Gappy Things That Branch and Change

IdentityImagine, in the early days of books, a small library consisting entirely of original manuscripts.  Some of them are very old, and have been attacked by mice.  Some have deteriorated so much that their pages crumble to dust when the custodian of the library tries to read them.  He mourns the loss of these books, and contemplates the inevitable decay of the remaining books with sorrow.  To be sure, new manuscripts are occasionally added to the library, but they cannot replace the volumes that are lost forever.  This goes on until, one day, the young assistant librarian has an idea.  “This book will be unreadable in five years,” he tells his elder.  “But I can read it now.  If I copy the words of this book onto sheets of new vellum, and bind them in a strong new binding, we will be able to read it for many decades to come.”  The old librarian tenderly strokes the cracked spine of the crumbling volume, and shakes his head.  “What good is a copy?  It wouldn’t be the same book.”

In the previous post, I summarized one of Derek Parfit’s main arguments that personal identity – being the same person over time – is not what matters in survival.

Human fission – one person ‘splitting’ into two – is clearly imaginable.  It is physically possible, and is not far from being technically possible.  Parfit argues compellingly that fission would preserve what is important in survival.  Specifically, if Parfit knew that both of his cerebral hemispheres were about to be separately transplanted into two separate bodies, he would have the same rational justification for anticipating the experiences of both of the post-op survivors as each of us has for anticipating his or her own future experiences.  This, despite the fact that the original Derek Parfit ceased to exist when he was divided.  In this case, ceasing to exist is very unlike ordinary death.  Ceasing to exist just consists in the fact that the two post-op survivors are different persons from one another, and neither one is the same person as the pre-op Derek Parfit.  Loss of identity of this kind does not matter.

Several attacks on Parfit’s theory stem from his philosophical opponents’ (Unger, Sosa, Johnston) unwillingness to abandon the idea that identity is, after all, what matters in survival.   Some of his sympathizers (Noszick, Lewis) have shown similar unwillingness.

I will introduce this subject with some general remarks on identity and concepts. Concepts are human artifacts.  Our concepts reflect our purposes.  Concepts subdivide reality into entities that are important to us.


Most material things we speak of have ‘natural’ boundaries in space and time.  Their boundaries are well defined on the scale in which most human action takes place.  They are not always well defined on a very small scale.  The spatial boundary of an animal is the outer surface of its skin, hair and nails.  As the animal moves through the world, almost all the material within that boundary moves.  However, if we were to examine the boundary at the molecular scale, we would see constant shedding of skin flakes, hairs, drops of perspiration, and airborne molecules of the animal’s scent.  Our concept of an animal, although as clear as any concept, does not precisely answer questions as to where the animal ends and its environment begins, or when a given molecule – of water perhaps, or of some organic compound – ceases to be part of the animal’s body.  There is a thin ‘grey area’ between what clearly is, and what clearly is not, part of the animal’s body.  There may be no correct answer to the question whether a given molecule, at a given time, is part of an animal’s body.  The reason there is no correct answer is that we deal with animals at a much larger scale.  Our concept of an animal does not decide exactly when an escaping molecule ceases to be part of the animal, because that is not something we normally care about in our dealings with animals.

The temporal boundaries of living organisms are often rather worse defined than the spatial ones.  An organism that reproduces sexually can reasonably be said to begin when sperm unites with egg and the chromosomes from each entwine in the double helix.  That process takes time, making it hard to pinpoint an animal’s beginning as precisely as one second, let alone a millisecond.  And the ‘moment’ of death is a rather protracted process. Within these periods of time at the beginning and end of an organism’s life, the question, “Does it exist now?” has no clear answer.

The fact that questions about boundaries of things often have no clear answers is not mysterious.  It is explained by concepts being human artifacts, devised for human purposes.  Whether a single hair from a calf’s tail drops off or remains attached does not affect the animal’s price at auction.  A single hair is not something we care about in our everyday dealings with animals.  The everyday concept of a calf serves everyday purposes without arbitrating precisely when a droplet of mucus passes through its nasal membrane and ceases to be part of the calf.

