Omniscience, timelessness, and A-theory

I’ve been thinking a lot this semester, in connection with my Philosophy of Time seminar, about whether the A-theory of time—the view that there is an objective present—can be made consistent with classical theism. I am now thinking there are two main problems here.

1. God’s vision of reality is a meticulous conscious vision, and hence if reality is different at different times, God’s consciousness is different at different times, contrary to a correct understanding of immutability.

2. One can only know p when p is true; one can only know p when one exists; thus, if p is true only at a time, one can only know p if one is in time. On an A-theory of time, there are propositions that are only true in time (such as that presently I am sitting), and hence an omniscient God has to be in time. Briefly: if all times are the same to God, God can’t know time-variable truths.

I stand by the first argument.

However, there may be a way out of (2).

Start with this. God exists at the actual world. Some classical theists will balk at this, saying that this denies divine transcendence. But there is an argument somewhat parallel to (2) here. If all worlds are the same to God, God can’t know world-variable truths, i.e., contingent truths.

Moreover, we can add something positive about what it is for God to exist at world w: God exists at w just in case God actualizes w. There is clearly nothing contrary to divine transcendence in God’s existing at a world in the sense of actualizing it. And of course it is only the actual world that God actualizes (though it is true at a non-actual world w′ that God actualizes w′; but all sorts of false things are true at non-actual worlds).

But given the A-theory, reality itself includes changing truths, including the truth about what it is now. If worlds are ways that all reality is, then on A-theory worlds are “tensed worlds”. Given a time t, say that a t-world is a world where t is present. Argument (2) requires God to exist at a t-world in order for God to know something that is true only at a t-world (say, to know that t is present).

Now suppose we have an A-theory that isn’t presentism, i.e., we have growing block or moving spotlight. Then one does not need to exist at t in order to exist at a t-world: on both growing block and moving spotlight our 2025-world has dinosaurs existing at it, but not in 2025, of course. But if one does not need to exist at t in order to exist at a t-world, it is not clear that one needs to exist in time at all in order to exist at a t-world. The t-world can have a “locus” (not a place, not a time) that is atemporal, and a being that exists at that atemporal locus can still know that t is present and all the other A-propositions true at that t-world.

Next suppose presentism, perhaps the most popular A-theory. Then everything that exists at a t-world exists at t. But that God exists at the t-world still only consists in God’s actualizing the t-world. This does not seem to threaten divine transcendence, aseity, simplicity, immutability, or anything else the classical theist should care about. It does make God exist at t, and hence makes God in time, but since God’s existing in time consists in God’s actualizing a t-world, this kind of existence in time does not make God dependent on time.

I still have some worries about these models. And we still have (1), which I think is decisive.

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.

Theism and presentism

Suppose presentism is true and truths about other times are grounded in tensed facts, such as the fact that there were once dinosaurs.

Given presentism and theism, God is in time. Suppose, as the Abrahamic religions hold, that God created all contingent things a finite amount of time ago. Before God created them, it was contingently true that God will create them. This truth would be grounded in a contingent tensed fact. Hence before God created all contingent things, there already was a contingent thing—the tensed fact that God will create. A contradiction.

So the presentist needs to have a different solution to the grounding problem than positing tensed facts. The best alternative is positing tensed properties. Thus before creation something will have to have the property of being such that God will create. There is only one candidate for that something—God. For nothing else exists before creation. So God has a contingent property, contrary to divine simplicity. Thus presentist theists need to deny divine simplicity. That’s a big price!

One solution is a restricted presentism like Feser’s on which everything that exists is either present or timeless. Then we can suppose that time begins with creation. There may be other problems there.

Presentism and B-theory

It’s common to say that presentism entails the A-theory. But that’s not so clear. Suppose that time can pass in the absence of change. Now imagine a world of with a beginning or an end of time, objects, but no change, no temporal parts, and no events except ones that last for all time. In that world, we automatically have a kind of presentism: all the objects and events that exist always exist presently. Yet a B-theorist could accept the possibility of such a world, too: the world need not have a distinguished present moment of time. Thus, a B-theorist could say that A-theory is impossible (say, because of McTaggart’s dubious arguments) but presentism is possible—though contingently false.

