Randomness and identity

Suppose an amoeba biologically symmetrically splits into two cells, A and B. Here are the main options for what happens metaphysically:

1. The parent perishes and the child cells are new organisms.

2. The parent becomes a scattered two-celled organism.

3. The parent becomes A, and B is a new organism.

4. The parent becomes B, and A is a new organism.

Typically, philosophers dismiss options (3) and (4) as arbitrary in cases where the splitting is symmetric. Option (2) is implausible, so that leaves option (1).

But now consider an option that the above argument for (1) does not consider:

5. Indeterministically, the parent has chance 1/2 of becoming A, with B being new, and chance 1/2 of becoming B, with A being new.

(Technically, this is not another option, but a further specification of (3) or (4).) Rule (5) is perfectly symmetric between A and B, so there is no arbitrary preference in the rule—though of course the random result may be said to be arbitrary.

I expect that the main reason (5) is usually not considered is that it is assumed that the answer as to which of (1)–(4) happens supervenes on qualitative biological features of the amoeba and offspring system. But if we have a “further fact” view about identity, or if we are dualists about amoebae—say, because we think that an amoeba has a non-physical soul or form that—then I think (5) is not at all crazy. There could well be indeterministic laws of how the “further fact” behaves or where the soul goes.

Of course, (5) is not the only indeterministic symmetric option that avoids scattered individuals. One could have a view where there is a 1/3 chance for each of options (1), (3) and (4). Or where there is a 2/3 chance of (1) and a 1/6 chance of each of (3) and (4).

Some people will think that amoebae do not have “further facts” or souls, but are entirely physically reducible. I am far from confident of that. But in any case, whether the indeterministic solution works for amoebae, it could well work for humans, whether in actual cases of early twinning or in science-fictional brain splitting thought experiments.

Here is another metaphysical difficulty where an indeterministic answer might work. Consider beginning and end of life issues: when do constituents come together as a new organism and when do organisms depart from life? It feels arbitrary to suppose, say, that when the damage exceeds some threshold, the organism must die there and then. But what if we suppose that there is a continuous distribution—say, something like an exponential one—with parameters continuously depending on the degree of damage, governing the random point at which the organism departs from this life if the damage is not changed? Of course, this kind of a story only makes sense on a non-naturalistic picture where there is some further unobservable fact about life.

I wonder what other metaphysical questions might have random answers.

Length and the memory theory of personal identity

1. That there is an entity that is 25 inches long in 1973 and 72 inches long in 1993 is not even partly grounded in facts about anybody’s memory.

2. If the memory theory of personal identity is true, the existence of such an entity is at least partly grounded in facts about my memory.

3. So, the memory theory of personal identity is false.

Premise (1) is a raw appeal to intuition.

Premise (2) follows from the following:

1. Normally an existentially quantified fact is grounded in each of its instances.

2. I was 25 inches long in 1973 and 72 inches long in 1993.

3. I was a person.

4. The case at hand is a relevantly normal case.

I suppose the memory theorist just needs to deny (1).

Identity and eternity

Suppose that you are an immortal who lived for an infinite amount of time, and each year, your body replaces all its cells with new cells constructed from the matter in your food. Furthermore, you only eat local food, and at the beginning of each year it is randomly chosen by a coin toss whether you will live in Australia or America. Moreover, in the world we are imagining, the food in Australia and America has no matter in common.

Consider these two plausible principles:

1. If x and y are people living in worlds w₁ and w₂, respectively, and at no time t in their lives do they have any matter in common, then x ≠ y.

2. The identity of an already existing person never depends on what will happen to that person in the future.

But now whether you exist in year n does not depends on what happens in year n, since you are immortal and by (2) your identity was already determined in year n − 1. By the same token, whether you exist in year n does not depend on what happens in year n − 1, and so on. In particular, it follows that whether you exist now does not depend on any particular coin toss. However, by (1) whether you exist does depend on the totality of the coin tosses, since if all the coin tosses go differently from how they actually do, the matter in the body would always be different, and hence by (1) the person would be different.

But it is quite paradoxical that your existence depends on the coin tosses collectively and yet each one is irrelevant. This points to the hypothesis that beings that are significantly changeable cannot be eternal (and slightly supports causal finitism).

