The evanescent world of becoming

An old idea in philosophy, going back to Plato, is that things that are becoming are less beings than things that are timeless. This is a mysterious view, but I have just found that my own preferred four-dimensionalism implies a clear and unmysterious version of this view.

On my preferred four-dimensionalism, material substances are four-dimensional entities. Since they are substances, they are explanatorily prior to any parts or accidents they may have. This four-dimensionalism, thus, cannot hold that four-dimensional entities are constructed out of three-dimensional time slices, or even that the slices are somehow ontologically on par with the four-dimensional substances.

Nonetheless, it makes sense to talk of a three-dimensional time slices as a kind of derivative entity.

It may, for instance, turn out to be like the Thomist’s “virtual entities”. The Thomist does not think that the electrons that help make up my body are substances, but thinks that our scientific language can be saved: the electrons “virtually exist” in virtue of my pattern of (accidental) causal powers.

Or it might even be that three-dimensional time slices just are accidents: that the four-dimensional entity that I am has an accident corresponding to every time at which it exists, an accident which itself is the bearer of further accidents. Thus, the fact that I have a certain three-dimensional shape s at a time t could be analyzed in terms of me having an existence-at-t accident E_t, and E_t in turn having an s-shape accident.

Virtual entities and accidents are unmysteriously less beings than substances: for them to be is to qualify a substance.

So, now, here is a reconstruction of the Platonic insight. A lot of our ordinary talk about material substances is most straightforwardly construed as about time slices rather than four-dimensional substances. When we talk of the shape of a flower, we mean its three-dimensional shape with respect to a particular slice, and so on. Now, we identify something like the Platonic world of becoming as the world of three-dimensional time slices. These are completely evanescent entities—they exist literally only for a moment each—and their being is derivative from the being of substances.

Presentists have long complained that four-dimensional entities are not really becoming. We can embrace an aspect of that insight. There is a way in which the four-dimensional entities form a world where time is less important. Granted, they indeed are spatio temporal entities: they do exist in time as well as in space. But there is little reason to think that their very being is somehow ontologically tied to time in the way that the presenists think the world of becoming is. On the other hand, the time slices are very much time slices: their very being is tied to their temporality.

Of course, this reconstruction of the Platonic insight into a world of becoming is in the end quite unfaithful to Plato: for we, who are four-dimensional substances, end up not being in the world of becoming, though we ground it. We are almost like Kantian noumena, grounding a world of becoming phenomena.

I don't know that the standard presentist can reconstruct the Platonist insight. For the standard presentist, to be is to be at present. The only difference between eternal things and things in the world of becoming is that eternal things were and will be in the same state, while things in the world of becoming were and/or will be in a different state. This is not a difference with respect to a way of being.

A fun little argument against four-dimensionalism

1. Spinning a rigid object cannot affect its shape.

2. If four-dimensionalism is true, spinning a rigid object can affect its shape.

3. So, four-dimensionalism is not true.

The easiest way to see that 2 is true is to imagine that space is two-dimensional. Then if objects are considered to be extended in time, as the four-dimensionalist says, an object intuitively thought of as a rectangle that stays still is really a rectangular prism, while if that rectangle is spun by 90 degrees, it looks like a twisty thing.

I don’t think it’s too costly to deny 2. And perhaps one can make sense of some notion of internal shape that doesn’t change no matter how a rigid object moves around.

The weird view that particles don't survive substantial change

I have a weird view: when a dog or another substance ceases to exist, all its particles cease to exist, being replaced by new particles with very similar physical parameters (with the new physical parameters being predictable via the laws of nature). Similar things happen when a new substance comes into existence, and when a particle is incorporated into or leaves a substance: no particles survive such things.

I have good Aristotelian reasons for this view. Particles are not substances, since substances cannot have substances as parts, and hence ontologically depend on substances for their existence. Thus, when the substance perishes, the particles do as well.

The view seems preposterously unparsimonious. I disagree. Let’s compare the view to some competitors. First of all, it’s clear to me that some version of four-dimensionalism is true, so let’s start with four-dimensionalist views.

A standard four-dimensionalism is perdurantism: four-dimensional objects are made up of instantaneous temporal parts—infinitely many of them if time is continuous. These instantaneous temporal parts come in and out of existence all the time, with very similar physical parameters to their predecessors. My weird view is compatible with the idea that particles actually all exist only instantaneously, akin to the perdurantist’s temporal parts. Such a view could be more parsimonious than standard perdurantism for two reasons: first, it needn’t posit temporal parts of substances, and, second, it needn’t posit wholes made up of the instantaneous particles.

An alternate version of my weird view says that particles do not survive change of substance, but live as long as they recognizably remain in the same substance. Imagine a particle that is eaten by a dog and some months later sloughed off. On my view, there are three particle-like objects in the story: the pre-dog particle, the in-dog particle, and the post-dog particle. On standard perdurantism, there are as many particle-like objects as moments of time in this story. Granted, some may think it weirder that the temporal boundaries in the existence of particles are determined by their allegiances to substances rather than by instants of time. But there is nothing weird about that if one takes seriously the priority of substances to their parts.

