronounced before the operation or placed within the scope of the temporal adverb 'before the operation'. The person-stage language also enables us to des-cribe the relationship between SJ, BJ, and Jones correctly. The temporal perspective absent from the branch language's truthrconditions for statements of personal identity is alive and thriving in the person-stage language. Sentences 1, 2, and 3, i f spoken before the operation, and their i n i t i a l adverb counterparts 1') Before the operation, SJ is the same person as J 2') Before the operation,1BJ i s the same person as J 36 3') Before the operation, SJ i s not the same person as BJ a l l have their<expected truth-valuei 1, 2, and 1* and 2' are true, since the stage named by 'Jones' before the opera-tion i s exactly the stage named by 'SJ* and 'BJ' at that time, and 3 and 3' are false because 'SJ* and 'BJ' name the same stage at that time. After the operation the situation is just the reverse. And again sentences 1, 2, and*3,iif spoken after the operation, and their adverbial versions 1'•) After the operation, SJ i s the same person as J 2*') After the operation, BJ i s the same person as J 3 ' ' ) After the operation, BJ i s not the same person as SJ have their expected truth-values. The person-stage language, then, at least at f i r s t blush, allows us to say what we want to say about Jones, SJ, and BJ. But the success of the person-stage language can on-ly be partial; for should the language be a correct account of English, i t would by the same token defeat Perry's pur-pose. How this clash arises is explained in the next section. B. Concept of a person versus the theory of personal identity As I mentioned at the beginning of this chapter, 37 Perry eventually rejects the person-stage language. In light of the* goal he sets himself in his paper there is a pressing reason why the language should be discarded, a reason Perry himself seems unaware of. The concept of a person which is at the base of the language implies that the theory of per-sonal identity Perry defends i s false. Given the facts of our example, the hypothesis that person-stages are persons and the theory of personal identity in question are incom-patible . To prove that the two are inconsistent, the facts about our example being what they are, we assume that the language's hypothesis about what makes up a person is correct, and then we show that the theory of personal identity cannot also be true. Suppose, then, that every person-stage cons-titutes a person. The theory of personal identity Perry supports i s i for any person-stages x and y, x and y are R-related i f and only i f there is a person to which x and y belong. Since the theory is expressed as a universally quantified b i -conditional, i t can be divided into a conjunction of two separate statements, A) i f a person contains stages x and y, then x and y are R-related, 38 and B) i f x and y are R-related, then some person con-tains x and y. Statement A is true i f a person is just a person-stage, because every person-stage is R-related to i t s e l f ; that i s , the R relation i s reflexive. More specifically, since person#stages x and y need not be distinct, statement A applies to two kinds of casest those where x and y are dis-tinct, and those where they are the same. Cases of the f i r s t kind never arise under the present concept of a person, a person being just a single person-stage. Only cases of the second type occur, and therefore statement A reduces . for this concept of a person to the statement that the person-stage forming a person i s R-related to i t s e l f . That state-ment is true, since every person-stage is R-related to i t -self. Statement B, however, is false i f a person consists merely of a single person-stage. Our example abounds with distinct person-stages that are R-related, stages sj and j , for example; yet no single person includes any such pair of stages, since each person contains exactly one person-stage. Insofar as there are distinct person-stages which are R-rela-ted, then, the person-stage language's concept of a person implies that statement B, and hence the entire theory of personal identity, i s false. The R relation f a i l s as a 39 sufficient condition of x and y's both belonging to the same person. Perry's ultimate aim in constructing the person-stage language, we must remember, i s to vindicate the theory of personal identity mentioned above. Since that theory is false i f the person-stage language is true, i t particular-ly behooves him to prove that language unacceptable. His evaluation of the language i s examined in the next section. C. Perry's assessment of the  person-stage language As we mentioned above, Perry rejects the person-stage language. He summarizes his reasonsas follows (Perry, p.48p)» He [the mentalistj cannot take refuge in the person-stage language, for i t denies what clearly i s truei that when I say of someone that he w i l l do such and such, I mean that he w i l l do i t . The events in my future are events that w i l l happen to me, and not merely events that w i l l happen to someone else of the same name. The theo-ry that English is the person-stage language violates our semantic intuitions; i t gives an unduly complicated ac-count of our language. Perry's objections to the person-stage language focus on i t s theory of truth-conditions for sentences of the form *N has F at t*. Consider again the situation of Johnson, who i s now in room 80 and w i l l be in room 90 in, say, a half-hour. Spoken now, the sentence Johnson w i l l be in room 90 in a half-hour is true in the person-stage language i f and only i f there i s in a half-hour a person-stage which is in room 90 and has R to the stage presently named by •Johnson". So Johnson, the person now named by 'Johnson', who i s now in room 80, w i l l be in room 90 in a half-hour not just in case he himself i s in that room in a half-hour, as we would expect, but just in case a totally different person, that i s , some other per-son-stage, who has R to the present Johnson, is in that room in a half-hour. What w i l l happen to the person now named •Johnson', then, depends on what w i l l happen to another per-son of the same name; that is what Perry objects to. Perry is right, I believe, when he claims that the person-stage language violates our semantic intuitions. Events, we would say, to be part of a given person's future, must happen to that person; otherwise, they belong not to that person's future but to someone else's. But in light of how Perry dismisses an earlier transgression of our seman-t i c intuitions i t is not certain that the present violation is ground for rejecting the person-stage language. By having proper names at different times of their use refer to different entities the person-stage language already ignores our notion that a proper name, i t i t refers ar a l l , refers to the same entity whatever the time of i t s use, at the risk of being improper i f i t does not. The proper name 'Johnson', for instance, would usually be understood to refer to the same entity regardless of the time of i t s use. Yet Perry 41 finds this f i r s t violation of our semantic intuitions no cause for abandoning the language; the fact that the ambi-guity of proper names is systematic explains our intuitions. He writes (Perry, p.477); . . . the name is systematically and coherently used, i n such a way that we are easily misled into supposing that i t names a single entity. But then, i f the fact that our use of an ambiguous name is orderly explains why we think the name refers to a single entity when i t actually refers at different times to different entities, the same fact might also account for our belief that that entity must have events occur to i t in order that they be events in i t s future, when in reality a l l that i s needed is that events occur to a future entity having R to that f i r s t entity. Just as the method in our use of ambiguous proper names explains the one belief about them, so i t would explain the other. Hence, the second violation of our semantic intui-tions might be no more reason for rejecting the person-stage language than the f i r s t . What the above considerations suggest i s that our semantic intuitions might be misleading. And i f the person-stage language does imply exactly what we would want to say about our example, as Perry indicates, then that i s a l l the more evidence that our intuitions are plainly wrong. Fortu-nately for our intuitions the person-stage language is not adequate for describing our example or even for describing 42 ordinary cases, like Johnson's; i t s failure to incorporate our intuitions creates for i t severe and crippoing problems. The next section describes the nature of these d i f f i c u l t i e s . D. The seamy side of the  person-stage language The d i f f i c u l t i e s inherent in the person-stage language surface in every one of i t s three components. Somw of the dif-f i c u l t i e s might be just hurdles that an elaborate version of that language would have to clear. Others, however, cons-titute serious faults which, I contend, warrant rejection of the language as i t stands. A d i f f i c u l t y of the f i r s t kind arises in the person-stage language's theory of persons as a direct result of the hypothesis that each person-stage forms a person. As I have said already, that hypothesis is extremely counterintuitive. Persons are iusually thought to be continuant entities, things that endure through time, and not more or less momentary ob-jects like person-stages, which last but for an instant or not much longer. That hypothesis, however, solves one of the branch language "s problems t i t gives the correct count for the number of persons alive at a definite instant, at least accor-ding to the theory of counting persons at a time which Perry adheres to. But in solving that problem i t creates anotheri how to count the number of persons existing not at a given instant of time but over a period of time. Suppose we con-43 sider the person-stages of Jones, BJ, and SJ, that i s , a l l the personsstages in our story, and also the period of time stretching from just before the birth of Jones to right after the deaths of SJ and BJ. How many persons lived during that time? To answer we need a theory of how to count persons over a stretch of time. Though the person-stage language offers no such theory, we can s t i l l experiment and apply what might be called the 'obvious' theory, that the number of persons existing over a certain span of time, given that a per son i s just a person-stage, i s the number of person-stages occurring during the period. But clearly, that theory gives a wrong answer; a myriad of persons did not live during that span of time. Of course the fact that the "obvious" theory of coun-ting i s inadequate is no reason to discard the hypothesis that each person-stage constitutes a person; but i t does point out the d i f f i c u l t y to be surmounted. The branch language's hypo-thesis gives rise to no such problem, at least for the span of time specified above; the number of people involved i n the story, again according to the "obvious" theory of counting persons over a period of time, i s two, which, i f anything, is a plausible answer. A different problem, a serious one this time, crops up in the theory of naming. That theory i s also very coun-terintuitive. Normally, proper names are not understood to 44 name different objects, depending on the time of their use, in the manner of definite descriptions. The particular way in which the person-stage language shifts the reference of proper names leads to dire consequences, which emerge most strikingly in that language's truth-conditions, or rather truth-values, for sentences of the form 'N has F at t'. Here is an example. Suppose, as before, that SJ is transported to room 102 right after the operation. Then after SJ has died i t is s t i l l true that he was in room 102 after the operation. That i s , the sentence 14) SJ was in room 102 after the operation does not become false because SJ has died. The event of his death would not alter or eradicate the fact that Jones was at that place at that time in his lifetime, just as even though Napoleon is long dead, i t is s t i l l true now that he was v i s i t -ing at Waterloo in 1815-Yet the person-stage language implies that sentence 14 is false i f spoken after SJ's death. Since no temporal adverb precedes the sentence, 'SJ' names only the person-stages that occur at the time the sentence is pronounced and have R to stage s j , the stage picked out at baptiam. But of the stages that have R to stage s j , none occurs at the time of utterance, since, as we would say, SJ is dead at that time. The name 'SJ*, then, f a i l s to refer and sentence 14 is false. For the same reasons, any sentence of the form 'SJ has F at t' 45 spoken after SJ's death is false; s t i l l more generally, so are a l l sentences of the form 'N has F at V voiced after N's death. Some of these sentences, though, we would say are true, sentence 14, for instance. Therefore the person-stage language i s not the language we use to describe our example; i t is not the English language. The foregoing argument constitutes solid evidence, I believe, for discarding the person-stage language. The argument does not even depend on any special feature of Perry's example; the same point could be made using ordinary persons in ordinary situations. The sentence Johnson was in room 90 at some point in his l i f e , for instance, i s false i f i t spoken after Johnson's death, for the same reason that 14 is false. Thus not only does the per-son-stage language f a i l to account for Perry's example; i t f a i l s to describe correctly ordinary situations. Nevertheless we should not infer that the person-stage language's concept of a person i s not ours because the language i s not English. It may be possible to concoct a version of the language which would retain the same concept of a person but present a different theory of naming and differ-ent truth-conditions, together with a suitable theory of coun-ting, a revised version which would meet the objections lev-eled against i t s parent. It is thus paramount that another 46 language be found that lacks the defects of the person-language and that supports the theory of personal identity Perry endorses. Such a language, Perry believes, is the lifetime language, his f i n a l attempt at constructing an adequate theory of how English operates. To that language we now turn. CHAPTER IV THE LIFETIME LANGUAGE "Thus the suggestion that persons are lifetimes (or at any rate entities correlated one-to-one with lifetimes) proves satisfactory," concludes Perry near the end of his ex-position of the lifetime language (Perry, p.485). According-ly, the last in Perry's t r i o of languages merits special attention; in i t we should find the resolution of the pro-blems besetting i t s predecessors. But whether or not the lifetime language overcomes the d i f f i c u l t i e s encountered by the branch and the person-stage languages, i t i s certainly as complicated as either, i f not more so; hence i t w i l l be wise to approach i t piece by piece, beginning with i t s theory of persons and ending with i t s theory of