We obviously don’t live in such a world. Though Parmenides may have thought he did.

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.

Presentism and the intrinsicness of past tensed properties

Many presentists think that objects have past-tensed properties. Thus an object that is now straight but was bent has the property of having been bent. (Some such presentists use these properties to ground facts about the past.)

But assuming for simplicity that being bent is an intrinsic property, we can argue that having been bent is an intrinsic property as well. Here’s why. If being bent doesn’t describe an object in relation to the existence, non-existence or features of any other object (assuming being bent is intrinsic), neither does having been bent. Nor is having been bent “temporally impure”—it does not describe the object in terms of anything happening at other times, since nothing can happen at other times on presentism. It does not describe the object in relation its past or future temporal slices or past or future events involving the object, since on presentism there are no past or future objects, and there are no past or future events.

But if having been bent is an intrinsic property of an object, it seems that, by a plausible patchwork principle or by intuitions about the omnipotence of God, an object could come into existence just for one instant and yet have been bent at that instant. Which is absurd.

Causation and the grounding problem for presentism

The past-grounding problem for presentism is of explaining what grounds facts about the past. The tensed-property solution is that presently existing objects have past-tensed properties like “Existing a hundred million years after a dinosaur” which ground the facts about the past.

Here is a problem. The presently existing objects exist at least partly because of how the world was a hundred million years ago. If how the world was a hundred million years ago is grounded in the properties of presently existing things, then we have a circularity in the order of explanation: the present objects’ existence is partly-explained by how the world was, and how the world was is grounding-explained by the objects’ possession of the properties, while the objects’ possession of the properties is partly ontologically explained by the objects’ existence.

Objection 1: This won’t bother one if one thinks one can have explanatory circularity as long as the explanations are of different sorts. But I think explanations of different sorts are still explanations, and circularity is still bad.

Objection 2: It seems that B’s being caused by A is explanatorily prior to B’s existing, so sometimes an instance of property possession is prior to existence. But I think this is mistaken. What’s prior to B is A’s exercise of causality, not B’s being caused by A.

Objection 3: If we solve the past-grounding problem by making use of past-tensed properties of God, then the problem disappears. For God doesn’t exist now because of how the world was a hundred million years ago. God exists now because God is a necessary being. I think this is a good response if one doesn’t believe in divine simplicity, but I am convinced of divine simplicity, which prohibits God from having contingent properties.

Appearances of atemporality

Here’s a way to think about presentism. We have a three-dimensional reality and temporal modal operators, such as Prior’s P, F, H and G (pastly, futurely, always-pastly and always-futurely), with appropriate logical rules.

But now imagine this scenario: Reality consists of an eternally frozen time slice from a complex two-way-deterministic Newtonian world resembling our world—“frozen Newtonian world” for short. There are particles at various positions with various momenta (I assume that q = mdx/dt is a law of nature rather than a definition of momentum, and momentum is fundamental), but they are ever still, unchanging in their Newtonian properties. Now if Q is one of the operators P, F, H and G, define the operator Q′ as follows:

• Q′p if and only if either (a) reality consists of an eternally frozen Newtonian world and in an unfrozen Newtonian world that agrees with reality on its present slice we would have Qp or (b) we have Qp and reality does not consist of an eternally frozen Newtonian world and we have Qp.

Then the primed operators behave logically just like the unprimed ones. But according to the primed operators, “there is change and motion”. For instance, for a typical particle z eternally frozen at location x, it will be the case that P′(z is not at x) and F′(z is not at x), since in an unfrozen Newtonian world whose present slice is just like our world’s, there will be past and future times at which z is not at x.

So what? Well, the presentist’s big intuition is that on a B-theory of time there is no change: there is just a four-dimensional block, where one dimension just happens to be called “time” and things are different at different locations along that dimension, but simply calling a dimension “time” doesn’t make it any different from the spatial ones.

But the B-theorist can respond in kind. On presentism there is no change: there is just a three-dimensional world related to other three-dimensional worlds via certain modal operators that are called “pastly”, etc., but simply calling a modal operator P “pastly” doesn’t make it any different from deviant operators like P′.