My view is admittedly less parsimonious than a four-dimensionalist view on which substances and particles are temporally extended, have no temporal parts, and particles outlast their substances. But such a four-dimensionalist has an implausible consequence. Many people will find plausible the idea that in some exceptional cases substances can share parts: conjoined twins are a standard example. But on this version of four-dimensionalism, it is now a matter of course that distinct substances share parts. The dog dies and some of its particles become a part of a flower: so the dog and the flower, considered as four-dimensional entities, have these particles as common parts. You and I share probably share parts with dinosaurs. So while my weird view is less parsimonious than a no-temporal-parts four-dimensionalism with particles that outlive substances, it is not less plausible.

The main alternative to four-dimensionalism is presentism. Is a presentist version of my view less parsimonious than a typical competing presentist view? In one sense, not. For at the present time, my view doesn’t posit additional present particles over and beyond those present particles posited by competing presentist views. And only present particles exist according to presentism! But more seriously, my view does posits that particles cease to exist and come into existence more than on typical presentist alternatives. So in that sense it is less parsimonious.

Thus, parsimony cuts against my view on presentism, but it may actually favor it on four-dimensionalism.

Temporary intrinsics and internal time

The main problem the literature presents for eternalist theories is the problem of temporary intrinsics: how an object can have an intrinsic property at one time and lack it at another.

The most common solution is perdurantism: four-dimensional objects have ordinary properties derivatively from their instantaneous temporal parts or slices having them, and since the slices only exist at one time, the properties can be as intrinsic as one likes.

Another solution that has found some purchase is a view on which the properties that we previously thought were intrinsic, such as shape and charge, are in fact fundamentally relational, defined by a relation to a time. Thus, to be square is to be square at some time or other. This results in a more commonsense ontology than perdurantism, but it has the problem of just denying that there are temporary intrinsic properties.

This morning it’s occurred to me that if we say that substances carry with them an internal time sequence that is intrinsic to them, then relationalism can admit temporary intrinsic properties. A property of a substance, after all, can be intrinsic even if the property is relational, as long as the relations that the possession of the property is grounded in are intrinsic to the object, say by being relations between parts or other metaphysical components of that object. After all, shape is seen as the paradigmatic case of an intrinsic property, and yet it is often seen as grounded in the relations between the particles making up an object. But on a view on which substances carry an internal time sequence, the internal times can be taken to be intrinsic aspects of the substance, and then ordinary properties can be seen as relational to the these internal times. Thus, to be square is more fundamentally to be square at some internal time or other.

What kinds of intrinsic aspects of the substance are the internal times? Here, there are multiple options. They could be sui generis aspects of the substance. They could be tropes—for instance, if substances all have beginnings, one could identify a time with the trope of having survived for a temporal duration D.

Internal times could even be time slices of the substance. This last option may seem to take us back to perdurantism, but it does not. For it is one thing to say that I am in pain because my temporal part ARP_t is in pain—it sure seems implausible to say that I am in pain derivatively from something else being in pain—and another to say that my being in pain is constituted by a relation to ARP_t, which part is in no pain at all. (That pain is constituted by a relation between the aspects of a substance is not at all strange and unfamiliar as a view: a materialist may well say that pain is constituted by relations between neuronal activities.)

Note, too, a view on which intrinsics are relational to internal times also solves another problem with views on which ordinary properties are relational to times: if those times are external, then time travel to a time at which one “already” exists is ruled out.

My own preferred view is that a nested trope ontology. I have a trope of being human. That trope then has an infinite number of temporal existence tropes, corresponding to all the different internal times at which I exist. These temporal existence tropes—or maybe even temporal human existence tropes—are then the internal times. And I can even say what the relation that makes a temporary intrinsic obtain at a temporal existence tropes t is: that temporary intrinsic obtains at t provided that it is a trope of t.

Perdurance and slices

One of the main problems with perdurance is thought to be that it makes intrinsic properties be primarily properties of slices, and only derivatively of the four-dimensional whole.

The most worrisome case of this problem has to do with mental properties. For if our slices have the mental properties primarily, and we only have them derivatively, then that leads to a sceptical problem (how do I know I am a whole and not a slice?) and besides violates the intuition that we have our mental properties primarily.

But someone who accepts a perdurantist ontology and accepts the idea that we are four-dimensional wholes does not have to say that intrinsic properties are primarily had by slices. For a property that involves a relation to one’s parts can still be intrinsic (having one’s parts is surely intrinsic!). Now instead of saying that, say, Bob has temporary property P at time t in virtue of his slice B_t at t having P, we can say that Bob has P in relation to B_t. This is very similar to how relationalist endurantists say that we have our temporary properties in relation to times, except that times are normally thought of as extrinsic to the object, while the slices are parts of the objects.

