Value supervenes on being

Consider this thesis, which both Augustine and Aquinas would accept:

1. Value supervenes on being (VSB): How valuable reality is is determined by what entities exist.

However:

2. It is good to have a true belief and bad to have a false belief.

We now have an argument against presentism (only present things exist) and growing block (only present and past things exist). Among our beliefs, we have beliefs about contingent future events. Some of these beliefs are contingently true and others are contingently false. (I am assuming a bivalent temporal logic.) The value of these beliefs is determined by what entities exist. But present and past entities are insufficient to determine whether the beliefs are true, and hence what the value of the beliefs is. Thus, contrary to presentism and growing block, there must be future things.

God and growing block

1. On the growing block theory of time, if God is in time, God grows.

2. God doesn’t grow.

3. So, God is not time or the growing block theory is not true.

Freedom: a problem for presentism and growing block

A number of people have told me that they have the intuition that a four-dimensional picture of reality like that in the B-theory undercuts free will.

I want to suggest that there is one way in which it is a presentist picture of temporal reality that undercuts free will. (A similar argument applies to growing block, but curiously enough not to shrinking block.)

Assume that open future views are false: there are always determinate facts about contingent future events. (If your reason for thinking that four-dimensional theories undercut free will is because you are an open futurist, then you won’t be impressed by what I say.) Suppose it is a fact that tomorrow morning I will have oatmeal for breakfast. On presentism, this fact can only be grounded in what is present, since on presentism, what is present is all there is. Maybe it’s grounded in the present existence of a future-tensed fact or maybe it’s grounded in my having a future-tensed property of being such that I will eat oatmeal in nine hours. But in any case, things right now are already such as to ground and guarantee that I will have oatmeal for breakfast. Moreover, this was already true five minutes ago—five minutes ago, things were also already such as to ground and guarantee that I will have oatmeal for breakfast tomorrow. This sure feels like it should undercut free will! It seems pretty intuitive that freedom isn’t compatible with there existing grounds that guarantee the action prior to the choice.

On the other hand, on a four-dimensional view while it is a fact that I will eat oatmeal for breakfast tomorrow, the grounds of this fact are not located in the present—and were never located in the past. Rather, the grounds of this fact are where they should be—at tomorrow morning. How things are on the present slice of reality, or on past slices, does not determine (assuming indeterminism) what I will have for breakfast tomorrow. That’s left for tomorrow.

The neatest way out for the presentist is to deny with Merricks that contingent truths about the future and past have any grounds. But that’s also costly.

After writing the above, I came across this related paper by Hunt. No time to revise right now to see what similarities or differences there are.

Growing Block and a time bias

Here’s a curious argument against Growing Block. Other things being equal, it is better to receive goods earlier in life and to receive bads later in life if Growing Block theory is true. For the earlier you receive X in life, the larger the portion of your life during which X is a part of your life. For X becomes a part of your life at its time, and on Growing Block remains a part of your life forever.

Thus, if you live to 70, and eat a chocolate cake at age 10, then for the next 60 years you are alive with a life that includes that happy event. But if you eat the cake at age 50, then it is only for 20 years that you are alive with a life that includes that happy event.

On Growing Block, this seems to be a good reason to put good things earlier in life and bad things later. But surely one does not have such a reason! So, we have evidence against Growing Block.

Existing and existing at a time

If we accept growing block or eternalism as our theory of temporal reality, we have to make a distinction between existing simpliciter (i.e., being in the domain of unrestricted quantifiers) and existing-at-a-time (including tensed existence at the present). To exist at time t is not the same as its being the case at t that one exists simpliciter.

Suppose, for instance, closed-future growing block. Then we can say the following about Bucephalus (circa 355 BC–326 BC):

1. In 330 BC: Bucephalus exists-in-330-BC.

2. In 330 BC: Bucephalus exists simpliciter.

3. In 2025: Bucephalus exists simpliciter.

4. In 2025: It’s not the case that Bucephalus exists-in-2025.

5. In 3000 BC: Bucephalus does not exist simpliciter.

6. In 3000 BC: Bucephalus exists-in-330-BC.

Existence-at-a-time is not really existence—it is just spatiotemporal locatedness. (Of course, we have a grounding problem about how on closed-future growing block facts about the future are grounded, but bracket that.)

