Any Way You Slice It: On Fission, Fusion and the Weighing of Welfare 1. [Please note: Citations have yet to be added.]

Jacob Ross University of Southern California Any Way You Slice It: On Fission, Fusion and the Weighing of Welfare 1 [Please note: Citations have yet to be added.] It is generally thought that there are certain persons to whose welfare we should give special weight. It is commonly held, for example, that we should give special weight to our own welfare. On the strongest version of this view, we should always give overriding weight to our own welfare, and so, in considering any set of alternatives, we should always prefer the one in which we fare best. Many people would reject this strong view, for two reasons. First, many people would hold that impersonal reasons (such as reasons of total utility) can sometimes outweigh, or at least counterbalance, reasons of self-interest. Further, many people think that reasons deriving from special personal relations can sometimes outweigh, or at least counterbalance, reasons of self-interest. We can, however, formulate a much weaker, and much more plausible, version of the selfinterest view that avoids both these problems. Let s first define a person s kin as anyone in the person s extended family (including himself). And let s define a person s kith very broadly as anyone with whom that person has ever interacted. We can now formulate the weak version of the self-interest view as follows. Weak Self-interest Thesis: For any two possibilities P 1 and P 2, if we should expect ourselves to fare better in P 1 than in P 2, and if we should not expect P 2 to be better than P 1 from an impersonal point of view, nor should we expect any of our kith or kin to fare better in P 2, then we should prefer P 1 to P 2. Even those who deny that we should give such special weight to our own welfare will typically hold that there are some people we should be especially concerned about to whose welfare she should give such special weight. Thus, it would seem that if one were comparing two possibilities, P 1 and P 2, such that P 1 is better than P 2 for one s child, and P 2 isn t better than P 1 either impersonally or for any of our kith or kin (including ourselves), then we should prefer P 1 to P 2. 1 I am grateful to Kenny Easwaran, David Manley, Derek Parfit, Mark Schroeder and Larry Temkin for very helpful discussions and comments concerning earlier drafts of this paper. My greatest debt is to Shieva Kleinschmidt for countless invaluable comments and discussions. 1

Let us now generalize. For any persons A and B, let us say that A gives special weight to the welfare of B just in case A prefers a possibility P 1 to a possibility P 2 whenever (i) A expects B to fare better in P 1 than in P 2 ; (ii) A does not expect P 2 to be better than P 1 from an impersonal point of view; and (iii) A does not expect any of her kith or kin to fare better in P 2 than in P 1. We may now define the Special Weight Thesis as follows. Special Weight Thesis: For some persons A and B such that A should be specially concerned about B, A should give special weight to B s welfare. Since the formulation of the Special Weight Thesis allows that A and B can be identical, the Weak Self-Interest Thesis can be thought of as a special case of the Special Weight Thesis, and so anyone who accepts the former should accept the latter. But the Special Weight Thesis should also be accepted by anyone who holds that we should give special weight to the welfare of our children, spouses, best friends, etc. Nonetheless, in what follows I will argue that the Special Weight Thesis is false, and I will propose an alternative principle in its place. My argument, like the pioneering arguments of Derek Parfit, will turn on cases involving fission and fusion. In presenting these arguments, I will not assume any particular interpretation of what goes on in such cases, but instead I will show that my conclusions follow regardless of which theory one adopts concerning what happens in cases of fission and fusion. I will proceed as follows. In part 1, after defining fission and fusion and arguing that everyone should allow for their possibility, I will present three claims about cases of fission and fusion which, I will argue, cannot plausibly be denied. I will then distinguish four alternative theories one can adopt concerning what happens in cases of fission and fusion. Then, in part 2, I will consider these four alternative theories in turn. And I will argue that, whichever of these theories one adopts, one cannot accept the Special Weight Thesis without denying one or other of the undeniable claims presented in part 1. Thus, any way you slice it, we should reject the Special Weight Thesis. In part 3, I will consider various responses that can be given to my arguments against the Special Weight Thesis, and I will argue that the best response is to adopt an alternative principle concerning the weighing of welfare, namely what I will call the Discounted Weight Thesis. 2

1. Thinking about Fission and Fusion 1.1 The Possibility of Fission, Fusion, and Switcheroo Let s begin with some definitions. For any person, A, let s say that a part, P, belonging to A is a replaceable part of A just in case A would survive an operation in which P is destroyed and immediately replaced with an exact duplicate of P, while the rest of A is left intact. Thus, for example, each of the buttons on my shirt is a replaceable part of my shirt, since my shirt would survive the destruction of any one of these buttons followed by its immediate replacement with an exact duplicate button. obtain. Next, let s define semi-replacement as a process in which the following conditions (i) (ii) Initially, there is a person who wholly consists of two non-overlapping, replaceable parts, L and R. Then R is either removed or destroyed, and it is immediately replaced with a molecular duplicate of R that is connected to L just as R had been previously. Here s an example of semi-replacement. Simple Semi-Replacement: Clive lies on the operating table of Dr. X, who possesses technology from the 24 ½th century. Dr. X scans Clive s body, recording its every detail. Then, using her Annihilation Ray, she destroys the right half of his body, including his brain. A nanosecond later, using her Materialization Ray, she generates a molecular duplicate of the half she just destroyed. From its origin, this newly-created half is connected to Clive s original left half just as his original right half had been. Next, let s define fission as a process in which the following conditions obtain. (i) (ii) Initially, there is a person who wholly consists of two non-overlapping, replaceable parts, L and R. Then L and R are separated from one another. As L is removed from R, it is replaced with a molecular duplicate of L which is connected seamlessly to R, just as L had been previously. And as R is removed from L, it is similarly replaced with a molecular duplicate of R. Here s an example of a fission case. Simple Fission: Dr. X then cleaves Clive down the middle, separating the right and left halves of his body (including his brain). A nanosecond later, she generates a molecular duplicate of Clive s original left which, from its origin, is connected to his original right half, and she likewise generates a molecular duplicate of Clive s original right half which, from its origin, is connected to 3