In fact, this helps save some intuitions of intrinsicness. For instance, it seems to be an intrinsic property of me that my heart is beating. But if t is now and A_t is my slice now, then A_t does not seem to intrinsically have the property of heart-beat. It seems that heart-beat is a dynamical property dependent not just on the state of the object at one time but also at nearby times. Thus, if we want to attribute heart-beat to A_t primarily, then heart-beat will not be intrinsic, as it will depend on A_t as well as slices A_t′ for t′ near t. But if we see my present heart-beat as a property of the four-dimensional worm, a property the worm has in relation to A_t (as well as neighboring times), then heart-beat can be an intrinsic property—and it can be had primarily by me, not my slices.

It is plausible that mental properties are dynamical as well: that one cannot tell just from the intrinsic properties of a three-dimensional slice whether thought is happening. (This is pretty much certain given materialism, but I think is plausible even on dualism.) So, again, mental properties aren’t going to be intrinsic properties of slices. But they can be primarily the intrinsic properties of four-dimensional persons, had in relation to their slices.

Persistence and internal times

Here are some desiderata for a view of the persistence of objects:

1. Ordinary objects can change with respect to intrinsic properties.

2. Ordinary objects are the primary bearers of some of the changeable intrinsic properties.

3. Ordinary objects are literally present at multiple times.

Endurantism is usually allied with some sort of view on which temporary properties are had in relation to times, and hence the temporary properties are relational and not intrinsic. Perdurantism violates 2: it is the stages, not the ordinary objects, that are the primary bearers of the temporary intrinsics. And no primary bearer of a property can change with respect to it. Exdurantism violates 3: ordinary objects only exist at a single time.

Here is a view that yields all three desiderata. Objects have internal times, and these internal times are literally parts of the objects. Changeable intrinsic properties are relational to the internal times: an object is, say, straight at internal time t₁ and bent at internal time t₂.

Let’s go through the desiderata. The internal times are parts of the object, and a property obtaining in virtue of relations between one’s own parts can still be intrinsic. Shape, for instance, might be had in virtue of the spatial relationships between the parts of an object—and yet this does not rule out shape being intrinsic (indeed, for David Lewis it’s paradigmatically intrinsic). Similarly, consciousness properties in a split brain might be had relationally to a brain hemisphere, but are still intrinsic since brain hemispheres are parts of the patient. Thus we can have (1).

Moreover, while parts—namely, internal times—are used to account for change, the parts are not the primary bearers of the changeable intrinsic properties. The changeable intrinsic properties to be relational between the ordinary object and the times, but that does nothing to rule out the possibility that some of these properties are primarily had by the object as a whole.

Ordinary objects can be literally present at multiple times. One can ensure this either in an endurantist way, so that the ordinary objects are multiply temporally located 3D objects, or in a four-dimensionalist way, so that the ordinary objects are 4D. Note that the endurantist version may require the ordinary object to have parts—namely, the internal times—that do not themselves endure but that only exist for an external instant. But there is no problem with an enduring object having a short-lived part.

There is another variant of the view. The internal times could be taken to be abstract objects instead of parts of the ordinary object. Arguably, a property that is had in virtue of a relation to an abstract object is not thereby objectionably extrinsic. If it were, then strong Platonists would all count as denying the existence of intrinsic properties.

Perdurance, Relativity and Quantum Mechanics

It is known that perdurantists, who hold that objects persisting in time are made of infinitely thin temporal slices, have to deny that fundamental particles are simple (i.e., do not have (integral) parts). For a fundamental particle is an object persisting in time, and hence will be made of particle-slices.

But what is perhaps not so well-known is that on perdurantism, the temporal slices a particle is made of will typically not be simple either, given some claims from standard interpretations of Quantum Mechanics and Special Relativity. The quick version of the argument is this: the spatial non-localizability of quantum particles requires typical temporal slices to be non-localized simples (e.g., extended simples), but this runs into relativistic problems.

Here is a detailed argument.

A perdurantist who takes Relativity seriously will say that for each inertial reference frame R and each persistent object, the object is made of R-temporal slices, where an R-temporal slice is a slice all of whose points are simultaneous according to R.

Now, suppose that p is a fundamental particle and that p is made up of a family F₁ of temporal slices defined by an inertial reference frame R₁. Now, particles are rarely if ever perfectly localized spatially on standard interpretations of Quantum Mechanics (Bohmianism is an exception): except perhaps right after a collapse, their position is fuzzy and wavelike. Thus, most particle-slices in F₁ will not be localized at a single point. Consider one of the typical unlocalized particle-slices, call it S. Since it’s not localized, S must cover (be at least partially located at) at least two distinct spacetime points a and b. These points are simultaneous according to R₁.

But for two distinct spacetime points that are simultaneous according to one frame, there will be another frame according to which they are not simultaneous. Let R₂, thus, be a frame according to which a and b are not simultaneous. Let F₂ be the family of temporal slices making up p according to R₂. Then S is not a part (proper or improper) of any slice in F₂, since S covers the points a and b of spacetime, but no member of F₂ covers these two points. But:

1. If a simple x is not a part of any member of a family F of objects, then x is not a part of any object made up of the members of that family.