The presentist will, presumably, say that it’s not just a matter of calling the operator P “pastly”, but rather the operator is the primitive pastly operator, so that if something pastly is different from how it’s now, it has changed. But now the B-theorist can just respond in the same way. It’s not just a matter of calling one of the four dimensions “time”, but rather the dimension is the primitive time dimension, so that if something is different at a different time from how it is now, it has changed or will change.

(Granted, a B-theorist does not need to think that the distinction between space and time is primitive. I am inclined not to, and hence I cannot make the above response.)

Presumably, even after this dialogue, the B-theorist’s alleged reality will look static to the presentist. But I think the presentist’s alleged reality can look atemporal to the B-theorist—it’s just a three-dimensional world with no time dimension and some modal operators relating it to other three-dimensional worlds.

Temporal purism

Say that a fact is temporally pure about an instantaneous time t provided that it holds solely in virtue of how things are at t. (The term is due to Richard Gale, but I am not sure he would have wanted the “instantaneous” restriction.) Thus, that Alice is swallowed the fatal poison at noon is not temporally pure because a part of why it holds is that she died after noon. The concept of a temporally pure fact is intuitively related to the Ockhamist notion of a hard fact: any fact that’s temporally pure about the past or present is a hard fact.

I will allow two ways of filling out “instantaneous time t” in the definition of temporal purity: the time t can be a B-theoretic time like “12:08 GMT on January 2, 2084 AD” and it can be an A-theoretic time like “exactly three hours ago” or “now”.

We can now define a theory:

• Temporal purism: Necessarily, all temporal facts are grounded in the temporally pure facts and/or facts about the existence (including past and future existence) of instantaneous times and of their temporal relationships.

Presentists, open futurists and eternalists can all embrace temporal purism.

Probably the best way to deny temporal purism is to hold that there are fundamental truths about temporal reality that irreducibly hold over an interval of times—this is the temporal equivalent of holding that there are fundamental distributional properties.

I think there are reasons to deny temporal purism. First, it is plausible that (a) some states of our consciousness are fundamental features of reality and (b) they irreducibly occur over an interval of time of some positive length. Claim (a) is pretty standard among dualists. Claim (b) seems to follow from the plausibility that no state of consciousness shorter than, say, a nanosecond can be felt by us, but of course there are no unfelt states of consciousness.

Second, temporal purism pushes one pretty hard to an at-at analysis of change, and many people don’t like that.

Eternalists can deny temporal purism. This is pretty clear: eternalists have no difficulty with temporally distributional properties.

I think it is difficult for open futurists to deny temporal purism. For suppose that some fundamental feature F of our temporal reality occurs over an interval from t₁ to t₂, and cannot occur over a much shorter interval. Then at some time very shortly after t₁, but well before t₂, the feature is already present. But its being present seems to depend on a future that is open. So open futurism plus temporal impurism pushes one to a view on which the present and even the near past is open, because it depends on what will happen in the future.

Closed-future presentists can deny temporal purism. However, this feels uncomfortable to me. There is something odd on presentism about the idea that a present reality depends on the near past and/or the near future. At the same time, many odd things are actually true.

I think the denial of temporal purism pushes one somewhat towards eternalism.

Presentism, multiverses and discrete time

Suppose time is in fact continuous and modeled by the real numbers.

It seems odd indeed to me that the real numbers should be the only possible way for time to run. The real numbers are a very specific mathematical system. There are other systems, such as the hyperreals or the rationals or even the integers, that seem to be plausible alternatives. I know of no argument that the time sequence has to be numbered by the real numbers.

Thus, given our initial supposition, it should be possible to have time sequences corresponding to ordered sequences numbered by the integers or the hyperreals. Here, then, is a further intuition. It is possible to have a multiverse with radically different spacetime structures in each universe of it. If so, then we would expect the possibility of a multiverse where different universes in a multiverse have time sequences based on very different ordered sets.