Now, on both growing block and eternalism, if something exists-now it exists simpliciter. Could one have a theory on which this inference is denied?

Perhaps Platonism denies it. Only timeless and unchanging things really are. Changing things in time become rather than really are. Similarly, it is said that God said to St Catherine of Siena: “I am he who is and you are she who is not.”

But is there a theory of time on which the inference is denied? I once explored a version of B-theory like that. Now I want to consider a version of A-theory like that.

Consider pastism, on which to exist simpliciter is to exist pastly, and take a version of pastism on which there are moments of time (probably the best version of pastism on offer is one where there are no moments). Suppose t₁ is the first moment of Bucephalus’ life. Then on pastism, at t₁ Bucephalus doesn’t exist, but Bucephalus exists-at-t₁. Is this coherent? It does have this odd consequence. Suppose t₁ is also the last moment of time (so Bucephalus exists at exactly one moment). Then Bucephalus exists-at-t₁, but it is never the case that Bucephalus exists simpliciter. Still, it’s not clear that a logical contradiction has occurred.

Nonetheless, it does seem absurd to suppose that something exists-now but doesn’t exist, even if it’s not strictly contradictory.

Some odd theories of temporal reality, with eschatological applications

The three major theories of temporal reality are presentism (reality includes only the present), growing block (reality includes the present and past) and eternalism (reality includes past, present and future).

A recent option that has been considered is thick presentism on which reality includes a short segment of time including the present. This lets one have some of the intuitive advantages of presentism (dinosaurs and Martian settlements don’t exist) while at the same time neatly solving the problem of diachronic causation. Moreover, it raises an interesting explanatory problem: why does our world have the kind of temporal reality it does.

I think that if thick presentism is metaphysically possible, likely so are a number of other views:

1. Very thick presentism

2. Time-variable thickness thick presentism

3. Growing block

4. Space-variable thickness thick presentism

5. Swiss-cheese temporal reality.

On very thick presentism, the band of reality in thick presentism becomes extremely thick, say a million years. For there seems to be no compelling reason why the band of reality posited by thick presentists would have to be thin.

On the time-variable thick presentism, we have a thick presentism where the thickness varies with time. This is likely something that the thick presentist has to countenance. For, plausibly, some moment within the thick present has to be distinguished as “very present” to avoid violating the law of non-contradictions (since objects will have contradictory properties within the thick present). Suppose that that moment happens to be at the middle of the thick present. Then when the very present gets closer and closer to the beginning or end of time, the band of reality must get thinner and thinner. Or suppose the moment happens to be at the end of the thick present (I think that may be the better theory). Then when the very present gets closer to the beginning of time, the band of reality gets thinner and thinner. We also get time-variable thick presentism by applying patchwork principles to recombine worlds with thick presentisms of different thicknesses.

Growing-block with a finite past is just a time-variable thickness thick presentism where the very present is at the end of the thick present and the thickness of the thick present at t is equal to the duration from the beginning of time to t. And if we allow it with a finite past, why not with an infinite one—assuming an infinite past is possible?

Applying patchwork principles to thick presentisms with different thicknesses, we can get a space-variable thick presentism—here, the present may be ten minutes thick, but there it may be ten years thick.

Once we allow that, why not go all the way and allow a swiss-cheese temporal reality, where at any given time various chunks of the four-dimensional manifold are included or left out in a pretty arbitrary fashion (perhaps subject to some restrictions to make causation work)?

Now, here’s a fun theological speculation. Some thinkers are worried about eternalism and growing block on theological grounds: they worry that these theories imply that horrendously evil events like the Holocaust will eternally be a part of reality, and that this is inappropriate. But once we have expanded the range of options as we have, we can have some interesting theological theories.

For instance, perhaps, growing block is true between now and the Second Coming. Then at the Second Coming the band of reality gets very thin, so that after the Second Coming, the band of reality includes only the times from the Second Coming to the then-present. We can think of this as giving a surprising reading of the “Behond, I make all things new” of Revelation 21:5—the past events and object suddenly get wiped out of reality. Or, as a variant, perhaps partial eternalism becomes true after the Second Coming: reality now includes all times from the Second Coming on.

But one may worry that that wipes out too much—for instance, it wipes out the glory of the Cross (I am grateful to a graduate student for this worry). Very well. Then we go for a swiss cheese version where we have selective removal from reality—the Holocaust goes but the Cross stays, say.