Thus, if S is simple, then S is not a part of our particle p, which is absurd. Therefore, for any reference frame R and particle p, a typical R-temporal slice of p is not simple.

I think the perdurantist’s best bet is supersubstantialism, the view that particles are themselves made out of points of spacetime. But I do not think this is a satisfactory view. After all, two bosons could exist for all eternity in the same place.

Without Relativity, the problem is easily solved: particle-slices could be extended simples.

It is, I think, ironic that perdurantism would have trouble with Relativity. After all, a standard path to perdurantism is: Special Relativity → four-dimensionalism → perdurantism.

I myself accept four-dimensionalism but not perdurantism.

My experience of temporality

This morning I find myself feeling the force of presentism. I am finding it hard to see my four-dimensional worm theory as adequately explaining why my experience only includes what I am experiencing now, instead of the whole richness of my four-dimensional life. I am also finding it difficult to satisfactorily explain the sequentiality of my experiences: that I will have different experiences from those that I have now, some of which I dread and some of which I anticipate eagerly.

When I try to write down the thoughts that make me feel the force of presentism, the force of the thoughts is largely drained. After all, to be fair, when I wrote that I have am having trouble “explaining why my experience only includes what I am experiencing now”, shouldn’t I have written: “explaining why my present experience only includes what I am experiencing now”, a triviality? And that mysterious sequentiality, is that anything beyond the fact that some of my experiences are in the future of my present experience?

The first part of the mystery is due to the chopped up nature of my consciousness on a four-dimensional view. Instead of seeing my life as a whole, as God sees it, I see it in very short (but probably not instantaneous) pieces. It is puzzling how my consciousness can be so chopped up, and yet be all mine. But we have good reason to think that this phenomenon occurs outside of temporality. Split brain patients seem to have such chopped up consciousnesses. And if consciousness is an operation of the mind’s, then on orthodox Christology, the incarnate Christ, while one person, had (and still has) two consciousnesses.

Unfortunately, both the split brains and the Incarnation are mysterious phenomena, so they don’t do much to take away the feeling of mystery about the temporal chopping up of the consciousness of my four-dimensional life. But they do make me feel that there is no good argument for presentism here.

The second part of the mystery is due to the sequentiality of the experiences. As the split brain and Incarnation cases show, the sequentiality of experiences in different spheres of consciousness is not universal. The split brain patient has two non-sequential, simultaneous spheres of consciousness. Christ has his temporal sphere (or spheres, if we take the four-dimensional view) of consciousness and his divine atemporal sphere of consciousness. But seeing the contingency of the sequentiality does not remove the mystery in the sequentiality.

It makes me feel a little better when I recall that the presentist story about the sequentiality has its own problems. If my future experiences aren’t real—on presentism they are nothing but stuff in the scope of a modal “will” operator that doesn’t satisfy the T axiom—then what am I anticipating or dreading? It seems I am just here in the present, and when I think about this, it feels just as mysterious as on four-dimensionalism what makes the future impend. Of course, the presentist can give a reductive or non-reductive account of the asymmetry between past and future, but so can the four-dimensionalist.

So what remains of this morning’s presentist feelings? Mostly this worry: Time is mysterious and our theories of time—whether eternalist or presentist—do not do justice to its mysteriousness. This is like the thought that qualia are mysterious, but when we give particular theories of them—whether materialist or dualist—it feels like something is left out.

But what if I forget about standard four-dimensionalism and presentism, and just try to see what theory of time fits with my experiences? I then find myself pulled towards a view of time I had when I was around ten years old. Reality is four-dimensional, but we travel through it. Future sufferings I dread are there, ahead of me. But I am not just a temporal part among many: there is no future self suffering future pains and enjoying future pleasures. The past and future have physical reality but it’s all zombies. As for me, I am wholly here and now. And you are wholly here and now. We travel together through the four-dimensional reality.

But these future pains and pleasures, how can they be if they are not had by me or anyone else? They are like the persisting smile of the Cheshire cat. (I wasn’t worried about this when I was ten, because I was mainly imagining myself as traveling through events, and not philosophically thinking about my changing mental states. It wasn’t a theory, but a way of thinking.) Put that way, maybe it’s not so crazy. After all, the standard Catholic view of the Eucharist is that the accidents of bread and wine exist without anything having them. So perhaps my future and past pains and pleasures exist without anyone having them—but one day I will have them.

Even this strange theory, though, does not do justice to sequentiality. What makes it be the case that I am traveling towards the future rather than towards the past?

And what about Relativity Theory? Why don’t we get out of sync with one another if we travel fast enough relative to one another? Perhaps the twin who travels at near light speed comes back to earth and meets only zombies, not real selves? That seems absurd. Maybe though the internal flow of time doesn’t work like that.