his original left half. Hence, a split second after the operation began, there are two individuals each of whom is just like Clive had been right before the operation. Next, let s define fusion as a process in which the following conditions obtain. (i) (ii) Initially, there are two persons, A and B, who are molecular duplicates of one another. Person A wholly consists of two non-overlapping, replaceable parts, L A and R A, and B wholly consists of two non-overlapping, replaceable parts, L B and R B, such that L B is a molecular duplicate of L A and R B is a molecular duplicate of R A. Then L A and R B cease to be connected to R A and to L B, respectively, and become connected instead, and in the very same manner, to one another. Here s an example of a fusion case. Simple Fusion: Initially, Clive and Cliff are molecular duplicates of one another. Then, within a nanosecond, Dr. X destroys the right half of Clive and the left half of Cliff, and she connects the remaining two halves to one another. Finally, let us define a kind of process that combines fission and fusion, which process we may call switcheroo. Let s say that switcheroo occurs just in case the following conditions obtain. (i) (ii) Initially, there are two persons, A and B, who are molecular duplicates of one another. Person A wholly consists of two non-overlapping, replaceable parts, L A and R A, and B wholly consists of two non-overlapping, replaceable parts, L B and R B, such that L B is a molecular duplicate of L A and R B is a molecular duplicate of R A. Then L A and R A are separated from one another, as are L B and R B. Then L A is immediately connected to R B just as L B had been, and L B is immediately connected to R A just as L A had been. Here s an example of a switcheroo case. Simple Switcheroo: Clive and Cliff are molecular duplicates of one another. Then, within a nanosecond, Dr. X cleaves Clive and Cliff each down the middle, and she attaches the left half of Clive to the right half of Cliff, and the left half of Cliff to the right half of Clive. Note that in this case, there are two processes of fission and two processes of fusion. There are some who would deny that human beings are capable of undergoing semi-replacement, fission, fusion, or switcheroo, as these terms have been defined above. Hence, they would deny that the cases described above (Simple Semi-Replacement, 4

Simple Fission, Simple Fusion, and Simple Switcheroo) are genuine examples of these processes. They might argue as follows. As you have defined these terms, someone can undergo semi-replacement, fission, fusion, or switcheroo only if she wholly consists of two non-overlapping, replaceable parts. But human persons aren t like that. The correct theory of personal identity is the animalist theory, according to which persons are living organisms and hence a person cannot survive the destruction of the living organism with which she is identical. And while there may be some living organisms that could survive the replacement of either half their bodies, humans aren t like that: if you destroyed and then replaced the left or the right side of a human, that living organism would cease to exist and a new one would appear in its place. Hence, the two sides of a human are not replaceable parts. Consequently, human persons can t undergo semi-replacement, fission, fusion or switcheroo as you have defined these terms. Suppose we grant, for the sake of argument, that the animalist view is correct, and we also grant that a human organism couldn t survive the replacement of either its right half or its left half. On these assumptions, the left and right halves of a human being won t constitute replaceable parts of a person, and so the cases described above won t count as genuine cases of semi-replacement, fission, fusion, or switcheroo. But even so, it won t follow that human persons don t wholly consist of two non-overlapping, replaceable parts, and so it won t follow that human persons can t undergo the processes defined above. Consider, for example, the whole consisting of the right half of every particle in a human body. Suppose this whole (and hence all the half-particles of which it consists) were annihilated and then replaced, a millionth of a nanosecond later, with an exact duplicate thereof. In this case, it could not plausibly be said that the human organism was destroyed. Instead we should say that the organism momentarily lost half its mass, and that the organism regained its original mass a moment later. Hence, even on the animalist view, the whole consisting of the right half of every particle in the human body will constitute a replaceable part of a human person. And the same will apply to the whole consisting of the left half of every particle in the human body. Hence, even on the animalist view, a human person wholly consists of two non-overlapping, replaceable parts, namely, the part consisting of the right halves of all the particles in her body and the part consisting in the left halves of all the particles in her body. Hence, it follows that, even on the animalist view, human persons can undergo semi-replacement, fission, fusion, and switcheroo. 5