Suppose presentism is necessarily true. Then even in such a multiverse, there would be an absolute present running across all of these timelines in the different universes. And that would be rather odd. Imagine that in one universe the time-line is corresponds to the integers and in the other it corresponds to the reals, and both are found in one multiverse. What happens in the universe whose time-line is based on the integers when the line of the present moves continuously across the uncountable infinity of times numbered by the real numbers? Does it stay for infinitely moments at the same integer? But then at infinitely many moments of time it would be at one moment, which is a contradiction. Or does the universe with the integer time-line pop out of existence when the present doesn’t meet up with these integers? Maybe that’s the best view, but it’s a weird view.

Perhaps the presentist’s best bet is to say that there is a privileged mathematical structure that models what a time-line could be like. If so, my intuition says that the only candidate for that privileged structure would be a discrete structure like the integers. For there are arguments in the history of philosophy for time having to be discrete (arguments from Zeno through myself), but none for time having to be modeled by specifically the real numbers, or the rational numbers, or some specific hyperreal field.

The Epicurean argument on death

The Epicurean argument is that death considered as cessation of existence does us no harm, since it doesn’t harm us when we are alive (as we are not dead then) and it doesn’t harm us when we are dead (since we don’t exist then to be harmed).

Consider a parallel argument: It is not a harm to occupy too little space—i.e., to be too small. For the harm of occupying too little space doesn’t occur where we exist (since that is space we occupy) and it doesn’t occur where we don’t exist (since we’re not there). The obvious response is that if I am too small, then the whole of me is harmed by not occupying more space. Similarly, then, if death is cessation of existence, and I die, then the whole of me is harmed by not occupying more time.

Here’s another case. Suppose that a flourishing life for humans contains at least ten years of conversation while Alice only has five years of conversation over her 80-year span of life. When has Alice been harmed? Nowhen! She obviously isn’t harmed by the lack of conversation during the five years of conversation. But neither is she harmed at any given time during the 75 years that she is not conversing. For if she is harmed by the lack of conversation at any given time during those 75 years, she is harmed by the lack of conversation during all of them—they are all on par, except maybe infancy which I will ignore for simplicity. But she’s only missing five years of conversation, not 75. She isn’t harmed over all of the 75 years.

There are temporal distribution goods, like having at least ten years of conversation, or having a broad variety of experiences, or falling in love at least once. These distribution goods are not located at times—they are goods attached to the whole of the person’s life. And there are distribution bads, which are the opposites of the temporal distribution goods. If death is the cessation of existence, it is one of these.

I wonder, though, whether it is possible for a presentist to believe in temporal distribution goods. Maybe. If not, then that’s too bad for the presentist.

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.

An Aristotelian argument for presentism

Here is a valid argument:

1. Matter survives substantial change.

2. It is not possible that there exist two substances of the same species with the very same matter.

3. If matter survives substantial change, it is possible to have two substances of the same species existing at different times with the very same matter.

4. So, it is possible to have two substances of the same species existing at different times with the very same matter. (1,3)

5. If presentism is not true, and it is possible to have two substances at different times existing with the very same matter, it is possible to have two substances of the same species existing with the very same matter.

6. So, if presentism is not true, it is possible to have two substances of the same species existing with the very same matter.

7. So, presentism is true. (2, 5)

Let’s think about the premises. I think Aristotle is committed to (1)—it’s essential to his solution to the alleged problem of change. Claim (2) is a famous Aristotelian commitment. Claim (3) is very, very plausible—surely matter moves around in the world, and it is possible to set things up so that I have the same atoms that Henry VIII had at some point in his life. Claim (5) follows when we note that the only two plausible alternatives to presentism are eternalism and growing block, and on both views if two substances of the same species exist at different times with the very same matter, then at the later time it is true that they both exist simpliciter.

However, given that there is excellent Aristotelian reason to deny presentism, the above argument gives some reason for Aristotelians to deny (1) or (2). Or to be more radical, and just deny that there is any such thing as the “matter” of traditional Aristotelianism.

Presentism, evil and privation

Suppose at 8 am, I promised you to call you before noon, and then I didn’t, even though I have no excuse. That’s an evil. When did this evil happen?