I do not think this is an attractive theory. It is the theory that best fits most of my experience of temporality, and that is a real consideration in favor of it. But it doesn’t solve the puzzle of sequentiality. I think I will stick with four-dimensionalism. For now. (!)

Acting without existing (any more)

Thesis: It is possible for an object to be acting while it does not exist.

Argument:

Imagine a rattlesnake that is ten light-years long, all stretched out. For all one hundred years of life it has been deliberately rattling its rattle. And then at the end of its hundred years, its head is destroyed, and I assume that the destruction of the head of a snake is sufficient for its death.

Rattling continues for at least about ten years even after the snake is dead, since the nerve signals the brain had sent while the snake was alive are continuing to rattle.

If this post-mortem rattle counts as the snake’s activity, the Thesis is established. But it is not clear that this ten years of post-mortem rattle is the snake’s activity.

But now consider the last year of pre-mortem rattling, call it R₉₉ (since it starts in year 99 of the snake’s life). Whatever one says of the post-mortem rattling, clearly R₉₉ is the snake’s activity. However, there is a reference frame—the way I set the length of the snake and the times in the story guarantees this—in which R₉₉ occurs after the snake’s head has been destroyed, and hence occurs after the death of the snake. But R₉₉ is the snake’s activity. Hence, there is a reference frame where an activity of the snake occurs after the snake is dead.

Scholium:

Obviously, only existent things can act. But while existence simpliciter is important for activity, existence-at-a-time does not have the same kind of significance. Obviously, often an actor’s action has a relationship R to some thing x that the actor itself does not have. For instance, an agent’s action may be known by me without the agent being known by me (here, R is being known and x is me).

Now, when we say that Elizabeth II exists as Queen of Canada, that is just an awkward way of saying that she has a monarchic relationship to Canada, rather than being a claim about that mysterious thing deep ontology studies: existence. I think we should think of existing-at-a-time as not really existence but simply as a particular kind of relationship—an occupation or presence relationship. It is not surprising in general that activities can stand in relationships that the agents do not. So, why can’t an activity stand in an occupation relationship to a time that the agent does not?

I think much confusion in philosophy comes from thinking of existence-at-a-time and existence-in-a-place as something special, somehow deeply ontologically different from other relations.

Extended simples

1. It is possible to have a simple that exists at more than one time.

2. Four-dimensionalism is true.

3. So, temporally extended simples are possible. (By 1 and 2)

4. If four-dimensionalism is true, the time and space are metaphysically very similar.

5. So, probably, spatially extended simples are possible.

From a dualism to a theory of time

This argument is valid:

1. Some human mental events are fundamental.

2. No human mental event happens in an instant.

3. If presentism is true, every fundamental event happens in an instant.

4. So, presentism is not true.

Premise (1) is widely accepted by dualists. Premise (2) is very, very plausible. That leaves (3). Here is the thought. Given presentism, that a non-instantaneous event is happening is a conjunctive fact with one conjunct about what is happening now and another conjunct about what happened or will happen. Conjunctive facts are grounded in their conjuncts and hence not fundamental, and for the same reason the event would not be fundamental.

But lest four-dimensionalist dualists cheer, we can continue adding to the argument:

5. If temporal-parts four-dimensionalism is true, every fundamental event happens in an instant.

6. So, temporal-parts four-dimensionalism is not true.

For on temporal-parts four-dimensionalism, any temporally extended event will be grounded in its proper temporal parts.

The growing block dualist may be feeling pretty smug. But suppose that we currently have a temporally extended event E that started at t₋₂ and ends at the present moment t₀. At an intermediate time t₋₁, only a proper part of E existed. A part is either partly grounded in the whole or the whole in the parts. Since the whole doesn’t exist at t₋₁, the part cannot be grounded in it. So the whole must be partly grounded in the part. But an event that is partly grounded in its part is not fundamental. Hence:

7. If growing block is true, every fundamental event happens in an instant.

8. So, growing block is not true.

There is one theory of time left. It is what one might call Aristotelian four-dimensionalism. Aristotelians think that wholes are prior to their parts. An Aristotelian four-dimensionalist thinks that temporal wholes are prior to their temporal parts, so that there are temporally extended fundamental events. We can then complete the argument:

9. Either presentism, temporal-parts four-dimensionalism, growing block or Aristotelian four-dimensionalism is true.

10. So, Aristotelian four-dimensionalism is true.

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.

4D, 3D and 2D

No three-dimensionalist has this ludicrous picture of the human being:

1. The human being is a three-dimensional whole whose functioning derives from the functioning of many two-dimensional slices that make her up.

But some four-dimensionlists have this picture of the human being:

2. The human being is a four-dimensional whole whose functioning derives from the functioning of many three-dimensional slices that make her up.

But it seems to me that (2) is not much better than (1). Just as we should be very dubious that there are any such things as two-dimensional slices of us—infinitely thin slices—we should be very dubious that there any such things as three-dimensional slices of us. And even if there are such slices, they are more like abstractions than components from which we derive our functioning.

