Divine timelessness

This is probably the simplest argument for the timelessness of God, and somehow I’ve missed out on it in the past:

1. God does not change.

2. Creation has a finite age.

3. There is nothing outside of creation besides God.

4. So, change has a finite age. (1–3)

5. There is no time without change.

6. So, time has a finite age. (4,5)

7. If something is in time, it has an age which is less than or equal to the age of time.

8. God does not have a finite age.

9. God is not in time. (6–8)

Premise (2) is supported by causal finitism and is also a part of Jewish, Christian and Muslim faith.

Some philosophers deny (3): they think abstract things exist besides God and creation. But this theologically problematic view does not affect the argument. For abstract things are either unchanging or they change as a result of change in concrete things (for instance, a presentist will say that sets come into existence when their members do).

The most problematic premise in my view is (5).

Time without anything changing

Consider this valid argument:

1. Something that exists only for an instant cannot undergo real change.

2. Something timeless cannot undergo real change.

3. There can be no change without something undergoing real change.

4. There is a possible world where there is time but all entities are either timeless or momentary.

5. So it is possible to have time without change.

Premises 1 and 2 are obvious.

The thought behind premise 3 is that there are two kinds of change: real change and Cambridge change. Cambridge change is when something changes in virtue of something else changing—say, a parent gets less good at chess than a child simply because the child gets really good at it. But on pain of a clearly vicious regress, Cambridge change presupposes real change.

The world I have in mind for (4) is one where a timeless God creates a succession of temporal beings, each of which exists only for an instant.

(I initially wanted to formulate the argument in terms of intrinsic rather than real change. But that would need a premise that says that there can be no change without something undergoing intrinsic change. But imagine a world with no forces where the only temporal entities are two particles eternally moving away from each other at constant velocity. They change in their distance, but they do not change intrinsically. This is not Cambridge change, for Cambridge change requires something else to have real change, and there is no other candidate for change in this world. Thus it seems that one can have real change that is wholly relational—the particles in this story are really changing.)

All that said, I am not convinced by the argument, because when I think about the world of instantaneous beings, it seems obvious to me that it’s a world of change. But even though it’s a world of change, it’s not a world where any thing changes. (One might dispute this, saying that the universe exists and changes. I don’t think there is such a thing as the universe.) This suggests that what is wrong with the argument is that premise (3) is false. To have change in the world is not the same as for something to change. This is more support for my thesis that factual and objectual change are different, and one cannot reduce the former to the latter.

Beyond metaphysical immutability

For years I was convinced that the extrinsic constitution model of divine knowledge, which theists who accept divine simplicity must accept, solves the problem of divine immutability in an A-theoretic world where truth changes. The idea was that God’s knowledge of contingent facts is constituted by God’s unchanging essential features (which given simplicity are God himself) together with the changing contingent realities that God knows, that God’s gaze extends to. (This idea is not original to me. Aquinas already had it and probably many contemporary people have independently found it.)

But I now think that this was too quick. For let’s take the idea seriously. The point of the idea is that an unchanging God can have changing knowledge. But now notice that God’s knowledge is conscious. The language of “God’s gaze” that I used above (and which Boethius also uses in his famous discussion of divine knowledge of free actions) itself suggests this—God sees the changing reality. At one time God sees Adam sinless. At another time God sees Adam sinful. This is a difference in conscious state. Granted, this difference in conscious state is entirely metaphysically constituted by the changing reality. But it still means that God’s conscious state changes. It changes in virtue of its extrinsic constituent, but it is still true that God at t₁ is conscious of one thing and God at t₂ is conscious of something else instead. And I submit that that is incompatible with divine immutability.

I think there are two responses the classical theist who believes in changing truths can give. The first is to deny that God is conscious of the changes. I think this is unacceptable. The more vivid and the more vision-like knowledge is, the more perfect it is. The idea that God has merely unconscious knowledge of contingents does not do justice to the perfection of omniscience.

The second response is to bite the bullet and say that God’s conscious state changes but this is compatible with immutability as long as this does not involve an intrinsic change in God. I think this is untenable. That God’s conscious state does not change is, I think, a central part of the content of immutability, regardless of whether this conscious state is intrinsically or extrinsically constituted. For a non-physical being, change of conscious mental state is a paradigmatically central kind of change—regardless of the metaphysics of how that change of conscious state comes about. When God says in Malachi 3:6 that he does not change, it seems very implausible to think that the listener is supposed to say: “Sure, but sometimes God has one conscious state and sometimes another, and because this change is grounded extrinsically, that’s OK.” Malachi isn’t doing heavy-duty scholastic/analytic metaphysics. Similarly, when the early Church Fathers say that God is unchanging I doubt they would tolerate the idea that God’s conscious state changes. The extrinsic constitution story is an explanation of what makes God’s conscious state change, and I expect the Church Fathers wouldn’t have cared what the explanation would be—they would just deny the change.