If time is continuous, there is no good candidate for the time of this evil. For the omission of calling happened before noon, so noon or later are not when the evil happened. But at any time before noon today, it wasn’t yet true that the promise was unfulfilled, since, if time is continuous, there was always a little bit more time (though, granted, once that time got short enough, it would have taken a miracle to call).

If time is discrete, there is exactly one somewhat plausible candidate for the time of the evil: the very last moment of time time before noon, call it t₁₂₋. It was then that the promise became unfulfilled, and yet that time was itself a time at which the promise was being broken. But even so, even though t₁₂₋ is a somewhat plausible candidate for the time of the evil, it’s not really a great candidate. For the omission didn’t just happen at the very end of the interval of times. It happened throughout the interval.

It seems that the right way to temporally locate the evil is to say that it happened on the time interval between 8 and 12. But note that this is interval-valued temporal location is intuitively different from the case of a headache that one might have from 10 to 11. For we can think of the whole evil of the headache as a sum of evils that are located at shorter intervals or even moments. But it seems the promise-breaking isn’t a sum of evils located at shorter intervals or moments, because the only shorter interval or moment that contains a relevant evil is an interval or moment that contains t₁₂₋ (and even that only if time is discrete). Rather, the promise-breaking is essentially spread over the interval from 8 to 12.

This provides a counterexample to the combination of presentism with a privation theory of evil. For on a privation theory of evil, each evil is constituted by a privation—a lack of something that should be there. But on presentism, things can only exist at specific times, and likewise privations can only be found at specific times. But the evil of promise-breaking is not at a time.

Thomism and presentism

According to Thomism:

1. That I exist is explanatorily prior to all the other facts about me.

Obviously:

2. That yesterday I safely crossed a street is explanatorily prior to the fact that I presently exist.

3. If presentism is true, the fact that I presently exist is the same fact as that I exist.

4. There are no circles of explanatorily priority.

5. That yesterday I safely crossed a street is a fact about me.

It logically follows from these that:

6. Presentism is not true.

(For from 2 and 3, if presentism is true, that I safely crossed a street is prior to the fact that I exist. But by 1 and 5 that I exist is prior to the fact that I exist. If presentism is true, we thus have a priority circle, so by 4, we don’t have presentism.)

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.

Simultaneous causation and occasionalism

In an earlier post, I said that an account that insists that all fundamental causation is simultaneous but secures the diachronic aspects of causal series by means of divine conservation is “a close cousin to occasionalism”. For a diachronic causal series on this theory has two kinds of links: creaturely causal links that function instantaneously and divine conservation links that preserve objects “in between” the instants at which creaturely causation acts. This sounds like occasionalism, in that the temporal extension of the series is entirely due to God working alone, without any contribution from creatures.

I now think there is an interesting way to blunt the force of this objection by giving another role to creatures using a probabilistic trick that I used in my previous post. This trick allows created reality to control how long diachronic causal series take, even though all creaturely causation is simultaneous. And if created reality were to control how long diachronic causal series take, a significant aspect of the diachronicity of diachronic causal series would involve creatures, and hence the whole thing would look rather less occasionalist.

Let me explain the trick again. Suppose time is discrete, being divided into lots of equally-spaced moments. Now imagine an event A₁ that has a probability 1/2 of producing an event A₂ during any instant that A₁ exists in, as long as A₁ hasn’t already produced A₂. Suppose A₁ is conserved for as long as it takes to produce A₂. Then the probability that it will take n units of time for A₂ to be produced is (1/2)^n + 1. Consequently, the expected wait time for A₂ to happen is:

• (1/2)⋅0 + (1/4)⋅1 + (1/8)⋅2 + (1/16)⋅3 + ... = 1.

We can then similarly set things up so that A₂ causes A₃ on average in one unit of time, and A₃ on causes A₄ on average in one unit of time, and so on. If n is large enough, then by the Central Limit Theorem, it is likely that the lag time between A₁ and A_n will be approximately n units of time (plus or minus an error on the order of n^1/2 units), and if the units of time are short enough, we can get arbitrarily good precision in the lag time with arbitrarily high precision.

