Time and extended wellbeing

It is said that when your friend has bad things happen, the occurrence of these bad things constitutes a loss of wellbeing for you. Not just because you are saddened, but simply directly in virtue of your interest in your friend’s wellbeing. This is said to happen even if you don’t know about your friend’s misfortune.

But when do you lose wellbeing? On the story above, you lose wellbeing when you friend suffers. But if we say that your loss of wellbeing is simultaneous with your friend’s, what does that mean, given that simultaneity is relative? What is the relevant reference frame?

There are two obvious candidates:

1. Your reference frame.

2. Your friend’s reference frame.

These may be quite different if you and your friend are traveling at high speeds through space. And there doesn’t seem to be a compelling argument for choosing one over the other. Furthermore, there really isn’t such a thing as the reference frame of a squishy object like a human being. Different parts of a human being are always moving in different directions. My chest moves away from my backbone, and soon moves towards it. It is tempting to define my reference frame as the reference frame of my center of mass. I am not sure this makes complete sense in the framework of general relativity (a center of mass is a weighted average of the positions of my parts, but when the positions like in a curved spacetime, I don’t know if a weighted average is well-defined). But even in special relativity there are problems, since it is possible for an organism’s center of mass to move faster than light. (Imagine that a knife moving at nearly the speed of light cuts a stretched-out snake in half, and the snake briefly survives. During the time that the knife moved through the thickness of the snake, the center of mass of the snake moved by a quarter of the snake’s length.)

Here is another option. Perhaps your friend’s misfortunes are yours precisely when a ray of light from the misfortune could have illuminated you, i.e., precisely when you are at the surface of the future lightcone centered on some portion of the misfortune. There is something a bit wacky about this: misfortune propagates just as idealized light (not taking into account collisions with matter) would. In particular, this means that misfortune is subject to gravitational lensing. That seems really weird.

All of the above seems like it’s barking up the wrong tree. Here is a suggestion. While some aspects of wellbeing or illbeing can be temporally localized—pains, for instance—others cannot be. Having a rich and varied life is not temporally localized. Perhaps the contribution to your illbeing from the misfortune of your friends is similarly not temporally localized in your life. It’s just a negative in your life as a whole.

But I am not very happy with that, either. For it seems that if your friend is in pain, and then is no longer in pain, there is some change in the wellbeing of your life.

I don’t know.

Spacetime and Aristotelianism

For a long time I’ve been inclining towards relationalism about space (or more generally spacetime), but lately my intuitions have been shifting. And here is an argument that seems to move me pretty far from it.

Given general relativity, the most plausible relationalism is about spacetime, not about space.

Given Aristotelianism, relations must be grounded in substances.

Here is one possibility for this grounding:

1. All spatiotemporal relations are symmetrically grounded: if x and y are spatiotemporally related, then there is an x-to-y token relation inherent in x and a y-to-x token relation inherent in y.

But this has the implausible consequence that there is routine backwards causation, because if I walk a step to the right, then that causes different tokens of Napoleon-to-me spatiotemporal relations to be found in Napoleon than would have been found in him had I walked a step to the left.

So, we need to suppose:

2. Properly timelike spatiotemporal relations are grounded only in the later substance.

But what about spacelike spatiotemporal relations? Presumably, they are symmetrically or asymmetrically grounded.

If they are symmetrically grounded, then we have routine faster-than-light causation, because if I walk a step to the right, then that causes different tokens of x-to-me spatiotemporal relations to be found in distant objects throughout the universe.

Moreover, on the symmetric grounding, we get the odd consequence that it is only the goodness of God that guarantees that you are the same distance from me as I am from you.

If they are asymmetrically grounded, then we have arbitrariness as to which side they are grounded on, and it is a regulative ideal to avoid arbitrariness. And we still have routine faster-than-light causation. For presumably it often happens that I make a voluntary movement and someone on the other side of the earth makes a voluntary movement spacelike related to my movement (because there are so many people!), and now wherever the spatiotemporal relations is grounded, it will have to be affected by the other’s movement.