In what follows, I will be focusing on versions of the processes under consideration where the replaceable parts of the persons that figure in these process are their left and right halves. However, readers who do not regard the left and right halves of persons as replaceable parts of these persons are welcome to instead consider versions of these cases where that parts of persons that are destroyed, divided, or connected are not the right or left sides of persons, but rather the collections of right or left particle-halves. 1.2 Three Self-Evident Truths Concerning such Cases In this section, I will consider some cases involving fission and the like, and I will argue that there are certain claims about these cases (the so-called Self-Evident Truths) that cannot plausibly be denied. This will prepare the way for part 2, where I will argue that, if one accepts the Special Weight Thesis, then one will be committed to denying some of these claims regardless of which theory one adopts concerning what happens in the cases in question. In considering the cases presented in this section, it isn t essential for the reader to commit them to memory the important thing is to appreciate the self-evidence of the three Self-Evident Truths. In each of the cases that I will describe in this section, I will use Cleo and Clive as variables ranging over persons (who may or may not be distinct), and t as a variable ranging over possible times. L and R will represent the objects which are, at t, the left and right halves of Clive, respectively. For convenience, I will introduce the following notation: where L A and R B refer to a left person-half and a right-person half, respectively, I will use the expression L A -R B to denote the individual (or individuals) whose left half at the time under consideration is L A and whose right half at the time under consideration is R B. Each of the cases will involve a pair of possibilities in which Clive figures, and in each case I will ask what Cleo s preference should be between these possibilities, on the supposition that she has special concern for Clive. The first of these cases, which I will call Divide and Torture, involves the following two possibilities. Single Torture: Beginning at t, Clive lives happily for x years. At the end of this time he undergoes semi-replacement wherein his right half is replaced. He is then tortured for y years and then destroyed. Double Torture: Beginning at t, Clive lives happily for x years. He then undergoes fission wherein his left and right halves (L and R) are separated from one another. As R is removed from L it is replaced by a newly-created molecular 6

duplicate R*, and as L is removed from R it is replaced with a newly-created duplicate L*. Then the two resulting individuals, L-R* and L*-R, are each torture, and then destroyed when the torture is completed. L-R* is tortured for y years, whereas L*-R is tortured for z years. In this case, it seems clear that if Cleo has special concern for Clive, then she should not prefer Double Torture to Single Torture. For these two possibilities agree with respect to what happens for the first x years after t, and they likewise agree with respect to what happens to the original left side of Clive, L, after t: it is connected to a newly created molecular duplicate of R, and the resulting individual is tortured for y years and then destroyed. The only differences between the two possibilities concerns to R beginning x years after t. In Single Torture, R is simply destroyed, whereas in Double Torture, R is connected to a newly created molecular duplicate of L, and the resulting individual is tortured for z years before being destroyed. And this difference doesn t seem to count in favor of Double Torture from an impersonal point of view, nor does it seem count in favor of Double Torture from the point of view of someone who cares about Clive. And so we should accept the following claim: regardless of who Cleo and Clive are, and regardless of when t is, and regardless of the values of x, y and z, if Cleo has special concern for Clive then she should not prefer Double Torture to Single Torture. 7

A second relevant case, which I will call Twin Divide and Torture, involves the following two options. Clive s Single Torture: At t, Clive has a molecular duplicate (Clive 2 ) who is neither kith nor kin to Cleo, but whose welfare is as important as that of Clive from an impersonal point of view. Then, beginning at t, Clive undergoes the same fate has he does in Single Torture: he lives happily for x years, and then he undergoes semi-replacement followed by y years of torture before being destroyed. Meanwhile, Clive 2 undergoes the fate that Clive undergoes in Double Torture: Beginning at t, Clive 2 lives happily for x years, and then he undergoes fission, whereupon the individuals with his original left and right halves undergo y and z years of torture, respectively, before being destroyed. Clive s Double Torture: This possibility is just like Clive s Single Torture, except that the fates of Clive and Clive 2 are reversed. Thus, in this possibility, it is Clive 2 who undergoes semi-replacement followed by y years of torture. And it is Clive who undergoes fission whereupon the individuals with his original right and left halves undergo y and z years of torture, respectively. In this case, it seems clear that if Cleo has special concern for Clive, then Cleo should not prefer Clive s Double Torture to Clive s Single Torture. For, from an impersonal point of view, these two possibilities are equally good, since the only difference between them is that the positions of two individuals are reversed, and the welfare of these two individuals is equally important from an impersonal point of view. And since what happens to Clive 8

in Clive s Single Torture is the same as what happens to him in Single Torture, while what happens to Clive in Clive s Double Torture is the same as what happens to him in Double Torture, it follows for the reasons already given that Cleo s concern for Clive shouldn t make her prefer Clive Gets Double Torture. And so we should accept the following claim (which, for future reference, it will be useful to name). Self-Evident Truth #1: for any persons Cleo and Clive, any time t, and any positive real values of x, y and z, if at t Cleo should have special concern for Clive, then Cleo should not to prefer Clive s Double Torture to Clive s Single Torture. In the remaining cases we will consider, we will need to specify not only the durations of experiences, but also their levels of intensity. Let s adopt a scale for levels of intensity of torture with the following features: 10 represents an extremely high level of torture, and anything above zero represents a level of torture at which life is worth ending. That is, any level of torture above zero is such that, other things being equal, one should prefer not to continue living if the remainder of one s life would consist in experiencing that level of torture. Similarly, let s adopt a scale for levels of intensity of pleasure with the following features: 10 represents an extremely high level of pleasure, and anything above zero represents a level of pleasure at which life is worth continuing. That is, any level of pleasure above zero is such that, other things being equal, one should prefer to continue living if the remainder of one s life would consist in experiencing that level of pleasure. Our third relevant case, which I will call Switcheroo Divide and Torture, involves the following two possibilities. Clive s Fusion Torture: At t, Clive has three molecular duplicate (Clive 2, Clive 3 and Clive 4 ) who are neither kith nor kin to Cleo, but whose welfare is as important as that of Clive from an impersonal point of view. Then Clive and Clive 2 undergo a process of fusion wherein the right half of Clive (R) and the left half of Clive 2 (L 2 ) are destroyed and the remaining two halves (L and R 2 ) are connected. The resulting individual (L-R 2 ) is then tortured at intensity-level 10 for ten years before being destroyed. Meanwhile, Clive 3 and Clive 4 undergo switcheroo, resulting in L 3 -R 4, who is tortured at intensity-level 10 for ten years before being destroyed, and L 4 -R 3, who is tortured at intensity level x for ten years before being destroyed. Clive s Switcheroo Torture: This possibility is just like Clive s Fusion Torture, except that Clive and Clive 3 exchange situations, as do Clive 2 and Clive 4. Thus, in this possibility, it is Clive 3 and Clive 4 who undergo a process of fusion, wherein R 3 and L 4 are destroyed and the remaining two halves are joined to 9