Another reason the grey areas of boundaries do not matter much, is that if they come to matter, we can always stipulate an answer.  That is what we do when there is vagueness about things that matter to us.  We add words, and increase the precision of our language.  If concepts carve up the world, then refining a concept is like sharpening a knife and using a magnifying lens when we cut.

Refining a concept through stipulation is sometimes arbitrary, but is more often guided by our contextual purposes.  An island is a body of land surrounded by water,  larger than an islet and smaller than a continent.  A peninsula is an island-sized body of land, connected to a larger landmass by a land-bridge, or isthmus, narrower than itself.  Is a body of land which is connected to a larger landmass only at low tide an island or a peninsula?  Dictionaries do not answer this question.  But the answer might be important to buyers and sellers of islands.  Suppose you are a realtor with a specialty in whole-island properties.  Your website extols the benefits of privacy, tranquillity, and security that come with owning an entire island.  If one of your clients was under the impression that he had bought an entire island, only to discover – too late – that it was connected to ‘another island’ by an easily walkable strip of sand at all by the highest tides, and that the ‘other island’ was occupied by a notorious motorcycle gang, he might have grounds for a lawsuit.  You might want to stipulate in your advertising that what you mean by an island is a body of land completely surrounded by water at all tides, since only an island meeting that description has the advertised benefits.  This stipulation is a non-arbitrary refinement of the concept of an island, which you might recommend to other realtors, and propose as an industry standard.  If the idea caught on widely, this refinement might become part of the common concept of an island, and eventually make its way into dictionaries.

I stress that concepts are human artifacts, tools which serve human purposes in clear communication, because I am about to propose a conceptual reform of the concept of a person, and I don’t want to run foul of the objection that my reformed concept is not the concept of a person because it is not the traditional concept.  As we have seen in past posts, the traditional concept of a person is not up to the demands we have begun to place on it.  It is unsatisfactory for describing cases of human teleportation and human fission.  Since technologies which can enable teleportation and fission are physically possible, economically desirable, and possibly not too far in the future, we need to think about replacing the traditional concept of a person with a more capable one.


Parfit and most of his critics seem to accept the view that personal identity is not preserved across a spatio-temporal gap.  On this view, if I am about to ‘travel’ by means of information-based teleportation, the person who will arrive at my destination will not be myself.  I will not be, strictly speaking, the same person at my destination as I was at my port of origin.  Although that person may be qualitatively identical to me (that is, exactly similar), he will not be numerically identical to me (that is, the same person), because of the spatio-temporal gap.

Another point often made is that identity of persons, and other things, cannot take a branching form.  If an amoeba undergoes mitosis, splitting into two amoebae, we say that the original organism no longer exists, and two new organisms have come into existence.  To say instead that the original amoeba survives the split as one, but not the other, would be arbitrary.  And to say that the original amoeba survives as both would require us, by the logic of identity, to say that the two survivors are a single amoeba.  That violates the convention by which we count amoebae.  Hence, the argument goes, when branching occurs, identity is lost.

Spatio-temporal continuity and adherence to the non-branching rule are both necessary for numerical identity of most kinds of physical objects, including biological organisms.  But for some other kinds of entities, neither are necessary.

Identity is a formal concept.  Numerical identity is defined by its formal properties.  Those properties belong to logic, the rules of discourse which allow us to communicate clearly and precisely.  There are four properties of identity.  (1) Reflexivity.  Every entity is identical to itself.  (2) Symmetry.  If any entity x is identical to any entity y, then y is identical to x.  (3) Transitivity. If x is identical to y, and y is identical to z, then x is identical to z.  (4) Identity obeys Leibniz’ Law.  If x is identical to y, then any statement that is true of x is also true of y.