All this has a certain resemblance to Hud Hudson’s hypertime story. But it’s different in two ways. First, it doesn’t need hypertime. Second, I am assuming here a variant of a standard presentist picture on which there are tensed truths, and the tensed truths function according to standard temporal logics. Thus, if it is true that p, it will always be true that it was true that p. What changes is what events and substances fall within the domain of restricted quantifiers—quantifiers do not commute with “at t” and other temporal operators.

For instance, on the “I make all things new” theories, right now all three of these are true:

1. There exists an x such that at 327 BC: x is a horse named “Bucephalus”

2. At 327 BC: there exists an x such that x is a horse named “Bucephalus”.

3. At 2000 AD: there exists an x such that at 327 BC: x is a horse named “Bucephalus”.

After the second coming, when the past objects and events are wiped out, we still have (b) and (c) holding, but (a) does not hold.

On a hypertime variant of “I make all things new”, once the past was wiped out, we would have none of (a)–(c).

I do not endorse any of these odd possibilities, because I am a die-hard B-theorist.

Wacky reality dynamics

The dynamics of reality over time vary between theories of time. On growing block, at each moment a new present slice is added to reality. On presentism, at each moment the formerly present slice is subtracted from reality and a new present slice is added to replace it.

But once we admit that there are at least these two such “reality dynamics”, other possibilities show up.

Centisecondism: At each moment, the slice one millisecond (i.e., 0.01 seconds) in the past (if there is one) is subtracted from reality, while a new present slice is added. As a result, except during an initial one centisecond warmup when reality is just growing, reality is always a one-centisecond thick chunk. Centisecondism is superior to presentism in multiple ways. First, it seems hard to fit consciousness in an infinitesimally long reality, as in presentism, but a centisecond is good enough. Second, a centisecond is long enough for diachronic causal relations to be unproblematic. Third, presentism suffers from the problem that on presentism we never see reality. Because of light-travel times, we always see the past, and the past is not real! On centisecondism, we have a chance to see reality as it is.

Of course, a centisecond is arbitrary. The actual slice thickness could be bigger or smaller. It may seem ad hoc what it is. But it’s no more ad hoc than, say, the fine structure constant or any other constant in the laws of nature. If there is a God, he can decide on the slice thickness, in his wisdom, just as he decides on the fine structure constant. If there is no God, the thickness constant can be brute.

Eschatological growing block: Presentism is true right now: reality is one-moment thick. But then comes an eschaton. At the eschaton, suddenly all those past slices that had disappeared due to presentism pop back into reality, and we stop subtracting from reality, and begin to just add. Now we have growing block. This could give us a kind of transcendent outlook on the past in the eschaton. The eschatological growing block has the interesting consequence that being-real-at is not a symmetric relation. For instance, the time of the eschaton is not real at 2023, but 2023 is real at the time of the eschaton. This may seem strange, but in fact is true on any growing block theory.

Eschatological eternalism: Presentism is true right now. But eternalism starts to be true at the eschaton—at the eschaton not just one moment, and not just the past, but the whole past, present and future pop into reality. This provides a kind of temporalized version of Leftow’s model of a timeless God’s relation to a presentism time—the beings in the eschaton have an eternalist relation to our presentist time.

One might think that these theories require hypertime. That is not true for centisecondism or eschatological growing block, because centisecondism and eschatological growing block have room for defining the present moment without moving to hypertime. The present moment on both theories is just the leading the edge of reality. On eschatological eternalism, if we could get in a moving spotlight, then we could define a present moment. (Or could we have an eschatological eternalism on which “at the eschaton” all the “past, present and future” are actually present?)

I think centisecondism and eschatological growing block are both coherent if standard growing block is coherent. If I were a growing blocker, I think I would think that God could make a world where presentism or centisecondism or eschatological growing block are true, or almost true (by that I mean that in those worlds there wouldn’t be time, but time^*).

But I am B-theorist eternalist, and I am just giving all these stories for fun. I suspect that they are all ultimately impossible, as are presentism (of a standard sort) and growing block.

The intrinsic badness of certain future tensed facts on presentism

It is bad that tomorrow someone will be in intense pain. On eternalism, we can easily explain this: tomorrow’s pain is just as real as today’s. But on presentism and growing block, future pains don’t exist.

