The Real Presence and Relativity Theory

Jesus Christ like all human beings has an internal clock. One can measure that clock in heartbeats or in lower level physical interactions or in some other way. Let’s measure it in “internal years”. If Jesus was born in 4 BC, then in 4 BC, his internal clock was at about a year (he was conceived about 0.75 years before he was born). In 1 BC, it was at 4 years, in 1 AD, it was at 5 years, and in 30 AD, it was at 34 years.

I don’t know what Jesus’s internal clock was at in 100 AD, and it’s not immediately obvious that the question makes sense. For it is not immediately obvious that there is a correlation between time on earth and time in heaven of such a sort it makes sense to ask “What is happening in heaven right now?” After all, according to Relativity Theory, it doesn’t make sense to ask “What is happening right now in the Andromeda Galaxy” without specifying a reference frame for the “right now”, and it’s not immediately clear that there is a common reference frame between heaven and earth.

However, the real presence of Jesus in the Eucharist does provide a temporal correlation between heaven and earth. Around 22:45 UTC today, Jesus will come to be present in our campus parish. Moreover, Jesus will be present as an adult glorified human, not as the three-year-old he was in 1 BC. There thus appears to be a fact of the matter as to what his internal clock will be showing when he comes to be present at 22:45 UTC in Waco today.

Interestingly, this gives a temporal ordering on events scattered across the earth apparently independent of our ordinary relativistic reference frames. For if the Eucharist is celebrated around 22:45 UTC in Waco and around 22:45 UTC in London, there is a fact of the matter whether Christ as present in Waco is older or younger or at the same age (according to his internal clock), and this fact provides a reference-frame independent temporal ordering between these two Eucharistic celebrations.

Indeed, since according to Catholic and Orthodox faith, Christ remains Eucharistically present in the tabernacles across the world, we constantly have a temporal ordering between events scattered spatially across the world. In principle, this defines a theologically privileged reference frame between scattered events—a Eucharistic reference frame. Events at locations z₁ and z₂ in spacetime are Eucharistically simultaneous, we might say, provided that Christ as Eucharistically present at z₁ and at z₂ has the same value of the internal clock.

Of course, some philosophers of time think there is an objective reference frame in the physical world. If they are right, then very likely the theologically privileged frame is the same as the objective one.

All that said, it is not completely clear to me that Christ as Eucharistically present has to have a well-defined value of his internal clock. But I suspect so, because of the intuition that it is the adult and not toddler Jesus who is Eucharistically present.

Computationalism and subjective time

Conway’s Game of Life is Turing complete. So if computationalism about mind is true, we can have conscious life in the Game of Life.

Now, consider a world C (for Conway) with three discrete spatial dimensions, x, y and z, and one temporal dimension, t, discrete or not. Space is thus a three-dimensional regular grid. In addition to various “ordinary” particles that occupy the three spatial dimensions and have effects forwards along the temporal dimension, C also has two special particle types, E and F.

The causal powers of the E and F particles have effects simultaneous with their causes, and follow a spatialized version of the rules of the Game of Life. Say that a particle at coordinates (x₀,y₀,z₀) has as its “neighbors” particles at the eight grid points with the same z coordinate z₀ and surrounding (x₀,y₀,z₀). Then posit these causal powers of an E (for “empty”) or F (for “full”) particle located at (x₀,y₀,z₀):

• If it’s an F particle and has less two or three F neighbors, it instantaneously causes an F particle at (x₀,y₀,z₀+1).

• If it’s an E particle and has exactly three F neighbors, it instantaneously causes an F particle at (x₀,y₀,z₀+1).

• Otherwise, it instantaneously causes an E particle at (x₀,y₀,z₀+1).

Furthermore, suppose that along the temporal axis, the E and F particles are evanescent: if they appear at some time, they exist only at that time, perishing right after.

In other words, once some E and F particles occur somewhere in space, they instantly propagate more E and/or F particles to infinity along the z-axis, all of which particles then perish by the next moment of time.