person counting. A. The lifetime language's  theory of persons In the lifetime language a person i s a lifetime. To every lifetime corresponds a person. Perry defines a l i f e -time as follows* a set of person-stages constitutes a lifetime i f and only i f there is in the set a person-stage having the relation R to a l l the members of the set and only to the mem-bers of the set. In our story three lifetimes can be discerned. One is 48 the set consisting of a l l the person-stages in the story, what Perry cal l s the "Y-shaped structure," composed of the branches assigned to 'SJ' and 'BJ* by the branch language. That set is a lifetime because i t contains an element—in fact, i t contains many, since any stage j , occurring before the oper-ation, can act as such an element—that has R to a l l the mem-bers of the set and to no other person-stage. The other two lifetimes are formed by the two bran-ches, respectively. The branch assigned to 'SJ* by the branch language i s a lifetime, since a l l i t s elements have R to stage s j , a post-operative stage of SJ, and no other person-stage in the story has R to i t . Likewise, the branch assigned to •BJ* by the branch language also composes a lifetime. In general, any branch i s a lifetime, but not vice-versa. It appears contradictory for Perry to suppose that persons are lifetimes after he has rejected the branch lan-guage. He explains (Perry, p.481)i At f i r s t sight the suggestion that persons are l i f e -times seems quite unpromising, leaving the mentalist worse off than the hypothesis that persons are branches. For the pre-operative stages of Jones belong to three lifetimes* the Y-shaped structure and each of i t s bran-ches. If i t was implausible to suppose that Jones was two persons a l l along, surely i t is more implausible by at least a half to suppose that he was three. Not only that? to Perry's explanation, we might add that the branch language at least made SJ and BJ one person each after the operation, supposing Perry's theory of counting to be 49 correct. The hypothesis that persons are lifetimes, on the other hand, seemingly implies that SJ and BJ each are two persons after the operation, since what we would c a l l their stages belong to two lifetimes. Jones, then, would be three persons before the operation, and each of BJ and SJ would be two persons each after the operation. This situation is clearly unsatisfactory, and Perry r e c t i f i e s i t by introdu-cing a principle which, in effect, excludes certain lifetimes when the theory of counting is applied. More about this principle in the section on the theory of person counting. B. The lifetime language's  theory of naming The lifetime language's theory of naming revolves upon the notion of determinability of a lifetime by a per-son-stage. A given person-stage determines a certain l i f e -time i f and only i f the lifetime contains just these person-stages that have R to the given person-stage, that i s , i f and only i f i t contains a l l the person-stages that have R to i the given person-stage, and only those person-stages. Any Here I have amended Perry's staged definition of determinability in order that i t conform with the use he makes of i t . On at least two occasions his definition omits the 'only i f * clause included in mine. On p.481 he writes, "But notice that each person-stage does identify a unique lifetime—the lifetime containing a l l person-stages that have R to i t , " and then, "Let us say that a person-stage deter-mines the lifetime i t identifies in the way just described— 50 stage j , then, which occurs before the operation, determines the Y-shaped lifetime, because that lifetime contains exact-ly those stages that have R to j i but such a stage j deter-mines neither branch, since none contains a l l the stages having R to j . Likewise any stage sj (or bj), which occurs after the operation, determines the branch iti belongs to but determines neither the other branch nor the Y-shaped l i f e -time, since they contain stages not R-related to stage sj (or bj). Furthermore, since every person-stage exists at a very definite time, a lifetime can be said to be determina-ble at a certain time according as i t i s determined by some person-stage occurring at that time. In that sense the Y-shaped lifetime i s determinable before the operation but not after, since any stage j determines i t , but no stage sj or bj does. On the other hand the two branches are not deter-minable before the operation because no stage j determines themj but after the operation the two branches are deter-minable, since any stage sj w i l l determine one and any stage the lifetime containing a l l person-stages with R to i t . " But clearly the 'only i f clause is necessary i f each person-stage is to identify a unique lifetime and i f , as an example of the use Perry makes of the notion,"The Y-shaped lifetime . . . i s not determinable after the operation"(p.481). Otherwise stage s j , for instance, which occurs after the oper-ation, determines both the branch containing i t and the Y-shaped lifetime, since both these lifetimes contain the per-son-stages that have R to stage s j . 51 bj the other. In brief the Y-shaped lifetime i s determin-able only before the operation, the two branches only after the operation. Now for the theory of naming proper7. Like i t s pre-decessors the lifetime language presupposes that persons are assigned names by the picking out of a person-stage at bap-tism. Where u is the stage singled out for assigning name N, the primary referent of N i s defined as the lifetime determined by u. Accordingly the primary referent of 'Jones* i s the Y-shaped lifetime, that of 'SJ' the branch containing stage s j , and that of 'BJ' the branch containing stage b j . As far as I can judge, primary referents play no role in the lifetime language. Their purpose i n l i f e i s merely to be compared to secondary referents, which w i l l be defined momentarily. It is not at a l l d i f f i c u l t to see why primary referents could hardly function within the lifetime language. If statements of the form 'N i s the same person as M' are to be analyzed in terms of s t r i c t identity between the ref-erents of the proper names *N* and *M*, and Jones, SJ, and BJ are a l l the same person before the operation, the ref-> erents of their names must be identical before the operation. But the primary referents of 'Jones', 'BJ', and 'SJ' are a l l different before the operation* therefore the primary ref-erents cannot be the referents of those names. And, indeed, 52 as we w i l l see below, the referents of proper names in sen-tences are their secondary referents. At a given time t, the secondary referent of a proper name N, assigned by isolating some stage u, i s defined as the lifetime determinable at t which contains u — f o r short, the lifetime identified at t by u. If there is no such l i f e -time, N has no secondary referent at t and hence i s improper at that time. Consequently the secondary referent of 'Jones* before the operation is the Y-shaped lifetime, since i t i s the only lifetime determinable before the operation and i t includes stage j . That i s , 'Jones''s secondary referent before the operation i s just i t s primary referent. After the operation, however, 'Jones' has no secondary referent, because there are two lifetimes then determinable which contain stage j . In like manner the secondary referent of 'BJ' and *SJ' before the operation i s the Y-shaped lifetime, since i t is the only lifetime determinable before the operation and i t contains stages sj and bj.. Their secondary referent before the oper-ation, then, i s not their primary referent. The situation is reversed after the operation? there, 'SJ' and 'BJ' regain their primary referents. In the lifetime language, then, proper names are sys-tematically ambiguous, as in the person-stage language. At different times of their use they refer to defferent enti-53 ties. That ambiguity, I s t i l l maintain, is necessary i f the sentences expressing the relationships among SJ, BJ, and Jones before and after the operation are to have their ex-pected truth-value and i f personal identity i s to be analyzed in terms of s t r i c t identity between the referents of the prop-er names occurring in the sentences. Moreover, proper names, i f they refer a t , a l l at a given time, refer only to lifetimes determinable at that time. This fact w i l l be of paramount importance in the evaluation of the lifetime language. C. The lifetime language's  truth-conditions The truth-conditions for sentences in the lifetime language display a refreshing simplicity reminiscent of the branch language. A sentence of the form N has F at t spoken at time t' is true in the lifetime language just in case the secondary referent of N at t' contains a person-stage which occurs at t and has property F. Otherwise, as when N has no secondary referent at t', the sentence is f a l -se. A sentence of the kind N is identicalitdsM v[ voiced at t' i s true i f and only i f the secondary referent of 'N' at t' and the secondary referent of 'M' at t* are identical. If either name i s improper at that time the sen-tence i s false. 54 Temporal adverbs i n i n i t i a l position play the same role as in the person-stage language. They guide the ref-erence of proper names occurring i n the sentence, and they f i x the time at which the sentence within the scope of the adverb is to be evaluated. Thus a sentence of type At V , N has F at t or of the kind At t', N i s identical to M is true i f and only i f the sentence following the adverb i s true i f spoken at time t'. We may note, f i r s t , that the truth-conditions make no mention of primary referents. Only secondary referents, which may vary from before the operation to after the oper-ation, are used to evaluate a statement's truth-value. It is i n this sense that primary referents play no role in the lifetime language. More importantly, the lifetime language meets Perry's objection to the person-stage language. A person has a prop-erty F at time t just in case his lifetime, and not someone else's, has at t a person-stage with property F. In addition the lifetime language, like i t s forerunner, describes correct-ly the relationships holding among SJ, BJ, and Jones, both before and after the operation. To the sentences 1) SJ i s the same person as J 2) BJ is the same person as J 3) SJ i s not the same person as BJ 55 and their adverbial counterparts the lifetime language assigns the truth-values we expect them to have. Sentences 1 and 2 are true and 3^false i f spoken before the operation, •Jones*, *BJ*, and 'SJ' a l l referring to the same entity, the Y-shaped lifetime. Voiced after the operation the sentences reverse truth-values, the proper names a l l then referring to different entities, or, in the case of 'Jones', not referring at a l l . Furthermore, again as in the person-stage language, the name 'Jones' refers before the operation but not after. So the sentence 9) Jones w i l l be in room 102 after the operation, for instance, and i t s parallel 9') Jones w i l l be in room 104 after the operation are both true provided they are spoken before the operation, when 'Jones* refers to the Y-shaped lifetime. However, the adverbial counterparts of these sentences, 10) After the operation Jones i s in room 102 and 12) After the operation Jones is in room 104, are both false, because 'Jones' f a i l s to refer after the operation. Bearing a l l the virtues yet lacking what he considered the unique vice of the person-stage language, the lifetime language appears to Perry "a satisfactory refuge for the mentalist." The one shortcoming Perry might acknowledge, 56 the ambiguity of proper names, he could easily account for by pointing out that the ambiguity arises only when division of persons takes place. In normal cases, that of Johnson's, say, where no branches overlap, the secondary referent of a proper name reduces to i t s primary referent and hence is the same whenever the secondary referent exists. Nevertheless I believe Perry was too quick to accept the lifetime language as definitive. Whatever qualities i t may possess, being a haven for the mentalist i s not one of them. The lifetime language suffers from the same problem as i t s precursor* should i t prove correct, the mentalist would be proven wrong. How this happens i s explained i n the next section. D. The lifetime language  and the mentalist Perry's chief objective i s to construct a language that w i l l exonerate a theory of personal identity seemingly plagued by contradiction. His f i n a l attempt, the lifetime language, i s internally consistent, as far as I can judge* no contradiction can be derived from i t . Nonetheless i t cannot serve to defend the theory of personal identity Perry supports, because the two are incompatible. If the lifetime language is correct and our concept of a person i s that of a lifetime, then the theory of personal identity i s false, the facts of our example being what they are. 57 The theory of personal identity in question can be stated ast For any person-stages x and y, x and y are R-related i f and only i f there is a person to which x and y belong. This universally quantified biconditional can be broken up into a conjunction of two distinct statements, A) i f a person contains stages x and y, then x and y are R-related and B) i f x and y are R-related, then some person contains x and y. It is statement A that clashes with the hypothesis that per-sons are lifetimes. For suppose that lifetimes are indeed persons. Then the Y-shaped structure, which is a lifetime, constitutes a person. That person contains stage s j , which is an a r b i t r a r i l y chosen stage of Smith-Jones after the oper-ation, and i t also contains stage bj, an arb i t r a r i l y chosen of Brown-Jones from after the operation. Yet stages sjrand bj are not R-related. Hence statement A i s false, and so i s the theory of personal identity, given that the Y-shaped L& structure i s a person? i t is not the case that any Itwo stages; of a person are R-related. If persons are lifetimes, the R-relation cannot be a necessary condition for person-stages x and y to be part of a single person. 