form an individual (L 3 -R 4 ) who is tortured at intensity-level 10 for ten years before being destroyed. And it is Clive and Clive 2 who undergo switcheroo, whereupon L-R 2 is tortured at intensity level 10 for ten years before being destroyed whereas L 2 -R is tortured at intensity level x for ten years before being destroyed. In this case, it seems clear that if Cleo has special concern for Clive, then she should not prefer Clive s Switcheroo Torture to Clive Fusion Torture. For, once again, these two possibilities are equally good from an impersonal point of view, since they differ only with respect to the identities of the persons involved. And once again, it doesn t seem that Cleo s special concern for Clive should give her any reason to prefer Clive s Switcheroo Torture to Clive Fusion Torture. For these two possibilities agree concerning what happens to the original left side of Clive, but they disagree concerning what happens to his original right side: in Clive s Fusion Torture, Clive s original right side is simply destroyed, whereas in Clive s Switcheroo Torture it is connected to the original left side of Clive 2, whereupon the resulting individual is tortured at intensity level x for ten years before being destroyed. And surely someone who has special concern for Clive should not regard this difference as counting in favor of Clive s Double Torture. And so 10

we should accept the following claim (which, again, it will be useful to name for future reference). Self-Evident Truth #2: for any persons Cleo and Clive, any time t, and any positive real value of x, if at t Cleo should have special concern for Clive, then Cleo should not to prefer Clive s Switcheroo Torture to Clive s Fusion Torture. The fourth relevant case, which we may call Hedonic Hustle, involves the following two possibilities. Unified Greater Pleasure: At t, Clive has a molecular duplicate (Clive 2 ) who is neither kith nor kin Cleo, but whose welfare is as important as that of Clive from an impersonal point of view. Then, beginning at t, Clive and Clive 2 each experience pleasure at intensity-level 10 for ten years before being destroyed. Neither Clive nor Clive 2 undergoes any unusual operation. Scattered Lesser Pleasure: At t, Clive and Clive 2 undergo a process of switcheroo, resulting in L-R 2 and L 2 -R. Then L-R 2 and L 2 -R each experience pleasure at intensity level (10 x) for ten years before being destroyed. In this case, it seems clear that if Cleo has special concern for Clive, then she should not prefer Scattered Lesser Pleasure to Unified Greater Pleasure. For these two cases differ 11

in two respects. First, Clive and Clive 2 remain intact in the first case but undergo switcheroo in the second. And second, the levels of intensity of the pleasure experienced in Unified Greater Pleasure exceed the levels of intensity of pleasure experienced in Scattered Lesser Pleasure. But neither of these differences would seem to count in favor of Scattered Lesser Pleasure either impersonally, or from the point of view of someone who has special concern for Clive. And so we should accept the following claim: regardless of who Cleo and Clive are, and regardless of when t is, and regardless of the value of x, if Cleo has special concern for Clive then she should not prefer Scattered Lesser Pleasure to Unified Greater Pleasure. The fifth relevant case is just like Hedonic Hustle, except that it involves torture instead of pleasure. In this case, which we may call Torture Tango, the two possibilities are as follows. Unified Greater Torture: At t, Clive has a molecular duplicate (Clive 2 ) who is neither kith nor kin to Cleo, but whose welfare is as important as that of Clive from an impersonal point of view. Then, beginning at t, Clive and Clive 2 are each tortured at intensity-level 10 for ten years before being destroyed. Neither Clive nor Clive 2 undergoes any unusual operation. Scattered Lesser Torture: At t, Clive and Clive 2 undergo a process of switcheroo, resulting in L-R 2 and L 2 -R. Then L-R 2 and L 2 -R are each tortured at intensitylevel (10 x) for ten years before being destroyed. In this case, it seems clear that if Cleo has special concern for Clive, then she should not prefer Unified Greater Torture to Scattered Pleasure. For these two cases differ in two respects: Clive and Clive 2 remain intact in the first case but undergo switcheroo in the second, and the level of intensity of torture are greater in the second case than in the first. And neither of these differences seems to count in favor of Unified Greater Torture from an impersonal point of view. Nor do they appear to count in its favor from the point of view of someone who has special concern for Clive. For just as in Scattered Lesser Pleasure the separation of Clive s two halves doesn t seem to make the ensuring pleasure any more desirable from the point of view of someone who has special concern for Clive, so in Scattered Lesser Torture the separation of Clive s two halves doesn t seem to make the resulting suffering more undesirable from the point of view of someone who has special concern for Clive. And so we should accept the following claim: regardless of who Cleo and Clive are, and regardless of when t is, and regardless of the value of x, if Cleo has special concern for Clive then she should not prefer Unified Greater Torture to Scattered Lesser Torture. 12