Given the Turing completeness of the Game of Life and a computational theory of mind, the E and F particles can compute whatever is needed for a conscious life. We have, after all, a computational isomorphism between an appropriately arranged E and F particle system in C and any digital computer system in our world.

But because the particles are evanescent, that conscious life—with all its subjective temporal structure—will happen all at once according to the objective time of its world!

If this is right, then on a computational theory of mind, we can have an internal temporally structured conscious life with a time sequence that has nothing to do with objective time.

One can easily get out of this consequence by stipulating that mind-constituting computations must be arranged in an objective temporal direction. But I don’t think a computationalist should add this ad hoc posit. It is better, I think, simply to embrace the conclusion that internal subjective time need not have anything to do with external time.

Pointy endpoints and internal space and time

In a series of recent posts, starting with this one, I argued that relativity theory gives us good reason to think that at the start and end of our lives we are pointlike in spatial extension. Crucial to these arguments was the idea that there is no privileged reference frame.

The conclusion is, of course, rather counterintuitive. While it is plausible that we start as a cell and that we shrink with old age, in neither case are we pointlike.

However, in some earlier posts, like this one, I explored the idea that substances may have internal space and internal time, in addition to the external spacetime of the universe.

Here is a suggestion that could save the intuition that we are not spartially pointlike at the beginning and end of life. We have internal space and time, and our internal space and time has an absolute simultaneity relation. With respect to internal time, at the first and last moments of our lives (I’m simplifying by assuming there are such moments), we have significant non-pointlike spatial extension. Of course, most external frames of reference do not agree with our internal simultaneity relation, and in most of them, we are pointlike at the beginning and end of our lives. But that’s fine: our intuition relates to our internal space and time.

The above suggestion is inspired by Rob Koons’ suggestion that our rest frame could be the privileged frame with respect to which we could have spatially non-pointlike endpoints of life. That suggestion doesn’t work for the technical reason, which Koons also noted, that there doesn’t seem to be a well-defined notion of a privileged frame of a squashy organism. (One might try to go with the rest frame of the center of mass. But an organism’s center of mass can move faster than light—e.g., in a fast amputation. And faster than light motion doesn’t define a reference frame.) But even if there isn’t a well-defined rest frame, there is a family of “approximate rest” frames that are intuitively close to what we would expect the rest frame to do. And then we could suppose that the internal simultaneity relation is pretty close to these approximate rest frames.

Note that we should not expect the internal simultaneity relations to align neatly between substances (except in the special case of substantial change where we might reasonably suppose that the old substances’s later internal simultaneity relations approximate the new substance’s earlier ones), and hence they do not define a global privileged simultaneity relation that would threaten relativity theory.

So now I think that my argument about spatially pointy endpoints of life gives us a choice between three options:

1. Accept spatially pointy endpoints.

2. Accept a global privileged reference frame.

3. Accept privileged reference frames specialized for individual substances.

In the last option, I think the best way is the way of internal space and time, but I suppose one could also think there are privileged external reference frames specialized for individual substances.

Accepting privileged reference frames specialized for individual substances could also help materialists deal with the problem of the unity of consciousness for a spatially extended brain.

Two implications of Aristotle's theory of time and locality

Aristotle thinks that time is infinitely subdivisible but only finitely subdivided. Thus, there will be moments t₁ < t₂ such that there is actually no moment between t₁ and t₂, but there could have been. What would make there have been a moment between t₁ and t₂? Presumably, this would be if something happened strictly between those times. Time is the measure of change, so if, say, some object started or finished changing at a time between t₁ and t₂, then there would have been a time between them, say t_1.5.

But here is a curious consequence. Suppose that in the actual world, w₀, I am living from t₁ to t₂, which are so close together in time that there are no time between them. But in another world, t₁, where everything in our galaxy was the same, in some other galaxy indeterministically an event happened between t₁ and t₂, namely at t_1.5. Then:

• In w₀, it is not true that I exist at t_1.5 (because there is no t_1.5).

• In w₁, it is true that I exist at t_1.5.

