Existential inertia and spacetime

According to the principle of existential inertia:

1. If x exists at t₁ and t₂ > t₁ and there is no cause of x’s not existing at t₂, then x exists at t₂.

This sounds weird, and one way to get at the weirdness for me is to put it in terms of relativity theory. Times are spacelike hypersurfaces. So, then:

2. If x exists somewhere on a spacelike hypersurface H₁ and H₂ is a later spacelike hypersurface and there is no cause of x’s not existing on H₂, then x exists on H₂.

This seems weird to me. Why should being in one specific area of spacetime metaphysically push one to exist in another specific area of spacetime? I can see how existing in one area of spacetime could physically push one to exist in another. But metaphysically? That seems odd.

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.

Divine conservation, existential inertia, presentism and simultaneous causation

As a four-dimensionalist, I have been puzzled both by the arguments that divine conservation is necessary secure the persistence of substances and the idea of existential inertia as a metaphysical principle.

Temporal extent seems little different metaphysically to me from spatial thickness, the “problem of persistence” seems to me to be a pseudo-problem, and both solutions to this pseudo-problem seem to me to be confused.

On the existential inertia side, a metaphysical principle that objects continue to exist unless their existence is interrupted by some other cause seems as ridiculous to me as a principle that objects are maximally thick (and long and deep) unless and until their thickness (or length or depth) is stopped by other causes. And divine action is needed to secure persistence only to the extent that it is needed to secure thickness (and length or depth). That said, I do think divine action is needed to secure thickness, as well as all other accidents of a thing, because substances are in some sense causes of their accidents, but all creaturely causation requires divine cooperation. But that, I think, is a slightly different line of argument from the arguments for persistence of substances (in particular, I don’t have a good argument for it that doesn’t already presuppose theism, while the arguments for conservation are supposed to provide reasons for accepting theism).

However, I now see how it is that presentism yields a real problem of persistence. Here’s the line of thought. First, note that contrary to the protestations of some presentists, it is very plausible that:

1. Presentism implies that all causation is simultaneous.

For something that exists, at least at the time at which it is caused, cannot have as its cause something that doesn’t exist. But given presentism, only something present exists. So at a time at which E is caused, if the cause of E did not exist, we would have the exercise of a non-existent causal power, which is absurd.

But even if all causation is simultaneous, nonetheless:

2. There is diachronic causal explanation.

Setting the alarm at night explains why it goes off in the morning, even if by the simultaneity thesis (1), setting the alarm cannot be the cause of the alarm going off. Diachronic causal explanation cannot simply be causation. So what is it? Here is the best presentist story I know (and it’s not original to me).

First, we can get some temporal extension by the following trick. Imagine a thing A persists over an interval of time from t₁ to t₂. At t₂ is causes a thing B that persists over an interval of time from t₂ to t₃. The existence of A at t₁ then causally explains the existence of B at t₃. Note, however, that the existence of A at t₁ does not cause the existence of B at t₃. Causation happens at t₂ (or perhaps over an interval of times—thus, A might persist until some time t_2.5 < t₃, and be causing B over all of the interval from t₂ to t_2.5), but not at any earlier time, since at earlier times A doesn’t exist. Thus, by supplementing the simultaneous causal relation between A and B at t₂ with the persistence of A before t₂ and/or the persistence of B after t₂, we have, we can extend the relation into what one might call a fundamental instance of diachronic causal explanation.

Thus, a fundamental link in diachronic causal explanation consists of an instance of causation preceded and/or followed by an instance of persistence of the causing thing and/or the caused thing respectively. And a non-fundamental instance of diachronic causal explanation is a chain of fundamental links of diachronic causal explanations. (It may be that these diachronic causal explanations are very close to what Aquinas calls per accidens causal sequences.)

But for this to be genuine explanation, the persistence of the cause and/or effect needs to have an explanation. Divine conservation provides a very neat explanation: God necessarily exists eternally, and is simultaneous with everything (there may be some complications, though, with a timeless being given presentism), so God can cause A to persist from t₁ to t₂ and B to persist from t₂ to t₃. Thus, fundamental links in diachronic causal explanations depend on divine conservation.

An existential inertia view also gives a solution, but a far inferior one. For existential inertia requires the earlier existence of A, together with the metaphysical principle of existential inertia, to explain the later existence of A. But such a cross-time explanatory relation seems too much like the already rejected idea of cross-time causation. For it’s looking like A qua existing at t₁ explains A existing at t₂. But at t₂, according to presentism A qua existing at t₁ is in the unreal past, and it is absurd to suppose that what is in the unreal past can explain something real now.

In summary, given presentism, all fundamental explanatory relations need to be simultaneous. But it is an evident fact that there are diachronic causal explanatory relations. The only way to build those out of simultaneous explanatory relations is by supposing a being that can be simultaneous with things that exist at more than one time—a timelessly eternal being—whose causal efficacy provides the diachronic aspects of the explanatory linkage.

That said, I think there are two serious weaknesses in this story. The first is that it’s a close cousin of occasionalism. For there is no purely non-divine explanatory chain from the setting of the alarm at night to the alarm going off in the morning—divine action explains the persistences that make the chain diachronic.

A second problem is the puzzle of what explains why A causes B at t₂ rather than as soon as A comes into existence. Why does A “wait” until t₂ to cause B? Crucial to the story is that A is the whole cause, which then persists from t₁ to t₂. But why doesn’t it cause B right away, with B then causing whatever effect it has right away, and with everything in the whole causal history of the universe happening at once? Again, one might give this an occasionalist solution—A causes B only because God cooperates with creaturely causation, and God might hold off his cooperation until t₂. But this makes the story even more occasionalist, by making God involved in the timing of causation.

Existential inertia and relativity

According to the doctrine of existential inertia, objects have a metaphysical tendency to continue existing absent interference. Existential inertia differs from ordinary physical inertia, in that existential inertia is supposed to come from the metaphysics of time and existence, while physical inertia comes from the laws of nature.

Let’s now imagine that Bob is a physical object that pops into existence at some point z₀ in spacetime, in a universe with nothing that would annihilate Bob (and with Bob lacking any means of self-annihilation). Then according to existential inertia, Bob will continue to exist. But what does that mean in a relativistic setting? Times correspond to spacelike hypersurfaces. A time is future with respect to z₀ provided that it corresponds to a spacelike hypersurface intersecting the future light-cone centered on z₀. Thus, what we get is:

1. If Bob exists at z₀, then for every spacelike hypersurface H that intersects the future light-cone of z₀, Bob exists at some location or other on H.

This is strange on two counts. First, it seems odd that for every spacelike hypersurface that intersects the future light-cone of z₀, we have some sort of a metaphysical guarantee that Bob is somewhere on it—not at any particular place, mind you, but somewhere or other on it. Maybe it doesn’t seem as odd to you as it does to me, though.

Perhaps more seriously, however, (1) describes a metaphysical tendency that makes crucial reference to the speed of light.

In fact, (1) seems to somehow make speed-of-light limits have some sort of metaphysical force. For suppose that Bob faster-than-light travels from z₀ to some point z₁ outside the light-cone of z₀. Then after that episode of faster-than-light travel, Bob could continue living a normal slower-than-light life, while violating (1) with respect to a number of hypersurfaces (that intersect the future cone of z₀). Thus, while violations of existential inertia are supposed to come from destructive powers, a violation of (1) can come from simple faster-than-light travel.

If we suppose that the metaphysics of time requires a privileged reference frame, the above problems disappear. They also disappear if we think that objects come along with a privileged internal time sequence, and that existential inertia is defined with respect to that internal time sequence.