58 The above argument affects only the capacity of the lifetime language to support Perry's theory of personal identity; i t says nothing about whether the language is correct or not. Should the language be right, though, the theory of personal identity would be wrong. Fortunately for the mentalist the lifetime language f a i l s to represent English in one important respect. Where i t f a l l s short is explained in the next section. E. The shortcomings of  the lifetime language What, we may ask, is the secondary referent of 'SJ' after SJ has died? The secondary referent of a proper name at a given time i s the lifetime determinable at that time which contains the stage singled out when the name was assigned. The secondary referent of 'SJ* after SJ's death, then, i s the lifetime determinable after SJ's death which contains stage s j . But the only lifetime determinable after SJ's death, i f BJ is s t i l l alive, is BJ's branch; and i t does not include stage s j . Hence *SJ' has no secondary ref-erent after SJ's death (though, of course, i t s t i l l has i t s primary referent). The lack of a secondary referent for 'SJ' after SJ has died creates some problems for the lifetime language. We know, for instance, that SJ was i n room 102 after the operation. Obviously, the fact that he was in room 102 at 59 that time s t i l l holds after his death. The event of SJ's death does not alter his history up to the time of his death. In other words the sentence 14) SJ was in room 102 after the operation i s true even after SJ's death. Yet the lifetime language deems that sentence false i f i t i s spoken after SJ's death, since 'SJ' does not refer then. The lifetime language does not assign to sentence lk the truth-value we expect i t to have. That discrepancy may be thought to be insignificant. After a l l , SJ i s special. He, like BJ, i s the product of personal division. Hence: to express in the lifetime lan-guage what lk means, we should use the adverbial counterpart of 14, 14') After the operation, SJ was i n room 102. That sentence i s true, both i n English and i n the lifetime lanfuage, and so there is no problem. But no, the problem remains, even though i t i s true that 14* has i n the lifetime language the same truth-value as 14 i n English. The failure of the lifetime language to give 14 i t s correct truth-value in no way depends on SJ's unusual status. The theory of naming causes an identical problem for ordinary cases as well. Taking another look at Johnson's situation, for instance, Johnson who indeed was in room 80 before being moved to room 90, we find that the sen-60 tence Johnson was in room 80 before being moved to room 90 is false after Johnson's death because no lifetime deter-minable then (we may suppose that there are some) con-tains any of Johnson's stages, and hence his name f a i l s to refer after his death. Moreover, nothing in the above argument turns on the properties chosen in the examples; we may say, in general, that N has F at t is false after N's death whether or not N i n fact has F at t. The lifetime language, therefore, f a i l s to account corrctly not only for how we wish to describe Perry's exam-ple but also for how we speak about ordinary instances, and hence ought to be rejected. This result should please the mentalist. If the lifetime language is indeed incorrect, as I have claimed above, then his theory of personal identity stands a chance of survival, since i t is not necessarily false i f the langua-ge i s . Again, as for the branch and person-stages languages, i t should be stressed that the fact that the lifetime lan-guage i s incorrect does not necessarily mean that i t s con-cept of a person i s at fault. Perhaps i t s theory of naming is wrong, or i t s truth-conditions, and not the concept that 61 persons are lifetimes. One facet of the lifetime language remains to be explored, i t s theory of person counting. This we do in the next two sections. F. The lifetime language's theory  of person counting Perry presents the lifetime language's theory of person counting by way of a sample question. He asks, "How many persons were there in Jones' room (room 100) before the operation?" (Perry, p. 484). His answer i s quite compressed, considering the complexity of the theory i t illustrates. Here is his response i n i t s f u l l short length (Perry, pp. 484 -5 )« On the one hand, "one" seems to be the correct answer; for there was only a single person, Jones, i n the room. On the other hand, Smith-Jones and Brown-Jones were both there; so "two" seems like the correct answer. But, after a l l , three lifetimes (the Smith-Jones branch, the Brown-Jones branch, and the Y-shaped structure) contain the person-stage i n room 100; so the answer would appear to be "three." A l l three answers are correct—but they are answers to different, and distinguishable, questions. Consider open sentences of the form x has F at t A person satisfies such an open sentence at a time, z satisfies the given open sentence at time t', i f and only i f z i s identifiable at t* and contains a person-stage that occurs at t and has F. The open sentence x is in room 100 before the operation is satisfied by exactly one person before the operation; so the answer to the question, "How many persons are in room 100?" asked before the operation (and to the ques-tion, "Before the operation, how many persons were in room 100?" asked at any time) i s "one." After the oper-ation, two distinct persons satisfy the open sentence; 62 so the answer to the question asked at that time (and to the question, "After the operation, how many persons were in room 100 before the operation?" asked at any time) i s "two." There i s no one time at which the correct answer to the question, "How many persons were i n room 100 before the operation?" is "three." But the lifetime lan-guage w i l l have to allow us to make assertions such as At some time, Brown-Jones was in room 100 before the operation, which w i l l be true just i n case there is some time t such that At t, Brown-Jones was i n room 100 before the operation, is true. The open sentence At some time, x was in room 100 before the operation, w i l l be satisfied by person z i f and only z is i d e n t i f i -able at some time and contains a person-stage occurring before the operation in room 100. This open sentence i s satisfied by three persons, and so the answer to "At any time, how many persons were in room 100 before the oper-ation?" is "three." The f i r s t thing to note about the theory is that the answer i t gives to Perry's i n i t i a l question, *How many per-sons were there in room 100 before the operation?', varies with time. When the question is asked before the operation, i t s answer is 'one'. But i f the question is asked after the operation, as Perry says, then the answer i s 'two*. In other werds, before the operation the number of persons in room 100 i s onei but right after the operation the number of persons there were in room 100 before the operation changes to two. Correspondingly, the answer to the question 'Before the operation, how many persons were in room 100?' is 'one*, whatever the time at which the question is posedi but the an-swer to 'After the operation, how many persons were in room 63 100 before the operation?*, regardless of when the question is asked, is 'two'. This variation i n the number of persons in room 100 before the operation is easily explained. Applied to the case at hand, the theory of counting implies that, at a given time, the number of persons there are or were in room 100 before the operation is just the number of lifetimes identifiable at the given time which have a stage in room 100 before the operation. Though Perry nowhere states what he means by a lifetime's being identifiable at a time, i t is f a i r to suppose that i t s definition can be obtained from that of a lifetime's being identified at a time by a person-stage, in much the same way that Perry, by existentially quantifying over person-stages, derives from the* notion of a lifetime's being determined at a time by a person-stage the notion of the determinability of a lifetime at a given time. On that supposition, then, and since a lifetime z i s iden-t i f i e d at time t by a person-stage u just i n case the l i f e -time z is the unique lifetime determinable at t which con-tains u, we obtain that a lifetime z i s identifiable at time t i f and only i f there exists a person-stage u such that z is the unique lifetime determinable at t which contains u, that i s , i f and only i f for some person-stage u, z i s deter-minable at t and contains u and i s the only such lifetime. Which lifetimes are identifiable when? Prom the 64 definition of i d e n t i f i a b i l i t y we can conclude straightaway that a lifetime is identifiable at a certain time only i f i t is determinable at that time. Hence the Y-shaped structure is not identifiable after the operation and the two branches are not identifiable before the operation. However, before the operation, the Y-shaped structure i s identifiable, since i t i s determinable at that time and there are stages which i t is the only such lifetime to contain, namely, any stage in the story. Likewise the BJ branch is identifiable after the operation, there being stages, stage bj, for instance, which the branch i s the only lifetime to contain while being determinable at that time. The same applies to the SJ branch. We find, then, that as far as our example goes, the lifetimes identifiable at a given time are just those l i f e -times determinable at that time. At a given time, therefore, the number of persons there were or are in room 100 before the operation is just the number of lifetimes determinable at the given time which have a stage in room 100 before the operation. A l l three lifetimes in our story have a person-stage in room 100 before the operation. /However, only one of these is determinable before the operation? hence, before the operation the number of persons who are in room 100 is one. After the operation, two lifetimes are determinable? hence, after the operation, the number of persons there were in room 100 before the 65 operation is two. The fact, then, that a lifetime must be determinable at a given time in order to be counted explains why the count varies from before the operation to after. In i t s f u l l generality, for any (basic) property F, the theory of person counting is as follows. At any given time t' the number of persons there are or were with a prop-erty F at time t is just the number of persons identifiable at t* which have or had a person-stage at t with property F. This theory of counting seems to have evolved in the following way. First Perry presupposes that C) at time t', a lifetime z has property F at time t i f and only i f at t', the sentence 'x has F at t' is satisfied by zt that i s , at t' a lifetime z has property F at time t just in case, intuitively speaking, the sentence 'xhas F at t' i s true when x is the lifetime z. Though i t is not explicit in Perry's exposition, that presupposition is nonetheless required for the reconstruction of the theory. For, from C, Perry reasons that the number of persons that, at V , had property F at time t is just the number of lifetimes identifiable at t' which contain a person-stage at t with property F. In other words, i t follows from C, Perry would say, that to ask at t*, 'How many persons were there with property F at time t?", is tantamount to asking, 'How many lifetimes satisfy, at:t', the open sentence 'x has F at t'?' 66 Next, Perry defines ' s a t i s f i a b i l i t y ' i D) a lifetime z satisfies at time t* the open sentence *x has F at t* i f and only i f z i s identifiable at t* and contains a person-stage that occurs at t and has F. Linking C and D gives E) at time t', a lifetime z has property F at time t i f and only i f z is identifiable at t* and contains a person-stage that occurs at t and has F. From E, using the same reasoning as for C, Perry concludes that the number, at t*, of persons with property F at time t is just the number of lifetimes identifiable at t* which contain a person-stage at t with property F. That theory of counting, I believe, is unsound.Why i t is so is explained in the next section. G. Criticism of the lifetime language  theory of person counting The flaw inherent in the lifetime language's theory of person counting i s akin to that in i t s truth-conditions. Suppose that, after the deaths of SJ and BJ, we ask the same question Perry asked in his exposition of the theory of countingi'How many persons were there in room 100 before the operation?' Its answer is just the number of lifetimes identifiable after SJ and BJ have died which have a person-67 stage in room 100 before the operation. However, no l i f e -time i s determinable after the deaths of BJ and SJ and hence none is identifiable. Consequently, after SJ and BJ have died, the number of persons there were in room 100 before the operation, according to the theory of counting, is zero. Quite clearly, that answer is wrong. The fact that the answer to that question varies from 'one' before the operation to 'two' after the operation i s odd enough in i t -self. If indeed there was only one person in room 100 prior to the operation, how could that number change after the oper-ation? How could events which occur during of after the oper-ation alter the count of persons in room 100 before the oper-ation? Even the division of the person in room 100 should not affect that count, no more than would his death. But i f the variation in the count from one before the operation to two right after the operation i s queer and objectionable, the further change to zero after the deaths of SJ and BJ i s intolerable. (Here, to simplify the dis>-cussion, I assume that SJ and BJ die at the same time.) Imagine again the case of Johnson, a normal human being, who, say, was alone in room 80 prior to being moved to room 90. The number of persons in his room, then, just before his being moved, is one. After his death, this number does not change? forever after Johnson has died, most of us would agree, i t i s s t i l l the case that there was only one person 68 in his room just prior to his being moved to room 90. Yet the lifetime language theory of counting implies that after Johnson's death, no one was in his room prior to his being moved to another room, there being after his death no one identifiable with a person-stage in room 80 just before the move. The theory, then, f a i l s to account even for ordinary cases of counting, l e t alone those involving the supposed division of a person, and so should be abandoned. Perhaps much of the intuitive appeal of the theory of counting l i e s i n the coincidence that there i s a ques-tion for which the answers the theory gives to Perry's question are correct. If we ask soon after the operation, •How many persons now alive were in room 100 before the oper-ation?', the answer is indeed 'two'. Both SJ and BJ are alive right after the operation and both were i n room 100 before the operation. Nevertheless the fact remains that there was only one person i n room 100 before the operation, since SJ and BJ were one and the same at that time. If after SJ and BJ have died we ask again, 'How many persons now alive were in room 100 before the operation?', the answer is obviously 'none*, neither SJ nor BJ being alive then. But again i t remains true that there was only one person in room 100 before the operation. There is yet a third question which the previous two must not be confused with, especially the f i r s t one. The 69 question i s , 'How many persons have been in room 100 before the operation?' In order to distinguish i t from the f i r s t question, 'How many persons were there in room 100 before the operation?', this third question might be paraphrased as, 'Of how many people is i t true to say that they were i n room 100 before the operation?' The answer, i f the question is posed after the operation, is 'two', since both SJ and BJ were in room 100 before the operation and they are now (after the operation) distinct. It is in this sense, and only in this sense, that i t is true to say that two people were in room 100 before the operation—that i s , that, after the oper-ation, even after the deaths of SJ and BJ, i t is true of two people that they were in