And what is responsible for that difference is that indeterministic event in another galaxy. So it seems that something in another galaxy is responsible, in a faster-than-light way, for whether I exist at t_1.5. In other words, the Aristotelian theory seems to imply highly non-local influences.

There is perhaps a way out. Perhaps fundamentally time sequences are internal to substances. Thus, I have a time sequence internal to me, you have one internal to you, and things in that other galaxy have time sequences internal to them. There are, additionally, connections (probably causal ones) between objects that allow one to form a global time sequence. That global time sequence will include moments that don’t correspond to any moments internal to me. For instance, it will include moments earlier than my conception, but more interestingly, it could be that for me t₂ immediately succeeds t₁, but something else has a time that fits between t₁ and t₂, and so global time could have times corresponding to t₁ and t₂, but also some intermediate time between them.

The difference between w₀ and w₁, then, would not be a difference in my internal time sequence. What happened in that other galaxy wouldn’t affect my internal time except perhaps once the light from that galaxy could reach me.

On this account, while it is true that I exist at t_1.5, my existing at t_1.5 is not an intrinsic feature of me. The difference between my existing at t_1.5 in w₁ and my not existing at t_1.5 in w₀ is a merely Cambridge difference.

I think it is hard to make this story fit with presentism. When t_1.5 is present, then it had better be intrinsic to me that I exist presently, i.e., at t_1.5. A similar point applies to growing block.

Maybe, though, there is a way of making this story fit with a moving spotlight A-theory. We could suppose that at global time t_1.5, what is “lit up” by the spotlight is the time t_1.5 for the thing in the other galaxy that has something happening to it then, but for me what is lit up is the entire interval between t₁ and t₂.

If I am right, then

1. Locality, and

2. Aristotle’s theory of time

seem to imply:

3. Internal time is primary

4. Eternalism is true.

There could still be a persistence-based cosmological argument even if there were existential inertia

Suppose that today at noon, Felix the cat enters a time machine and travels back to the time of the dinosaurs, where he spends the rest of his life hunting small reptiles. According to the doctrine of existential inertia, objects have a blockable tendency to continue existing.

Question: If Felix has existential inertia, was his inertial tendency to continue existing blocked at noon when he time-traveled to the past, and hence failed to exist past today’s noon?

My intuition is that the answer is negative. Existential inertia seems to me to be about “having a future” and today at noon, Felix does have a future, even if that future is in the distant past. In other words, if there is such a thing as existential inertia, it concerns what I call “internal” rather than “external” time.

Beyond mere intuition, here is a reason for a defender of existential inertia to agree with me. If existential inertia concerns external time, then in a relativistic world it is a doctrine that says that an object that exists at point z of spacetime has a tendency to exist somewhere or other in the forwards lightcone centered on z. But there is something odd about a metaphysical principle, like existential inertia is supposed to be, that impels an object to continue to exist in some location or other in some infinite set of locations (say, the infinite number of locations in the forward lightcone one second away from the present in some reference frame), without impelling the object to exist in any particular location, or even imposing any kind of probability distribution on where it is to exist. Moreover, it is not clear why the forward lightcone would be so metaphysically special that a fundamental metaphysical principle would coordinate with lightcones so neatly.

Perhaps this is not completely convincing. But it has some legs. There is thus some reason to think that existential inertia applies to internal rather than external time. But if so, then existential inertia has not removed all that needs to be explained about persistence. For a normal cat not only tends to continue to exist in its internal-time future, but also tends to continue to exist in its external-time future, since normally there is no time travel. And this external-time persistence is not explained by existential inertia, if existential inertia concerns the external-time future. So there is a persistence to explain, and theism offers an explanation. There is still room for an argument for theism from persistence.

Here is a closely related explanatory problem: Why is it that internal and external time tend to be correlated, so that internal-time persistence tends to imply external-time persistence?

Suppose that, contrary to my relativity theory intuitions, one insists that existential inertia concerns external-time persistence rather than internal-time persistence? Then there is still something to be explained: the correlation between internal and external time.

