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.

Self-causation, persistence and presentism

Fido exists now because of various things Fido did a couple of minutes ago, such as breathe, pump blood with his heart, etc. So, it seems, Fido's existence is caused by Fido. But self-causation is absurd. So what's going on? Well, that depends on the theory of persistence.

Perdurantists and exdurantists have no problem at all. One temporal part causes another. There isn't even a whiff of absurd self-causation, either. Four-dimensionalist worm-theorists who don't believe in temporal parts can say that Fido doesn't cause his existence, but only aspects of his spatiotemporal dimensions. So on four-dimensional theories, we don't have absurdity.

But what about three-dimensionalist theories? Suppose Fido wholly exists at this time. Then it seems that all of Fido (now) is caused by Fido (five minutes ago), and that would be absurd. But that's not quite right. The eternalist or growing block three-dimensionalist can distinguish. Fido doesn't cause Fido's existing simpliciter. Fido only causes Fido's existing now. If we want more precision, we can say that Fido in virtue of existing five minutes ago causes himself to exist now. No problem, again.

That leaves the other three-dimensionalist option: presentism. And now we have a problem. According to presentism, to exist is to exist presently. Fido's present existence is (was? -- the tenses are hard to get right) caused by Fido. But that just means that Fido's existence is caused by Fido. And that's self-causation.

But perhaps we should take account of the sorts of things presentists say about the problem of transtemporal causation. Maybe it's not quite correct to say that Fido's existence is caused by Fido, but rather that Fido's existing is caused by Fido's having existed five minutes ago. Plus, talking like this makes causation a relation between states of affairs, and some will prefer that. But we still have a problem. For Fido's having existed five minutes ago is a state of affairs involving Fido. But it's absurd for Fido's existing to be caused by any state of affairs involving him, since Fido's existing is explanatorily prior to any state of affairs involving Fido.

Perhaps, though, the presentist can bring in Fido's haecceity H. Fido's existing is caused by H's having been instantiated five minutes ago. That is, I suspect, the presentist's best bet here. But there is a problem for that. For it sure seems like the state of affairs that caused Fido's present existence isn't a state of affairs of his haecceity having had something happen to it (say, being co-instantiated with respiration), but but it is the state of affairs of Fido having done certain things five minutes ago, like breathing. If it is states of affairs about haecceities that are causally relevant, then it looks like the things that are fundamentally involved in causation aren't particulars like Fido but are are abstracta like haecceities. And that's not right.

There is a direct argument here against presentism, too.

1. Fido's presently existing is caused by Fido's having existed five minutes ago.
2. If presentism is correct, Fido's presently existing is Fido's existing.
3. Fido's having existed five minutes ago is a state of affairs of which Fido is a constituent.
4. No state of affairs of which Fido is a constituent causes Fido's existing.
5. So, if presentism is correct, Fido's existing is caused by Fido's having existed five minutes ago. (1, 2).
6. So, if presentism is correct, Fido's existing is caused by a state of affairs of which Fido is a constituent. (3, 5).
7. So, presentism is not correct. (4, 6)

The completed infinite

It is very hard to deny that it is logically possible that every rabbit has at least one offspring and there are no loops (no rabbit is its own ancestor). But in that situation, there will be infinitely many rabbits.

"Not so fast!" say the defenders of the distinction between the potential and the completed infinite. This is a case of a potential but not a completed, or actual, infinite. But why? On the scenario in question, there are infinitely many humans. A standard answer is to embrace a theory of time, like growing block or presentism, on which there are no future entities, and then to say something like this about the scenario:

• Infinitelymany rabbits will come into existence, but there are only finitely many rabbits and at any given future time there will only be finitely many then.

Not only does this require abandoning eternalism, which the correct theory of time, but it requires further work to explain why it couldn't also be the case that every rabbit has the property that its offspring take half as long as it did to produce offspring.[note 1] But in that case, after a finite amount of time there would be infinitely many rabbits. Further, this approach requires either nominalism or a special story about why concrete objects like rabbits can't form a complete infinity, while mathematical entities like prime numbers can (not a big problem for me, since I'm not a Platonist).

My proposal is that we should see the denial of a completed infinite differently. Rather than seeing it ontologically as saying that there are not infinitely many of anything, we should see it causally. A student has completed a class provided that the class is available for her to build on, either in her future thinking and work or as a prerequisite for other classes. Likewise, a process is completed provided that its product is available for other processes to build on.

A completed infinity, I propose, is the sort of infinity that can be causally built upon. The rabbits in my initial scenario cannot be built upon: they aren't all causally available to anyone. In that initial scenario, there is a plausible explanation about this in terms of time: there is no time at which there are infinitely many rabbits, so there is no time at which you can build on all of them.