I suppose routine faster-than-light causation isn’t too terrible if it can’t be used to send signals, but it still does seem implausible. It seems to me to be another regulative ideal to avoid nonlocality in our theories.

What are the alternatives to relationalism? Substantivalism is one. We can think of spacetime as a substance with an accident corresponding to every point. And then we have relationships to these accidents. There is a lot of technical detail to work out here as to how the causal relationships between objects and spacetime points and the geometry of spacetime work out, and whether it fits with an Aristotelian view. I am mildly optimistic.

Another approach I like is a view on which spacetime position is a nonrelational position determinable accident. Determinable accidents have determinates which one can represent as values. These values may be numerical (e.g., mass or charge), but they may be more complex than that. It’s easiest in a flat spacetime: spacetime position is then a determinable whose determinates can be represented as quadruples of real numbers. In a non-flat spacetime, it’s more complicated. One option for the values of determinate positions is that they are “pointed spacetime manifold portions”, i.e., intersections of a Lorentzian manifold with a backwards lightcone (with the intended interpretation that the position of the object is at the tip of the lightcone). (What we don’t want is for the positions to be points in a single fixed manifold, because then we have backwards causation problems, since as I walk around, the shifting of my mass affects which spacetime manifold Napoleon lived in.)

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.

Property dualism and relativity theory

On property dualism, we are wholly made of matter but there are irreducible mental properties.

What material object fundamentally has the irreducible mental properties? There are two plausible candidates: the body and the brain. Both of them are extended objects. For concreteness, let’s say that the object is the brain (the issue I will raise will apply in either case) Because the properties are irreducible and are fundamentally had by the brain, they are are not derivative from more localized properties. Rather, the whole brain has these properties. We can think (to borrow a word from Dean Zimmerman) that the brain is suffused with these fundamental properties.

Suppose now that I have an irreducible mental property A. Then the brain as a whole is suffused with A. Suppose that at a later time, I cease to have A. Then the brain is no longer suffused with A. Moreover, because it is the brain as a whole that is a subject of mental properties, it seems to follow that the brain must instantly move from being suffused as a whole with A to having no A in it at all. Now, consider two spatially separated neurons, n₁ and n₂. Then at one time they are both participate in the A-suffusion and at a later time neither participates in the A-suffusion. There is no time at which n₁ (say) participates in A-suffusion but n₂ does not. For if that were to happen, then A would be had by a proper part of the brain then rather than by the brain as a whole, and we’ve said that mental properties are had by the brain as a whole.

But this violates Relativity Theory. For if in one reference frame, the A-suffusion leaves n₁ and n₂ simultaneously, then in another reference frame it will leave n₁ first and only later it will leave n₂.

I think the property dualist has two moves available. First, they can say that mental properties can be had by a proper part of a brain rather than the brain as a whole. But the argument can be repeated for the proper part in place of the brain. The only stopping point here would be for the property dualist to say that mental properties can be had by a single point particle, and indeed that when mental properties leave us, at some point in time in some reference frames they are only had by very small, functionally irrelevant bits of the brain, such as a single particle. This does not seem to do justice to the brain dependence intuitions that drive dualists to property dualism over substance dualism.

The second move is to say that the brain as a whole has the irreducible mental property, but to have it as a whole is not the same as to have its parts suffused with the property. Rather, the having of the property is not something that happens to the brain qua extended, spatial or composed of physical parts. Since physical time is indivisible from space, mental time will then presumably be different from physical time, much as I think is the case on substance dualism. The result is a view on which the brain becomes a more mysterious object, an object equipped with its own timeline independent of physics. And if what led people to property dualism over substance dualism was the mysteriousness of the soul, well here the mystery has returned.

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.

Relativity and an argument for incompatibilism

A common argument for the incompatibility of freedom and determinism goes something like this (where premises 1, 2 and 3 are implicitly assumed to hold at all times):

1. It is currently possible that I will do A only if the past and the laws are compatible with my future doing of A.

2. If determinism is true, then the past and the laws are only compatible with my future doing of what I will in fact do.