Substance dualism and relativity theory

Here is an interesting argument against substance dualism:

1. Something only exists simultaneously with my body when it exists in space.

2. My mind now exists simultaneously with my body.

3. So, my mind now exists in space.

4. Anything in space is material.

5. So, my mind is material.

If this argument is right, then there is at least one important respect in which property dualism and physicalism are better off than substance dualism.

The reasoning behind (1) is Relativity Theory: the temporal sequence that bodies are in cannot be separated from space, forming an indissoluble unity with it, namely spacetime.

One way out of the argument is to deny (4). Perhaps the mind is immaterial but in space in a way derivative from the body’s being in space and the mind’s intimate connection with the body. On this view, the mind’s being in time would seem to have to be derivative from the body’s being in time. This does not seem appealing to me: the mind’s spatiality could be derivative from the spatiality of something connected with the mind, but that the mind’s temporality would be derivative from the temporality of something connected with the mind seems implausible. Temporality seems too much a fundamental feature of our minds.

However, there is a way to resolve this difficulty, by saying that the mind has two temporalities. It has a fundamental temporality of its own—what I have elsewhere called “internal time”—and it has a derivative temporality from its connection with spatiotemporal entities, including the body. When I say that my mind is fundamentally temporal, that refers to the mind’s internal time. When we say that my mind is derivatively temporal, that refers to my mind’s external time.

If this is right, then we have yet another reason for substance dualists to adopt an internal/external time distinction. If this were the only reason, then the need for the distinction would be evidence against substance dualism. But I think the distinction can do a lot of other work for us.

A simpler formulation of the paradox of short pains

On reflection, my paradox of short pains can be simplified. Start with:

1. Whether I have had a pain does not depend on the future.

2. It is impossible for me to have a pain that lasts less than a picosecond.

3. I once started to be in pain for the first time in my life.

Now imagine that the first pain in my life just started half a picosecond ago. Then anybody who has the power to annihilate me in the next quarter (say) picosecond has the power to make it be the case that I had not yet had a pain, since if they so annihilate me, then I won’t have had a pain by (2). But whether someone will annihilate me in the next quarter second is a fact about the future, so whether I have had a pain depends on the future.

To put this in Ockhamist terminology, if we accept (2), then we have to accept that facts about whether one has had a pain can be soft facts.

I like the idea of denying (1), though I think this may make presentists (and others) uncomfortable.

I also like the idea of saying that the argument equivocates between phenomenal and physical time. The duration of pain is a phenomenal duration that does not correspond in a precise way to a physical duration.

More on the problem of short pains

Consider these two very plausible theses:

1. Whether I have pain at time t does not depend on any future facts.

2. There is a length of time δt such that you cannot have a pain lasting no more than δt, but you can have a pain lasting 4δt.

Now imagine that I feel a pain that lasts from t₀ to t₂ = t₀ + 4δt. Let t₁ = t₀ + (1/2)δt. Suppose it is now t₁. Then I am in pain. But now I claim that this counterfactual is true:

3. Were it to be the case that I was to be annihilated at t₀ + (3/4)δt, I wouldn’t have felt any pain now.

Why? For if I were so annihilated, my pain could only have lasted (3/4)δt, which is too short for a pain by (2).

But by (3), whether I feel pain now depends on whether I will shortly be annihilated, contrary to (1).

Hence, we need to reject one of (1) and (2).

It is hard to reject (2). After all, imagine the sequence of times: a second, a quarter second, a sixteenth of a second, …, 2⁻⁴⁰ seconds. Clearly I can feel a pain that lasts a second. The last of these is less than a picosecond, and clearly I can’t feel a pain that short. So somewhere in that sequence I must reach a δt which is too short for a pain, but where 4δt isn’t too short for a pain.

I think denying (1) isn’t as bad as it may seem.

But perhaps a less counterintuitive move is to deny that phenomenal times and physical times are as closely correlated as they intuitively seem. Here is a possible story. Phenomenal times are discrete points while physical times are continuous (or discrete on a much finer timescale). You can feel a pain that is located at exactly one phenomenal time. The spacing between the phenomenal times corresponds to a fairly large (and non-uniform) spacing between physical times, say of the order of magnitude of a millisecond. So, you can feel a pain that is there one millisecond and gone the next, but you may feel it at exactly one point of phenomenal time.

