A theory of personal identity is a theory of what makes one person P2 at a later time t2 the same person as a person P1 at an earlier time t1, for example what makes George, accused in 2020 of having committed a murder in 1960, the same person as a person called ‘George’ who committed that murder in 1960. This question is not as such the question of whether the later person has the same personality as the earlier person. Someone's personality (= character) is a matter of whether they are strong willed, knowledgeable, intelligent, sympathetic and so on. We say that someone's personality has changed if they – that is, the very same person – gains or loses some of these characteristics. But the question about personal identity is a question about whether a person is the same person as an earlier person, even if his or her personality has changed. (However, as we shall see, on some theories but only on some theories, of personal identity, a person's character does have some role in determining their identity.)

One apparently obvious answer to the question of what makes P2 the same person as P1 is that P2 is the same person if and only if P2 has the same body. But how much of the same body? Surely if someone has a heart transplant, they still continue to exist but with a new heart; and similarly for any transplant of any other bodily organ except the brain. What makes the brain special is that our conscious life depends on the operation of our brains. We move our limbs only by causing some brain event which causes the motion of our limbs; and we see and hear what is happening in the world only because light or sound waves cause changes in our eyes and ears which cause brain events which in turn cause our perceptual experiences; and our memories and character depend on the operation of our brain. Without the operation of our brain we would not have any conscious experiences at all. So perhaps the answer to our question is that P2 is the same person as P1 if and only if P2 has the same brain as P1. But again the same question arises – how much of the same brain does P2 need in order to be the same person as P1? While most cells in other parts of our body are replaced gradually over the course of seven years or so by new cells, probably most brain cells (that is, neurones) remain the same over the course of a normal human life; and that is perhaps an additional reason for taking our brain as what makes us who we are. But although natural processes may not lead to gradual replacement of brain parts, surgical operations could do so. Surgeons often remove diseased parts of the brain. Although at present it is not possible for surgeons to replace a damaged brain part with a part transplanted from another body, this should become possible within the next century. Surgeons are now just beginning to be able to reconnect severed spinal nerves: and so they are on the way to being able to connect a severed nerve to a new nerve obtained from elsewhere, and the nerves which connect brain parts with other brain parts are nerves of the same kind as spinal nerves. Hence it should become possible for them to remove some brain part by severing the nerves which connected it to the rest of the brain and join the severed nerves to a part of the same kind taken from another brain. So how much of someone's brain could be replaced before that person ceases to exist?

One important fact about the brain which highlights this issue is this. The brain consists of two cerebral hemispheres, left hemisphere and right hemisphere, and also a lower part, the cerebellum. Our conscious life depends on the upper part of the cerebral hemispheres, the cerebral cortex. Patients suffering from some otherwise incurable epilepsy due to a malfunctioning hemisphere sometimes have parts of one hemisphere removed and may even have the whole hemisphere removed in an operation called an ‘anatomical hemispherectomy’. What then happens is that most of the functions of that part or whole hemisphere are taken over by another part or the other hemisphere; and the patient thinks and behaves in much the same way as before (except for not having epileptic fits), at least in the respect that their memories remain largely the same and their character is not very different. (There is some effect on their capacities to move their limbs.) And this is the case, whichever of the two hemispheres is removed – which shows that there is very considerable overlap between the brain states of the two hemispheres which give rise to conscious memories and character. So suppose when one of the hemispheres is removed from one person, let's call him John, it is replaced by a hemisphere transplanted from the brain of a different person, James. Then it is to be expected that the resulting person will have some memories and aspects of character deriving from the experiences of James, as well as the ones that John had previously. So is the resulting person John or James, or neither of these? If you think that the answer is that the resulting person is John because he still has most of John's brain, then consider a more radical surgical operation in which both hemispheres are removed from a different person whom I will call Alexandra and also from two other persons, Alex and Sandra; Alexandra's left hemisphere is then connected to Alex's brain, and Alexandra's right hemisphere is connected to Sandra's brain. Then both of two subsequent persons would have equal claims to be Alexandra, and there would seem to be no possible subsequent experiment which could show which (if any) of Alexandra, Alex, or Sandra, was still alive.