But my causal finitism suggests that the same is true on my modified scenario where the rabbits breed faster and faster. Maybe that scenario can produce an infinite number of rabbits in a finite amount of time. But nonetheless, only finitely many of the rabbits will irreducibly work together causally. (I wonder whether irreducibility rules out overdetermination. Worth thinking about...) Let's say you cast a glance at that infinity of rabbits. You will only see finitely many at a time—your field of view is only finitely large and finitely sharp. Only finitely many of them will eat up your garden. And so on.

If we see a "completed infinity" as a causal notion, then we have no worries about Platonist mathematics. For mathematical entities are typically taken to be causally inert, and even if for some epistemological reason we do not take them so, we could still think that only finitely many are involved in any one causal interaction.

The importance of the future

It would be bad for me to permanently cease to exist in five minutes. But why? Suppose first a metaphysics of time on which there is no future, namely Growing Block or Presentism. On such a metaphysics there is no such thing as my future life, so how could it be bad for there to be a cessation of it?

Since the only tenable alternative to Growing Block and Presentism is Eternalism, the view that the past and future are real (oddly, there are no Futurists who think the future is real but deny the reality of the past), Eternalism is true.

Now, given Eternalism, we have a choice for three visions of our persistence through time. On one vision, Exdurantism, we are instantaneous stages that do not persist through time at all—at most we have temporal counterparts at other times. This does not fit with the intuition of my radical incompleteness should I cease to exist in five minutes. The second vision is Endurantism: I am wholly present at each time at which I exist. But then if the present moment is real, and eternally will be real, and I wholly exist at this present moment, then the intuition about the deep incompleteness I would have were my existence to permanently end in five minutes is undercut. So that can't be right either.

What remains is a family of views on which we are strung out four-dimensionally. The most common member of the family is Perdurantism: I am four-dimensional but have three-dimensional stages localized at times. A less common view is that I am four-dimensional, but not divided up into stages. Both of these views do justice to the idea that my existence is deeply incomplete, in something like the way it would be if I were missing an arm, should I cease to exist in five minutes.

As far back as I thought much about time (probably going back to age 10) I was an Eternalist. Until a couple of years ago, I was an Endurantist. Then I started being unsure whether Endurantism or a stageless four-dimensional view is right. The above argument strongly pushes me towards a four-dimensional view, and since I don't believe in stages, a stageless one.

Moreover, the above may help with a puzzle I used to have, which was how a B-Theorist should think about the badness of impending evils (especially death). How can a B-Theorist make sense of the badness of being closer and closer to something bad? But that may primarily be a problem for the Endurantist, since the Endurantist thinks we are three-dimensional beings wholly located in the here and now (as well as in the there and later, of course).

Eternalism and presentism

Here is an argument against eternalism:

1. If eternalism is true, times are like places.
2. Times are not like places.
3. So, eternalism is false.

There are a number of arguments for (2). Many, though not all, of them have something to do with the directionality of time, given that space lacks such directionality. Now consider this parallel argument against presentism, and hence for eternalism:

4. If presentism is true, times are like worlds.
5. Times are not like worlds.
6. So, presentism is false.

There are a number of arguments for (5). Here's a fun one. If I am happy now and miserable at all other times, I'm really unfortunate. If I am happy in the actual world and miserable at all other worlds, I'm really lucky one. In general, misery at other times matters in a way in which misery at other worlds does not.

So how to break this impasse? One way would be to opt for a theory other than eternalism and presentism, say growing block. Another way is to keep on adding disanalogies between times and places or between times and worlds until one of the disanalogies ends up being much stronger. Yet another way, and I think the most promising, is to embrace both (2) and (5), but explain the disanalogy in a way that is compatible with presentism or eternalism (whichever is one's preference).

One should also note that arguments from analogy tend not to be the strongest.

Time and sacrifice

Suppose that I am now undergoing suffering S on account of a greater good G. If there was no way of gaining G or something comparable without S or something comparable, and if G obtains, then I would rationally say: "It was worth it."

Notice that for the "It was worth it" judgments, it does not matter whether G is past, present or future. All that matters is that G be actual. You may wonder briefly how one can undergo suffering on account of a greater good. Time travel is the exotic case—I can get a tetanus shot in order to avoid getting tetanus in the Cretaceous. But the humdrum case is where S is a cost of the good G: perhaps I worked really hard to gain G yesterday, and today I am suffering exhaustion.

Suppose, on the other hand, I now undergo suffering S in account of a greater good G that occurs in some other possible world. For instance, I endure penury because I have spent my money building a robot that digs in my backyard looking for diamonds. I fully know that there are no diamonds in Texas, but there is a possible, though I am quite sure non-actual, situation where tomorrow someone will bury a treasure trove of diamonds in my backyard. In that possible situation, I will get very rich. But it is silly to endure actual penury for the sake of merely possible riches.

So for a good G to make a sacrifice S worthwhile, it matters a great deal that the good occur in the actual world. But it does not matter whether G occurs in the past, present or future.