If you think that your identity also depends on your memories, add that in Australia and America you form different memories. If you think that your identity depends on your soul, then instead of running the argument about a human being, run it against something soulless.

If you think all complex objects have something like soul (as I do), the argument may not impress.

Identity and quantification

One way of posing the question of diachronic identity is to ask for an explanation of facts like

1. The xs compose the very same object at t₁ as the ys compose at t₂

where we do not use sameness or identity or similar concepts in the explanation.

This task turns out to be quite easy. The following is logically equivalent to (1) and does not use sameness or identity:

2. There is an object z such that the xs compose z at t₁ and the ys compose z at t₂.

This is a variant of the point made here.

Two brutenesses

Some philosophers think identity over time is brute: diachronic identity facts are not further explained. Markosian proposed (though later rejected) a view on which composition is brute: whether a bunch of simples make up an object at a time has no further ground.

It seems to me that it would be very natural to hold the two views together in the case of objects composed of simples. Consider the thesis:

• When we have a plurality of particles at t₁ and a plurality of particles at t₂, it is brute whether there is one object which both pluralities compose.

If the pluralities are the same and t₁ = t₂, then as a special case we get the bruteness of composition. And if we presuppose that both pluralities compose, then we get the following bruteness of identity for objects composed of simples: namely, it being brute whether the object at t₁ composed of the xs is identical with the object at t₂ composed of the ys. Since bruteness of diachronic identity for simples is itself extremely plausible, and it is very plausible (pace gunkiness) that everything is either simple or composed of simples, it follows that the above thesis very plausibly yields bruteness of diachronic identity in general.

While one could hold to bruteness of diachronic identity without holding to bruteness of composition or vice versa, it does not seem very natural to me to do so.

Reality is strange

The doctrines of the Trinity, the Incarnation and transubstantiation initially seem contradictory. Elaborate theological/philosophical accounts of the doctrines are available (e.g., from St. Thomas Aquinas), and given these, there is no overt contradiction. But the doctrines still seem very strange and they feel like they border on contradiction, with the accounts that remove contradiction sometimes looking like they are ad hoc designed to remove the contradiction from the doctrine. This may seem like a good reason to reject the doctrines.

But to reject the doctrines for this reason alone would be mistaken. For similar points can be made about Relativity Theory and Quantum Mechanics. To say that simultaneity is relative or that a physical object has no position but rather a probability distribution over positions borders on contradiction, and the philosophical moves needed to defend these seem ad hoc designed to save the theories. If we’ve learned one thing from physics in the 20th century, it is that the true physics of the world is very strange indeed.

Nor are theology and science the only places where things are strange. Similar things can be said about the mathematics of infinity, or even just common sense claims such as that there is change (think of Zeno’s paradoxes) or that material objects persist over time (think of the Ship of Theseus and the paradoxes of material composition).

We can, thus, be very confident that created reality is very strange indeed. And hence, shouldn’t we expect similar strangeness—indeed, mystery—in the Creator and his relationship to us?

Why my present existence can't depend on future events

I find very persuasive arguments like this:

1. If theory T is true, then whether I exist now depends on some future events.

2. Facts about what exists now do not depend on future events.

3. So, theory T is not true.

For instance, some four-dimensionalist solutions to problems of fission according to which the number of people there are now depends on whether fission will are subject to this criticism.

But I’ve had a nagging worry about arguments like this, that in accepting (2), I am not being faithful to my eternalist four-dimensionalist convictions: why should the present aspects of the four-dimensional me have this sort of priority? Moreover, I didn’t really have an argument for (2). Until today.

Here is an argument for (2). Start with this.

4. If facts about my present existence depend on future events, then facts about my present existence depend on future events that happen to me.

For instance, suppose that whether I exist now depends on whether some surgeon cuts my brain in half tomorrow. Well, then, some of the events that my present existence depends on will be events that happen entirely to someone else—for instance, whether the surgeon gets to work on time. But other events, such as the cutting or non-cutting of the brain, will happen to me. It would be absurd to think that facts about my present existence or identity depend on future events that happen entirely to something other than me.

Then add:

5. Any events that happen to me in the future depend on my present existence.

For, such events presuppose my future existence, and my future existence is caused by my present existence.