As far as I can tell, it is not possible to run the annihilation argument while keeping careful track of the continuous physical and discrete phenomenal timelines. I guess this is a way of rejecting (2) by making it not make sense.

Here is a third way out of the argument. Imagine that what it is to have a pain at t is to have had some constitutive physical or spiritual process P have lasted some threshold period of time δt. On this view, before P lasted over a period of δt, there was no pain: pain only starts once P has lasted δt. We might now suppose that δt is something like a millisecond. Then it is possible to have a pain that lasts only a picosecond: for that, all we need is the underlying process P to have lasted δt plus a picosecond—and only the last picosecond of that process would have constituted a pain. But we no longer need to make the implausible claim that we can be aware of picosecond-scale stuff. For in paining, our awareness is the awareness of the underlying process P, and that process always needs to have taken something in the millisecond range for it to constitute a paining.

This way out of the argument also has the consequence that it is not possible to have a pain before completing the first δt of one’s existence. Pain is not a momentary property.

The third way out will not appeal to dualists who think phenomenal states are fundamental.

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.

Two attempts at deriving internal time from the causal order of modes

It would be nice to define the internal time of a substance in terms of the causal order of its accidents.

For each mode (i.e., accident or substantial form) α that a finite substance x has, there is the event c_α of α’s being caused. Causal priority provides a strict partial ordering on the events c_α.

Perhaps the simplest theory of the internal time of the substance x is that the moments of internal time just are the events c_α and their order just is the causal priority order.

This has the consequence that internal time need not be totally ordered, since one can have cases where α ≠ β but there is no priority relation between c_α and c_β. This consequence is welcome and unwelcome. It is welcome, as it allows one to give a nice account of bilocation involving the bifurcation of internal time. It is unwelcome, as intuitively time is linear. Let’s see if we can do something to reduce the unwelcome consequence.

Let’s suppose—as per causal finitism—that causal interactions are discrete. Then we can define a fundamental distance between the moments of internal time: d(c_α, c_β) is the length of the longest unidirectional causal priority chain between c_α and c_β. One might reasonably hypothesize that d(c_α, c_β) is something of the order of magnitude of the temporal distance between c_α and c_β in the rest frame of the substance in units of the order of Planck time. (Note that d is not a metric because of the unidirectionality constraint on the chains.)

This lets us have a second way of defining the internal time of a substance x. Let f be x’s substantial form. Then we can define “the start time” of a mode α as d(f, α): the length of the longest internal causal priority chain from c_f to c_α. Now likely some modes will have a simultaneous internal start time—they will have the same distance to c_f.

For this to define an intuitively plausible time sequence, we need the substance to have lots of interconnections between its accidents. Ordinary substances do seem to have that.

And perhaps some accidents won’t have an internal start time—if God turns me blue right now, my blueness won’t have an internal start time. But nonetheless that blueness can be “attached” to my internal temporal sequence by noting that it will be close according to d to some of my near-future accidents. For that miraculous blueness will interact with some of my other accidents to produce new accidents that are properly in my middle age. For instance, it will interact with my memories of observations of things not turning blue to generate the accident of surprise.

A variant of the at-at theory of change

It’s occurred to me that some of the difficulties with the at-at theory of change nicely disappear if the theory is expressed in terms of the internal time of an object: x changes provided that it is F at internal time t₁ and not-F at internal time t₂ such that t₁ < t₂ or t₂ < t₁.

For instance, consider this difficulty: Fred is bilocated and is sitting all day today and he is standing all day today. So at 10 he is not standing (and standing!) and at noon he is standing (and not standing!). On an external-time at-at theory of change, Fred has changed: at one time he is standing and and at another he isn’t. But that doesn’t seem right.