The final relevant case, which we may call Switcheroo Torture Tango, involves the following two possibilities. Clive s Unified Greater Torture: At t, Clive has two molecular duplicate (Clive 2 and Clive 3 ) who are neither kith nor kin Cleo, but whose welfare is as important as that of Clive from an impersonal point of view. Then, beginning at t, Clive undergoes the same fate as he does in Unified Greater Torture: he is tortured at intensity-level 10 for ten years before being destroyed, without having first undergone any unusual operation. Meanwhile, at t, Clive 2 and Clive 3 undergo the fates that figure in Scattered Lesser Torture: they undergo a process of switcheroo wherein L 2 -R 3 and L 3 -R 2 are formed, each of whom is then tortured at intensity-level (10 x) for ten years before being destroyed. Clive s Scattered Lesser Torture: This possibility is just like Clive s Unified Greater Torture, except that the fates of Clive and Clive 3 are reversed. Thus, in this possibility, it is Clive 3 who is tortured at intensity-level 10 for ten years without having undergone any unusual operation. And it is Clive who undergoes switcheroo with Clive 2, resulting in L-R 2 and L 2 -R, each of whom is then tortured at intensity-level (10 x) for ten years before being destroyed. In this case, it seems clear that if Cleo has special concern for Clive, then she should not prefer Clive s Unified Greater Torture to Clive s Scattered Lesser Torture. For from an impersonal point of view, the two possibilities are equally good, since they differ only in 13

the positions of two equally important individuals. Moreover, since what happens to Clive in these two possibilities is the same as what happens to him in Unified Greater Torture and in Scattered Lesser Torture, respectively, it follows for reasons already given that Cleo s concern for Clive shouldn t make her prefer Clive s Unified Greater Torture. And so we should accept the following claim (which, again, it will be useful to name). Self-Evident Truth #3: for any persons Cleo and Clive, any time t, and any positive real value of x, if at t Cleo should have special concern for Clive, then Cleo should not to prefer Clive s Unified Greater Torture to Clive s Scattered Lesser Torture. While everyone should accept all three Self-Evident Truths, I will argue that the proponent of the Special Weight Thesis cannot do so. Before this can be shown, however, we must first consider some alternative ways of interpreting the cases in question. 1.3 Four Theories about what Would Happen in such Cases What would happen to someone if she were to undergo fission or fusion? What makes this question difficult to answer is that there are prima facie plausible claims about fission and fusion cases that are jointly inconsistent. Consider the following claims. (1) Anyone who undergoes fission or fusion survives the process. (2) Because of the symmetry of fission and fusion, it can t be that one, but not the other, of those who emerge from fission survived it, nor can it be that one, but not the other, of those who undergo fusion survives it, (3) Because of the transitivity of identity, it can t be that one person survives fission as two distinct persons, nor can it be that two distinct persons survive fusion as the same person. (4) For any time t and any two person-halves L and R that are connected together in the ordinary manner at t, there is one and only one person A such that L and R are, at t, the two halves of A. These four claims can t all be true. They conflict in cases fission, and they likewise conflict in cases of fusion, but let s focus on cases of fission. Suppose that at t Clive were to undergo a process of fission in which his original left half (L) is connected to a duplicate of his original right half (call it R*) and in which his original right half (R) is connected to a duplicate of his original left half (call it L*). If (4) is true, then prior to t Clive would be the only person whose two halves are L and R, and so he would be the 14

only person who undergoes the fission process. Similarly, if (4) is true then after t there would be exactly one person (call him Lefty) whose two halves are L and R*, and there would likewise be exactly one person (call him Righty) whose two halves are L* and R. From (1) it follows that Clive would survive the fission, and from (3) it follows that he would survive it as one or other of Lefty and Righty, but not as both. But if Clive is the only one who would undergo the fission, and if Clive would survive it as Lefty or as Righty but not as both, then it would have be true of only one of Lefty and Righty that someone survives the fission as that person, contrary to (2). Thus, we cannot consistently hold all four of these intuitively plausible claims. We can, however, consistently hold any three of them, resulting in four possible views involving minimal departures from our natural intuitions. First, one can reject (1) while retaining the other assumptions, and claim the following: No Survivor View: No one survives fission: the person who undergoes it ceases to exist in the process, and the two individuals who emerge from it come into existence in the fission process. Similarly, no one survives fusion. The two people who undergo fusion cease to exist in the process, and the individual who emerges from it comes into existence in the fusion process. Alternatively, one can reject (2) while retaining the other assumptions, and claim the following: Solitary Unbranching Survivor View: If someone were to undergo fission, then she would survive as one or other of the two individuals who emerge from it, while the other such individual would come into existence in the fission process. Similarly, if two persons were to undergo fusion, then one or other of them would survive the process, while the other would cease to exist in the process. The third option is to reject (3) while retaining the other assumptions, and to claim the following. Solitary Branching Survivor View: If someone were to undergo fission, then she would survive as each of the two individuals who emerge from it. Similarly, if two persons were to undergo fusion, then they would each survive as the individual who emerges from it. The fourth option is to reject (4) while retaining the other assumptions, and to claim the following. Colocated Unbranching Survivor View: If someone were to undergo fission, then prior to the fission she would be one of two distinct colocated persons sharing 15