room 100 before the operation. This does not mean or imply, however, that there were two persons in room 100 before the operation. The third question, 'How many persons have been in room 100 before the operation', must also be differentiated from the second question, 'How many persons now alive were in room 100 before the operation?' The difference manifests i t s e l f when the questions are asked after the deaths of SJ and:BJ. The answer to the second question i s obviously 'none', since both SJ and BJ have died, whereas the answer to the third i s s t i l l 'two', since i t is s t i l l true of two per-sons that they were in. room 100 before the operation. More w i l l be said about these questions and their 70 answers in Chapter VI. H. Chapter summary The lifetime language i s Perry's f i n a l attempt at constructing a theory that would exculpate the theory of personal identity he espouses. This last language shares many features with i t s predecessor. Its proper names are systematically ambiguous, referring at different times to different entities? temporal adverbs play the same role as in the person-stage language? statements of personal iden-t i t y , as i n the person-stage language, are analyzed in terms of s t r i c t identity between the referents of proper names oc-curring in the statement, making personal identity tran-siti v e , reflexive, and symmetric? and, i n fact, the lifetime language assigns to a l l the sentences we have considered so far the same truth-value as does the person-stage language, describing correctly the relationship holding among Jones, BJ, and SJ before the operation and after. Furthermore, the lifetime language, in an important respect, i s a refinement over i t s predecessor. It meets the single objection which had led Perry to reject the person-stage language. A sentence of the kind 'N w i l l have F at t' is true at t' just in case i t i s the referent of N at t' which has property F at time t, and not merely some other entity which is R-related to the referent, as in the person-stage language. And accordingly. Perry declares the l i f e -71 time language satisfactory. But Perry's hope i n the lifetime language is mis-placed; for as well as possessing many of the advantages of the person-stage language, the lifetime language suffers suffers from i t s two worst defects. First, the lifetime language, like the person-stage language, i s inconsistent with the theory of personal identity Perry defends, given the facts about Perry's example. Hence i f either of the two languages is correct, the theory of personal identity i s incorrect. Second, as in the person-stage language, any sentence of the type 'N has Fiat t' is false after N ceases (or has yet) to exist, and therefore neither language can account for the truth-value of certain very ordinary state-ments about ordinary persons. Moreover, the theory of per-son counting associated with the lifetime language i s i t s e l f unsound. The lifetime language, then, neither defends Perry's theory of personal identity nor explains how a supposed case of personal division can be described consistently in the same terms as those used to make statements about ordinary persons. A language which accomplishes both these aims has yet to be found. This chapter ends the discussion of Perry's solution to the problem. In the next chapter David Lewis' contri-bution w i l l be reviewed. 72 CHAPTER V DAVID LEWIS AND THE FISSION OF PERSONS In a l l the languages he developed i n order to protect a certain theory of personal identity , Perry adhered to the view that personal identity statements are to be analyzed in terms of s t r i c t identity between persons. Thus sentences of the form N is the same person as M, spoken at some time t, are true just in case the referent of N and that of M are s t r i c t l y identical at time t, the refer-ents of N and M being a lifetime, a person-stage, or a branch, depending on what the specific language assumes a person to consist of. Yet, the theory of personal identity the langua-ges are meant to defend states, not under what conditions persons are the same, but under what conditions person-stages belong to a single person; moreover, the theory is couched not in terms of the s t r i c t identity of person-stages but in terms of a weaker relation, the R-relation, holding between person-stages. There i s , then, a discrepancy i n character between the languages* truth-conditions for personal iden-t i t y statements, on the one hand, and the theory of personal 73 identity the languages were created to defend, on the other. Since a l l three languages, by way of their concept of a per-son, are meant to contain the theory of personal identity, they can be seen as attempts on Perry's part to show there is no conflict between the theory of personal identity he endorses and the view that statements of personal identity are to be analyzed in terms of s t r i c t identity between per-sons . In "Survival and Identity" David Lewis pursues very nearly the same goali to bring together the theory of per-sonal identity in question and the view that personal iden-t i t y is a matter of s t r i c t identity between persons. I say "very nearly" the same goal, because Lewis* and Perry's approaches differ in minor though noteworthy respects. First, what Perry and I, following him, have called the "theory of personal identity" appears under a different guise in Lewis, as the thesis that the R-relation is the I-relation. This relation Lewis defines as "the relation that holds among the stages of a single continuant" (Lewis, p. 21). In logical notation the definition can be stated as (x) (y) ( I x y t r d f ^ z(Pz & x«z & yez)) where, as before, 'x' and *y* range over person-stages, 'z' ranges over sets of person-stages, and 'P* i s the predicate * is a person*. Using the usual criterion for the individua-tion of relations, that of coextensiveness in a l l possible 74 cases, we can express as (x)(y)(Rxy*»Ixy) the thesis that the I-relation is just the R-relation, which, as we can see from the definition of the I-relation, is equivalent to (x)(y)(Rxy*»3z(Pz & xez & yez)). But the above quantified biconditional is merely a state-ment of Perry's theory of personal identity (cf. pp. 13-14 above). To say that the I-relation is the R-relation, therefore, is just to assert that the theory of personal identity Perry espouses is true. Second, Lewis, like Perry, is committed to the view that s t r i c t identity i s a correct analysis of personal iden-t i t y . But unlike Perry, he provides no theory of naming or truth-conditions for statements of certain kinds, but only a theory of what a person consists of and also a theory of counting. In the following sections, what these theories are and how they apply to the division of persons w i l l be explained. A. Lewis' concept of  a person Lewis advances the following hypothesis (Lewis, p.22)i . . . something is a continuant person i f and only i f i t is a maximal R^-iriterrelated aggregate of person-stages. That is i i f and only i f i t is an aggregate of person-stages, each of which is R-related to a l l the rest (and to i t s e l f ) , and i t is a proper part of no other such aggregate. 75 Since a branch is nothing but a maximal R-interrelated set of person-stages, Lewis' definition of a person i s the same, or almost the same, as the one Perry had proposed in the branch language. The difference between the two l i e s in the fact that Lewis' definition is more general than Perry's. Whereas Perry stipulates, at least i n i t i a l l y , that a person is a set of person-stages, Lewis leaves i t open what kind of aggregate a person consists of (see Lewis, p. 39, n. 4). In order to make the two definitions the same, I w i l l take Lewis' persons to consist also of sets of person-stages. We can say, then, that, for Lewis, persons are bran-ches. Accordingly the person-stages in Perry's story form two branches, which Lewis designates 'CI' and *C2'. These two branches correspond to Perry's SJ and BJ branches. Which of CI and C2 corresponds to SJ and which to BJ is arbitrary, since Lewis gives us no means of distinguishing between the two branvhes. Is the branch hypothesis of a person adequate? The branch language is the f i r s t language Perry developed, and i t is also the f i r s t one he rejected. He discarded i t for two related reasonsJ the branch hypothesis implied, in his judgment, that Jones, the person undergoing the operation, was two persons before the operation, when, obviously, he was only one person* and the branch language entailed that no one in the story was named 'Jones', when, again, someone 76 was. Lewis has rejoinders to both these objections, in the form of a theory of counting. That theory i s explained in the next section. B. Lewis' theory of  person counting When Perry concluded that the branch hypothesis of a person implied that two persons existed before the operation, he reasoned as follows. Even though only one stage exists at any one instant before the operation, any such stage be-longs equally to two branches; hence two persons are alive at any time before the operation. In other words, Perry used the following theory of counting; given that a person is a branch, the number of persons existing at a time equals the number of branches with a stage at that time. That theory of counting, in conjunction with the branch hypothesis, led to a count of persons before the operation which clashes with what we might c a l l the "accepted" count of one. Lewis agrees; the count of the number of persons alive before the operation is one. He writes (Lewis, p.26)i The count of stages is the count we accept; yet we think we are counting persons, and we think of persons as con-tinuants rather than stages. How, then, can we tolerate overlap? For instance, we say that in a case of fission one person becomes two. By describing fission as i n i t i a l stage sharing we provide for the two, but not for the one. There are two all.„along. It is a l l very well to say from an eternal or postfission standpoint that two persons (with a common i n i t i a l segment) are involved, but we also demand to say that on the day before the fission only one person entered the duplication center; 77 that his mother did not bear twins; that until he f i s -sions he should only have one vote; and so on. Counting at a time, we insist on counting a person who w i l l f i s -sion as one. We insist on a method of counting persons that agrees with the result of counting stages, though we do not think that counting persons just is counting (simultaneous) stages. The dilemma Lewis poses i s an intriguing one. We want to count the number of persons existing at a given time, having assumed that persons are branches. If, per-sons being branches, we add up the number of branches with a stage at the given time, as Perry does, we obtain what we re-gard to be a wrong answer. On the other hand, i f we count the number of stages at the time, we get the right count, though i t appears we have not counted what we intended to count in the f i r s t place, namely, persons. Lewis' solution to this dilemma is to deny that we must count by identity, that i s , that we must count as one person alive at time t any continuant which has a stage at time t and is not identical to any other such continuant. Instead we might count by a weaker relation which Lewis dubs "tensed identity" and defines as follows* continuants C3 and Ck are identical-at-time-t i f and only i f G3 and C4 both have stages at time t and a l l and only stages of C3 at t are stages of C4 at t. To put the definition more simply, continuants C3 and C4 are identical-at-time-t just in ease they completely over-78 lap during that time. Despite i t s name suggesting the con-trary, tensed identity is not the relation of identity, sin-ce i t may hold between continuants which are not identical. Lewis proposes that continuants be counted not by identity but by identity-at-a-time. On that proposal, a l l continuants sharing the same stages at time t count as one person alive at time t. It i s easy to see that that theory of counting gives the right count. The number of persons alive after the operation is two, since two continuants have stages at that time, and they do not share stages then. Before the operation, however, the number of persons alive is one, because the two branches that have stages occurring before the operation share their stages then and hence count only as one. Lewis' theory of person counting, then, removes one of the objections that led Perry to reject the branch hypothesis. Next we examine the second of those objections. C. Naming in Lewis' discussion of fission The second reason why Perry abandons the branch language is that i t implies that no one in the story i s named 'Jones', since the stage singled out in assigning the name belongs to more than one branch. Once again, then, i t is the overlapping of the two branches which causes problems, as i t did in attempts to count the number of persons alive before the operation. 79 How does Lewis handle this second dif f i c u l t y ? Though, as we mentioned earlier in the chapter, Lewis offers no theo-ry of naming, as Perry had in each of his three languages, the few remarks he makes on the matter suggest he finds no serious problem with the name 'Jones'. Both branches in the story would bear the name, and hence 'Jones' would be ambi^ guous anytime i t i s used. But at least someone in the story would be named 'Jones'i before the operation, only one person exists in the story (this we know from the theory of counting), and he i s named 'Jones't after the operation two persons are alive, and both bear the name. .As solution to Perry's naming problem, then, Lewis could invoke the fact that before the operation, only one person exists, and therefore that that person can be baptized, even though the stage that would be singled out in baptism belongs to two continuants. That i s , Lewis could say that, in order to name a person, i t i s not requisite that the stage isolated belong to only one branchj what is necessary i s that the stage isolated belong to only one person existing at that that time, the time the ceremony is performed. And that this condition is met in Perry's story is insured by Lewis' theory of counting, which implies that only one person exists before: the operation. This relaxed view, however, of what is necessary for baptism to function leaves us with the ambiguity of 'Jones', 80 there being over the period of time the story takes place two persons bearing that name. This ambiguity, Lewis be- . : lieves, would be harmless in sentences that hark back to prior to the operation, since such sentences would be true on both disambiguations of 'Jones', or false on both. Sen-tences that refer to after the operation, though, like pre-dictions made before the operation, would be problematict no doubt Lewis would deem such a sentence false (or perhaps just without truth-value), be i t true on either disambigua-tion of the name or false on either. In connection with the topic of naming i t i s worth remarking that Lewis uses 'CI' and 'C2* not only to desig-nate what i n our discussion of Perry was called the SJ and the BJ branches but also to name the two persons correspon-ding to the two branches. For instance, he says, ''How many persons entered the duplication centre yesterday? We may reply» CI entered and C2 entered . . . " (Lewis, p. 2 7 ) . 