The theories of personal identity prevalent in the English-speaking world of the last few centuries have been of three kinds – physical theories or mental (= psychological) theories or mixed theories. A physical theory analyses P2 being the same person as P1 in terms of having (all or some of) the same body or same brain as P1. A mental theory analyses P2 being the same person as P1 in terms of P2 having many largely true memories of the actions of P1 and a similar character to P1, these memories and character of P2 being causally dependent on those of P1. A mixed theory contains elements of both physical and mental theories. Faced with the difficulties which I have described, any physical theory has to tell us how much of the (body or) brain of P1 P2 needs to have in order to be P1. A mental theory needs to tell us how many of the memories of P1's experiences P2 needs to have, and how similar to P1 P2's character needs to be in order for P2 to be P1; and a mixed theory needs to tell us what combination of brain parts and memories would make P2 identical to P1. All of these theories are what are known as ‘complex theories’, in that P2 being the same person as P1 is to be analysed in terms of a certain degree of ‘continuity’ of one or more separate features of P2 with those of P1. P2's brain is continuous with the brain of P1 to the degree to which any replacement of parts of P1's brain is gradual; and P2's memory and character are continuous with those of P1 to the degree to which any loss of memory is gradual, being gradually replaced by new memories of more recent experiences. Some of these theories also require some degree of what has been called ‘connectedness’ of one or more separate features of P2 with those of P1. The ‘connectedness’ of P2's brain with that of P1 is a matter of how much of the original brain remains after any gradual replacement; and the connectedness of P2's memory and character with that of P1 is a matter of how many of P1's memories P2 retains, and how similar their characters are. For example, a detailed brain theory of personal identity might have a ‘continuity’ requirement that P1 is the same as P2 if and only if over any period of five years separating them no more than 10% of P1's brain has been replaced by a part taken from the brain of some other person. And it may add a ‘connectedness’ requirement that, for example even if over many years much of the brain of P1 is gradually replaced (with no more than 10% being replaced every 5 years), the resulting person P2 must retain 40% of the original brain in order to be that original person. So P1 would be the same person as P2 if after 5 years only 9% of P1's brain has been replaced but not if 11% of P1's brain has been replaced. A detailed mental theory will need to specify whether there needs to be a chain of intermediate persons between P1 and P2, such that there is one person P1* at t₁* immediately after t₁ whose memories and character are almost the same as those of P1, and then another person P1** at t₁** whose memories and character are almost the same as those of P1*, and so on until we get to P2. Or it may allow gaps in the chain. And it will need to specify just how many memories and how much character needs to be how similar to those of the preceding instant for the succession to guarantee that P2 is P1. A mixed theory typically specifies that there must be continuity (and sometimes connectedness) of memory and character between P2 and P1, caused by brain continuity. And again, in order to be a precise theory, it needs to fill in the details.

All such ‘complex’ theories are open to the arbitrariness objection. It seems highly arbitrary to suppose that P2 is the same as P1 only if no more than 10% of P1's brain has been replaced over 5 years, but not P1 if more than 10% has been replaced. The same objection will go for any other brain theory which contains different numbers (for example, ‘no more than 10% in one operation’). And a similar objection applies to mental and mixed theories; it seems highly arbitrary to suppose P2 is the same as P1 only if he can remember at least 5% of P1's experiences after 5 years. No conceivable experiment could show which of such theories was correct; all that an experiment could show is that P2 had such and such brain matter and had such and such memories and character. But the issue is whether the person who did have such and such brain matter and such and such memories and character is P1, and there could not be the slightest reason for preferring any one detailed theory which philosophers might offer over a slightly different one. But which is the right theory is a very important matter which will rightly influence human decisions. Consider the case of a patient who has a serious brain disease which can only be cured, not merely by removing a certain part of the brain but by replacing it with a part obtained from another brain. Before they agree to undergo the operation the patient will need to know whether they are likely to survive the operation. A neuroscientist might be able to tell the patient whether the operation is likely to be successful in the sense that after the operation there will be a living conscious person, and the neuroscientist might be able to tell the patient how much of their past memory the subsequent person will have and perhaps whether the subsequent person will have a similar character to the present patient. But unless he or she has access to a true philosophical theory of personal identity, the neuroscientist will not be able to tell the patient whether they themself will survive the operation.