Presumably, the presentist and growing blocker will say that the tensed fact of there being an intense pain tomorrow is bad, and this bad tensed fact presently exists.

Is this badness of the future tensed fact about the pain an instrumental or non-instrumental badness? If it’s instrumental, it is not clear what it could be instrumental to. The main candidate (apart from special cases where there is an obvious candidate, such as when the pain leads to despair) is that the fact that there will be a pain tomorrow is instrumental to tomorrow’s pain. But the fact that tomorrow there will be pain won’t cause that pain—otherwise, it would be trivial that every future event has a cause.

So the present badness of there being a pain tomorrow would be non-instrumental. But now imagine two scenarios with finite time lines.

• Scenario A: There is a mindless universe with a day of random particle movement, followed by the formation of a brain which has intense pain for a minute, followed by the end of time.

• Scenario B: There is a mindless universe with a century of random particle movement, followed by the formation of a brain which has intense pain for a minute, followed by the end of time.

Let’s suppose we find ourselves at the last moment of time in one scenario or the other. Then in Scenario A, there was a day of the obtaining of a “future pain fact”, and in Scenario B, there was a century of the obtaining of a “future pain fact”. If a future pain fact is a non-instrumentally bad thing, then there was non-instrumentally bad stuff in Scenario B for a much longer period of time than in Scenario A, and so Scenario B is much worse than Scenario A with respect to future pain. But that seems mistaken: the greater length of time during which there is a future pain fact does not seem any reason to prefer one scenario over another.

Should the A-theorist talk of tensed worlds?

For this post, suppose that an A-theory of time is true, so there is an absolute present. If we think of possible worlds as fully encoding how things can be so that:

1. A proposition p is possible if and only if p holds at some world,

then we live in different possible worlds at different times. For today a Friday is absolutely present and tomorrow a Saturday is absolutely present, and so how things are is different between today and tomorrow (or, in terms of propositions, that it’s Saturday is false but possible, so there must be a world where it’s true). In other words, given (1), the A-theorist is forced to think of worlds as tensed, as centered on a time.

But there is something a little counterintuitive about us living in different worlds at different times.

However, the A-theorist can avoid the counterintuitive conclusion by limiting truth at worlds to propositions that cannot change their truth value. The most straightforward way of doing that is to say:

2. Only propositions whose truth value cannot change hold at worlds

and restrict (1) to such propositions.

This, however, requires the rejection of the following plausible claim:

3. If (p or q) is true at a world w then p is true at w or q is true at w.

For the disjunction that it’s Friday or it’s not Friday is true at some world, since it’s a proposition that can’t change truth value, but neither disjunct can be true at a world by (2).

Alternately, we might limit the propositions true at a world to those expressible in B-language. But if our A-theorist is a presentist, then this still leads to a rejection of (3). For on presentism, the fundamental quantifiers quantify over present things, and the quantifiers of B-language are defined in terms of them. In particular, the B-language statement “There exist (tenselessly) dinosaurs” is to be understood as the disjunction “There existed, exist or will exist dinosaurs.” But if we have (3), then worlds will have to be tensed, because different disjuncts of “There existed, exist or will exist dinosaurs” will hold at different times. A similar issue comes up for growing block.

So on the most popular A-theories (presentism and growing block), we have to either allow that we inhabit different worlds at different times or deny (3). I think the better move is to allow that we inhabit different worlds at different times.

Heaven, the goods of others and the defeat of evil

There is a delight in competing athletically with one’s child: if they win, it feels good, and if one wins, it feels good, too. (The hedonic ideal is achieved when the child wins about 60% of the time; then one feels proud of their superiority, but not rarely one has the pleasure of beating a stronger opponent.)

Parental love makes it easy to love another as oneself (to paraphrase what C. S. Lewis says about Eros). It thus gives us an image of what it is like to be in heaven: we will greatly enjoy the goods had by others. This gives us an attractive picture of how the joy of heaven could fit with enduring differences in personal characteristics. Perhaps being an extrovert would not be true to my self and to God’s vocation for me, and so maybe even over an eternity in heaven I won’t be extroverted. But if so, I will still be fully happy for the joy of the heavenly extroverts, without any regret that I am not one of them, while they will be fully happy for me introverted joys, also without any regret that they are not like me.