'CI' and 'C2', then, also serve as proper names, no less than 'Smith-Jones' and 'Brown-Jones' in Perry. This fact is hardly surprising, of course) I point i t out only because I w i l l use 'CI' and 'C2' as names in a later section. D. An evaluation of Lewis' theory of counting As far as I can judge, Lewis' theory of counting is adequate. Unlike the theory Perry presented in relation to 81 the lifetime language, Lewis' theory has no d i f f i c u l t y clear-ing the f i r s t hurdle, namely, to account for normal cases, those in which no continuants overlap. But then, neither has i t s r i v a l , the counting-by-identity theory, according to which the number of persons alive at a time equals the num-ber of continuants with a stage or with stages at that time. It too gives the accepted count for normal cases. Such cases, therefore, do not constitute a basis for choosing be-tween the two theories, since they support each theory equally. The second hurdle consists of fission cases, and Lewis' theory seems to be the sole competitor to progress beyond i t . It alone implies that there is only one person alive before the operation and two after; the counting-by-identity theory entails that there were two persons a l l along, contrary to our intuitions. Fission cases, then, provide evidence in favor of Lewis' theory but against the counting-by-identity theory. But adequate as i t may be, Lewis' theory of person counting nonetheless harbours an oddity which must be ex-posed. In the passage quoted earlier (p. 76-77 above), Lewis stresses how the method of counting we are seeking must agree with the result of counting person-stages, while at the same time be a method of counting persons, since we 82 believe we are counting persons, not person-stages. The theory he proposes appears at f i r s t blush to meet this re-quirement. To count the persons alive at a certain time we count the continuants having stages at that time, but with the proviso that continuants which overlap during that time are counted as one person instead of two. Persons being continuants, i t certainly looks as though we are coun-ting persons. The very phrase 'counting continuants by tensed identity* suggests we are indeed counting continuants, though in some strange but legitimate manner. It may well be that, i n some weak sense of the word 'counting', we are counting continuants when we count them by tensed identity. S t r i c t l y speaking, however, we are not* we are counting groups or classes of continuants. To put the point technically, we are counting equivalence classes formed by the relation of tensed identity holding among con-tinuants. Relations of tensed identity, as Lewis himself points out (Lewis, p. 28), are equivalence relations, being reflexive, transitive, and symmetric. Such a relation has the property of dividing into distinct groups, called 'equi-valence classes', the objects among which i t holds. In the case of a relation of tensed identity each equivalemce class contains just those continuants that are identical.^at-that-time. The relation of being identical-before-the-operation, for instance, groups into equivalence classes a l l those con-83 tinuants that are identical-before-the-operation. Each group of continuants which overlap before the operation forms a single equivalence; class. In Perry's story CI and C2 are identical-before-the-operation, and no other conti-nuant bears that relation to them; hence they form an equi-valence class under that relation, in effect the only equi-valence class, since there are no other continuants i n the story. On the other hand, under the relation of being identical-after-the-operation, CI and C2 each forms an equivalence slass on their own, since the relation f a i l s to hold between them. The decision to count as one person continuants that are identical-at-a-time, when counting the number of persons alive at that time, is tantamount to counting the equivalence classes formed by that relation, because each equivalence class contains just those continuants-that are identical-at-that-time. It follows, therefore, that to count continuants according to tensed identity is not to count continuants. Rather i t is to count equivalence classes formed by that relation. The point can be expressed succintly as followst when one counts two (or more) continuants as one person, one is not counting continuants any more; one i s counting groups of continuants, even though the groups themselves consist of continuants, perhaps even single continuants, and the rela-84 tion that generates the groups i s a relation holding among continuants. Since, according to Lewis* concept of a person, a group of continuants does not constitute a person, at least not when i t contains two or more continuants, i t is s t i l l a f a i r question to ask how i t is that a count of groups of continuants could possibly give us an accurate count of the number of persons existing at a time. Until that question is answered, Lewis' method of counting persons is as ad hoc as that of counting stages. Lewis, then, as far as I can see, has not resolved the dilemma he himself set. E. A criticism of Lewis' analysis  of personal identity As I mentioned in the introduction to this chapter, Lewis wishes to analyze personal identity i n terms of s t r i c t identity. One answer to the question of what matters in survival, he asserts, i s "a compelling commonsense answer, an unhelpful platitude that cannot credibly be deniedt what matters i s identity between myself, existing now, and myself, s t i l l existing in the future"(Lewis, p. 18). This answer holds not only for questions of survivals i t applies as well to questions of personal identity, even the problem casest "At the same time we can consistently agree with common sense (and I think we should) that what matters i n questions of personal identity—even in the problem cases— i s 85 identity" (Lewis, p. 19). Furthermore, by 'identity' Lewis means s t r i c t iden-t i t y , as he stresses in the following passagei"But this verbal manoeuver jcalling the R-relation ' identity Qwould not meet the need on those who think, as I do, that what matters in survival i s l i t e r a l l y identity* that relation that everything bears to i t s e l f and to no other thing" (Lewis, p. 20). And in matters of personal identity the relation of identity must hold among continuants, not among person-stagesi"He who says that what matters in survival i s identity, on the other hand, must be speaking of identity among temporally extended continuant persons with stages at various times" (Lewis, p.20). "Likewise for other questions of personal identity," he adds later on (Lewis, p. 21). No mistake i s to me made, then* Lewis analyzes questions of personal identity in terms of the s t r i c t identity of con-tinuants. Whether CI and C2 are the same person before the operation i s such a question, and hence, according to Lewis, CI and C2 are the same person before the operation j u s t in case CI and C2 are s t r i c t l y identical then. Clearly they are not s t r i c t l y identical, either before the operation or at any other time. Therefore CI and C2 are not the same person before the operation. This consequence of Lewis'analysis of personal 86 identity is contrary to our intuitions about Perry's story. It seems that, before the operation, CI and C2 are the same person. Perry, for one, would reject this analysis right then and there, as he did the branch language, because i t f a i l s to imply that CI and C2 are the same person before the operation. His f i n a l language, the lifetime language, did imply that CI and C2 (actually, Smith-Jones and Brown-Jones) were the same person before the operation, and he considers that language satisfactory. But furthermore, the result that CI and C2 are not the same person before the operation creates a severe ten-sion, i f not an inconsistency, between Lewis' analysis of personal identity and his method of counting. That method, we have already seen, implies that only one person existed before the operation, but two after. CI and C2 being the only two persons alive during that entire timespan, that i s , alive both before the operation and after, i t must be they who are one before the operation and two after. Very reasonably, then, we can suppose that the theory of counting also entails that CI and C2 are one person before the oper-ation and two after the operation. Here I am assuming that to say that CI and C2 are one person before the operation is to say just thatt that, before the operation, CI and C2 count as a single person. Thus we arrive at the following awkward situation. 87 Lewis* method of counting implies that CI and C2 are one person before the operation; yet his analysis of personal identity entails that CI and C2 are not the same person before the operation. Before the operation, then, CI and C2 are one person but not the same person. This statement is not a l i t e r a l contradiction. None-theless i t sounds extremely odd. But though the source of that statement's oddity is hard to pinpoint, i t is not at a l l d i f f i c u l t to see how Lewis placed minself in this pre-dicament. The relation he proposes to count persons by and the relation he uses to determine personal identity are not the same relation. Two (or more) persons count as one at a certain time just in case they are identical-at-that-time, whereas two (or more) persons are the same person at that time just in case they are identical. Since continuants that are identical are also identical-at-all-times, i t never happens, for example, that CI and C2 are the same per-son at some time but not one person at that time. However, the reverse does not hold. Continuants that are identical-at-some-time may not be identical, that i s , identical-at-all-times j and hence i t may happen, as in the case of CI and C2 before the operation, that persons that are one at some time are not the same person at that time. This conflict between Lewis' method of person coun-ting and his analysis of personal identity, i f indeed i t is 88 a conflict, can be resolved in either of two ways* by altering the theory of counting, or by changing the analy-sis of personal identity. The method of counting, as I have maintained earlier, needs no adjustment, insofar as i t implies exactly what we wish to say about the number of per-sons in Perry's story. Therefore the analysis of personal identity must be to blame for any conflict. That analysis, I conclude, is unsatisfactory on two countst i t clashes with our intuition that CI and C2 are the same before the operation; and i t is at odds with Lewis' theory of coun-ting, a theory which i s satisfactory to the extent that i t predicts just what we would expect. F. Chapter summary In his discussion of the division of persons David Lewis pursues the same goal as Perry« to reconcile the view that person-stages belong to a single person just in case they are R-related and the view that persons are the same just in case they are identical. Like Perry, then, Lewis believes that personal identity is a matter of the s t r i c t identity of persons. To effect the reconciliation, he assumes, as Perry had in the branch language, that persons are branches. The f i r s t problem Perry encountered, the apparent crowding in Jones' room before the operation, Lewis overcomes by proposing to count persons according to 89 tensed identity rather than according to identity. On that proposal only one person exists before the operation. Hence the population problem is solved. The second problem Perry faced, the failure of Jones to be baptized 'Jones', can also be surmounted by appealing to the theory of coun-ting, provided the conditions necessary for baptism to function are relaxed. If, instead of requiring that the stage singled out during baptism belong to only one conti-nuant, we demand that only one person be baptized, that i s , that, at the time the ceremony takes place, only one person exist which i s being baptized , and that i t include the stage singled out, then someone in the story w i l l indeed be named 'Jones'. In fact, there w i l l be one such person before the operation, but two after, with the consequence that 'Jones' w i l l be ambiguous. Those solutions to Perry's branch language problems are, I believe, satisfactory. Lewis' analysis of personal identity in terms of s t r i c t identity, however, is not ac-ceptable, because i t conflicts with our belief that CI and C2 are the same person before the operation and is at vari-ance with Lewis' own method of person counting. As was the case for a l l of Perry's languages, though, the fact that the st r i c t identity analysis of personal identity is incorrect does not mean that the concept of a person to which the ana-ly s i s is applied is i t s e l f at fault. The analysis i t s e l f may be defective. 90 CHAPTER VI THE B LANGUAGE Perry's and Lewis' attempts at describing coherently the supposed instance of personal division taking place in Perry's story are not entirely successful. Though every se^ mantic theory they present captures some of the story's features, no one theory by i t s e l f implies everything we would like to say about that example. A theory that im-proves substantially upon Perry's and Lewis' efforts can be developed, I believe, and the present chapter is devoted to describing such a theory. In order to distinguish i t from i t s two ancestors, Perry's branch language and Lewis' own theory, the present language w i l l be called the "B language," where 'B' i s meant to suggest 'branch'. The following sections describe i t s various elements, starting as usual with the language's concept of a person. A. Persons in the  B language The B language concept of a person is the same as the one in the branch language or in Lewis' theory: persons 91 are branches. As before, then, the person-stages in Perry'i story form two branches, with the stages occurring before the operation belonging to both branches alike. As we proved in Chapter II, the hypothesis that persons are branches logically implies the theory of per-sonal identity that Perry defends, namely, that person-stages x;;and y are R-related just in case some person con-tains both x and y. Or, to put i t in Lewis' terms, the hypothesis that persons are branches entails without fur-ther ado that the I-relation i s the R-relation. No need, therefore, to examine various d i f f i c u l t cases of personhood: i f persons are branches, the I-relation holds just when the R-relation does. B. The B language's theory  of person counting The basic method of person counting in the B lan-guage is as follows. The number of persons there are during a certain period of time es equal to the number of branches formed by the person-stages occurring only during the period. According to the present theory, then, i t is not necessary to consider a l l the person-stages occurring in, say, Perry's story, in order to determine the number of persons there are during a given time period. Rather, only those person-stages which occur during the given time internal need be taken into account. 