Many of such ‘complex’ theories are open to a second objection, the more-than-one-candidate objection. I mentioned earlier the possibility of an operation in which both hemispheres are removed from one person, Alexandra, and also from two other persons, Alex and Sandra; Alexandra's left hemisphere is then connected to Alex's brain, and Alexandra's right hemisphere is connected to Sandra's brain. Then on a theory which claims that in order to be P1 a subsequent person needs only to have 10% of P1's brain and to be able to remember 5% of the past experiences of P1, both of the subsequent persons would be Alexandra. But that is not possible, since they now have quite independent lives and think quite different thoughts from each other. This objection does not apply to theories which demand a great degree of continuity and connectedness between P1 and P2 for P2 to be identical to P1, for then it would only be possible for one later person to have that degree of continuity and connectedness – for example only one later person could have 60% of P1's brain. Some theories which would otherwise be open to this objection avoid it by adding a condition that P1 cannot be P2 if there is some other person P2* who satisfies the other conditions of continuity and connectedness with P1 as well as or better than does P2. Thus Robert Nozick (‘The Identity of the Self’ in his Philosophical Explanations) claimed that to be P1, P2 has to be the ‘closest continuer’ of P1. Continuity, he claims, consists in the brain states of P1 causing subsequent brain states of P2, which in turn cause P2 to have memories and character continuous with that of P1 – so long as there is no rival candidate P2*who satisfies these criteria better than does P2.

It is because of the extreme arbitrariness of any attempt to make such theories precise (and also in the case of many such theories, because of the more-than-one-candidate objection), that philosophers who produce such theories have typically not filled them out in detail. Rather, some philosophers have produced what Harold Noonan (Personal Identity, chapter 6) calls a ‘semantic indecision’ theory. This holds that replacing a relatively small amount of P1's brain matter and making relatively small differences to P1's memory and character over a relatively short interval has the consequence that the resulting person is still P1; and that replacing a relatively large amount of P1's brain matter and making relatively large differences to P1's memory and character over a relatively large interval has the consequence that the resulting person is not P1. But it claims that it is ‘neither true nor false’ that the person resulting from replacing an intermediate amount of brain matter and making intermediate differences to P1's memory and character is P1. After all, when a surface is reddish-blue, it is neither definitely true that the surface is red nor definitely false that the surface is red. So why should we not say the same sort of thing about personal identity?

My answer to that question is that the arbitrariness objection resurfaces in a different form. For the question then arises as to how small are the differences to P1's brain and memory over how short a time which guarantee that P2 is definitely the same person as P1, and how large are the differences to P1's brain and memory over how long a time which guarantee that P2 is definitely not the same person as P1. How wide is the border region of differences from P1 such that it is ‘neither true nor false’ that P2 is P1? Any answer to this question will be extremely arbitrary Why say that if no more than 10% of P1's brain is replaced over 5 years P2 is definitely P1, and if more than 30% of P1's brain is replaced over 5 years is definitely not P1: but intermediate amounts of replacement over intermediate periods have the consequence that it is ‘neither true nor false’ that P2 is P1. But, unlike in the case of it being ‘neither true nor false’ that the surface is reddish-blue, it matters greatly to someone about to go undergo an operation whether they will definitely survive the operation, or whether it will be ‘neither true nor false’ that the subsequent person will be them. They would certainly prefer definitely to survive the operation; and they might well wonder what it would be like for there to be a subsequent person who was neither them nor not-them. And whatever that state was like, they would almost certainly prefer it to a state in which they definitely did not survive the operation. But any philosophical theory which told them the minimum degree of continuity with themselves which would make it definitely that case that the succeeding person was them, and the minimum degree of continuity, having less than which would make it definitely the case that the subsequent person was not them would be extremely arbitrary. And so there would not be the slightest reason to believe any one such theory.