3. So, if determinism is true, the only things that it is currently possible that I will do are the things that I will in fact do.

4. Freedom requires that at some time it be possible that I will do something other than what I will in fact do.

But given relativity theory, it is not clear what “the past” means in the above arguments, since past is always relative to some reference frame. There are at least four ways of reading (1):

• Strongest: It is now possible for me to do A only if the events in the complement of my present closed future light-cone and the laws are compatible with my doing A.

• Stronger: It is now possible for me to do A only if for every reference frame R, the past according to R and the laws are compatible with my doing A.

• Weaker: It is now possible for me to do A only if for some reference frame R, the past according to R and the laws are compatible with my doing A.

• Weakest: It is now possible for me to do A only if the events in my present open past light-cone and the laws are compatible with my doing A.

Now, generally we should prefer less strong premises. So we should avoid the Strongest and Stronger readings of (1). But I claim that the analogue of (2) is unjustified if we take the Weaker reading of (1). For suppose A would be a future action. Then the past open light-cone of A will be strictly larger than my current past open light-cone. Determinism tells us that A or its absence is nomically determined by the events in its past open light-cone. But that past open light-cone is strictly larger than my current past open light-cone. And it could be that some event E that is in A’s past open light-cone but not in my current past open light-cone makes a difference as to whether A happens. Then there will be a reference frame R such that this event E would be outside my current past according to R. Thus, A’s or its absence’s being determined by the events in its past open light-cone leaves open the possibility that some event E that isn’t in my current past according to R makes a difference as to whether A happens, and hence that A or its absence need not be determined by the events in my current past according to R.

So, for the argument (1)–(4) to work given relativity, it seems we need the Stronger or Strongest reading for (1).

Is there a better way to fix the argument relativistically? Maybe. I like the idea of replacing (1) with an atemporal formulation:

5. Action A is only free if its non-occurrence is compatible with the laws and the subset of events in A’s causal history that are outside of my life.

Mystery and religion

Given what we have learned from science and philosophy, fundamental aspects of the world are mysterious and verge on contradiction: photons are waves and particles; light from the headlamp on a fast train goes at the same speed relative to the train and relative to the ground; objects persist while changing; we should not murder but we should redirect trolleys; etc. Basically, when we think deeper, things start looking strange, and that’s not a sign of us going right. There are two explanations of this, both of which are likely a part of the truth: reality is strange and our minds are weak.

It seems not unreasonable to expect that if there were a definitive revelation of God, that revelation would also be mysterious and verge on contradiction. Of the three great monotheistic religions, Christianity with the mystery of the Trinity is the one that fits best with this expectation. At the same time, I doubt that this provides much of an argument for Christianity. For while it is not unreasonable to expect that God’s revelation would be paradoxical, it is a priori a serious possibility that God’s revelation might be so limited that what was revealed would not be paradoxical. And it would also be a priori a serious possibility that while creation is paradoxical, God is not, though this last option is a posteriori unlikely given what we learn from the mystical experience traditions found in all the three monotheistic religions.

So, I am not convinced that there is a strong argument for Christianity and against the other two great monotheistic religions on the grounds that Christianity is more mysterious. But at least there is no argument against Christianity on the basis of its embodying mysteries.

Simultaneity, A-Theory and Relativity

Here is a standard story about Special Relativity and the A-theory of time:

• There is an objective metaphysical simultaneity, but

• this metaphysical simultaneity does not affect physical events and is unobservable.

Let’s assume the A-theory is correct and this story is also correct.

Now, when people talk about this metaphysical simultaneity, they normally think they it aligns with the frame-relative simultaneity of Special Relativity for some privileged reference frame. This seems reasonable. But it is an interesting question to ask for an explanation of this alignment.

Causation may put some constraints on metaphysical simultaneity. For instance, perhaps, there shouldn’t be any possibility of future to past causation. But a metaphysical simultaneity relation can satisfy such constraints without coinciding with any frame-relative simultaneity.