Jumping from the Church Fathers to the modern period, Calvin says that God “cannot be touched with repentance, and his heart cannot undergo changes. To imagine such a thing would be impiety.” But if God’s conscious states are extrinsically constituted and can change, there would be nothing to prevent the idea of God’s “heart” undergoing changes: when people behave well, God feels pleased; when people behave badly and deserve vengeance, God feels vengeful. The differences in God’s feeling would be, one could imagine, constituted by the differences in human behavior and divine response to it. But it would be implausible to think that Calvin would say “Well, as long as the change is extrinsically constituted, it’s OK.” We then wouldn’t need Calvin’s famous story—itself going back to the Church Fathers—of the accommodation of divine speech to our needs. When Calvin insists that God’s heart cannot undergo changes, he isn’t just concerned about divine metaphysics. He is rightly concerned about a picture of a God with a changing mental life. And here at least, Calvin is with the mainstream of the Christian tradition.

If I am right in the above, there is a disanalogy between how God’s mental state behaves across possible worlds and across times. We have to say that in different possible worlds God has different (extrinsically constituted according to divine simplicity) conscious states. But we cannot say that God has different conscious states at different times.

Some thinkers, especially open theists, want the doctrine of divine immutability not to be about metaphysics but about the constancy of God’s character, purposes and promises. I think they are wrong: the doctrine of immutability really does include what we might call metaphysical immutability, that God has no intrinsic change. But metaphysical immutability is not enough. A mental and especially conscious immutability is also central to how we understand divine immutability.

And this is not compatible with the A-theory of time, given omniscience. Which is too bad. While I myself am a B-theorist, the reasoning in yesterday’s post was giving me the hope that we could detach the A- and B-theoretic debate from theism, so that the theist wouldn’t need to take a stand on it. But, alas, I think a stand needs to be taken.

What is real change?

I am starting to think that it’s rather mysterious what real change—i.e., non-Cambridge change—is. (Cambridge change is illustrated by examples like: Alice became shorter than her son Bob because Bob grew.)

It is tempting to say:

1. x undergoes non-Cambridge change if and only if there is an intrinsic property that x gains or loses.

But it could well turn out that one can undergo non-Cambridge change with respect to relational, and hence non-intrinsic, properties. The radical, but I think quite possibly correct, example is that it could turn out that all creaturely properties are relational because they all involve participation in God. (Thus, to be green is to greenly participate in God.)

However, there could be less radical cases. For instance, plausibly, shape properties are constituted by relations between an object’s parts and regions of space. But an object’s changing shape is a paradigm example of a non-Cambridge change. Or it might be that a Platonism on which we have an “eye of the soul” that changingly gazes at timeless Platonic objects. It seems like the change in the eye of the soul in coming to gaze on Beauty Itself could be entirely relational and fundamental. In particular, the “gaze” might not be constituted by any non-relational features of the eye of the soul. And yet the change is not a Cambridge change.

It seems to me that this worry gives one some reason to accept this Aristotelian account:

2. x undergoes non-Cambridge change if and only if x has a passive potentiality that is actualized.

I would rather not do that—I have long tried to avoid passive potentialities—but I don’t right now know another alternative to (1). I dislike passive potentialities sufficiently that I am actually tempted to deny that there is an account of the difference between Cambridge and non-Cambridge change. But that would come at a serious cost: it would be hard to account for divine immutability.

Two kinds of change

I ran across this old post of mine and it made me think that there is an interesting distinction between two kinds of change which one might label as objectual and factual change. Objectual change is change in objects, including both an object’s acquiring or losing properties and an object’s coming or ceasing to be. Factual change is change in reality itself—the facts of reality themselves change, with future facts coming to be present (and on open future views getting filled out) and present facts coming to be past. We can put this in terms of change of facts, change of truth value of (“fully closed”) propositions, or change of reality as a whole.

When A-theorists accuse B-theorists of having a static picture of the universe and B-theorists respond with the at-at theory of change (change is a thing’s having a property at one time and lacking it at another), they are talking past each other to some degree. The A-theorist is talking of factual change. The B-theorist is talking of objectual change. The A-theorist is simply right that on the B-theory there is no factual change: the facts about reality were, are and will ever be the same. That there is objectual change on the B-theory does not contradict this. But at the same time, the A-theorist’s accusation of static factuality is something the B-theorist should proudly admit as a feature and not a bug: truth does not change.

That there is objectual change is a part of our uncontroversial data about the world. That there is factual change is the A-theory in a nutshell, and hence begs the question against the B-theorist.