So just as all three-dimensionalists deny 2D-slicism, all four-dimensionalists should deny 3D-slicism.

Now, let’s turn to three-dimensionalists. The following proposition is crazy:

1. The human being is two-dimensional.

But some think:

2. The human being is three-dimensional.

Why think (1) is false? The best reason is that the characteristic functioning of a human being requires more than just an infinitely thin section. Any thin section—whether infinitely thin or of non-zero thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

But the same reason applies against (2). Any temporally thin section—whether infinitely thin or of non-zero temporal thickness—through a human being is going to be quite unnatural, being intimately connected causally to other sections that are just as important to the characteristic functioning of a human being.

A secondary reason against (1) is that it is implausible that are privileged 2D slices. But likewise it is implausible (though maybe a bit less so) that there are privileged 3D slices.

Where does all this leave us? We should be at least four-dimensionalists (there might turn out to be more dimensions), and we should not think of ourselves as derivative from 3D or thinner slices. We should, indeed, be sceptical of the existence of such slices.

Four-dimensionalism and caring about identity

In normal situations, diachronic psychological connections and personal identity go together. A view introduced by Parfit is that when the two come apart, what we care about are the connections and not the identity.


This view seems to me to be deeply implausible from a four-dimensional point of view. I am a four-dimensional thing. This four-dimensional thing should prudentially care about what happens to it, and only about what happens to it. The red-and-black four-dimensional thing in the diagram here (up/down represents time; one spatial dimension is omitted) should care about what happens to the red-and-black four-dimensional thing, all along its temporal trunk. This judgment seems completely unaffected by learning that the dark slice represents an episode of amnesia, and that no memories pass from the bottom half to the upper half.

Or take a case of symmetric fission, and suppose that the facts of identity are such that I am the red four-dimensional thing in the diagram on the right. Suppose both branches have full memories of what happens before the fission event. If I am the red four-dimensional thing, I should prudentially care about what happens to the red four-dimensional thing. What happens to the green thing on the right is irrelevant, even if it happens to have in it memories of the pre-split portion of me.

The same is true if the correct account of identity in fission is Parfit’s account, on which one perishes in a split. On this account, if I am the red four-dimensional person in the diagram on the left, surely I should prudentially care only about what happens to the red four-dimensional thing; if I am the green person, I should prudentially care only about what happens to the green one; and if I am the blue one, I should prudentially care only about what happens to the blue one. The fact that both the green and the blue people remember what happened to the red person neither make the green and blue people responsible for what the red person did nor make it prudent for the red person to care about what happens to the green and blue people.

This four-dimensional way of thinking just isn’t how the discussion is normally phrased. The discussion is normally framed in terms of us finding ourselves at some time—perhaps a time before the split in the last diagram—and wondering which future states we should care about. The usual framing is implicitly three-dimensionalist: what should I, a three-dimensional thing at this time, prudentially care about?

But there is an obvious response to my line of thought. My line of thought makes it seem like I am transtemporally caring about what happens. But that’s not right, not even if four-dimensionalism is true. Even if I am four-dimensional, my cares occur at slices. So on four-dimensionalism, the real question isn’t what I, the four-dimensional entity, should prudentially care about, but what my three-dimensional slices, existent at different times, should care about. And once put that way, the obviousness of the fact that if I am the red thing, I should care about what happens to the red thing disappears. For it is not obvious that a slice of the red thing should care only about what happens to other slices of the red thing. Indeed, it is quite compelling to think that the psychological connections between slices A and B matter more than the fact that A and B are in fact both parts of the same entity. (Compare: the psychological connections between me and you would matter more than the fact that you and I are both parts of the same nation, say.) The correct picture is the one here, where the question is whether the opaque red slice should care about the opaque green and opaque blue slices.

In fact, in this four-dimensionalist context, it’s not quite correct to put the Parfit view as “psychological connections matter more than identity”. For identity doesn’t obtain between different slices. Rather, what obtains is co-parthood, an obviously less significant relation.

However, this response to me depends on a very common but wrongheaded version of four-dimensionalism. It is I that care, feel and think at different times. My slices don’t care, don’t feel and don’t think. Otherwise, there will be too many carers, feelers and thinkers. If one must have slices in the picture (and I don’t know that that is so), the slices might engage in activities that ground my caring, my feeling and my thinking. But these grounding activities are not caring, feeling or thinking. Similarly, the slices are not responsive to reasons: I am responsive to reasons. The slices might engage in activity that grounds my responsiveness to reasons, but that’s all.

So the question is what cares I prudentially should have at different times. And the answer is obvious: they should be cares about what happens to me at different times.

About the graphics: The images are generated using mikicon’s CC-by-3.0 licensed Gingerbread icon from the Noun Project, exported through this Inkscape plugin and turned into an OpenSCAD program (you will also need my tubemesh library).