6. Circular dependence is impossible.

7. So, facts about my present existence do not depend on future events.

Note that (6) is a very strong premise, and is one place the argument can get attacked. Many people think that you can have circular dependence when the dependence in the two directions is of a different sort. In the case at hand, facts about my present existence might depend constitutively on future events, while the future events depend causally on my present existence. Nonetheless, I think (6) is true, even if the dependence in the two directions is of a different sort.

Another move is to describe the future events on which my existence depends without reference to me. Don’t describe what the surgeon does as the splitting of my brain, but as the splitting of brain x. Then we could say that the future event of the surgeon’s splitting my brain does depend on my present existence, but my present existence doesn’t depend on that event. Instead, it depends on the future event of the surgeon’s splitting brain x. This objection denies (5): while the splitting of my brain depends on my present existence, the splitting of brain x does not, and yet it happens to me.

I think this is mistaken. The splitting of brain x depends on the future existence of that brain, and that brain depends on me, because parts depend on wholes—that is a deep Aristotelian premise I accept. Thus I think (5) is true. An event that happens to me is an event that involves at least a part of me, and none of my parts could exist without me. Granted, a brain like mine could exist without me. But token events are individuated in part by the things caught up in them. A splitting of a brain merely like mine would be a different event from the splitting of this particular brain. And it is a token event that my present existence is supposed to depend on.

The above argument won’t move non-Aristotelians who think that wholes depend on parts rather than parts depending on wholes. But it works for me. And hence it assuages the worry that in accepting (2), I am being unfaithful to my views about time.

All that said, I don’t really want to affirm (2) in an exceptionless way. If I am a time-traveller born in the year 2200, then my present existence does depend on what will happen in the future. But it only depends on what will happen in the external-time future not on what will happen in my internal-time future. And, crucially, I think time-travel is only possible when it doesn’t result in causal loops. So even if I am a time-traveller from the future, I cannot affect anything that is causally relevant to whether I will be born, etc. This probably means that if time-travel is possible, it is possible only in very carefully limited settings.

The identity of countries and persons

Suppose Canada is dissolved, and a country is created, with the same people, in the same place, with the same name, symbols, and political system. Moreover, the new country isn’t like the old one by mere happenstance, but is deliberately modeled on the old. Then very little has been lost, even if it turns out that on the correct metaphysics of countries the new country is a mere replica of Canada.

On the other hand, suppose Jean Vanier is dissolved, and a new person is created, with the same matter and shape, in the same place, with the same name, apparent memories and character. Moreover, the new person isn’t like the old one by mere happenstance, but is deliberately modeled on the old. Then if on the correct metaphysics of persons the new person is a mere replica of Jean Vanier, much has been lost, even if Vanier’s loving contributions continue through the new person.

This suggests an interesting asymmetry between social entities and persons. For social entities, the causal connections and qualitative and material similarities across time matter much more than identity itself. For persons, the identity itself matters at least as much as these connections and similarities.

Perhaps the explanation of this fact is that for social entities there is nothing more to the entity than the persons and relationships caught up in them, while for persons there is something more than temporal parts and their relationships.

[Note added later: This was, of course, written before the revelations about Jean Vanier's abusiveness. I would certainly have chosen a different example if I were writing this post now.]

Relative identity and relative shape

Take a classic case of relative-identity. At time 1, we have a lump of clay, Lumpy1, that is formed into a statue of a horse, a statue I will call "Bucephalus". At time 2, the lump continues to exist as Lumpy2, but is reformed into into a statue of a big man, a statue I will call "Goliath". Then Lumpy1 is the same lump as Lumpy2, Lumpy1 is the statue as Bucephalus, Lumpy2 is the same statue as Goliath, but it does not follow that Lumpy1 is the same statue as Lumpy2, since we only have transitivity of relative identity when we keep the kind fixed.

Now suppose a four-dimensionalism that says that ordinary objects are four-dimensional (no further commitments on temporal parts, etc.). Then it seems we have a very odd thing. Lumpy1 the lump has a different shape and size from Bucephalus the statue. For Lumpy1 the lump is extended temporally up to and including at least time 2, while Bucephalus the statue does not extend temporally up to time 2. So shape and size are kind-relative. As a lump, Lumpy1 has one four-dimensional shape and size. As a statue, it's Bucephalus and it has a different four-dimensional shape and size. The causal powers are different, too. Lumpy1 can still be seen at time 2, while Bucephalus can no longer be seen then (except in photographs). So the causal powers of a thing are kind-relative, too. Moreover, this kind of thing happens routinely--it's not a miracle as when Christ is omnipresent qua God but only in Jerusalem qua human. It seems implausible that we would have routine kind-relative variation of size and shape.