At this point it seems we have an impasse. Where should the debate go? I think one thing to figure out is whether one of the kinds of change depends on the other. Suppose it turns out that objectual change would need to depend on factual change. Then the A-theorist has won: the B-theory has no change at all. Note that the at-at theory of change is not a sufficient response to a claim that objectual change depends on factual change. For the at-at theory depends on the concept of time (change is having different properties at different times), and if time itself requires factual change, then the at-at theory itself requires the A-theory. This suggests that if the at-at theory is going to be the B-theorist’s response, the B-theorist owes the A-theorist an account of what makes time be time (McTaggart insisted on the latter point).

What about the other direction? That one is kind of interesting, too. One might think that factual change would need to arise from objectual change. Aristotle apparently did. It’s not clear, however, how one gets the A-theorist’s change of reality, where future facts become present and present facts become past, out of changes in objects. Perhaps one can read McTaggart’s infamous argument against the coherence of the A-theory as an attempt to show that this task can’t be done, at least in the special case where the objects are events.

Can we offer such an argument? Maybe. We aren’t going to be able to get factual change simply from the fact that objects have different ordinary properties at different times, say a light being green at t₁, orange at t₂, and red at t₃. For there is no way to use such facts to ground which of these times are past, present or future. So it seems that if we’re to get factual change from objectual change, we’re going to have go the route McTaggart suggests, and try to ground it in terms of objects’ temporal A-properties, say this light’s being past, present, or future. But that seems problematic. For the change between past, present and future does not happen in the lifetime of the light. During the lifetime of the light, the light is always present—it is only past after its existence and it is only future before its existence! But a change that does not happen during an object’s lifetime is, of course, a Cambridge change, like a horse’s becoming posthumously famous. And Cambridge change must always be relative to something else changing really. But then it is in the latter change that we should be grounding our factual change. And now we are off on a vicious regress, much as McTaggart (perhaps for somewhat different reasons) thought.

This suggests to me that just as the B-theorist denies that objectual change depends on factual change, the A-theorist should deny that factual change arises from objectual change. As more than one philosopher has noted, the A-theorist should respond to McTaggart by taking A-temporality, understood as factual change, as primitive.

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.

Change and matter

Aristotle’s positing matter is driven by trying to respond to the Parmenidean idea that things can’t come from nothing, and hence we must posit something that persists in change, and that is matter.

But there two senses of “x comes from nothing”:

1. x is uncaused

2. x is not made out of pre-existing materials.

If “x comes from nothing” in the argument means (1), the argument for matter fails. All we need is a pre-existing efficient cause, which need not be the matter of x.

Thus, for the argument to work, “x comes from nothing” must mean (2). But now here is a curious thing. From the middle ages to our time, many Aristotelians are theists, and yet still seem to be pulled by Aristotle’s argument for matter. But if “x comes from nothing” means (2), then theism implies that it is quite possible for something to come from nothing: God can create it ex nihilo.

There are at least two possible responses from a theistic Aristotelian who likes the argument for matter. The first response is that only God can make things come from nothing in sense (2), and hence things caused to exist by finite causes (even if with God’s cooperation) cannot come from nothing in sense (2). But there plainly are such things all around us. So there is matter.

Now, at least one theistic Aristotelian, Aquinas, does explicitly argue that only God can create ex nihilo. But the argument is pretty controversial and depends on heavy-duty metaphysics, about finite and infinite causes. It is not just the assertion of a seemingly obvious Parmenidean “nothing comes from nothing” principle. Thus at least on this response, the argument for matter becomes a lot more controversial. (And, to be honest, I am not convinced by it.)

The second and simpler response is to say that it’s just an empirical fact that there are things in the world that don’t come from nothing in sense (2): oak trees, for example. Thus there in fact is matter. This response is pretty plausible, but can be questioned: one might say that we have continuity of causal powers rather than any matter that survives the generation.

Finally, it’s worth noting that I suspect Aristotle misunderstands the Parmenidean argument, which is actually a very simple reductio ad absurdum:

3. x came into existence.
4. If x came into existence, then x did not exist.
5. So, x did not exist.
6. But non-existence is absurd.

The crucial step here is (6): the Parmenidean thinks the very concept of something not existing is absurd (presumably because of the Parmenidean’s acceptance of a strong truthmaker principle). The argument is very simple: becoming presupposes the truth of some past-tensed non-existence statements, while non-existence statements are always false. Aristotle’s positing matter does nothing to refute this Parmenidean argument. Even if we grant that x’s matter pre-existed, it’s still true that x did not exist, and that’s all Parmenides needs. Likewise, Aristotle’s famous actuality/potentiality distinction doesn’t solve the problem. Even if x was pre-existed by a potentiality for existence, it’s still true that x wasn’t pre-existed by x—that would be a contradiction.