On an internal-time account of bilocation, we need to ask: is an internal time at which Fred is standing earlier or later than an internal time at which Fred is sitting? And what the answer is depends on how the bilocation was arranged. Suppose Fred was sitting all day, and at the end of the day he activated a time machine and went back to the beginning of the day and stood all day. Then he was sitting internally-earlier than he was standing, and so we do have change—just as we should. But suppose that Fred is just leading two parallel bilocated lives, without any time travel involved. Then his internal time splits into two streams when the bilocation begins and rejoins when they reunite. And plauusibly there are no earlier-than or later-than relations between the two parallel streams. And so there is no change.

An argument against time travel or for temporal parts or for internal time

Start with this plausible claim:

1. If two objects are composed of the very same particles at the same time, then they have the same shape.

But now consider a statue of a horse that is reshaped into a statue of a tree and then time-travels back to sit besides the statue of the horse. Then the statue of the horse and the statue of the tree are composed of the very same particles at the same time, and yet they do not have the same shape.

I see three ways out of this paradox.

2. Deny the possibility of time travel.

3. Subscribe to temporal parts theory and modify (1) to speak of temporal parts of particles instead of particles.

4. Distinguish external and internal time, and qualify (1) to refer to internal time.

My preference is (4).

Internal reference frame

Suppose a long snake is stretched out and its front half is annihilated instantaneously. This presumably instantly destroys the snake's form or soul. So the tip of the snake's tail instantly ceases to be informed by the snake form. But then there will be a reference frame according to which the front half is annihilated before the tail loses its form. In that frame, the tip of the tail still has a snake form at a time at which the snake's front half doesn't exist. That seems wrong. So it seems there should be a privilege to reference frames where the front half is destroyed simultaneously with the tail losing its form. But a global privileged frame is unattractive. Maybe, however, we should suppose that particular substances carry along privileged frames of their own, frames internal to them. Then there will be a privilege frame for each substance, but these frames need not cohere into a global privileged frame.

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.

Internally eternal life

Suppose that starting this year (2019), I and all people who are important to me will do the following: We will live for 20 years on a delightful planet, and then travel through spacetime both 20 years back and to another delightful planet, and repeat ad infinitum.

Then, we won’t exist after the year 2039. But notice that this needn’t matter to us! Indeed, we are no worse off than if we skipped the time travel, and lived forever, moving between delightful planets every 20 years.

This is yet another thought experiment showing that what is important to us is internal and not external time.

Probabilistic propensities and the Aristotelian view of time

Consider an item x with a half-life of one hour. Then over the period of an hour, it has a 50% chance of decaying, over the period of a second it only has a 0.02% chance of decaying. Imagine that x has no way of changing except by decaying, and that x is causally isolated from all outside influences. Don’t worry about Schroedinger's cat stuff: just take what I said at face value.

We are almost sure that x will one day decay (the probability of decaying approaches one as the length of time increases).

Now imagine that everything other than x is annihilated. Since x was already isolated from all outside influences, this should not in any way affect x’s decay. Hence, we should still be almost sure that x will one day decay. Moreover, since what is outside of x did not affect x’s behavior, the propensities for decay should be unchanged by that annihilation: x has a 50% chance of decay in an hour and a 0.02% chance of decay in a second.

But this seems to mean that time is not the measure of change as Aristotle thought. For if time were the measure of change, then there would be no way to make sense of the question: “How long did it take for x to decay?”

Here is another way to make the point. On an Aristotelian theory of time, the length of time is defined by change. Now imagine that temporal reality consists of x and a bunch of analog clocks all causally isolated from x. The chances of decay of x make reference to lengths of time. Lengths of time are defined by change, and hence by the movements of the hands of the clocks. But if x is causally isolated from the clocks, its decay times should have nothing to do with the movements of the clocks. If God, say, accelerated or slows down some of the clocks, that shouldn’t affect x’s behavior in any way, since x is isolated. But an Aristotelian theory of time, it seems, such an isolation is impossible.

I think an Aristotelian can make one of two moves here.

First, perhaps the kinds of propensities that are involved in having an indeterministic half-life cannot be had by an isolated object: such objects must be causally connected to other things. No atom can be a causal island. So, even though physics doesn’t say so, the decay of an atom has a causal connection with the behavior of things outside the atom.