That is the classical definition of numerical identity.  There are philosophical challenges to the classical definition, and competing definitions are on offer.  I don’t intend to examine those challenges and competitors in this project.  Classical identity is adequate for this discussion.

Because identity is a formal concept, defining logical rules of discourse, it is equally applicable to all sorts of entities.   Its rules apply equally to entities that people commonly talk about – for example, rabbits – and to entities that people rarely talk about – for example, rabbit-stages.  (A rabbit-stage is a time-slice of a rabbit.  Only philosophers talk about rabbit-stages.)  Jojo, my neighbour’s pet rabbit, ate yesterday and is eating at this moment.  Jojoy, the time-slice of my neighbour’s rabbit that existed at the moment of noon yesterday, was asleep, not eating.  Jojoy – who existed only for a moment – never ate anything.  (Since eating takes time, it is arguable that a time-slice can’t eat anything.)

I introduce rabbit-stages to illustrate how different concepts divide reality in different ways.  The concept of a rabbit-stage is coherent, even useful on occasion (although for most practical purposes we are better served by talking about rabbits).  The concept of the set containing all red face cards plus the eight of spades is even less useful, but is perfectly clear.

For materialists, the spatio-temporal boundaries of persons coincide closely with the boundaries of our biological organisms.  I have argued that a means of physically separating them may be available in the not-too-distant future.  Some object that the idea of separating them is incoherent, because persons are identically biological organisms.  The thought-experiments of personal identity challenge that view.  They persuade people that a person, unlike the organism it depends on, can cross a spatio-temporal gap by teleportation, that is, ‘travelling as information’.  Parfit says no, the person would not survive teleportation, because the technology that makes teleportation possible can also produce branching, and identity would be lost if there were branching; however, teleportation would preserve what is important in personal survival.  If the technology worked reliably, we should not fear it.  We should not regard teleportation as death.

Why Identity May Matter After All

Several of Parfit’s critics balk at his view that ‘personal identity does not matter.’  They do not accept that someone who is about to be teleported to Australia can reasonably expect to have the experiences and live the life of the post-teleportation person in Australia, without being that person.

Their argument has force.  The force of it, I think, has to do with the fact that our concept of a person is tightly bound to what is important to us about being the same person – which includes the relation (whatever it is) that justifies us (we think) in expecting to have future experiences, and in feeling responsible for our past actions.  Parfit recommends divorcing the concept of a person from one of the things that is most important to us about being a person – perhaps the most important thing!   No wonder it is hard to swallow.  Our concepts reflect what is important to us.  If we cannot define an entity whose identity conditions coincide with the extremely important relation that ‘matters’ in survival, perhaps there is something wrong with our ideas.  Without a concept of an entity, we have difficulty even talking clearly about these matters.

I think that Parfit, in accepting the conventional wisdom that personal identity cannot survive a spatio-temporal gap and cannot branch, may have missed an opportunity.  Although the identity criteria for biological organisms obey those rules, the case can be made that persons are not, identically, biological organisms.  This case can be made without abandoning materialism; it does not imply that persons are ‘separately existing entities’ or ‘spiritual substances’.

Things that are Gappy, Things that Branch

Some things can cross spatio-temporal gaps, and can also survive branching.  These are not ‘artificial’ entities that only appear in philosophical examples, but entities that figure in everyday speech, because they are central to human concerns.

Consider books.  Derek Parfit’s book, Reasons and Persons, is in my personal library.  The same book is, I’m fairly sure, in his library.  The same book is in university libraries around the world.

The word “book” is ambiguous.  It refers to two types of entity.  One type is a printed volume, with physical attributes such as weight, location, and some number of dog-eared pages.  The other type of book is an intellectual work, with attributes like word count, subject matter, and number of citations in peer-reviewed journals.  We describe entities of the former type as ‘copies’ of entities of the latter type.