If the probability of each event triggering the next at an instant is made smaller than 1/2, then the expected lag time from A₁ to A_n will be less than n, and if the probaility is bigger than 1/2, the expected lag time will be bigger than n. Thus the creaturely trigger probability parameter, which we can think of as measuring the “strength” of the causal power, controls how long it takes to get to A_n through the “magic” of probabilistic causation and the Central Limit Theorem. Thus, the diachronic time scale is controlled precisely by creaturely causation—even though divine conservation is responsible for A_i persisting until it can cause A_i + 1. This is a more significant creaturely input than I thought before, and hence it is one that makes for rather less in the way of occasionalism.

This looks like a pretty cool theory to me. I don’t believe it to be true, because I don’t buy the idea of all causation being simultaneous, but I think it gives a really nice.

Divine conservation, existential inertia, presentism and simultaneous causation

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

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

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

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

1. Presentism implies that all causation is simultaneous.

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

But even if all causation is simultaneous, nonetheless:

2. There is diachronic causal explanation.

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

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

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

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

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

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

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

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

Eternalism and future non-existence

I go back and forth on whether this is a strong argument against eternalism:

1. Given eternalism, it is guaranteed to be eternally the case that one exists simpliciter, even if one’s existence comes to an end.

2. Given eternalism, one’s existence coming to an end is just finitude in the forwards temporal direction.

3. If it is guaranteed to be eternally the case that one exists simpliciter, finitude in the forwards temporal direction would not be something to be dreaded.

4. So, given eternalism, one’s existence coming to an end would not be something to be dreaded. (1–3)

5. One’s existence coming to an end would be something to be dreaded.

6. So, eternalism is false. (4–5)

(As a theist, I think our existence does not come to an end. Hence the hypothetical “would” in (5).)

The intuition behind (3) is that finitude in the forwards temporal direction, given that one exists simpliciter, is akin to finitude in the backwards temporal direction or along a spatial axis, and these are clearly not to be dreaded.

But, on reflection, I think the eternalist can make very good sense of the appropriate attitudes to an end of existence. Consider this: If I were threatened with amputation of the part of me below the head—i.e., with being reduced to a head in a life-support tank—that would be something to be dreaded. It would be something to be dreaded, because the kind of functioning that is natural to human beings requires the below-the-head portion of the body. On the other hand, we could imagine sessile aliens that are very much like human heads, and there is nothing dreadful about the life of these aliens. These aliens’ lack of the below-the-head functioning normal humans enjoy would not be a deprivation.

Thus, human flourishing has spatial requirements: we require all of our body to fully flourish. Similarly, human flourishing has a robust temporal requirement: it requires an eternal future. This is because of the nature of human flourishing. Plausibly, human flourishing has a drive to infinity, requiring endless growth knowledge of reality and relationship with others. (This is probably not the whole story, but it will do for this post.) But our flourishing does not require spatial unlimitedness—on the contrary, there is a maximum size along each spatial axis such that a human being that is too big along that axis is not a fully flourishing human being.

We are four-dimensional beings, and we require a specific four-dimensional shape to flourish: a shape that is not too small and not too large in the three spatial directions and that is infinite in the forwards temporal direction. A finite future is a terrible truncation.

Now not every animal is like humans. Brute animals do not require an eternal future to be fully flourishing: they can achieve complete flourishing in a finite life, say because the lack the drive to the infinite that humans have. If we were like that, it would not be appropriate for us to dread future non-existence. Not being inclined to dread future non-existence is hard for us to imagine, because the drive to the infinite arises from such deep features of our nature. But philosophically, it makes perfect sense to think that there could be beings that can complete their flourishing in a finite compass.

The eternalist’s seeing a future end of existence of a human as a terrible truncation, but as not necessarily a terrible truncation in a non-human, seems very compelling. On the other hand, I think it is harder for a presentist to make sense of the difference here. Future non-existence seems really bad, because future non-existence on presentism would imply that eventually one will not exist simpliciter, and that seems dreadful. But the dreadfulness of this seems to have to do with the value of existence simpliciter, and not with our nature. Thus, we may have a story as to why it would make sense for a presentist to dread an end to existence, but that story proves too much: for that story would apply even if the presentist were the kind of non-human that doesn’t need an infinite future for flourishing.