92 For example, suppose we ask how many persons there are after the operation. Since the only stages that occur then are the post-operative stages of SJ and of BJ, we find, considering these stages in isolation from the rest, that they form two branches, that i s , two maximal R-inter-related setsj one consists of a l l of BJ's post-operative stages, and the other of a l l of SJ's post-operative stages. The number of persons there are after the operation, then, is two. Before the operation, however, only one person exists, since the stages that occur then, which are the pre-operative stages of Jones, by themselves form a single branch. Likewise, the number of persons existing over the entire period of time the story takes place is two, since a l l the person-stages occurring in the story form two bran-ches. This basic method of person counting applies to instants as well as to intervals of time. The person popu-lation at a given instant is just the number of branches formed by the person-stages occurring only at that instant. So, for instance, the number of persons alive at an instant shortly after the operation i s two, since each of the two person-stages occurring then i s R-related to i t s e l f but not R-related to the other stage and hence forms a maximal R-in-terrelated set by i t s e l f . On the other hand the number of 93 of persons there are at an instant soon before the opera-tion is one, since only one stage exists at any such ins-tant, and i t forms a branch on i t s own, being R-related to i t s e l f . In general, then, for either a given interval of time or instant of time, the number of persons there are at that time i s equal to the number of branches formed by the stages occurring only during or at that time. In the case of a period of time, i t should be added, the phrase 'the number of persons there are during a given time period' is open to another interpretation. It could mean the number of persons alive at every instant of that period, in contrast to existing at some instant or other during the period. When the phrase i s so construed, a con-dition must be attached to our present theory, stipulating that the branches formed by the stages occurring only du-ring the period in question have a stage at every instant of the period. The number of people there are during a given period of time, therefore, where this is interpreted to mean the number of persons existing during the entire period, i s just the number of branches which are formed by the stages occurring only during that period and which have stages at every instant of that period. The distinction made here between persons that exist at some instant or other during a given time period and persons existing during the entire period is not peculiar to the B language's 94 theory of counting? the same distinction must be made for any theory. The B language's theory of counting appears to be successful. It accords with What we regard to be the accep-ted count of persons at various times during Perry's story. Moreover, i t displays an elegance absent im. Lewis' theory. Persons are branches, and to count persons, according to the present theory, we simply count branches. Yet, despite i t s success and elegance, the theory i s suspect. We do not seem to be counting the right kind of branches. When we assumed persons to be branches, we t a c i t l y assumed that the branches which compose persons are the largest such bran-ches possible} that i s , that the time span considered i s long enough to include a l l the possible stages a person might have. And hence i t does not seem right to be coun-ting branches that occur within a limited time span. Those limited branches, we might say, are not persons; they are merely parts of persons. S t i l l , whether or not the method of counting is philosophically satisfying, i t s success at giving the right count begs for explanation. This problem w i l l occupy us in a later section. For now, we turn to the theory of naming. C. The B language's theory  of naming Like Perry's three languages the B language's theory 95 of naming presupposes that a name can be assigned to a per* son by the picking out of a stage during some baptism cere-mony. Let u be the stage singled out? then, provided the stage u belongs to exactly one person at the time of bap-tism, the name N names, not just the branch, but every branch of which u is a stage. If u f a i l s to belong to a single person at the time of baptism, then baptism does not take place; the name 'N'names no one. Whether u does belong to exactly one person or not is decided by the lan-guage's method of person counting. Applying the theory of naming to Perry's story, we obtain the following results. First we should note that, according to the theory of person counting, the person-stages j , bj, and s j , which are the stages isolated i n assigning the names 'Jones', 'BJ', and 'SJ', respectively, each belong to only one person at the time the names are assigned, since each such stage by i t s e l f forms a branch at that time. So there i s no possibility of the naming procedure's f a i l i n g . Then, we find that the branch with a person-stage in room 102 after the operation i s called 'SJ* and that that with a person-stage in room 104 after the operation is named 'BJ', as in the branch language. But furthermore, each branch i s also called 'Jones', in con-trast to the branch language, where neither branch bears that name. 96 In the B language, therefore, someone in the story is named 'Jones*. In fact, over the time span the story un-folds, there are two such persons. Before the operation, only one person exists, and he bears the name 'Jones*, as well as 'BJ' and 'SJ's after the operation, two persons exist, of whom one is named 'BJ', the other 'SJ', and both of whom are called 'Jones'. D. The B language's truth-conditions  for statements of the form  'N has F at t' Before tackling the B language's truth-conditions for sentences of the kind 'N has F at t', i t w i l l be ins-tructive to re-examine those of the branch language and ask whether they could not be transferred without alteration to the B language. Doing so w i l l help to explain why the B language's truth-conditions must differ from those of the branch language. Where N is a proper personal name, F a basic prop-erty, and t a time, a sentence of type ,'N has F at t* is true in the branch language just in case the branch referred to by N contains a person-stage at t with F. If the branch contains no such person-stage or i f the name N f a i l s to refer, the sentence i s false. Under those truth-conditions sentences containing the names 'SJ' and *BJ* w i l l have the truth-values we expect. For instance the sentences 97 15) SJ is in room 100 before the operation 16) BJ i s in room 100 before the operation are true, as are 1?) SJ is i n room 102 after the operation 18) BJ i s in room 104 after the operation? but sentences 19) SJ i s in room 104 after the operation 20) BJ is in room 102 after the operation are false, again as we would expect. However, any sentence containing the name 'Jones' is false under those truth-conditions, because two branches bear the name and hence the name f a i l s to refer. So, where-as in the branch language 'Jones' f a i l s to refer because no branch bears the name, here 'Jones' would f a i l to refer because more than one branch bears the name. In either case the result i s the samei sentences in which 'Jones' occurs are false. This result i s problematic. The fact is that we do use the name 'Jones' in sentences, and these sentences are not always false. Perry, for one, uses the name when he relates the story: i t is Jones who enters hospital, i t is Jones whose brain i s triplicated, i t i s Jones whose heart is f a i l i n g , etc. So i t seems that in at least some ins-tances the name 'Jones' i s not ambiguous and does refer, and hence the truth-conditions of the branch language need 98 to be modified. But in what way should they be changed? It is quite clear that the name is not ambiguous when i t occurs in present-tense sentences spoken before the operation, as in, say, 'Jones is now in room 100'. At that time Jones i s , obviously, one person. On the other hand, though i t may hot be as clear, i t i s also true, I believe, that in most contexts the name is ambiguous when i t occurs in pre-sent-tense sentences voiced after operation. Thus 'Jones is presently in room 102' i s ambiguous after the operation, I hold, because Jones has divided by then, and, as the theory of naming and the theory of counting support, there are in existence after the operation two persons named •Jones'. The same applies to the sentence 'Jones w i l l be in room 102 after the operation', say? even though i t may be uttered before the operation, when only one Jones exists, the sentence i s nevertheless false (or without truth-vlaue), since Jones w i l l have divided by the time mentioned in the sentence. These observations, i f such they are, can be incor-porated within the B language by modifying the branch lan-guage's truth-conditions as follows* a sentence of the form 'N has F at t' is true just in case a l l the branches of name N are identical-at-time-t and have a person-stage with F at t. 99 Otherwise the sentence is false. In case only one branch bears a given name N, the condition that a l l the branches of name N be identical-at-time-t is automatically satisfied, since every branch is identical-at-any-time with i t s e l f . This condition insures that a name like 'Jones', which names more than one branch, w i l l refer just in case a l l the branches form a single person at the time referred to by the sentence containing such a name. It does not insure that the name w i l l refer when only one person named 'Jones' exists at the time referred to by the sentence, even though i t may be the case that only one person named'Jones' exists when that name does refer. Imagine, for example, that BJ outlives SJ by a substantial number of years. Then only one person would be named 'Jones' after SJ had died. None-theless a sentence like 'Jones is now in room 110*, spoken long after has died, would be deemed false by the B language even i f BJ were indeed in room 110 at the given time. Here are a few illustrations. Our perennial exam-ple, 'Jones i s in room 100 before the operation*, i s true, since the two branches named 'Jones' overlap before the operation and have at that time a stage in room 100. The same goes for 'Jones entered hospital before the operation'. However, 'Jones is in room 102 after the operation' is f a l -se, since the two branches of name 'Jones' do not overlap at that timej similarly for 'Jones w i l l be in room 102 after 100 the operation'. The B language's truth-conditions, then, seem to work properly. E. The B language's truth-conditions  for statements of the form  'N is the same person as M at time t' The analysis of personal identity statements pre-sented in this section differs from that of Perry and Lewis. Rather than being analyzed in terms of s t r i c t iden-t i t y , statements of personal identity in the B language are analyzed in terms of identity-at-a-time, that i s , i n terms of tensed identity. Persons are the same at a given time (either an instant or an internal) just in case they are identical-at-that-time, that i s , just in case their bran-ches completely overlap whenever they occur during the given time. Thus BJ and SJ are the same person before the operation, since their branches overlap at any time they have stages before the operation. For just the opposite reason, SJ and BJ are not the same person after the oper-ation, nor during their entire lifetime. Likewise Jones, before he undergoes the operation, is the same person as BJ and as SJ, since what we would c a l l his person-stages at that time are just those of BJ and SJ before the operation. After the operation, however, two Jones exist, and hence any reference to Jones i s ambi-guous. 101 The truth-conditions which entail the results des-cribed above are the following. A statement of the kind N i s the same person as M at time t is true just in case a l l branches of name N and a l l bran-ches of name M are identical-at-time-t. In other words, the statement i s true just in case the stages which occur during time t and belong to a given branch bearing either name M or name N are identical to the stages which occur during time t and belong to any other such branch. Other-wise, the sentence i s false. The reason why the truth-conditions demand that a l l branches bearing name N and a l l branches bearing name M be identical-at-time-t, rather than merely the branch named N and the branch named M, is to acconodate sentences contain-ing a name l i k e 3 'Jones', which names more than one branch. As in the truth-conditions for sentences of the kind 'N has P at t', we want 'Jones' to refer just i n case the sentence containing i t refers to a time when the two branches with that name form a single person. Requiring that the two branches bearing that name be identical-at-the-time insures that the name w i l l refer only when a l l these branches form a single person. This claim w i l l be justifi e d in a later section. Under the B language's truth-conditions, the senten-ces 102 1•) Before the operation, SJ is the same person as J 2') Before the operation, BJ is the same person as J 3**) Before the operation, SJ i s the same person as BJ are a l l true, as we would like them to be. On the other hand, the sentences 1'•) After the operation, SJ is the same person as J 2'•) After the operation, BJ i s the same person as J 3*'') After the operation, SJ is the same person as BJ are a l l false. Sentences 1*' and 2*' are false because •Jones' f a i l s to refer after the operation, the two bran-ches bearing that name not being identical-after-the-oper-ationj and 3'' is false because the SJ branch and the BJ branch are not identical-after-the-operation. The B lan-guage, then, correctly describes the relationships among SJ, BJ, and Jones. Furthermore, proper names in the B language are not ambiguous i n the undesirable way they were in the lifetime language. In that language, the sentence 'SJ i s now the same person as BJ' i s true before the operation and false 103 after, because 'SJ* and 'BJ' change referents with the cour-se of time. Before the operation they both refer to the Y-shaped lifetime; after the operation they refer to their respective branches. This shift is extremely counterintui-tive, I believe. In the B language, that same sentence, 'SJ is now the same person as BJ', is both true before the operation and false after the operation without the refer-ent of 'SJ', or that of 'BJ*, shifting from one time to the other. The names keep the same referents whenever they occur. And, in general i n the B language, a name that has a referent keeps that referent for a l l times, as we would expect. In a way this holds even for 'Jones', for, to put the point paradoxically, i t has no referent even when i t does refer. That i s , even in the cases where we would say that 'Jones' does indeed refer, say, for example, in the sentence 'Jones is in room 100 before the operation*, where •Jones' refers to the one person existing before the opera-tion, the B language assigns no referent to the name; i t merely