This makes relative identity not so plausible given four-dimensionalism. But four-dimensionalism (in the weak sense I'm using) is clearly true. :-)

Relative identity and relative parthood

Advocates of relative identity say that identity is always relative to a kind. This seems to have an interesting and underappreciated consequence: If there is such a thing as parthood, it's relative to a kind too. For:

1. Necessarily: x=y if and only if x is a part of y and y is a part of x.

This is very plausible and is a consequence of the antisymmetry of parthood axiom. So if we had an absolute parthood relation, we would automatically get an absolute identity relation out of it.

Is it crazy to think parthood is relative to a kind? Maybe not. Consider classic apparent counterexamples to the transitivity of parthood like: My right foot is a part of me and I am part of the Admissions Committee, but my right foot is not a part of the Admissions Committee. Well, we could say: my right foot is a part of me qua organism, while I am a part of the Admissions Committee qua organization. It's unsurprising that can't chain "___ is a part of ___ qua F" and "___ is a part of ___ qua G" together. On the other hand, perhaps we can say that my right foot is a part of me qua physical object and I am a part of the Admissions Committee qua physical object, so my right foot is a part of the Admissions Committee qua physical object. That sounds just right! So the kind-relativity of parthood seems to be a helpful thesis, at least in this regard.

Still, having to say that parthood is kind-relative is additional baggage for the relative identity theorist to take on board. Can she escape from the weight of that load? Maybe. She could say that diachronic identity is relative but synchronic identity is absolute. If she says that, then she could say that (1) holds but only for synchronic identity and synchronic (three-dimensionalist) parthood. (I think, though, that one shouldn't make diachronic identity be any different from synchronic identity. They are both, just, identity.)

Vague mental states

I've been thinking through my intuitions about vagueness and mental states, especially conscious ones. It certainly seems natural to say that it can be vague whether you are in pain or itching, or that it can be vague whether you are sure of something or merely believe it strongly. But I find very plausible the following mental non-vagueness principle:

• (MNV) Let M be a maximally determinate mental state. Then it cannot be vague whether I am in M.

MNV is compatible with the above judgments. For if I am in a borderline case between pain and itch, it is not vague that I have the maximally determinate unpleasant conscious state U that I have. Rather, what is vague is whether U is a pain or an itch. Intuitively, this is not a case of ontological vagueness, but simply of how to classify U. Similarly, if I am borderline between sureness and strong belief, there is a maximally determinate doxastic state D that I have, and I have it definitely. But it's vague whether this state is classified as sureness or strong belief.

Interestingly, though, MNV is strong enough to rule out a number of popular theories.

The first family of theories ruled out by MNV is just about any theory of diachronic personal identity that allows personal identity to be vague. Psychological continuity theories, for instance, are going to have to make personal identity be vague (on pain of having a very implausible cut-off). More generally, I suspect any theory of personal identity compatible with reductive materialism will make personal identity be vague. But suppose it's vague whether I am identical with person B who exists at a later time t. Then likely B has, and surely could have, a maximally determinate mental state M at t that definitely nobody else has at that time. Then if it's vague at t whether I am B, it's vague at t whether I have M, contrary to MNV.

I suppose one could weaken MNV to say that it's not vague whether something is in M. I would resist this weakening, but even the weakened MNV will be sufficiently strong to rule out typical (i.e., non-Aristotelian) functionalist theories of mind. For suppose that my present maximally determinate mental state M is constituted by computational state C. But now imagine a sequence of possible worlds, starting with the actual, and moving to worlds where my brain is more and more gerrymandered. Just replace bits of my brain by less and less natural prosthetics, in such ways that it becomes more and more difficult to interpret my brain as computing C. (For instance, at some point whether something counts as a computational state may depend on whether it's raining on a far away planet.) Suppose also nothing else computing C is introduced. Then there will be a continuum of worlds, at one end of which there is computation of C and at the other of which there isn't. But it would be arbitrary to have a cut-off as to where M is exemplified. So it's vague whether M is exemplified in some of these worlds, contrary to MNV.