her person-halves. At the time of fission these two persons would part company, and one would survive as the individual with the original left half while the other would survive as the individual with the original right half. Similarly, if two persons were to undergo fusion, then they would both survive as two distinct but colocated persons sharing the same person-halves. The four alternative views just considered are not the only logically possible views one can take about cases of fission and fusion, as other views are available if one rejects more than one of assumptions (1) through (4), stated above. However, since these four alternative views involve the minimal departures from our ordinary intuitions, they are the least implausible views one can adopt about such cases. And they are also the views that have been most prominently defended. I will therefore focus on these four views in what follows. 2. Why We Should Reject the Special Weight Thesis In the second part of the paper, I will argue that if the defender of the Special Weight Thesis adopts any one of the four views just outlined, then she must deny at least one of the Self-Evident Truths. In particular, if she adopts the No Survivor View, the Solitary Unbranching Survivor View, or the Colocated Unbranching Survivor View, then she will be committed to denying Self-Evident Truth #1. And if she adopts the Solitary Branching Survivor View, then she will be committed to denying either Self-Evident Truth #2 or Self-Evident Truth #3. 2.1 The Problem for the No Survivor View In this section, I will argue that the conjunction of the Special Weight Thesis and the No Survivor View is incompatible with Self-Evident Truth #1. I will therefore focus on the second case described in section 1.2 above, namely Switcheroo Divide and Torture, since Self-Evident Truth #1 concerns this case. Let us suppose, for the sake of argument, that the Special Weight Thesis is true. And let us consider a version of Switcheroo Divide and Torture in which Cleo and Clive are persons who instantiate the Special Weight Thesis. That is, let us consider a version of Switcheroo Divide and Torture where Cleo and Clive are persons with the following features: Cleo should have special concern for Clive, and Cleo should give special weight to Clive s welfare assuming the Special Weight Thesis is true, there must be such 16

persons, and so we are entitled to consider the version of the case where such persons figure. Let us further suppose that the No Survivor View (NS) is correct. This view implies that if someone were to undergo fission, then he would not survive, and the two individuals who would emerge from the fission would be newly-created molecular duplicates of this person. This view thus implies that the outcomes of the two possibilities that figure in Switcheroo Divide and Torture are as follows. Clive s Single Torture NS : Beginning at t, Clive and Clive 2 each live happily for x years. Then Clive goes on to be tortured for y years before being destroyed. By contrast, Clive 2 undergoes fission, at which point he ceases to exist. Two molecular duplicates of Clive 2 are formed in his place, one of whom is tortured for y years before being destroyed and the other of whom is tortured for z years before being destroyed. Clive s Double Torture NS : Just like the above, except that the positions of Clive and Clive 2 are reversed. Thus, in this outcome it is Clive 2 who is tortured for y years before being destroyed, and it is Clive who ceases to exist before any torture occurs, and whose fission gives rise to two newly-created individuals who are tortured for y years and z years respectively. It s clear that Clive fares better in Clive s Double Torture NS than in Clive s Single Torture NS, since in the latter he is tortured for y years before being destroyed whereas in the former he ceases to exist before any torture occurs. Moreover, none of Cleo s kith or kin fares better in Clive s Single Torture NS than in Clive s Double Torture NS. For apart from Clive, the only persons who figure in these outcomes are Clive 2 and the two individuals who emerge from the fission. We have stipulated that Clive 2 is neither kith nor kin to Cleo, and, since those who emerge from the fission are newly-created molecular duplicates of Clive, they are persons with whom Cleo has never interacted, and so they too are neither kith nor kin to Cleo. Thus, Cleo should expect Clive to fare better in Clive s Double Torture NS than in Clive s Single Torture NS, and she should not expect Clive s Single Torture NS to be better impersonally, nor should she expect any of her kith or kin to fare better in Clive s Single Torture NS. And so, from our supposition that Cleo should give special weight to Clive s welfare, it follows that Cleo should prefer Clive s Double Torture NS to Clive s Single Torture NS. But recall that, according to the No Survivor view, Clive s Single Torture NS and Clive s Double Torture NS are the outcomes of Clive s Single Torture and Clive s Double Torture, respectively. And so it follows from the No Survivor view that Cleo should 17