If God exists, I guess we might suppose that metaphysical simultaneity coincides with a frame-relative simultaneity because it’s more elegant if it does.

Reality is strange

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

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

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

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

Perdurance and particles

A perdurantist who believes that particles are fundamental will typically think that the truly fundamental physical entities are instantaneous particle-slices.

But particles are not spatially localized, unless we interpret quantum mechanics in a Bohmian way. They are fuzzily spread over space. So particle-slices have the weird property that they are precisely temporally located—by definition of a slice—but spatially fuzzily spread out. Of course, it is not too surprising if fundamental reality is strange, but maybe the strangeness here should make one suspicious.

There is a second problem. According to special relativity, there are infinitely many spacelike hyperplanes through spacetime at a given point z of spacetime, corresponding to the infinitely many inertial frames of reference. If particles are spatially localized, this isn’t a problem: all of these hyperplanes slice a particle that is located at z into the same slice-at-z. But if the particles are spatially fuzzy, we have different slices corresponding to different hyperplanes. Any one family of slices seems sufficient to ground the properties of the full particle, but there are many families, so we have grounding overdetermination of a sort that seems to be evidence against the hypothesis that the slices are fundamental. (Compare Schaffer’s tiling requirement on the fundamental objects.)

A perdurantist who thinks the fundamental physical entities are fields has a similar problem.

A supersubstantialist perdurantist, who thinks that the fundamental entities are points of spacetime, doesn’t run into this problem. But that’s a really, really radical view.

An “Aristotelian” perdurantist who thinks that particles (or macroscopic entities) are ontologically prior to their slices also doesn’t have this problem.

Van Inwagen's ear

Van Inwagen holds that:

1. All and only things whose activity constitutes a life (properly) compose a whole.

2. Whether a plurality of things composes a whole depends only on their internal relations.

He considers a counterexample to (1) and (2) of the following sort. Let the xs be the particles in van Inwagen outside the right ear.

3. If van Inwagen were to have lost the right ear, the activity of the xs would have constituted a life (his life) and composed a whole (namely, van Inwagen).

4. But in fact, the activity of the xs does not constitute a life, but only partly does so, along with the activity of the right ear particles.

5. However, the internal relations between the xs were he to have lost his right ear would have been the same as they are now.

This is a problem: for by (4) and (1), the xs do not compose a whole, but by (3) they would have had he lost his right ear, and by (5) they would have had the same internal relations then, which contradicts (2).

Van Inwagen attempts to escape this problem by denying (5), saying that the internal relations between the particles in his body in the vicinity of the right ear would be affected by the ear not being there. For they would no longer experience forces from the ear particles.

But let d be the closest distance between a right-ear particle and a van Inwagen particle not in the right ear (i.e., one of the xs). But now if God were to suddenly annihilate the right ear, then it seems that none of the xs would be in any way affected until influences traveling at the speed of light could bridge the distance d. I.e., until d/c (where c is the speed of light) had passed, the xs would be without the ear just as they are with the ear. Hence, if we specify that the time of severance in (3) is less than d/c ago, van Inwagen’s response seems to fail.

One might try to get out of this by invoking (non-Bohmian) quantum mechanics, and saying that all particles have fuzzy positions, and the ear particles overlap positionally with the non-ear particles, so that the disappearance of the ear particles affects the non-ear particles instantly. But the instant part of the effect is slight. We can imagine that the disappearance of the ear is so orchestrated as to never split any molecules or atoms. But particles in different molecules are fairly localized to their respective molecules, and the effect of the tails of the wavefunction on what is going on in a neighboring molecule will presumably be negligible.

Of course, a negligible effect is still an effect. But we could imagine a third scenario: van Inwagen loses his ear, and God miraculously tweaks the movements of the xs in a slight and biologically negligible way during the d/c period so that they behave just as they do in the actual world where the ear is attached. In that scenario, the xs would compose van Inwagen, but they would have exactly the same internal relations as they do in the actual world.

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.

Time and marriage

Consider this sequence of events:

• 2000: Alice marries Bob.