The psychological theory of personal identity

Let's suppose that personal identity over time is secured by continuation of psychological states. Now imagine Jim and Sally are robots who are persons (if you don't think robots could be persons, just suspend disbelief for a while until I get back to the issue) and have almost all of their psychological states on their hard drives. According to the psychological theory, if you swap Jim and Sally's hard drives, Jim and Sally will go with the hard drives, rather than with the rest of their hardware. But here is something odd. When you unplug Jim and Sally's hard drives during the swap, either Jim and Sally continue existing or they don't. If they do continue existing, then by the psychological theory, they are surely located where the hard drives are, since that's where the memories are. They are basically reduced to hard drives.

There is a case to be made that they do continue existing, at least given the psychological theory of personal identity. First: To kill an innocent person, even temporarily (after all, many people, including me, believe that all our deaths are temporary!), is seriously wrong. But swapping hard drives doesn't seem problematic in this way. Second: There is some reason to think temporally gappy existence is impossible, and if gappy existence is impossible, then if Jim and Sally exist before and after the swap, they exist during it. Third (and specifically to the psychological theory): It is plausible that if the identity of a person across time is secured by a part of the person, then the person can exist reduced to that part. Thus, if the identity of a person comes from the soul, then the person can survive reduced to a soul.

So we have this: Given the psychological theory, Jim and Sally exist reduced to hard drives. But that's absurd! For we can replace hard drives by cruder mechanisms. We can suppose a computer where memory is constituted by writing in a large book. It is absurd to think a person can exist reduced to a book. So we should reject the psychological theory.

Well, that assumed that robots could be persons. Maybe they can't. And our memories do not sit on a convenient isolated piece of hardware in the brain. Indeed, that is true. But surely agents could have evolved whose memories are stored on a convenient isolated piece of hardware, and such agents could be persons. And the argument could be run for them.

Brains and animalism

Animalists hold that we are animals. It is widely accepted by animalists that if a brain were removed from a body, and the body kept alive, the person would stay with the bulk of the body rather than go with the brain.

I wonder how much of the intuition is based on irrelevant questions of physical bulk. Imagine aliens who are giant brains with tiny support organs—lungs, heart, legs, etc.—dwarfed by the brain. I think we might have the intuition that if the brain were disconnected from the support organs, the animal would go with the brain. In the case of beings that dwarf their brains, it feels natural to talk of a certain operation as a brain transplant. But in the case of beings that are almost all brain, the analogous operation would probably be referred to as a support-system transplant. Yet surely we should say exactly the same thing metaphysically about us and the aliens, assuming that the functional roles of the brains and the other organs are sufficiently similar.

This isn't a positive argument that we'd go with our brains. It's just an argument to defuse the intuition that we wouldn't.

What about cerebra? Here's a widely shared intuition. If the cerebrum is removed from the skull of an animal and placed in a life-support vat, the animal stays with the rest of the body.

But now suppose that we granted that the animal goes with the whole brain. Let's say, then, that I am an animal and sadly become a brain in a life-support vat, losing the rest of my body. Suppose that next my brain is cut and the upper and lower brains are placed in separate life-support vats. It does not seem particularly plausible to think that the animal goes with the lower brain. (Maybe the animal dies, or maybe it goes with the upper brain.) So once we've granted that the animal would go with the brain, the primacy of the lower brain for animal identity seems somewhat undermined.

Maybe, though, one could accept both (a) the common intuition that if the cerebrum were removed the human animal would go with the rest of its body, and (b) my intuition that if the human animal were first reduced to a brain, and the brain then cut into the cerebrum and lower brain, the animal would go with the cerebrum. There is no logical contradiction between these two intuitions. Compare this. I have a loaf of bread. Imagine the loaf marked off into five equally sized segments A, B, C, D and E. If I first cut off the 2/5 of the loaf marked D and E, it's plausible that the loaf shrinks to the ABC part, and DE is a new thing. And then if I cut off C, the same loaf shrinks once again, to AB. On the other hand if I start off by cutting off the AB chunk, the loaf shrinks to CDE. So the order of cutting determines whether the original loaf ends up being identical to AB or to something else. (We can also make a similar example using some plant or fungus if we prefer a living example.) Likewise, the order of cutting could determine whether the animal ends up being just a cerebrum (first remove brain, then cut brain into upper and lower parts) or whether it ends up being a cerebrumless body.