This is unsurprising to eternalists. But it should be puzzling to presentists and growing blockers who think that present goods really exist while future ones do not.

Spinoza and reductionistic determinism

According to some presentist theories of time, facts about the future are grounded in facts about the present and in the laws of nature. What grounds the fact, if it is a fact, that tomorrow the sun will rise is that the present conditions together with the laws of nature entail that the sun will rise tomorrow. Alan Rhoda played with a similar view in regard to the past: facts about the past are grounded in facts about God's present memories.

Suppose determinism holds and there is an initial time t₀. Let L be the laws. Then we can imagine a view which we might call initialism in the place of presentism. According to initialism, facts about what happens at a time t>t₀ reduce to facts about what the laws are and what the initial conditions are. More precisely, if I is the initial conditions of the world at t₀, according to initialism, what it is for a state of affairs to obtain at a time t>t₀ is for I and L to jointly entail that it obtains at t. Thus, what it is for there to be humans in the world is for the world to have had initial conditions and laws such as to guarantee the arising of humans.

According to initialism, none of us are substances, because facts about our existence reduce to facts about the initial conditions and laws. In Spinozistic terminology, we are modes of laws and initial conditions or of whatever grounds the laws and initial conditions.

Initialism has some obvious problems. It assumes that determinism holds and that there is an initial time t₀. But determinism is in tension with quantum mechanics, and probably the best interpretation of the Big Bang is that although the universe has finite age, there was no initial moment.

There is a strong resemblance between initialism and Spinoza's metaphysics. To make the resemblance closer, we will make some modifications.

Modification 1: Take time to discrete. Thus, there is a finite number of moments of time between t₀ and the present. If we do this, we can get a nested view closer to Spinoza's. Instead of reducing the conditions at time t_n to the laws and the conditions at t₀, we reduce them to the conditions at t_n−1 and the laws. Now our present time slices are modes of modes of ... modes of the initial conditions and laws.

The second move we can make is to remove the initial time t₀. Instead, there is a doubly infinite sequence of times ...,t₋₂,t₋₁,t₀,t₁,t₂,.... How things are at each time reduces to the laws and how they were at the preceding time. Thus, in Spinozistic terminology, we are modes of modes of modes of ....

The third move is to reintroduce something outside of the whole sequence of modes, in which the sequence of events is grounded. After all, the idea of a sequence of modes without any substance seems absurd. One move would be to take that which is outside the sequence to be the lawmaker of L—that entity in virtue of which L is law, the truthmaker of the proposition that L is law. We may perhaps call this entity "Natura Naturans", nature naturing, or if we are pantheistically inclined like Spinoza, "Deus sive Natura" (though the latter identification would be taking a stand on whether Spinoza's Deus is Natura Naturans or the whole shebang of nature, in favor of the former). If we like, we can call the mereological sum of the modes "Natura Naturata", nature natured. The Natura Naturans, then, is the substance of which the temporal modes are ultimately (though with an infinite chain intervening) are modes.

The final move, to make the view be more like Spinoza's, is to take out the reference to times. Instead, we just have a sequence of entities—objects and/or events—that are each reduced to previous ones.

I think one puzzle about this view is how the Natura Naturans is related to the sequence of temporally qualified, "determinate", modes. We could take this relationship to be one of reduction once again: the whole infinite sequence of times reduces to the laws. This fits with much of what Spinoza says. It is, however, in some tension with Spinoza's idea that from the idea of God qua eternal, and it is this which seems to fit best with this eternal lawmaker, temporally determinate facts do not follow.

This exegetical difficulty can perhaps be overcome.

Here is one way. Accept a relationist B-theory of time, and then say that something is determinate insofar as we can delineate the times of its beginning and end. But on a relationist B-theory, sub specie aeternitatis, we just have a doubly infinite sequence without time-as-a-container, and no non-relative, non-arbitrary way of identifying times like "November 15, 2011". Of course, we can stipulate names for beginning and end times of some events, and then with this stipulative delineation in hand, we can delineate temporally when other events will happen. Thus, if a match struck just before noon, it will come on fire just after noon. Thus, to derive facts about when events happen we need facts about when other events happen. We cannot derive when-facts from eternal laws. Spinoza is clear on his view that times are the product of human beings divisions of duration.

If all there was to being a determinate mode was having a beginning and end time, I think that would be a satisfactory answer. But I think temporally determinate modes may be prior on his view to times. Perhaps, though, his thought is this. What we can derive from L is the whole sequence of things, but considered as an undivided sequence, and all divisions and delineations in the sequence are due to us. And from a delineated cause—say, a match's being struck, which is delineated from what comes before (the movement of the match) and what comes after (the fire)—there can be derived a delineated effect. Again, on this reading, the division in the modes is arbitrary.

Actually, I am not sure that Spinoza's mode-to-haver relationship is reductive. But I think it gives an illuminating reading.