Here are two controversial (for very different reasons) applications of this. First, there is a genuine and distinctive good in being a woman and there is a genuine and distinctive good in being a man, and it seems to make sense for a person to desire the goods of the other sex, regardless of whether it is possible to have them oneself. In heaven, however, Joseph can enjoy Mary’s good in being a woman and Mary can enjoy Joseph’s good in being a man, without Joseph regretting that he personally “only” has the good of manhood and Mary regretting that she personally “only” has the good of womanhood. That is what total love is like.

Second, given an eternalist or moving block theory of time, the past will always be fully real. This in turn gives us a solution to the problem that various important goods, such as marriage and self-sacrifice, will not be available in heaven. For we will be able to rejoice in others’ past possession of these goods, without regret for the fact that they aren’t ours and now.

The second point, however, raises the following problem: Won’t we also grieve for others’ past—and even present, if hell is a reality (as I think it is)—subjection to great evils? Maybe, but in God’s plan there is a crucial asymmetry between good and evil. Evils are defeated. How this defeat happens is deeply mysterious. But because of this defeat, I suspect the grief for a defeated evil will not hurt, precisely because of the evil’s being defeated, while goods remain undefeated and hence the joy for them will always delight.

In fact, the last point suggests something to me. A lot of philosophers of religion have said that it’s not enough for theodicy if evils are justly compensated for or their permission is in some way justified. We need these evils to be defeated. I think this is mistaken if all we are after is a response to the problem of evil. But we also need a response to the problem of why the past and present suffering of others doesn’t cause the saints pain in heaven. And it is here that we need the defeat of evil.

Presentism, promises and privation

It appears that the presentist (and maybe even growing blocker) may not be able to accept either the privation theory of evil, which says that every evil is the lack of a due good, nor the privation theory of evilmaking, which says that every evil either is the lack of a due good or is made evil by the lack of a due good.

For suppose I promise you that one unspecified day I will do A for you. But it turns out that I never do it. That’s an evil, and intuitively it is an evil because of the lack of fulfillment of the promise, which sure sounds like a privation. But when do we have this evil? Either when I make the promise or at some later time. The nonexistence of future promise fulfillment isn’t the lack of a due good given presentism or growing block. For the nonexistence of future action A is automatic given presentism or growing block, and something automatic like that can’t be an evil. Another way to put the point is that something that would have to be future can’t be such as to be due to exist. Suppose, now, the evil is at some later time. But no later time is such that I ought on that day to do A, since the day for doing A was not specified, so on no day is my failure to do A a lack of a due good.

The growing blocker might at least say that at the last moment of my life the nonexistence of A during the present and past is the lack of a due good—but even that won’t work if I live forever and never do A.

The eternalist, on the other hand, can say that the non-existence of A throughout a finite or infinite interval of times can count as the lack of a due good, regardless of whether these times are past, present or future.

Presentism and the Cross

1. It is important for Christian life that one unite one’s daily sacrifices with Christ’s sufferings on the cross.

2. Uniting one’s sufferings with something non-existent is not important for Christian life.

3. So, Christ’s sufferings on the cross are a part of reality.

4. So, presentism is false.

Theories of time and truth-supervenes-on-being

Truth supervenes on being is the thesis that if two worlds have the same entities, they are otherwise the same. I just realized something that should be pretty obvious. One cannot hold on to all three of the following:

• A-theory

• eternalism

• truth supervenes on being.

For according to eternalism, at any two different times, the facts about what exists are the same. So if truth supervenes on being, at any two different times, all facts are the same—and in particular the facts about what time is objectively present will be the same, which contradicts A-theory.

In other words, just as the best version of presentism (that of Trenton Merricks) rejects that truth supervenes on being, so does the best version of the moving spotlight theory. Moreover, closed-future growing blockers—and, in particular, classical theist growing blockers—will also want to reject that truth supervenes on being since substantive truths about the future won’t supervene on being given growing block.

All this suggests that we are left with only two major theories of time available to those who accept that truth supervenes on being:

• B-theoretic eternalism

• growing block with an open future.

Grace and theories of time

1. All grace received is given through Christ’s work of salvation.
2. Christ’s work of salvation happened in the first centuries AD and BC.
3. One cannot give something through something that does not exist.
4. Abraham received grace prior to the first century BC.
5. So, Abraham’s grace was given through Christ’s work of salvation.
6. So, it was true to say that Christ’s work of salvation exists even when it was yet in the future.
7. So, presentism and growing block are false.