provides truth-conditions that allow a sentence con-taining the name to be given a truth-value. The lack of a referent for 'Jones* when the name occurs in a true sentence is not eminently satisfactory, of course; but supplying •Jones' with a referent—the set of stages occurring before the operation is a prime candidate—would substantially complicate the B language. In any event, the fact remains 104 that unproblematic cames like *BJ' and 'SJ° retain the same referent whenever they are used, while the sentences con-taining them are assigned the truthr-values we expect them to have. This i s more than can be said about the lifetime language, not to mention i t s various other shortcomings. The B language, then, though not ideal, is a vast improve-ment over the lifetime language. As for Lewis' theory, no comparison can be made between i t and the B language in this respect, since Lewis offers no formal theory concern-ing names. We might also note that temporal adverbs do not play in the B language the dual role they f u l f i l l e d in the lifetime language. They serve only one function* to indi-cate at which time the subject or subjects have a given property. Hence their position in the sentence is quite irrelevant . Sentences 1' to 3*'' could just as well have been written with the temporal adverbs at the end of the sentence, rather than at the beginning. F. Tensed identity and i t s relation  to s t r i c t identity The B language has now been presented in f u l l . S t i l l , much needs to be said about the theory. We have seen in the previous section, for instance, that tensed identity is the better relation for analyzing statements of personal identity. But why should that relation work? 105 What interpretation of i t w i l l account for i t s success? The idea behind analyzing personal identity state-ments in terms of tensed identity is in reality quite straightforward. When we ask whether SJ and BJ are the same person before the operation, for example, we are asking by the same token whether SJ and BJ, at that time in their l i f e , are the same person. Consequently, in order to answer that question and establish whether, at that time, SJ and BJ are the same person, we need only examine them at that point in their lifetime, that i s , examine their person-stages at that time, and see i f the person-stages are iden-t i c a l . No need, therefore, for a l l of SJ's stages and a l l of BJ's stages to be identical, which is what the s t r i c t identity analysis of personal identity requires, in order for SJ and BJ to be the same person before the operation. An analogy might help to c l a r i f y the point. No one would insist that a l l of SJ's stages be in room 100 in order for i t to be true that SJ i s in room 100 before the operation. It need only be the case that SJ be there at the time in question—that i s , that his person-stage at that time be in room 100. Similarly, in order for SJ to be the same person as BJ ats.a given time, i t is not necessary for a l l of SJ's stages to be identical to a l l of BJ's , as the identity analysis requires. It need only be the case that his person-stages at that time be identical to those of BJ 106 at that time, that i s , that SJ and BJ be identical-at-that-time. And this is just what the tensed identity analysis demands. Yet, despite i t s requirement that only some of a person's stages be compared, the tensed identity analysis attributes to personal identity the same important logical characteristics that a s t r i c t identity analysis would* ten-sed identity, like s t r i c t identity, i s an equivalence rela-tion, and hence the relation of personal identity, under either analysis, i s transitive, symmetric, and reflexive. For the remainder of this section the implications of the two analyses w i l l be compared for a variety of situ-ations. We w i l l find that they do not always conflict. In fact, more often than not, the two analyses give the same results. In normal situations, for instance, when no bran-ches overlap, the two analyses agree* i f a sentence of the kind 'N i s the same person as M at time t' i s true accor-ding to one analysis, i t is true according to the other. For, i f no branches overlap, no stages are shared among branches, and hence any stage u singled out for assigning a given name belongs to only one branch. The names N and M, therefore, name a single branch i f they name at a l l . Now, the sentence 'N and M are the same person at time t' is true according to one analysis just in case N and M are identical-at^time-ts according to the other, the sentence 107 is true just in case N and M are s t r i c t l y identical. But since there is no overlap among branches, branches are identical-at-a-given-time only i f they are s t r i c t l y iden-ticals and moreover, branches which are identical are iden-tical-at-any-time. Consequently, N and M are identical-at-a-given-time just in case they are identical, and the sen-tence 'N and M are the same person at t' is true according to the tensed identity analysis when and only when i t is true according to the s t r i c t identity analysis. Normal cases, then, are always instances of the two analyses' agreeing. Normal cases are not the only situations in which the two analyses accord. The problem cases also provide instances of agreement, though they do not always do so, obviouslys for i f they did, there would be no practical difference between the two theories. Suppose, for example, that long after their demise, we ask, 'Were SJ and BJ the same person?' The correct an-swer would be 'No, they were not', I believe. Some things are true of the one person which are not true of the other. SJ was in room 102 after the operation, for instance, while BJ was not. So SJ and BJ were not the same person. This reasoning suggests that a correct analysis of the sentence 'SJ is the same person as BJ' should be one in terms of s t r i c t identity, that SJ and BJ are the same person just in 108 case they are s t r i c t l y identical. That analysis is ade-quate, I believe, since i t implies the answer we obtained above. But i t i s adequate only i f the ' i s ' in the senten-ce ' SJ is the same person as BJ' is interpreted as a tense-less ' i s ' . A s t r i c t identity analysis of statements of personal identity would not be adequate4-this i s one of the central contentions of this t h e s i s — i f the sentence i s taken to mean ' SJ and BJ are now the same person'. Sentence 3*» however, 3*) SJ i s the same person as BJ, could be analyzed in terms of tensed identity just as well. To say tenselessly that SJ i s the same person as BJ is to say that they are the same person at any time; and hence, according to the B language, 3* i s true just in case SJ and BJ are identical-at-all-times. More generally, taking into account the possibility of names like 'Jones' occurring, we can say that a sentence of the form N is (tenselessly) the same person as M is true just in case a l l branches bearing name N and a l l branches bearing name M are identical-at-all-times. Apply-ing this analysis to the SJ and BJ example, we again obtain that SJ and BJ are not the same person, as we obtained with the s t r i c t identity analysis. Why the two analyses should work equally well is not d i f f i c u l t to see. Both imply that the statement 'BJ is 109 (tenselessly) the same person as SJ* is true just in case the stages of BJ are identical to a l l those of SJ, or, more generally, a l l the stages of branch N are just those of branch M. Such statements, then, are instances where the tensed identity analysis reduces to the s t r i c t identity analysis. So for such statements, the two analyses w i l l always agree, not only in problem cases, like the example above, but in normal cases as well. Thus far, we have seen that the two analyses always agree for sentences of the type *N is (tenselessly) the same person as M', whether the statements are made about problem cases or not, and that the two analyses also always agree for sentences of the kind *N i s the same person as M at a given time t' when the statements are made about normal cases. Therefore the only cases l e f t to consider, which must be the ones for which the two analyses may differ, are problem cases about which statements of the kind ' N is the same person as M at a given time t* are made. The great majority of the statements we have made about Perry's story are of this kind. About these cases we can say only what holds of a l l cases in general, namely, that a statement which is true under the s t r i c t identity analysis w i l l also be true under the tensed identity analysis. If ' N and M are the same per-son at time t* i s true under the s t r i c t identity analysis, 110 theniN and M refer to only one branch eaeh, and N and M are identical. Clearly, N and M are thus identical-at-any-time and hence the sentence i s true under the tensed identity analysis as well. However, i f N and M are identical-at-some-time-t and the case we are dealing with i s a problem case, i t need not be true that a l l branches named 'N' and a l l branches named 'M' are identical. Hence i f 'N is the same person as Mat a given time V is true under the tensed identity ana-l y s i s , i t may not be true under the s t r i c t identity analysis. The two analyses, therefore, w i l l differ only as regards statements of the kind *N is the same person as M at a given time t' made about problem cases; and when they do differ i n such cases, the statements are deemed true by the tensed identity analysis but false by the s t r i c t iden-t i t y analysis. In the case of Perry's story, for instance, the statement that could not be accounted for by the identi-ty analysis was 'SJ is the same person as BJ before the op-eration'. It considered that statement false, while the tensed identity analysis deems i t true. From this exhaustive comparison of the two analyses, an important conclusion can be drawn. Since the two anal-yses are in complete agreement over a l l cases except the problem ones about which statements of the form 'N and M are the same person at a given time' are made, i t follows I l l that only these cases can serve to separate the two anal-yses i f , as appears to be the case, both can adequately ac-count for the cases in which they do agree. Normal cases, then, those in which no overlap occurs among branches, do not enable us to choose one analysis over the other. G. Personal identity and person  counting in the B language Lewis' analysis of personal identity and his method of counting, i t w i l l be remembered from Chapter V, are not always in harmony. In certain situations a severe tension develops between the two. A case in point is the example of SJ and BJ before the operation. On the one hand the method of counting implies that SJ and BJ are one person before the operation, their branches being identical-at-that-time. On the other hand, the analysis of personal identity entails that SJ and BJ are not the same person before the operation, since their branches are not identi-cal. Taken together, then, Lewis* analysis of personal identity and his method of person counting imply that SJ and BJ are one but not the same person before the operation. This dislocation, I wish to say, is unnatural and unintui-tive. It seems that once a definition i s given of what a person i s , that i s , once a certain concept of a person is taken for granted, persons that are one should be the same, and vice-versa. 112 In the B language no such dislocation arises. Per-sons that are one at a given time are also the same at that time, provided the following definition is accepted of what i t is for two persons to count as one. Two persons count as one at a given time in the B language just in case one person has stages during the given time whenever the other does, and these stages form a branch within that period of time. Given this definition, i t can be shown that persons are the same at a given time when they are one at that time; at least, I can find no counterexample. The B language, then, i s free from yet another problem that plagued Lewis' treatment of Perry's story. Its analysis of personal iden-t i t y and i t s theory of counting are in perfect accord. H. The B language's theory of person  counting compared to Lewis'  method In a l l the situations we have examined so far, Lewis' method of person counting and the B language's theory have produced identical results. For both normal cases and Perry's story the two theories imply what we re-gard to be the correct count. Nonetheless these two ways of counting persons are not equivalent. Their count some-times desagree, as the next; example w i l l i l l u s t r a t e . Imagine a case of simple overlap, where two bran-ches exist at different times except for the part they 113 share. This kind of situation might well result from our man Johnson, a normal patient, age 30, now in room 80 but about to be moved to room 90, receiving a blow on the head, a blow severe enough to eradicate a l l memories he has of the f i r s t 25 years of his l i f e . Up until time b, then, the time of the incident, a l l of Johnson's stages are R-inter-related, just as they would be i f Johnson were not to re-ceive a blow. But since he does get h i t and the stages occurring after time b are not R-related to his early stages, the stages occurring up un t i l time b form a maxi-mal R-interrelated set, namely, a branch. Furthermore, the stages occurring after the i n c i -dent are R-related among themselves. But they are also R-related to a l l the stages occurring after time a, when Johnson is 25 years old. Hence a l l the stages occurring after time a form a second branch. In a l l , therefore, Johnson's stages ( i f we may c a l l him 'Johnson' even after he suffers the blow) form two branches, which overlap between time a and time b. Now, i t may not be obvious just what we would say about Johnson after he receives a blow as severe as the one described,whether he is the same person, for instance, and whether he i s s t i l l Johnson. But i t is quite clear, I believe, that, at least until he is injured by the blow, Johnson is a single person, since he i s , until that time, 114 exactly like any other normal person, and hence should count as only one person. Yet, not both of the theories under comparison give that result. The B language's theory of counting implies that only one person exists before time b, the time of the incident, since a l l the stages occurring before then form a single branch. Lewis' method, however, entails that there are two persons in existence before time b, because two con-tinuants, that i s , two branches, have stages at that time, and those stages are not identical; in other words, the two branches are not identical-before-time-b. Evidently, therefore, the B language's theory of person counting and Lewis' method are not equivalent. Also obviously, the case of simple overlap can serve as a counterexample to Lewis* method of person counting, since our intuitions about the case do not agree with the count given by the method. We would say that Johnson is a single person before the receives the blow, whereas the method implies that two persons existed before the incident occurred. In a way we can explain why Lewis' method f a i l s . It allows events which happen after a given period of time to influence the count of persons there are during the period, when i t should not. The fact that Johnson's character and memory are affected by the blow he receives should be i r r e -115 levant to how many persons there are before the incident. That much is clear. But what is not clear is whether the failure is due to what might be called the counting method proper, the idea that continuants ought be to counted accor-ding to the relation of tensed identity, or whether the method's failure i s due to what continuants are assumed to be:*.: namely, branches. In other words, the failure of Lewis' method in the present instance might be attributable to the branch concept of persons i t s e l f rather than to Lewis' way of counting these branches. The fact that the B language's theory of counting implies the correct count would be helpful i f i t were ob-vious that that theory i s also based on the branch concept of a person. We could then maintain that i t must be Lewis' method of counting per se which i s at fault, since there would then be other ways of counting, based on the same concept of a person, which would give the right count. Alas, i t is not at a l l certain, at least to my mind, that the B language's theory of counting is indeed based on exactly the same concept of a person as i s Lewis' method. This is yet another problem that must be settled. At least our example illustrates one nice feature of the B language's theory of person counting! The only stages that need to be considered are those that occur during the time for which we wish to know the? population. This proce-116 dure is very much in line with how we normally count persons. That i s , we do so without inquiring about people's pasts and futures. A l l we take note of are the persons as they are at the time the count i s being taken. Finally, we should ask, does the B language's theo-ry of person counting resolve Lewis' dilemma? The dilemma, i t w i l l remembered, was the following. To count the person population at a time, we can either count the number of per-son-stages at the time, or we can count the number of bran-ches there are with a stage at that time. These, i t seems, are the only two plausible choices. If we count the per-son-stages there are at the time in question, we get the correct count; however, i t appears that, by doing so, we have not counted what we set out to count, namely, persons, since we have not counted branches. On the other hand, i f we count the branches with a stage at the time in question, we are seemingly counting what we intend to count, namely, persons; the problem here is that the count so obtained is wrong. Lewis' solution to the dilemma is to count branches by tensed identity. That method gives the accepted count, at least for Perry's story; that i s , i t gives the count that would be obtained by counting stages. However, Lewis' solution is not really a solution, I believe; for to count continuants by tensed identity cannot correctly be said to 117 be a way of counting continuants. Rather i t is a method for counting groups of continuants. The B language also gives a count that matches the count of stages at the time. But does i t count persons? It does count branches, but not the same kind of branches as those Lewis envisaged. The branches counted by the B language are what we termed 'limited' branches, branches that can be formed within a limited period of time, whereas the branches Lewis had in mind are the largest possible branches, that i s , branches formedffrom a l l possible per-son-stages. In fact, i t is quite l i k e l y that, to the B language's proposal that persons be counted at a time by counting the (limited) branches during that time, Lewis would object that one is merely counting parts of persons, and not entire persons. He almost says just that when developing his definition of a person, in the following passage (Lewis, p. 22)t A continuant person is an aggregate of person-stages, each one I-related to a l l the rest (and to i t s e l f ) . For shorti a person is an I-interrelated aggregate. Moreover, a person i s not part of any larger I-interrelated aggregate? for i f we l e f t out any stages that were I-related to one another and to a l l the stages we included, then what we would have would not be a whole continuant person but only part of one. The argument Lewis gives in this passage is phrased in terms of the I-relationj but Lewis would make similar assertions in terms of the R-relation, since he believes that the 118 I-relation i s nothing but the R-relation. To Lewis* objection I have no solid reply. The fact that the B language's theory of counting is success-ful ,perhaps even more so than Lewis' own theory i f we take into account the case of simple overlap, is too striking to be a mere coincidence. But since I have no explanation for the theory's success, Lewis' dilemma s t i l l stands. I. Extending the B language's  theory of person counting The basic method of person counting presented in section B can be generalized to answer queries like Ques-tion 1, 'How many persons were there in room 100 before the operation?', which Perry used to present his own theory of counting. That i s , from counting the number of persons there are at a given instant the method can be extended to count only those persons with a certain basic property F. For example, given that the number of persons there were before the operation is just the number of branches that can be formed by the person-stages occurring only at that instant, the number of persons there were at that time who were also in room 100 is just the number of those branches that have a person-stage in room 100. Clearly, then, the answer to the question is 'one', since the only branch that can be formed at that instant also has a person-stage in room 100. Here i t is assumed that the adverb 'before the 119 operation' refers to a specific instant, as Perry had in his own exposition. Answers in terms of the theory of counting can also be given to Questions 2 and 3» which we claimed must be kept apart from Question 1. Question 2, 'How many persons now alive were in room 100 before the operation?', can be answered by extending the basic method of counting as f o l -lows. A person who is alive now and who was in room 100 before the operation clearly must be alive during (though not necessarily throughout) the period between now and be-fore the operation. Hence i t is f a i r to suppose that the number of persons now alive who were in room 100 before the operation i s equal to the number of persons there are during that interval who have a person-stage in room 100 before the operation and also a stage now. In terms of the method of counting extended to intervals of time, this number is just the number of branches that can be formed from person-stages occurring only during the interval and that have a stage now and one in room 100 before the operation. Now, suppose the question is asked before the operation but after the instant designated as the one when Jones is in room 100. Its answer, according to the theory above, is 'one', since only one branch can be formed from the person-stages occurring during that interval and i t has a stage in room 100 before the operation and one at the time 120 the question is asked. On the other hand, i f the question is asked after the operation but before the death of SJ and BJ, i t s answer i s 'two*, again according to the theory. However, i f the question is posed after SJ and BJ have died, i t s answer is 'zero*, since neither of the two branches existing in the interval has a stage occurring after SJ's and BJ's death. The answers the theory providesy; then, match what we believe to be the correct answer. It is very interesting, though, that the same theory breaks down when the temporal perspective i s reversed and a question like question 2 is asked before the operation about a time after the operation. Imagine, for instance, that BJ and SJ are brought to room 105 after the operation in order to be interviewed, and that before the operation, we ask, 'How many persons now alive w i l l be in room 105 after the operation?* The answer, according to the theory we just used, i s 'two', since two branches can be formed by a l l the person-stages occurring between the time the question i s asked and the time SJ and BJ are brought to room 105, and each branch has a stage at the time the ques-tion is asked and a stage in room 105 at the time of the interview. But 'two' cannot be the right answer, because there is only one person alive before the operation. Nor is 'one' the correct answer, I think? i t cannot properly be said, I believe, that Jones w i l l be in room 105 after the 121 operation. The point remains, though, that the theory of person counting as modified to answer Question 2 cannot be applied to questions such as the one introduced above. Question 3t 'How many persons have been to room 100 before the operation?', which might be paraphrased as, 'Of how many persons i s i t true to say that they were in room 100 before the operation?' can also be accomodated within the framework of the method of counting. Question 3 i s the same as Question 2, except that the requirement that the persons be alive now, i.e. alive at the time the question is asked, is removed. Accordingly, i t s answer in terms of the method of counting i s just the number of branches that are formed by person-stages occurring only between the time the question is asked and the time designated as being before the operation, and that have a person-stage i n room 100 at the time designated. Before the operation the answer to the question is 'one'; after the operation the answer is 'two', even after the death of SJ and BJ. So once again, the theory of counting accords with what we consider to be the facts about the example. J. Chapter summary and  conclusion The B language is a descendant of Perry's branch language and Lewis' own theory, in that i t too is founded on the branch concept of a person. Therefore, like i t s two 122 ancestors, the B language implies the theory of personal identity Perry and Lewis endorse, which, in Lewis' par-lance, is the thesis that the I-relation is the R-relation. The branch concept of a person, however, is the only element the B language shares with i t s two predecessors. The rest of i t s elements depart in some way or other from the corresponding elements in the branch language or in Lewis' theory, and more ofter than not, improve upon them. The B language's theory of counting, for instance, differs radically from i t s only plausible alternative, Lewis' method. And even though, surprisingly enough, this radical difference does not give rise to different counts, at least as far as Perry's story and normal cases are con-cerned, the B language can nevertheless boast of using only those stages which occur at or during the time for which the population is being counted, a procedure which mirrors the one actually followed when, say, we count the number of persons in a room. Moreover, the B language's theory of person counting seems to work for cases of simple overlap, where Lewis* method f a i l s . The next theory in the B language, the theory of naming, is also an improvement over i t s parent theory, the branch language's theory of naming (Lewis presents no such theory). The B language's theory implies that both SJ and BJ are named 'Jones' and hence that someone before the 123 operation is called by that name, whereas the branch lan-guage entails that no one existing either before or after the operation bears that name, contrary to our intuitions. Lewis, for his part, offers no formal theory of namingJ but, as we mentioned in Chapter V, evidence suggests he would agree f u l l y with the B language's theory. The B language's truth-conditions for sentences of the kind *N has F at t' are nothing more than a refinement of the branch language's truth-conditions. The revision allows a sentence containing the name 'Jones' to be true when the sentence refers to a time when the two Jones are a single person, which is any time before the operation. Though this is not reflected in the truth-conditions, •Jones' in effect refers to SJ and BJ's common segment. As a result the B language assigns to Jones, BJ, and SJ exact-ly the properties we would say they do have. The truth-conditions for statements of the form •N and M are the same person at time t', on the other hand, are morethan a mere elaboration of either Lewis' views or of the branch language's truth-conditions for such state-ments. They embody the view that statements of personal identity are to be analyzed in terms of tensed identity, rather than in terms of s t r i c t identity. The analysis in terms of tensed identity is the only one which i s accep-table; for, as we explained at length in section F, the 124 two analyses give different results only for sentences such as ' SJ and BJ are the same person before the operation', and, for such sentences, only the analysis i n terms of tensed identity gives the truth-value we would expect. The B language's truth-conditions for statements of personal identity, then, are a vast improvement over i t s predecessor; they alone imply exactly what we wish to say about the rela-tionships holding among Jones, SJ, and BJ, before the oper-ation and after. But though the B language i s thoroughly satisfactory as far as implying what we believe to be true about Perry's story and normal cases, i t does not fare much better than Lewis' theory as far as satisfying our philosophical intui-tions. The incongruous element in both theories is the theory of counting. In Lewis the method of counting i s ad hoc because i t does not seem to direct us to count what we assume persons to be, namely, branches. The B language's theory of counting, on the other hand, displays the formal elegance absent in Lewis, in that the B language does indeed count branches to count persons. Nevertheless, the theory is just as ad hoc as Lewis', since the branches counted by the B language do not appear to be the branches that are assumed to be persons. The B language, then, is not ideal. Some of i t s elements could be upgraded, not in order to produce 125 different implications—the present ones, as far as I can judge, are those we want—but in order to secure the p h i l -osophical underpinning of the theory. S t i l l , the fact re-mains, I believe, that the B language i s an undeniable im-provement over i t s predecessors, and hence, I hope, a step to a yet better theory. 126 BIBLIOGRAPHY Lewis, David. "Survival and Identity." In The Identities  of Persons, pp. 17-40. Edited by Amelie Oksenberg Rorty. Berkeley! University of California Press, 1976. Parfit, Derek. "Personal Identity." Philosophical Review 80 (January 1971)« 3-27. Perry, John. "Can the Self Divide?" The Journal of Phil- osophy 69 (September 9, 1972)» 463-88. Prior, Arthur. "Opposite Number." Review of Metaphysics 11 (December 1957)» 196-201. . "Time, Existence, and Identity." Proceedings of the Aristotelian Society 66 (1965-6 ) 1 183-192. Williams, B.A.O. "Personal Identity and Individuation." Proceedings of the Aristotelian Society 57 (1956-7)t 229-52. 

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