A theological argument for four-dimensionalism

One of the main philosophical objections to dualist survivalism, the view that after death and prior to the resurrection we continue existing as disembodied souls is the argument that I am now distinct from my soul and cannot come to be identical with my soul, as that would violate the transitivity of identity: my present self (namely, I) would be identical to my future self, the future self would be identical to my future soul, my future soul would still be identical to my present soul, and so my present self would be identical with my present soul.

(This, of course, won’t bother dualists who think they are presently identical with souls, but is a problem for dualists who think that souls are proper parts of them. And the latter is the better view, since I can see myself in the mirror but I cannot see my soul in the mirror.)

It’s worth noting that this provides some evidence for four-dimensionalism, because (a) we have philosophical and theological evidence for dualist survivalism, while (b) the four-dimensionalist has an easy way out of the above argument. For the four-dimensionalist can deny that my future self is ever identical with my future soul, even given dualist survivalism. My future self, like my present self, is a four-dimensional temporally extended entity. Indeed, the future self and the present self are the same four-dimensional entity, namely I. My future soul, like my present soul, is a temporally extended entity (four-dimensional if souls have spatial extension; otherwise, one-dimensional), which is a proper part of me. And, again, my future soul and my present soul are the same temporally extended entity. At no future time is my future self identical with my future soul even given dualist survivalism. At most, it will be the case that some future temporal slices of me are identical with some future temporal slices of my soul.

Death, harm and time

For the sake of this post, stipulate death to be permanent cessation of existence. Epicurus famously argues that death is not a harm to one, because the living aren’t harmed by death while the dead do not exist.

As formulated, the argument appears to require presentism—the view that only presently existing things exist. If eternalism or growing block is true, the dead would exist, albeit pastly. This would give us a nice little argument against presentism:

1. If presentism is true, the Epicurean argument is sound. (Premise)

2. The conclusion of the Epicurean argument—namely, that death is not a harm—is absurd. (Premise)

3. So, presentism is false.

But things aren’t quite so simple, because one can reconstruct an Epicurean argument without presentism.

4. One is intrinsically harmed by x iff there is a time t at which one is intrinsically harmed by x. (Premise)

5. One is intrinsically harmed at t by x only if one exists at t. (Premise)

6. One is not intrinsically harmed by death at any time at which one exists. (Premise)

7. One is not intrinsically harmed by death at any time. (5 and 6)

8. One is not intrinsically harmed by death. (4 and 7)

This argument distinguishes intrinsic from extrinsic harm. Here’s an illustration of the distinction I have in mind: if I lose a finger, that’s an intrinsic harm; if people say bad things about me behind my back, that’s an extrinsic harm—unless it causally impacts me in some negative way. Epicurus didn’t seem to think there was such a thing as extrinsic harm, so he formulated his argument in terms of harm as such. But, really, his argument was only plausible with respect to intrinsic harm, in that a no longer existent person certainly could suffer extrinsic harms, say by losing reputation or having loved ones suffer harm. And the conclusion that death is not an intrinsic harm is implausible enough. Death seems to be among the worst of the intrinsic harms. (In particular, I think my little argument against presentism remains a good one even if we weaken the conclusion of the Epicurean argument to say that death is not an intrinsic harm.)

Of course, the conclusion (8) is still false! So which premise is false?

Here is a pretty convincing argument for (5):

9. One is intrinsically harmed at t by x only if has or lacks an intrinsic property at t because of x. (Premise)

10. One does not have or lack any intrinsic properties at times when one doesn’t exist. (Premise)

11. So, (5) is true.

Premise (6) is also pretty plausible.

Premise (4) is also plausible.

But there is a way out of the argument. If four-dimensionalism is true, we have a good way to reject (4). Consider first the spatial analogue of (4):

12. One is intrinsically harmed by x if and only if there is a point z in space at which one is intrinsically harmed by x.

But (12) is implausible. Consider a spherical plant that suffers the harm of being made cylindrical. To be distorted into an unnatural shape seems to be an intrinsic harm. But it need not an intrinsic harm locatable at any point in space. At any point in space where the plant is not, surely it’s not harmed. At points where the plant is, it might be harmed—say, by the stresses induced by the unnatural shape—but it need not be. We could, in fact, suppose that the plant is nowhere stressed, etc. The harm is simply the intrinsic harm of being deformed. For another example, suppose materialism is true, and consider an animal in pain. The pain is an intrinsic harm, plausibly, but there is no harm at any single point of the brain—only at a larger chunk of the brain.

What the examples show is that spatially extended objects can be intrinsically harmed in respect of properties that cannot be localized to a single point. If four-dimensionalism is true, we are also temporally extended. We should then expect the possibility of being intrinsically harmed in respect of properties that cannot be localized to a single instant of time, and hence we should not believe (4). And death seems to be precisely such a case: one is harmed by having only a finite extent in the temporally forward direction. This could be just as much an intrinsic harm as being spatially distorted.