Two puzzles about pain and time

Supposing the growing block theory of time is correct and you have a choice between two options.

1. You suffer 60 minutes of pain from 10:30 pm to 11:30 pm.
2. You suffer 65 minutes of pain from 10:50 pm to 11:55 pm.

Clearly, all other things being equal, it is irrational to opt for B. But supposing growing block theory is true, there are only past and present pains, and no future pains, so why is it irrational to opt for B?

Well, maybe rationality calls on us to make future reality be better, and we have:

1. If you opt for A, then at 11:55 reality will contain 60 minutes of pain

2. If you opt for B, then at 11:55 reality will contain 65 minutes of pain.

Opting for B will make reality worse (for you) at 11:55, so it seems irrational to choose B. However, we also have facts like these:

3. If you opt for A, then at 11:30 reality will contain 60 minutes of pain.

4. If you opt for B, then at 11:30 reality will contain 55 minutes of pain.

Thus, opting for A will make reality worse at 11:30. Why should the 11:55 comparison trump the 11:30 comparison?

One answer is this: The 11:55 comparison continues forever. If you choose B, then reality tomorrow, the day after tomorrow, and so on will be worse than if you choose B, as on all these days reality will contain the 65 minutes of past pain instead of the mere 60 minutes if you choose A.

However, this answer isn’t the true explanation. For suppose time comes to an end tonight at midnight. Then it’s still just as obvious that you should opt for A instead of B. However, now, it is only during the ten minute period after 11:50 pm and before midnight that reality-on-B is worse than reality-on-A, while reality-on-A is better than reality-on-B during the whole of the 80 minute period strictly between 10:30 pm and 11:50 pm. It is mysterious why the comparison during the 10 minute period starting 11:50 pm should trump the comparison during the 80 minute period ending at 11:50 pm.

I suppose the growing blocker’s best bet is to say that later comparisons always trump earlier ones. It is mysterious why this is the case, though.

The story is also puzzling for the presentist, as I discuss here. But there is no problem for the eternalist: on B reality always contains more pain than on A.

However, there is a different puzzle where the growing blocker can tell a better story than the eternalist. Suppose you will live forever, and your choice is between:

3. You will feel pain from 10 pm to 11 pm every day starting tomorrow
4. You will feel pain from 9 am to 11 am every day starting tomorrow.

Intuitively, you should go for C rather than D. But on eternalism, on both C and D reality includes an equal infinite number of hours of pain. But on growing block, after 9 am tomorrow, reality will be worse for you if you choose D rather than C. Indeed, at every time after 9 am, on option D reality will contain at least twice as much pain for you as on option C (bracketing any pains prior to 9 am tomorrow). So it’s very intuitive that on growing block you should choose C.

Maybe, though, the eternalist can say that utility comparisons involving infinities just are going to be counterintuitive because infinities are innately counterintuitive, as our intuitions are designed/evolved for dealing with finite cases. Moreover, we can tell similar puzzles involving infinities without involving theories of time. For instance, suppose an infinite line of people numbered 1,2,3,…, all of whom are suffering headaches, and you have a choice whether to relieve the headache of the persons whose number is even versus the headache of the persons whose number is prime. The intuition that C is better than D seems to be exactly parallel to the intuition that it’s better to benefit the even-numbered rather than the prime-numbered. But the latter intuition is not defensible. (Imagine reordering the people so now the formerly prime-numbered are even-numbered and vice-versa. Surely such a reordering shouldn’t make any moral difference.) So perhaps we need to give up the intuition that C is better than D?

Asymmetric temporal attitudes and time travel

Philosophers sometimes use thought experiments concerning the asymmetry of attitudes towards future and past events as arguments for a metaphysical asymmetry between past and future. For instance, the fact that I would prefer a much larger pain in my past to a smaller pain in the future is puzzling if the past and future are metaphysically on par.

Here’s a thesis I want to offer and briefly defend:

• It is not rationally consistent to give use thought experiments in this way and to accept the possibility of backwards time travel.

The reason is quite simple: if backwards time travel is possible, our asymmetric attitudes track personal time, not objective time. If I am going to travel 100 million years back in six minutes, I will prefer a smaller pain in five minutes to a much larger pain 100 million years ago, since both of these pains will be in my personal future and only a minute of personal time apart. But the metaphysical asymmetry between past and future tracks external time, not personal time.