We distinguish between the two types of book – the printed volume and the intellectual work – because both are important to us.  The two types have very different identity conditions.  My volume of Reasons and Persons came into existence when it was bound at the printer.  Perhaps it will be destroyed when my heirs clean house after my death.  But that will not be the end of Parfit’s intellectual work, because it will continue to exist in other volumes in other libraries, and in electronic files, and – perhaps – also in manuscript.

The intellectual work, Reasons and Persons, is not spatio-temporally continuous; it is distributed over many copies in different places.  And books branch, in a straightforward sense, whenever they are copied.

The reason there are two concepts of book is that books are easy to copy.  There was a time when copying books rarely occurred.  We can imagine debates, in that ancient time, about the identity of books.  The potential confusion between the two concepts of book is illustrated by the little story with which I began this post.

There is more to that story than confusion of two concepts with the same name.  The old librarian’s confusion lay in losing sight of what is important about books.  What is important about a book continues to exist as long as at least one copy of the book exists.  Any copy will do.

I suggest that when persons become easy to copy, as they will when we develop the scanning/replicating technology that supports teleportation, we will start to distinguish between two kinds of entities that we now tend to conflate.  We use the word “person” for both.   One kind has the identity conditions of human organisms; indeed, a ‘person’ in this sense is (identically) a biological organism.  The other kind of ‘person’ is the sort of thing that can cross spatio-temporal gaps, and can branch.  This sort of person can survive teleportation and duplication.  Like a book, this sort of person can survive destruction of one ‘copy’ if another ‘copy’ exists, or can be constructed on the basis of stored information.  And most of what is important about persons will be true of this sort of person.  Because this concept captures what is most important about persons, I recommend using the word “person” to refer to this kind of (potentially gappy, potentially branching) entity, rather than to the biological organism.

Persons are, I claim, like books (the intellectual work, not the bound volume) in that a good copy preserves what is most important.  A book can exist in one or several copies, in one medium or different media.  It is only destroyed if all copies are destroyed.

Books are, of course, unlike persons in many ways.  Books are not conscious.  Neither are they alive.  They do not change, much.  The fact that a book does not change, much, after it comes into existence makes it relatively easy for us to answer questions of the form, “Is a the same book as b?”  If a and b have the same author, and the same, or almost the same, word content, then a and b are the same book.   The concept of a book does allow for some changes, including typographical corrections and the modest addenda that may be found in successive editions.  If the differences between editions are important to us, we have no difficulty in making ourselves clear.  (“I am in the market for a first edition, signed by the author.”  “The passage I quoted is on p. 394 of the 1990 edition.”)  But for most of our book-related questions, like “Have you read Moby Dick?”, edition doesn’t matter.

It’s interesting to contrast books and paintings.  In the fine arts world, the distinction between original and copy is of paramount importance.  A copy of a book is the book, whereas a copy of a painting is a forgery.  Although the market value of a painting derives largely from the artistic qualities of the image, most of that value inheres only in the original.  A photograph of the painting, no matter how faithfully it captures the image, has low market value.  Books are not like that.  We will pay more for a finely bound edition than for a paperback; but that difference reflects costs of production.   We will pay more for a copy signed by the author; but in that case we are paying for the signature.  When we buy a painting by Tom Thomson, on the other hand, we are investing in a unique artifact.  If it is destroyed in a fire, no copy, even of the highest quality, can preserve our investment.

Musical compositions are like books, and unlike paintings.  Beethoven’s Fifth is the same symphony when played in Vienna in 1808 or in Vancouver in 2010.  Songs and dances are like that too.  But unlike books and classical symphonies, songs and dances are volatile.  Performers often adapt them.  Verses are added to songs, or dropped; the tempo of a dance may change to suit the age and spirit of the dancers, and new steps are introduced.  Over time, a song or dance may change so much that we call it a different song or a different dance.  When a song or dance is adopted by two different groups and begins to diverge, we are quick to recognize two distinct entities.  Because they are so volatile, the identity of songs and dances is soon lost when they branch.