In fact, once we see the analogy between harm not located at a point of space and harm not located at a point of time, it is easy to find other counterexamples to (4). Consider a life of unremitting boredom. Suppose someone lives from t₁ to t₂ and is bored at every time. At every time t between t₁ and t₂ she suffers the intrinsic harm of being bored; but she has the additional temporally non-punctual intrinsic harm of being always bored. Or suppose that materialism is true. Then just as pains do not happen in respect of properties at a single spatial point, they probably do not happen in respect of properties at a single instant either: pain likely requires a sequence of neural events.

In fact, the multiplication of examples is sufficiently easy that even apart from the more abstruse question of the harms of death, someone whose theory of time or persistence forces her to endorse (4) is in trouble.

But on reflection, the moves against three-dimensionalism and maybe even presentism were too quick. Maybe even the presentist can say that we have intrinsic properties which hold in virtue of how we are over a temporally extended period of time.

Accretion, excretion and four-dimensionalism

Suppose we are four-dimensional. Parthood simpliciter then is an eternal relation between, typically, four-dimensional entities. My heart is a four-dimensional object that is eternally a part of me, who am another four-dimensional object.

But there is surely also such a thing as having a part at a time t. Thus, in utero my umbilical cord was a part of me, but it no longer is. What does it mean to have a part at a time? Here is the simplest thing to say:

1. x is a part of y at t if and only if x is a part of y and both x and y exist at t.

But (1) then has a very interesting metaphysical consequence that only a few Aristotelian philosophers endorse: parts cannot survive being accreted by or excreted from the whole. For if, say, my finger survived its removal from the whole (and not just because I became a scattered object), there would be a time at which my finger would exist but wouldn’t be a part of me. And that violates (1) together with the eternality of parthood simpliciter.

This may seem to be a reductio of (1). But if we reject (1), what do we put in its place, assuming four-dimensionalism? I suspect we will have to posit a second relation of parthood, parthood-at-a-time, which is not reducible to parthood simpliciter. And that seems to be unduly complex.

So I propose that the four-dimensionalist embrace (1) and conclude to the thesis that parts cannot survive their accretion or excretion.

Dualist survivalism

According to dualist survivalism, at death our bodies perish but we continue to exist with nothing but a soul (until, Christians believe, the resurrection of the dead, when we regain our bodies).

A lot of the arguments against dualist survivalism focus on how we could exist as mere souls. First, such existence seems to violate weak supplementation: my souls is proper part of me, but if the body perished, my soul would be my only part—and yet it would still be a proper part (since identity is necessary). Second, it seems to be an essential property of animals that they are embodied, an essential property of humans that they are animals, and an essential property of us that we are humans.

There are answers to these kinds of worries in the literature, but I want to note that things become much simpler for the dualist survivalist if she accepts a four-dimensionalism that says that we are four-dimensional beings (this won't be endurantist, but it might not be perdurantist either).

First, there will be a time t after my death (and before the resurrection) such that the only proper part of mine that is located at t is my soul. However, the soul won’t be my only part. My arms, legs and brain are eternally my parts. It’s just that they aren’t located at t, as the only proper part of me that is located at t is my soul. There is no violation of weak supplementation. (We still get a violation of weak supplementation for the derived relation of parthood-at-t, where x is a part-at-t of y provided that x is a part of y and both x and y exist at t. But why think there is weak supplementation for parthood-at-t? We certainly wouldn’t expect weak supplementation to hold for parthood-at-z, where z is a spatial location and x is a part-at-z of y provided that x is a part of y and both x and y are located at z.)

Second, it need not follow from its being an essential property of animals that they are embodied that they have bodies at every time at which they exist. Compare: It may be an essential property of a cell that it is nucleated. But the cell is bigger spatially than the nucleus, so it had better not follow that the nucleus exists at every spatial location at which the cell does. So why think that the body needs to exist at every temporal location at which the animal does? Why can’t the animal be bigger temporally than its body?

Of course, those given to three-dimensional thinking will say that I am missing crucial differences between space and time.

Four-dimensionalism and interpersonal connections

I have thought about reality as four-dimensional since I was ten years old. Yesterday morning I was sitting in a conference room, and I decided to imagine what it would be like to think of the people there as if presentism were true and they were all merely three-dimensional. I then saw the people as small, disconnected lone individuals. I've since been reflecting on the way that four-dimensionalism can change how we see people.

If four-dimensionalism is true, we are four-dimensional stalks, branching off from our mothers, with a slightly less direct connection to our fathers. Together we all form an interwoven mat of upward growing stalks, stalks in contact where we, say, shook hands, hugged, kissed or even fought. The picture is no longer one of lone individuals, but of a complex multiply interconnected system. It's like a family tree where the branches are all twisted around each other.

Of course, the presentist will say that it is true that we came from our mothers, that we were begotten by our fathers, that we shook hands, hugged, kissed or fought, and so on. But on presentism these connections are past, over and done with. We are basically lone individuals, who at a variety of past times came in a variety of contacts. It is the four-dimensionalist who has a metaphysics that captures the fact that no one of us is an island.

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. :-)