Presentism and counting future sufferings

I find it hard to see why on presentism or growing block theory it’s a bad thing that I will suffer, given that the suffering is unreal. Perhaps, though, the presentist or growing blocker can say that is a primitive fact that it is bad for me that a bad thing will happen to me.

But there is now a second problem for the presentist. Suppose I am comparing two states of affairs:

1. Alice will suffer for an hour in 10 hours.
2. Bob will suffer for an hour in 5 hours and again for an hour in 15 hours.

Other things being equal, Alice is better off than Bob. But why?

The eternalist can say:

1. There are more one-hour bouts of suffering for Bob than for Alice.

Maybe the growing blocker can say:

2. It will be the case in 16 hours that there are more bouts of suffering for Bob than for Alice.

(I feel that this doesn’t quite explain why it’s B is twice as bad, given that the difference between B and A shouldn’t be grounded in what happens in 16 hours, but nevermind that for this post.)

But what about the presentist? Let’s suppose preentism is true. We might now try to explain our comparative judgment by future-tensing (1):

3. There will be more bouts of suffering for Bob than for Alice.

But what does that mean? Our best account of “There are more Xs than Ys” is that the set of Xs is bigger than the set of Ys. But given presentism, the set of Bob’s future bouts of suffering is no bigger than the set of Alice’s future bouts of suffering, because if presentism is true, then both sets are empty as there are no future bouts of suffering. So (3) cannot just mean that there are more future bouts of suffering for Bob than for Alice. Perhaps it means that:

4. It will be the case that the set of Bob’s bouts of suffering is larger than the set of Alice’s.

This is true. In 5.5 hours, there will presently be one bout of suffering for Bob and none for Alice, so it will then be the case that the set of Bob’s bouts of suffering is larger than the set of Alice’s. But while it is true, it is similarly true that:

5. It will be the case that the set of Alice’s bouts of suffering is larger than the set of Bob’s.

For in 10.5 hours, there will presently be one bout for Alice and none for Bob. If we read (3) as (4), then, we have to likewise say that there will be more bouts of suffering for Alice than for Bob, and so we don’t have an explanation of why Alice is better off.

Perhaps, though, instead of counting bouts of suffering, the presentist can count intervals of time during which there is suffering. For instance:

6. The set of hour-long periods of time during which Bob is suffering is bigger than the set of hour-long periods of time during which Alice is suffering.

Notice that the times here need to be something like abstract ersatz times. For the presentist does not think there are any future real concrete times, and so if the periods were real and concrete, the two sets in (6) would be both empty.

And now we have a puzzle. How can fact (6), which is just a fact about sets of abstract ersatz times, explain the fact about how Bob is (or is going to be) worse off than Alice? I can see how a comparative fact about sets of sufferings might make Bob worse off than Alice. But a comparative fact about sets of abstract times should not. It is true that (6) entails that Bob is worse off than Alice. But (6) isn’t the explanation of why.

Our best explanation of why Bob is worse off than Alice is, thus, (1). But the presentist can’t accept (1). So, presentism is probably false.

From a dualism to a theory of time

This argument is valid:

1. Some human mental events are fundamental.

2. No human mental event happens in an instant.

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

4. So, presentism is not true.

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

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

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

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

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

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

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

8. So, growing block is not true.

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

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

10. So, Aristotelian four-dimensionalism is true.

Cessation of existence and theories of persistence

Suppose I could get into a time machine and instantly travel forward by a hundred years. Then over the next hundred (external) years I don’t exist. But this non-existence is not intrinsically a harm to me (it might be accidentally a harm if over these ten years I miss out on things). So a temporary cessation of existence is not an intrinsic harm to me. On the other hand, a permanent cessation of existence surely is an intrinsic harm to me.

These observations have interesting connections with theories of persistence and time. First, observe that whether a cessation of existence is bad for me depends on whether I will come back into existence. This fits neatly with four-dimensionalism and less neatly with three-dimensionalism. If I am a four-dimensional entity, it makes perfect sense that as such I would have an overall well-being, and that this overall well-being should depend on the overall shape and size of my four-dimensional life, including my future life. Hence it makes sense that whether I undergo a permanent or impermanent cessation of existence makes a serious difference to me.