• 2010: Bob dies.

• 2020: Alice marries Carl.

• 2030: Alice and Carl invent time machine and travel to 2005 where they meet Bob.

Then, in 2005, Alice is married to Bob and Alice is married to Carl. But she is not a bigamist.

Hence, marriage is not defined by external times like 2005, but by internal times, like “the 55th year of Alice’s life”. To be a bigamist, one needs to be married to two different people at the same internal time. A marriage taken on at one internal time continues forward in the internal future.

And while we’re at it, the twin paradox shows that it is possible for two people to be married to each other and for one to have been married 10 years and the other to have been married 30 years. Again, it’s the internal time that matters for us.

Absolute relativistic simultaneity

If we accept relativity theory as providing a metaphysically correct theory of time, the folk concept of temporal simultaneity needs revision. The standard way to revise it has been to relativize it to a reference frame. Instead of simultaneity being a binary relation between events (A is simultaneous with B) it becomes a ternary relation between events and a frame (A is simultaneous with B in F).

But another revision of the folk concept is possible: We keep simultaneity a binary relation, and specify that two events are simultaneous if and only if they are colocated in spacetime (this is roughly the same as saying that they are simultaneous according to every frame). Spatially distant events, on this revision, are never simultaneous.

The downside of the absolute simultaneity revision is that a lot of first-order
simultaneity judgments become false. Leibniz and Newton were not developing calculus simultaneously. I am not typing this at the same time as my daughter is playing a game on another laptop. Etc.

The upside is that colocation is a much more fundamental concept given relativity theory than the concept of a reference frame.

So we have a choice: We can keep our ordinary first-order judgments as to what events are in fact simultaneous or we can preserve the arity of the simultaneity relation and the judgment about the fundamentality of simultaneity. I think cases of revision of ordinary concepts, preserving ordinary first-order judgments tends to trump other things. So I am inclined to think the standard revision is superior as a way of doing justice to the language.

But the absolute revision may be better as a philosophical heuristic. For we might think that fundamental philosophical concepts should be frame-invariant, like fundamental physical concepts are.

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.

Relativity, simultaneity, minds and brains

This is very much a thinking-in-progress post rather than a finished argument. But I've been toying with this line of thought:

1. The simultaneity relations between conscious mental states of an ordinary human (e.g., "itching while feeling cold") are not relative to reference frame.
2. The simultaneity relations of spatially extended states of an object are relative to a reference frame.
3. If conscious mental states are identical with or wholly constituted by brain states, then they are spatially extended states.
4. So, conscious mental states of an ordinary human are neither identical with nor wholly constituted by brain states.

The restriction to ordinary people rules out cases where someone has two or more centers of consciousness at a given time (e.g., due to brain-splitting, time travel, or multiple personalities). In the case of such a non-ordinary person, we can run the argument for each center of consciousness and conclude that the center's states are not identical with or constituted by brain states.

What makes this argument tricky—and this is the part I need think more about—is that of course the relativistic effects between different bits of the brain are practically negligible. The kind of time difference that would be involved in trying to see whether I started itching before starting to feel cold or whether it was the other way around would be so minuscule that I couldn't tell the difference as to which state started earlier or whether they started simultaneously. Nonetheless, there is some plausibility in thinking that there is a fact of the matter as to which state started earlier or whether they started simultaneously. Moreover, maybe we could imagine beings with bigger and faster brains where the effects would be real--and (1) plausibly isn't just a fact about us, but about any discursive agents with a single center of consciousness.

Here's an interesting thing. Suppose that one responds to the argument by saying that there is an absolute reference frame, despite relativity theory, much as defenders of the A-theory of time hold. That response doesn't get one completely out of the argument. We can argue: the absolute frame is insignificant for physics; yet it is significant for mind; so mind doesn't reduce to physics.

I also think the argument (though perhaps not the absolute-frame variant) may lead to some problems for supervenience theories of mind. But that's for future research.