Many entities that branch, including recipes, games, and software programs, are intellectual artifacts.  Some are not.  The HBB gene associated with sickle-cell anemia is a naturally occurring entity, which is widely distributed over space and time in the chromosomes of myriad human cells.  Genes branch through mutation.  Biological species are natural entities that branch as a result of evolutionary changes following the physical separation of breeding populations.

Things that Branch and Change

Recipes are a good example of a kind of thing that can span spatio-temporal gaps, branch, and change over time.  A recipe can be in many places at once.  The recipe for Wilma’s Ginger Snaps is on the Rolodex in my kitchen; the same recipe is in the kitchens of most or all of Wilma’s six children; and the same recipe is on the eMom recipe wiki.  Recipes are volatile.  Cooks are always changing recipes in response to family tastes, dietary restrictions, ‘healthy eating’ fads, and available ingredients.  Omitting a quarter teaspoon of salt from my waffle recipe is a minor adjustment which does not justify calling it a new recipe.   But many minor changes, over time, may add up to major changes which would induce us to talk about different recipes.  If I start with a recipe for orange cake, but substitute lemons for oranges because I relish the sourness of lemon; and a friend of mine, starting from the same recipe, substitutes ground almonds for flour because of a family member’s gluten allergy, we pretty soon have two recipes.  Although clearly distinct, and meriting two names (Flourless Orange Cake, Gordon’s Lemon Cake) the two recipes have a shared past in the cookbook from which my friend and I both started, and in the entire history of that recipe prior to its inclusion in that cookbook.

Recipes provide a model for things that can cross spatio-temporal gaps, and can branch.  Unlike books, recipes often change substantially after being copied.

A recipe is a simple thing.  When a recipe changes substantially, it unproblematically ceases to be the same recipe.  This is because the history and origins of recipes are, for common purposes (culinary purposes) relatively unimportant.

Persons – A Proposal

The history and origins of individual persons are very important.  It strains the concept of a person to say that, if a person is divided in the way Parfit imagines (preserving memories, personality, skills, and even important physical attributes such as general appearance, genome and bodily age) then two new persons begin to exist at the time of division, and the original person ceases to be.

I think society will discourage, perhaps outright ban, the making of multiple concurrent copies of a human being.   But I also think it is likely to happen occasionally.  Accidents, like the one in the story Forking, will happen.  Some people will act outside the law.  Governments may make exceptions, under exceptional circumstances.   If human replication technology had been available during WW II, the U.S. government might have been sorely tempted to accelerate the Manhattan Project by making a few copies of Fermi and other key personnel.

If and when human replication happens, it will become important to distinguish between the copies of each person.  Each post-split individual will require a unique social security number.  Arguably, each will deserve a vote, and should be counted in a census.  Each will be responsible for his own post-split actions, and for paying taxes on his earnings.  Because they will live separate lives, we will count them as two post-split persons, not a single person with two bodies.

But it will also be important to recognize the connection of post-split individuals to their shared past.  It will not do for an adult to give her age as three weeks on the grounds that her existence began on the split date.  Since age from birth is tied to many rights and obligations, that attribute should be inherited by the post-split individuals.  So should country of origin.  So should educational degrees and diplomas.  So should moral and legal responsibility for pre-split actions.

The concept of a person which preserves all those important characteristics in branching cases has the form of David Lewis’ model in “Survival and Identity”.  If a person divides into two, then there are two post-split persons.  Both persons began to exist long before the split occurred. They have a shared past.  It follows from the logic of identity that there were two persons all along, before the split as well as after.

This is startling.  But it does not, I think, do unacceptable violence to the concept of a person.

Consider the two Elliots in Forking, post-split.  When discussing their shared past, they find it natural to use the pronoun “we”.

“Remember,” [Elliot] finally says, “how we smoked Mike Partridge?”  As he sees, in the other’s sudden change of expression, the memories flooding back, his sense of their radical kinship deepens profoundly.