prefer Clive s Double Torture to Clive s Single Torture. And this contradicts Self- Evident Truth #1. Thus, anyone who accepts the Special Weight Thesis and the No Survivor View will be committed to denying Self-Evident Truth #1. 2.2 The Problem for the Solitary Unbranching Survivor View In this section, I will argue that the Solitary Unbranching Survivor View, like the No Survivor View, is incompatible with Self-Evident Truth #1 when conjoined with the Special Weight Thesis. Once again let us suppose, for the sake of argument, that the Special Weight Thesis is true. And so let us again consider a version of Switcheroo Divide and Torture in which Cleo and Clive are persons who instantiate the Special Weight Thesis. Let us suppose, in other words, that Cleo should have special concern for Clive and should give special weight to his welfare. In addition, let us suppose that that Solitary Unbranching Survivor View (SUS) is correct. Recall that according to this view, when someone undergoes fission she survives as one or other of the persons who emerge from the fission, while the other is a newly-created molecular duplicate of her. Thus, when someone undergoes fission in which her left and right halves are divided, there are two things that might happen: she might survive as the person with her original left half, or she might survive as the person with her original right half. And it doesn t seem that Cleo would be in a position to know which of these possibilities would obtain if Clive or Clive 2 were to undergo fission. Thus, since Clive 2 undergoes fission in Clive s Single Torture, the SUS view implies that Clive s Single Torture can be thought of as a gamble (Call it the Clive 2 Gamble) between the following two outcomes. Clive 2 Gets y: Beginning at t, Clive lives happily for x years and is then tortured for y years before being destroyed. Meanwhile, Clive 2 lives happily for x years and then survives fission as the fission-product who is tortured for y years before being destroyed. The other fission-product, who is tortured for z years before being destroyed, is a newly-created molecular duplicate of Clive 2. Clive 2 Gets z: Just like the above, except that in this outcome it s Clive 2 who survives as the fission products who is tortured for z years, and the fission product who is tortured for y years is a newly-created molecular duplicate of Clive 2. 18

Similarly, since Clive undergoes fission in Clive s Double Torture, the SUS view implies that Clive s Double Torture can be thought of as a gamble (Call it the Clive Gamble) between the following two outcomes. Clive Gets y: Beginning at t, Clive 2 lives happily for x years and is then tortured for y years before being destroyed. Meanwhile, Clive lives happily for x years and then survives fission as the fission-product who is tortured for y years before being destroyed. The other fission-product, who is tortured for z years before being destroyed, is a newly-created molecular duplicate of Clive. Clive Gets z: Just like the above, except that in this outcome it s Clive who survives as the fission products who is tortured for z years, and the fission product who is tortured for y years is a newly-created molecular duplicate of Clive. So long as z is less than y, Cleo should expect Clive to fare better in the Clive Gamble than in the Clive 2 Gamble. For in the former gamble, Clive has a chance of being tortured for y years and a chance of being tortured for only z years, whereas in the latter gamble he is guaranteed to be tortured for y years. Thus, since the SUS View implies Cleo should regard Clive s Single Torture as equivalent to the Clive 2 Gamble and Clive s Double Torture as equivalent to the Clive Gamble, it follows from the SUS View that Cleo should expect Clive to fare better in Clive s Double Torture than in Clive s Single Torture. Moreover, she should expect these two possibilities to be equally good from an impersonal point of view, since they differ only with respect to the identities of the persons involved. And since, aside from Clive, no one who figures in either of these possibilities is kith or kin to Cleo, it follows that, apart from Clive, she should not expect any of her kith or kin to fare better in Clive s Single Torture than in Clive s Double Torture. Consequently, so long as z is less than y, Cleo should expect Clive to fare better in Clive s Double Torture, and she should not expect Clive s Single Torture to be better either impersonally or for any of her kith or kin. Therefore, from the supposition that Cleo should give special weight to Clive s welfare, it follows that, so long as z is less than y, Cleo should prefer Clive s Double Torture to Clive s Single Torture. But this contradicts Self-Evident Truth #1. And so anyone who accepts the Special Weight Thesis and the SUS View is committed to denying Self-Evident Truth #1. 19

2.3 The Problem for the Colocated Unbranching Survivor View In this section, I will argue that the Colocated Unbranching Survivor View, like the two views considered in the last two sections, is incompatible with Self-Evident Truth #1 when conjoined with the Special Weight Thesis. Once again let us suppose that the Special Weight Thesis is true. And so let us again consider a version of Switcheroo Divide and Torture in which Cleo should have special concern for Clive and should give special weight to his welfare. In addition, let us suppose that that Colocated Unbranching Survivor View (CUS) is correct. Recall that, according to this view, when someone undergoes fission she survives as one or other of the persons who emerge from the fission, while the other is a distinct person who was colocated wither prior to the fission and who parts company with her at the time of fission. Thus, when someone undergoes fission in which her left and right halves are divided, there are two things that might happen: she might survive as the person with her original left half, and the person with whom she is colocated might survive as the person with her original right half, or vice versa. And it doesn t seem that Cleo would be in a position to know which of these possibilities would obtain if Clive or Clive 2 were to undergo fission. Thus, since Clive 2 undergoes fission in Clive s Single Torture, the SUS view implies that Clive s Single Torture can be thought of as a gamble (Call it the 2 nd Clive 2 Gamble) between the following two outcomes. Clive 2 Gets y*: Beginning at t, Clive lives happily for x years and is then tortured for y years before being destroyed. Meanwhile, Clive 2 lives happily for x years during which he is colocated with a distinct person (call him Clive 2 *). Then Clive 2 and Clive 2 * undergo fission, and Clive 2 survives as the fission-product who is tortured for y years before being destroyed, whereas Clive 2 * survives as the fission-product who is tortured for z years before being destroyed. Clive 2 Gets z*: Just like the above, except that in this outcome it s Clive 2 who survives as the fission-product who is tortured for z years and Clive 2 * who survives as the fission-product who is tortured for y years. Similarly, since Clive undergoes fission in Clive s Double Torture, the SUS view implies that the outcome of Clive s Double Torture can be thought of as a gamble (Call it the 2 nd Clive Gamble) between the following two outcomes. Clive 2 Gets y*: Beginning at t, Clive lives happily for x years and is then tortured for y years before being destroyed. Meanwhile, Clive 2 lives happily for x years during which he is colocated with a distinct person (call him Clive 2 *). Then Clive 2 and Clive 2 * undergo fission, and Clive 2 survives as the fission-product 20