It is because of the continuity between persons who have less and less of the brain matter of some person P1, and less and less of the memories and character of P1, that most of those who advocate complex theories of personal identity have moved to a theory of personal identity which reflects that continuity. This is a theory of ‘partial identity’. (The term ‘partial identity theory’ to describe these theories is mine, but that is in effect their nature.) The claim is that the less and less of P1's brain matter and/or memories and character a subsequent person P2 has, and the less and less gradual is the process by which the change occurred, the less is the identity of the subsequent person P2 with P1. Among the eminent philosophers who have advocated such a theory are Robert Nozick, David Lewis and Derek Parfit. Nozick (‘The Identity of the Self’ in his Philosophical Explanations) described later persons who evolved causally from earlier persons as being their ‘continuers’; Lewis (‘Survival and Identity’ in his Philosophical Papers, vol. 1) wrote of personal identity as ‘a matter of degree’ of a relation (of continuity and connectedness) which he calls the ‘R relation’: Parfit (Reasons and Persons, Part 3) wrote of later persons being (to different degrees) ‘survivors’ of the earlier person (to the extent to which they have physical and mental continuity and connectedness with them). For all these writers the facts which a theory of personal identity needs to describe are the extent of such continuity and connectedness, which is in effect the ‘partial identity’ of a person with an earlier person. According to these philosophers, to call a future person really ‘identical’ with a past person is to use an imprecise ordinary language term to describe the case where some person has a very great degree (perhaps the maximum degree) of continuity and connectedness with a past person, and (as Nozick insisted) a greater degree of continuity and connectedness with that person than with other persons. Advocates of these theories point out that the identity of a later inanimate physical object with an earlier one is a matter of degree. A later table is naturally described as being ‘partly the same’ as an earlier table, if it is made of only some of the parts of the earlier table, for example if it has all the legs of the earlier table but a different tabletop. The facts in virtue of which we might say that a later table is ‘totally the same’, ‘partly the same’ or ‘hardly the same’ are the degree of continuity of its parts with those of the earlier table. It has greater continuity with the earlier table if it has most of the parts of the earlier table, and so is ‘more identical’ to it than it would be if it only had a few parts of the earlier table. Why should we not say the same about persons, perhaps taking into account the continuity of their memories and character as well as of their brain matter?

There is, however, an enormous difference between persons and inanimate things such as tables in that an earlier person being identical with a later person entails that the earlier person is going to experience the experiences of the later person. Inanimate things do not have experiences; and so their identity can rightly be analysed in terms of the continuity (and perhaps connectedness) of their parts. But if personal identity is ultimately a matter of the degree of continuity between successive persons, it must give an account in terms of continuity of why and when a person has reason to fear the bad experiences and to hope for the good experiences of any person who is a close ‘continuer’ or ‘survivor’. Presumably it must say that a person has more reason to fear or hope for the experiences of a future person to the extent to which that future person is a close continuer of themself. But that leads to what I regard as a conclusive objection to any such ‘partial identity’ theory. While only some of the complex theories that I discussed earlier, which entail that any future person either definitely is or definitely is not identical to the earlier person, are open to the more-than-one-candidate objection, all ‘partial identity’ theories are open to a form of this objection. On any theory on which continuing to exist is a matter of degree, it is always possible for P1 to have more than one continuer (or whatever), although one of them may be a closer continuer than another. For example, if P2 has only 70% of P1's brain, then the remaining 30% can be given to P2*; and so while P2 is a close continuer of P1, P2* is also a continuer, although a less close one. But since they are both continuers, then P1 will be going to have (to different degrees) both the experiences of P2 and the experiences of P2*. So if P1 knows in advance what is going to happen to his brain, and also knows that P2 is going to have a happy life, and P2* is going to have a miserable life, then P1 must expect to have a life that is partly happy and partly miserable (although of course more happy than miserable, because P2 is a closer continuer than P2*). But what can that mean, since no future person is going to have a life that is partly happy and partly miserable? P2 and P2* will have quite different lives, and neither of their lives will include a mixture of happiness and misery. So perhaps the suggestion is that, as with tables, part of P1 is going to have a happy life and part of P1 is going to have a miserable life. But experiences are properties of persons, not properties of parts of persons: while part of my brain may be the cause of me hearing a sound and part of my brain may be the cause of me feeling pain, it is I who co-experience both the sound and the pain. It cannot be the case that one part of me looks forward with pleasure to P2's experiences, and a different part of me looks forward with fear to P2*'s experiences. So the partial identity of both P2 and P2* with P1 cannot consist in P2 being identical with one part of P1 and P2* being identical with a different part of P1. For these reasons it seems impossible to make sense of the notion of a future person being partly identical to an earlier person; degree of continuity of brain or memories cannot be what personal identity consists in.