Shape is not an intrinsic property

1. (Premise) If an object can change in shape without undergoing intrinsic change, shape is not an intrinsic property.
2. (Premise) If the diameter[note 1] of an object changes while its perimeter does not, the object changes in shape.
3. (Premise) An object can change in diameter but not in perimeter without undergoing intrinsic change.

The thought behind (2) is that the shape of an object determines the ratios of distances between parts.

Now I argue for (3). Imagine a giant hula-hoop, a light-year in diameter, without anything inside. Suppose that God creates a massive star in the middle. This distorts the spacetime manifold in the vicinity of the star, changing the distances between diametrically opposed points on the hula-hoop. But it will take half a year for the changes in the spacetime manifold to propagate to the hula-hoop. Thus the perimeter of the hula-hoop is unchanged for half a year. Furthermore, surely, the creation of a star half a light-year from any part of an object doesn't intrinsically change the object for at least half a year.

So, the hula-hoop (a) is intrinsically unchanged, (b) its perimeter is unchanged, and (c) its diameter is changed, which yields (3).

This is a modification of an argument in a paper of mine on the Eucharist.

Absolute simultaneity and common sense

It's common sense that there is absolute simultaneity, whether directly so or because it's common sense that there is an objective present. It is sensible for philosophers to want to hold on to what is common sense. But here we should not be so quick. For consider some common sense claims:

1. There is absolute simultaneity.
2. If A and B are absolutely simultaneous and C and D happen t units of time after A and B respectively, then C and D are absolutely simultaneous.
3. Properly functioning clocks correctly measure lengths of time.
4. Clocks continue to properly function when moving, as long as they are not accelerated so quickly as to damage them.

But while (1)-(4) are all common sense, we have empirical data (assuming some uncontroversial claims of how to determine cases of absolute simultaneity for side-by-side events) that they are not all true, namely the data confirming the Twin Paradox.

Now when a number of common sense claims cannot all be held together, it is not responsible simply to say that one of them is common sense and therefore true. For the same thing could be said about the others. One would need to say something about how one's preferred claim is more commonsensical than the others, and that's a judgment that may well go beyond common sense.

I think most defenders of absolute simultaneity will reject (3) or (4). But if we look at how we actually acquire our concepts of durations of time by using clocks, watches and internal timers, it's plausible that we are committed to (3). And our practices of blithely using clocks even after coming to think that the earth is rapidly moving around the sun suggest (4).

I actually think that an interesting strategy for defending absolute simultaneity is to deny (2). This would lead to a view with absolute simultaneity but purely relative temporal durations.

That said, I am happy to deny (1).

The essential properties of our spacetime

Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?

There are three different views one could have about some kind K of potential properties of a spacetime:

1. All the properties in K that Spacey has are essential to Spacey.
2. None of the properties in K are essential to Spacey.
3. Some but not all the properties in K that Spacey has are essential to Spacey.

Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).

Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)

Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.

The flow of time

Famously, D. C. Williams ridiculed the deep-seated intuition (at the heart of Bergson's thought, of course) that there is a flow of time, asking how fast time is flowing, if it's flowing. Some wits have tried to respond: "Always at a second per second." But there is a much better and less trivial answer. And interestingly it is an answer that has a home in the B-theory of time.

The Twin Paradox suggests that we should distinguish the internal time of an individual from something like the generally shared external time of the human community. Thinking about time travel suggests a similar distinction, as Lewis has noted. But once we have a distinction between internal and external time, then we can give a non-trivial answer to Williams' question. The flow of time is measured in terms of external units of time per internal units of time. If external time is defined by the shared life of the human community (that's one among a number of options—we should probably understand "external time" in a context-sensitive way), normally time flows at one external second per second. But if I were to engage in travel at relativistic speeds, it could be that in a month of internal time, eight years of external time would elapse. And if I were to engage in gradual backwards time travel, then I would have a negative rate of time's flow: maybe I would be moving at −1 external century per internal second. (In non-gradual time travel, the rate would be undefined.)

The distinction between internal and external time fits best with the B-theory. So the notion of time's flow, surprisingly, seems to have its home in the B-theory.