We might have a rough general principle: The animal when cut in two tends to go with the functionally more important part. Thus, perhaps, when the human animal is cut into a brain and a rest-of-body, it goes with the brain, as the brain is functionally more important in the brainier animals. When that brain is subsequently cut into upper and lower brains, the brainy animal goes with the upper brain, as that's functionally more important given its distinctively brainy methods for survival. On the other hand, if the human animal is cut into a cerebrum and a cerebrumless-rest-of-body, perhaps (I am actually far from sure about this) the animal goes with the cerebrumless-rest-of-body, because although the upper brain is more important functionally than a lower brain, the lower brain plus the rest of the body are collectively more important than the upper brain by itself. So the order of surgery matters to identity.

Two questions about identity

Here is an interesting line of thought.

Consider these two questions:

1. What is it for x and y to be identical?
2. What necessary and sufficient conditions can be given for a person to be identical with a person?

These two questions seem respectively exactly parallel to:

3. What is it for an action to be permissible?
4. What necessary and sufficient conditions can be given for a killing of a person to be permissible?

Here, (3) is a metaethics question while (4) is an applied ethics question.

One way to notice the difference I'd like to highlight between (3) and (4) is to consider the kinds of answers one might get. For instance, on a fairly standard natural law theory, the answer to (3) is that an action is permissible if and only if it does not conflict with one's nature, while the answer to (4) is, perhaps, that the killing be a proportionate act of justice or self-defense and not otherwise impermissible. On a Kantian theory, the answer to (3) is that an action is permissible if and only if it treats no person as a mere means. But the answer to (4) may be exactly like the natural law answer. On a divine command theory, the answer to (3) is that what makes an action permissible is its not being forbidden by God, but again the answer to (4) might just like on the other theories.

Observe, thus, what we are very unlikely to get from standard answers to (4): we are very unlikely to find out what the permissibility of a killing consists in. If we want an answer to that question, the natural lawyer will say that the permissibility of a killing consists in its comformability to our nature, the Kantian that it consists in its not treating anyone as a mere means, and the divine command theorists that it consists in its not being forbidden by God. None of these answers will answer the applied ethics question we want, as these answers are at too high a level of generality: we can replace "killing" by any other action type, and they remain applicable.

Now go back to the metaphysics. I have no idea how to answer (1). It's hard to think of anything more fundamental than identity to answer it in terms of. But I think the analogy with the ethics question suggests this. If we can get a substantive answer to (2), it's not going to be an answer to the question of what identity of persons consists in. It's simply going to be an answer as to what interesting necessary and sufficient conditions for identity are in the special case where it is given that the relata are persons.

If we want to know what the identity of persons (or at least finite persons) consists in, the correct answer will not be so informative: what makes person a be identical with person b is that (i) a is a person, (ii) b is a person, and (iii) Iab, where "Iab" is a stand-in for whatever identity in general consists in. I have no idea what "Iab" will say, but I know that it won't say anything about memories, gradual replacement of cells, etc. For, "Iab" is the general account of identity, and that is beyond the details of particular kinds of beings.

This line of thought is attractive, but resistable. One might instead insist that identity is something different in different types of beings. (This may or may not involve the further step of accepting a relative identity theory.) Here, the "types" could be categories—substances, accidents, relations, etc. Or they could be kinds—dogs, persons, photons, electromagnetic fields, etc. I prefer the first option, but what I say applies in both cases. One way to flesh out such views is with a theory of analogy. There is no one thing that identity consists in: there is a relation between a substance and substance, and a relation between an accident and an accident, and so on, and these are all analogous (maybe one of them is focal?). Or if one prefers the second type of "type", one might say: there is a relation between a dog and a dog, and a relation between a person and a person, and so on, and these are all analogous.

On this kind of view, we might well have something substantive to say about what identity between, say, a person and a person consists in, which does not reduce simply to saying: this is a person, and this is a person, and this equals this. I think very naturally such a view will call for a typed logic. (Query to self: In a typed logic of this sort, should there be a quantification over types of quantification?)

I wonder if the argument of my recent AJP paper on diachronic identity is vulnerable to this sort of view. Quite possibly. But I still think the reduction of diachronic to synchronic identity that I perform in that paper is plausible.