Second, perhaps any item that can have a half-life or another probabilistic propensity in isolation from other things has to have an internal clock—it has to have some kind of internal change—and the Aristotelian dictum that time is the measure of change should be understood in relation to internal time, not global time.

External time as such doesn't matter to us

Suppose a deity threatened to move us all to a universe where everything is pretty much as in our world, except that electric charges are reversed and the laws of nature are tweaked to ensure that this reverse doesn’t affect our lives. Thus, in that world, we are based not on carbon atoms, but on anti-carbon anti-atoms (they will have six anti-protons and six positrons, etc.), but the laws are tweaked so that the anti-atoms would behave just like atoms.

Assuming we can survive the shift, it seems that except for sentimental considerations (maybe when Grandma’s old wedding ring is replaced by a ring of anti-gold, it’s no longer the same ring) it would make no difference to us.

Similarly, if the deity threatened to spatially rotate the world by 180 degrees around some axis, that would make no difference to us.

What if the deity offered to rotate our world in time by 180 degrees, with causation now running temporally backwards, with us being born in the future and dying in the past, but everything being kept intact. It seems to me that this would make no difference to us.

Similarly, it seems to me that if the deity offered to rotate our four-dimensional world so that the temporal dimension and a spatial dimension were swapped, so that we would be born and die at the same time, but in different places along a spatial axis, and causation would run unidirectionally along the spatial axis, again that would make no difference to us.

I think these thought experiments suggest that external time as such is not important. What matters is how the distribution of things interacts with the causal order.

To be honest, though, I am not completely confident that any of these thought experiments make sense. It could be that any dimension along which causation runs much as causation runs along the temporal direction in our world is therefore a time dimension. But if so, then I think it's still true that it is causation, not external time as such, that matters.

I am less confident of this in the case of internal time.

Simultaneous and diachronic causation

The main problem with the idea that all causation is simultaneous is to make sense of the obvious fact of diachronic causation, as when setting an alarm in the evening causes it to go off in the morning. Here is a theory that has both simultaneity and diachronicity that bears further examination:

• All causation between substances is simultaneous

• There is diachronic causation within a substance.

We now have a model of how setting the alarm works, on the simplifying assumption that the alarm clock is a substance. In the evening, by simultaneous causation, I cause the clock to have a certain state. A sequence of diachronic causal interactions within the clock—accidents of the clock causing other accidents of the clock, say—then causes the alarm to go off. The alarm’s going off then, by means of simultaneous causation between substances, causes particles in the air to move, etc. In other words, the diachronicity of the causation is all internal to the substances.

An even more interesting theory would hold that:

• All causation between substances is simultaneous

• All causation within a substance is diachronic.

If we were willing to swallow this, then we would have a very elegant account of the internal time of a substance as constituted by the causal relations within the substance (presumably, the causal relations between the accidents of the substance).

Time and clocks

Einstein said that time is what clocks measure.

Consider an object x that travels over some path P in spacetime. How long did the travels of x take? Well, if in fact x had a clock traveling with it, we can say that the travels of x took the amount of time indicated on the clock.

But what if x had no clock with it? Surely, time still passed for x.

A natural answer:

• the travels of x took an amount of time t if and only if a clock would have measured t had it been co-traveling with x.

That can’t be quite right. After all, perhaps x would have traveled for a different amount of time if x had a clock with it. Imagine, for instance, that x went for a one-hour morning jog, but x forgot her clock. Having forgot her clock, she ended up jogging 64 minutes. But had she had a clock with her, she would have jogged exactly 60 minutes.

That seems, though, a really uncharitable interpretation of the counterfactual. Obviously, we need to fix the spacetime path P that x takes. Thus:

• the travels of x over path P took an amount of time t if and only if a clock would have measured t had it been co-traveling with x over the same path P.

But this is a very strange counterfactual if we think about it. Clocks have mass. Like any other massive object, they distort spacetime. The spacetime manifold would thus have been slightly different if x had a clock co-moving with it. In fact, it is quite unclear whether one can make any sense of “the same path P” in the counterfactual manifold.