who is tortured for y years before being destroyed, whereas Clive 2 * survives as the fission-product who is tortured for z years before being destroyed. Clive 2 Gets z*: Just like the above, except that in this outcome it s Clive 2 who survives as the fission-product who is tortured for z years and Clive 2 * who survives as the fission-product who is tortured for y years. As before, so long as z is less than y, Cleo should expect Clive to fare better in the 2 nd Clive Gamble than in the 2 nd Clive 2 Gamble. For in the former gamble, Clive has a chance of being tortured for y years and a chance of being tortured for only z years, whereas in the latter gamble he is guaranteed to be tortured for y years. Thus, since the SUS View implies Cleo should regard Clive s Single Torture as equivalent to the 2 nd Clive 2 Gamble and Clive s Double Torture as equivalent to the 2 nd Clive Gamble, it follows from the SUS View that Cleo should expect Clive to fare better in Clive s Double Torture than in Clive s Single Torture. 21 Moreover, she should expect these two possibilities to be equally good from an impersonal point of view, since they differ only with respect to the identities of the persons involved. The only remaining question, therefore, is whether Cleo should expect any of her kith or kin to fare better in Clive s Single Torture than in Clive s Double Torture. Now besides Clive, the only person who figures in either of these possibilities who might be kith or kin to Cloe is Clive*. For the only other persons involved are Clive 2 and Clive 2 *. We have stipulated that Clive 2 is neither kith nor kin to Clive, and since Clive 2 * is colocated with Clive 2 up to and including the time under consideration (t), the same will be true of Clive 2 *. We must therefore ask whether Cleo should expect Clive* to fare better in Clive s Single Torture than in Clive s Double Torture. There appear to be three alternative ways in which this question might reasonably be answered. First Answer: Clive* does not exist in Clive s Single Torture, though he does exist in Clive s Double Torture. But if a person does not exist in a first possibility and exists in the second, then he cannot fare better in the first possibility than in the second. Hence, Clive* cannot fare better in Clive s Single Torture than in Clive s Double Torture. And so Cleo should not expe ct Clive* to fare better in Clive s Single Torture. Second Answer: Clive* does not exist in Clive s Single Torture, though he does exist in Clive s Double Torture. But if a person does not exist in a first possibility and exists in the second, then it is possible for him to fare better in the first possibility than in the second: he will fare better in the first possibility than in the second just in case, in the second possibility, his level of lifetime welfare is below the level at which life ceases to be worth living or, as we may put it, just in case in the second possibility he lives a sub-neutral life.

Thus, Cleo should expect Clive* to fare better in Clive s Single Torture than in Clive s Double Torture just in case she should expect Clive* s life in Clive s Double Torture to be sub-neutral. Now whether Cleo should expect this will depend on several factors: it will depend on how good Clive* s life was before t, and it will also depend on the values of x, y and z. No matter how good Clive* s life was before t, if x is sufficiently small and y and z are sufficiently large, then Cleo should expect Clive* s life in Clive s Double Torture to be subneutral. Conversely, no matter how bad Clive* s life was before t, if x is sufficiently large and y and z are sufficiently small, then Cleo should not expect Clive* s life to be sub-neutral. Thus, so long as x is sufficiently large and y and z are sufficiently small, Cleo should not expect Clive* to fare better in Clive s Single Torture than in Clive s Double Torture. Third (Lewisian) Answer: It s true that, strictly speaking, Clive* does not exist in Clive s Single Torture. But then, strictly speaking, the same individual never exists in two alternative possibilities. If a given individual exists in a given possibility, then only a counterpart of that individual can exist in another possibility. And what would happen to a given individual A if some alternative possibility P were to obtain is whatever does happen to the counterpart of A in possibility P. And the counterpart of Clive* in Clive s Single Torture is Clive, since Clive is the one who, up until t, is just like Clive*. Thus, since what does happen to Clive in Clive s Single Torture is that is lives happily for the first x years after t and is then tortured for y years before being destroyed, this is what would happen to Clive* if Clive s Single Torture were to obtain. By contrast, if Clive s Double Torture were to obtain, then there s a chance that Clive* s x years of happiness would be followed by y years of torture, and a chance that it would be followed by z years of torture. Therefore, Cleo should expect that Clive* would fare better if Clive s Single Torture were to obtain than if Clive s Double Torture were to obtain just in case Cleo should expect a certainty of y years of torture to be better than a chance of y years of torture and a chance of z years of torture. And the latter will be true only if z is greater than y. Consequently, so long as z is not greater than y, Cleo should not expect Clive to fare better in Clive s Single Torture than in Clive s Double Torture. All three of these answers imply that, under certain conditions, Cleo should not expect Clive* to fare better in Clive s Single Torture than in Clive s Double Torture. The First Answer implies that she should never expect this; the Second Answer implies that she should not expect this if x is sufficiently large and y and z are sufficiently small; and the Third Answer implies that she should not expect this if z is no greater than y. It follows, therefore, that if x is sufficiently large, y and z are sufficiently small, and z is no greater than y, then regardless of which of these answers is correct, Cleo should not expect Clive* to fare better in Clive s Single Torture than in Clive s Double Torture. 22