The naturalness of this way of talking supports the idea that there were two.

But the idea remains startling.  Pre-split, they would not have been counted as two.  Nothing about them indicated duality, or distinguished them from any other individual who was just one person because a split was not in his or her future.

Besides persons, are there other kinds of entities that branch this way?   If persons are the only kind of thing that takes this form, that should cause some discomfort.

The comparison to recipes, songs and dances breaks down, because their history is not so central to their identity as in the case of persons.   They are comparatively simple artifacts, lacking an analog to the important unifying relation of psychological connectedness and continuity.

Software programs may be a better model.  Like books, recipes and songs, programs are easy to copy.   They change frequently, not only by versions, but by builds.  My computer is now running FireFox version 3.5, build 30729.  Some programs are complex, and their history is fairly important.  Subtle attributes of programs, including latent bugs, are inherited from earlier versions. Programs can branch like recipes (but do so less frequently).

Some programs can modify their behaviour in response to input, in ways that resemble learning from experience.  Such programs begin to diverge whenever they are copied and run.  But the identity conditions of programs that change by ‘learning’ are not intuitively obvious.  That may be because few such programs exist, and they aren’t important to many people.  A comparison to software programs does not give us strong reasons for favouring a particular model of personal identity.

I cannot think of a compelling analog for branching persons, and therefore I am still a little uncomfortable with the recommendation.

But I am not uncomfortable with the idea that persons resemble books, dances, games, recipes, and genes in being the kind of thing that can span spatio-temporal gaps.  Persons can do so because everything important about a person can be captured as information, which can be used to make a replica.  This is true of a broad class of entities, which I will call “informational entities.”  The idea that persons are informational entities captures the intuition that if someone is teleported to Australia, he is not mistaken in his belief that he is the same person who left Ottawa earlier that day.  This idea seems to me illuminating.   We can be teleported successfully because we are more like intellectual works than like printed volumes.

On this view, we are not identically biological organisms.   We do depend, for our existence, on our organisms.  Each of us requires an organism, as software requires hardware to run.  And until we develop replication technology, or the ability to surgically transplant two hemispheres into separate bodies as Parfit describes, the spatio-temporal boundaries of ourselves and our organisms will continue to coincide very closely.

Parfit’s Division is not unlike amoebic division, surgically induced.  A flatworm can be replicated successfully by being cut in two.  The identity conditions for biological organisms dictate that the number of organisms surviving the operation is two, not one, and that neither of them is identical with the original organism, which ceases to exist when its brain is removed.  But Derek Parfit, born in 1942, survives the operation.

If Parfit’s double transplant surgery is successful, two persons exist afterwards.  By the logic of identity, there were two all along.  That remains startling, but is less so when we realize that persons are informational entities.  The fact that, pre-split, there is no evidence of more than one person is no more mysterious than the fact that a single recipe may branch, in different kitchens, into two or more recipes.  Because persons are not biological organisms, we should not be too surprised that they are not counted like biological organisms.  And because they have, until now, always coincided with organisms, we should not be surprised that we are startled by that conclusion.


Johnston, Mark (1997) “Human Concerns Without Superlative Selves”, in Martin and Barressi, ed. (2003) Personal Identity

Lewis, David (1983) “Survival and Identity”, in Martin and Barressi, ed. (2003) Personal Identity

Nozick, Robert (1981) “Personal Identity Through Time”, in Martin and Barressi, ed. (2003) Personal Identity

Parfit, Derek (1984) Reasons and Persons

Sosa, Ernest (1990) “Surviving Matters”, in Martin and Barressi, ed. (2003) Personal Identity

Unger, Peter (1990) “Fission and the Focus of One’s Life”, in Martin and Barressi, ed. (2003) Personal Identity

Wiggins, David (1967) Identity and Spatio-Temporal Continuity

Leave a Reply