We can try to control for the mass of the clock. Perhaps in the counterfactual scenario, we need to require that x lose some weight—that x plus the clock have the same mass in the counterfactual scenario as x alone had in the actual scenario. Or, more simply, perhaps we can drop x altogether from the counterfactual scenario, and suppose that P is being traveled by a clock of the same mass as x.

But we won’t be able to control for the mass of the clock if x is lighter than any clock could be. Perhaps no clock can be as light as a single electron, say.

I doubt one can fix these counterfactuals.

Perhaps, though, I was too quick to say that if x had no clock with it, time still passed for x. Ordinary material substances do have clocks in them. These clocks may not move perfectly uniformly, but they still provide a measure of length of time. Alice’s jog took 396,400 heartbeats. Bob’s education took up 3/4 of his childhood. Maybe the relevant clocks, then, are internal changes in substances. And where the substances lack such internal changes, time does not pass for them.

Disconnected bodies and lives

We can imagine what it is like for a living to have a spatially disconnected body. First, if we are made of point particles, we all are spatially disconnected. Second, when a gecko is attacked, it can shed a tail. That tail then continues wiggling for a while in order to distract the pursuer. A good case can be made that the gecko’s shed tail remains a part of the gecko’s body while it is wiggling. After all, it continues to be biologically active in support of the gecko’s survival. Third, there is the metaphysical theory on which sperm remains a part of the male even after it is emitted.

But even if all these theories are wrong, we should have very little difficulty in understanding what it would mean for a living thing to have a spatially disconnected body.

What about a living thing having a temporally disconnected life? Again, I think it is not so difficult. It could be the case that when an insect is frozen, it ceases to live (or exist), but then comes back to life when defrosted. And even if that’s not the case, we understand what it would mean for this to be the case.

But so far this regarded external space and external time. What about internally spatially disconnected bodies and internally temporally disconnected lives? The gecko’s tail and sperm examples work just as well for internal as well as external space. So there is no conceptual difficulty about a living thing having a disconnected body in its inner space.

But it is much more difficult to imagine how an organism could have an internal-time disconnect in its life. Suppose the organism ceases to exist and then comes back into existence. It seems that its internal time is uninterrupted by the external-time interval of non-existence. An external-time interval of non-existence seems to be simply a case of forward time-travel, and time-travel does not induce disconnectes in internal time. Granted, the organism may have some different properties when it comes back into existence—for instance, its neural system might be damaged. But that’s just a matter of an instantaneous change in the neural system rather than of a disconnect in internal time. (Note that internal time is different from subjective time. When we go under general anesthesia, internal time keeps on flowing, but subjective time pauses. Plants have internal time but don’t have subjective time.)

This suggests an interesting apparent difference between internal time and internal space: spatial discontinuities are possible but temporal ones are not.

This way of formulating the difference is misleading, however, if some version of four-dimensionalism is correct. The gecko’s tail in my story is four-dimensional. This four-dimensional thing is connected to the four-dimensional thing that is the rest of the gecko’s body. There is no disconnection in the gecko from a four-dimensional perspective. (The point particle case is more complicated. Topologically, the internal space will be disconnected, but I think that’s not the relevant notion of disconnection.)

This suggests an interesting pair of hypotheses:

• If three-dimensionalism is true, there is a disanalogy between internal time and internal space with respect to living things at least, in that internal spatial disconnection of a living thing is possible but internal temporal disconnection of a living thing is not possible.

• If four-dimensionalism is true, then living things are always internally spatiotemporally connected.

But maybe these are just contingent truths Terry Pratchett has a character who is a witch with two spatially disconnected bodies. As far as the book says, she’s always been that way. And that seems possible to me. So maybe the four-dimensional hypothesis is only contingently true.

And maybe God could make a being that lives two lives, each in a different century, with no internal temporal connection between them? If so, then the three-dimensional hypothesis is also only contingently true.

I am not going anywhere with this. Just thinking about the options. And not sure what to think.