I conclude that no complex theory can possibly analyse what it is for one person to be identical with a later person, because no such theory can analyse what it is for an earlier person to be about to have the experiences which some later person is going to have. It simply isn't enough for there to be any degree of continuity and connectedness between the experiences of the earlier and the later persons. In contrast to ‘complex theories’, a ‘simple theory’ claims that personal identity cannot be analysed in terms of any properties or substances of which there can be different degrees or quantities, since – for the reasons which I have given – personal identity is all or nothing; each person is or is not the same person as an earlier person, and there is no intermediate possibility. Certainly, the greater the continuity (and connectedness) between P1 and P2 of brain, memory and character, the more probable it is that P2 is P1, but this continuity is only probabilistic evidence of personal identity, which is something different from that continuity. (Just as a footprint in the sand makes it probable that someone walked there, but someone having walked there is something quite different from there being a footprint in the sand.) But then in what does personal identity consist? Why not just say that it is ultimate and unanalysable, and that P2 being the same as P1 cannot be analysed further? Why not just say that either P1 is the same person as P2 or P1 is not the same person as P2 are unanalysable truths, even if we cannot know which one is the true one?

The problem with this is that it is incompatible with a highly plausible principle which I call ‘the principle of the identity of composites’, and which I will now explain. A substance is a thing which has properties, a component of the world, and it may or may not have other substances as parts. Thus, the Milky Way, my house, my desk, and each of the atoms of which my desk is made are all substances; they all have properties including properties of shape, mass, volume, colour and such like. Persons are substances. The principle of the identity of composites states that:

Consider a certain car C1 parked at a certain time in a car park. It has many different parts – engine, wheels, seats, and so on – arranged in a certain way. The car has had a certain history during which it has gained or lost various properties and parts. Each of its parts has had a certain history during which the part has gained and lost various properties. Now is it possible that instead of this car, there could be instead of C1 a different car C2 parked in the same place at that same time which was made of all the same parts arranged in just the same way, parts which had all the same properties as C1 at each moment as the other, and yet is a different car? It doesn't make sense to suppose this. The history and the properties of the car, and the history and properties of its parts, fully determine which car it is; it is simply not compatible with all that I have described being the same, that C2 could be a different car from C1.

Now reconsider the earlier example of P2 being formed of some of the parts of and having some of the memories of the experiences of P1. A person is a substance. So, by the principle of the identity of composites any person P2* formed from exactly the same parts (obtained from P1) as P2 (including brain parts), arranged in the same way as these parts, having had the same properties and history as those of P2, and having exactly the same memories of P1's experiences as does P2, and exactly the same degree of similarity of character to P1 as does P2, would be P2. It follows that if the only parts of P2 are physical parts, and it and the parts have had a certain past history (including having certain past experiences), then it would not be possible for P2 still to be either P1 or not P1 (and so some other person). The principle does not determine whether P2 is P1, but it does follow that either it is a logical consequence of its past history and all its parts that it is P1 or it is a logical consequence of its past history that it is not P1 – if the only parts it has are physical parts. But given a ‘simple theory’ for which I have argued, the physical parts and their properties (mental and physical) of P2 may be quite insufficient to determine whether P2 is or is not P1. So P2 must have another part which determines whether the future person is or is not P1. That part must be a non-physical part; and it must be an indivisible part, since if it was divisible the problems discussed above would reappear in the form of a problem of what proportion of that part would be necessary for P2 to be P1. This non-physical indivisible part is what we call P1's ‘soul’. And, given that there is a person P2 who has P1's soul, any suggestion that physical parts or mental or physical properties are also necessary in order for P2 to be P1, would also be open to those same difficulties about what proportion of these features would be necessary. Hence, I conclude that if there is a person P2 who has P1's soul, then P2 is P1; and if a person P2 does not have P1's soul, then P2 is not P1. Normally, no doubt, when there are no large brain transplants or amnesia, our soul goes where our brain goes: but in the puzzle situations, no one can know where our soul goes. Nevertheless, in all circumstances our soul determines who we are.Footnote ¹