But suppose I am three-dimensional and consider these two scenarios:

1. In 2017 I will permanently cease to exist.

2. In 2017 I will temporarily cease to exist and come back into existence in 2117.

I am surely worse off in (1). But if I am three-dimensional, then to be worse off, I need to be worse off as a three-dimensional being, at some time or other. Prior to 2117, I’m on par as a three-dimensional being in the two scenarios. So if there is to be a difference in well-being, it must have something to do with my state after 2117.

But it seems false that, say, in 2118, I am worse off in (1) than in (2). For how can I be better or worse off when I don’t exist?

The three-dimensionalist’s best move, I think, is to say that I am actually worse off prior to 2017 in scenario (1) than in scenario (2). For, prior to 2017, it is true in scenario (1) that I will permanently cease to exist while in (2) it is false that I will do so.

It can indeed happen that one is worse off at time t₁ in virtue of how things will be at a later time t₂. Perhaps the athlete who attains a world-record that won’t be beaten for ten years is worse off at the time of the record than the athlete who attains a world-record that won’t be beaten for a hundred years. Perhaps I am worse off when publishing a book that will be ignored than when publishing a book that will be taken seriously. But these are differences in external well-being, like the kind of well-being we have in virtue of our friends doing badly or well. And it is counterintuitive that permanent cessation of existence is only a harm to one’s external well-being. (The same problem afflicts Thomas Nagel’s theory that the badness of death has to do with unfinished projects.)

The problem is worst on open future views. For on open future views, prior to the cessation of existence there may be no fact of the matter of whether I will come back into existence, and hence no difference in well-being.

The problem is also particularly pressing on exdurantist views on which I am a three-dimensional stage, and future stages are numerically different from me. For then the difference, prior to 2017, between the two scenarios is a difference about what will happen to something numerically different from me.

The problem is also particularly pressing on presentist and growing block views, for it is odd to say that I am better or worse off in virtue of non-existent future events.

Of the three-dimensionalists, probably the best off is the eternalist endurantist. But even there the assimilation of the difference between (1) and (2) to external well-being is problematic.

Times that never become present

Could there be times that are never present? At first sight, this seems a contradiction: surely, each time t is present at itself. Given the B-theory of time, this indeed is automatically true.

Not so, however, for A-theories. There is no contradiction in the growing block growing by leaps and bounds. Imagine that suddenly a whole minute is added to the growing block. The times in the middle of that minute never got to be at the leading edge of reality, and hence never got to be present, since to be present is to be at the leading edge of reality, given growing block. Or consider the moving spotlight: the spotlight could jump ahead in the spacetime manifold by a minute or an hour or a year, skipping over the intervening bits of the manifold. It's less clear whether it is possible to have times that aren't ever present given presentism. Still, Dean Zimmerman has considered an eccentric version of presentism on which there still is a four-dimensional spacetime manifold. On such a view, times could be identified with hypersurfaces in some preferred foliation, and there might be some such hypersurfaces that never become present.

So, apart from the B-theory and many versions of presentism, we have a possibility of times that are never present. Why would we want to countenance such a nutty option, though?

I can think of two reasons. The first would be to reconcile Aristotle's theory of time with many physical theories. According to Aristotle, times are endpoints of changes, and any interval of time contains at most finitely many changes, so that time is discrete. (Causal finitism might be a reason to adopt such a theory.) But in many modern physical theories, from Newton at least through Einstein, time is a continuous coordinate. One can try to reconcile the two views by supposing that time is continuous, as Newton and Einstein suppose, but that only those times which are the endpoints of changes are ever present. Aristotle then may be right that times are discrete, as long as we understand him to be speaking only about the times that matter, namely those that ever become present. The second motivation would be to have a flash ontology--an ontology on which physical things exist only during the discrete moments of quantum collapse--while softening the counterintuitive consequence that at most times the universe is empty. For we could identify the times that ever become present with the times at which a flash occurs. Then even if at most times, in the broad sense of the word "times", the universe is empty, still the universe is non-empty at all the times that matter, namely at all the times that become present.

Neither a B-theorist nor a standard presentist can suppose times that are never present. But she might still suppose something that plays a similar functional role. She could think of abstract times as numbers or as hypersurfaces in an abstract continuous manifold. Then real time could be discrete, while abstract time is continuous.