To solve Parmenides’ problem, however, we do not need to posit matter or potentiality or anything like that. We just need to reject the idea that negative existential statements are nonsensical. And Aristotle expressly does reject this idea: he says that a statement is true provided it says of what is that it is or of what is not that it is not. Having done that, Aristotle should take himself as done with Parmenides’ problem of change.

Trope theory and merely numerical differences in pleasures

Suppose I eat a chocolate bar and this causes me to have a trope of pleasure. Given assentiality of origins, if I had eaten a numerically different chocolate bar that caused the same pleasure, I would have had had a numerically different trope of pleasure.

Now, imagine that I eat a chocolate bar in my right hand and it causes me to have a trope of pleasure R, and immediately as I have finished eating that one chocolate bar, I switch to eating the chocolate bar in my left hand, which gives me an exactly similar trope of pleasure, L, with no temporal gap. Nonetheless, by essentiality of origins, trope L is numerically distinct from trope R.

To some (perhaps Armstrong) this will seem absurd. But I think it’s exactly right. In fact, I think it may even an argument for trope theory. For it seems pretty plausible that as I switch chocolate bars, something changes in me: I go from one pleasure to another exactly like it. But on heavy-weight Platonism, there is no change: I instantiated pleasure and now I instantiate pleasure. On non-trope nominalism, likewise there is no change. It’s trope theory that gives us the change here.

Events and the unreality of time

When I think about McTaggart’s famous argument against the A-theory of time—the theory that it is an objective fact about the universe what time it is—I sometimes feel like it’s just a confusion but sometimes I feel like I am on the very edge of getting it, and that there is something to the argument. When I try to capture the latter feeling in an argument that actually has a chance of being sound, I find it slipping away from me.

So for the nth time in my life, let me try again to make something of McTaggart style arguments. Last night I gave a talk at University of North Texas. When I gave the talk, it was present, and afterwards it became past, and every second that talk is receding another second into the past, becoming more and more past, “older and older” we might say. There is something odd about this, however, since the talk doesn’t exist now. Something that no longer exists can’t change anymore. So how can the talk recede into the further past, how can it become older and older?

Well, we do have a tool for making sense of this. Things that no longer exist can’t really change, but they can have Cambridge change, change relative to something else. Suppose a racehorse is eventually forgotten after its death. The horse isn’t, of course, really changing, but there is real change elsewhere.

More generally, we learn from McTaggart that events can’t really change, but can only change relative to real change in something other than events. The reasoning above shows that events can’t really change in their A-determinations. And they can’t change in their intrinsic non-temporal features, as McTaggart rightly insists: it is eternally true that my talk was about God and mathematics; all the flaws in the talk eternally obtain; etc. So if events can’t really change, but only relatively to real change elsewhere, and yet all of reality is just events, then there is no change.

But reality isn’t just events, and in addition to events changing there is the possibility for enduring entities to change. Here’s perhaps the simplest way to make the story go. The universe is an enduring entity that continually gets older. My talk, then, recedes into the past in virtue of the universe ever becoming older than it was when I gave the talk. (If one is skeptical, as I am, that there is such an entity as the universe, one can give a more complex story about a succession of substances becoming older and older.)

Can one run any version of the McTaggart argument against a theory on which fundamental change consists in a substance’s changing rather than in the change of events? I am not sure, but at the moment I don’t see how. If a person changes from young to old, we have two events: their youth A and their old age B. But we can now say that neither A nor B changes fundamentally: A recedes into the past because of the person’s (or the universe’s) growing old.

If this line of thought is right, then we do learn something from McTaggart: an A-theorist should not locate fundamental change in events, but in enduring objects.

A slight tweak to the at-at theory of change

The at-at theory of change says:

1. Change is things being one way at one time and another way at another time.

McTaggart complained that this was like saying a poker changes because it’s hot at one and end cold at the other. It seems that (1) just fails to capture the “dynamism” in change.

A slight modification to (1) takes care of these, and some other, problems.

2. Change is things being one way at one time and another way at a later time.

You might think there is no real difference, because if there are two times, one must be later than the other. First, that’s not obvious, actually. In a Minkowski space-time, a time from one reference frame will be neither earlier nor later than a time from another reference frame.

But in any case, even if it were true that one time must be later than another, putting it in the definition makes a difference. First, McTaggart’s poker: one end isn’t earlier than the other! Second, dynamism: you can put all the dynamism you like in the “later”. You can say that t₂ is later than t₁ just in case at t₁, t₂ is future, is impending, is approaching, is a time of the actualization of a potential found at t₁, etc. The dynamism all goes into the “later”.

The fleetingness of being

Imagine it’s the last moment of time. What’s next for you? Nothing! It’s a terrifying time, but it’s one that’s hard to describe well. Phrases like “You’re about to perish” don’t fit it logically, because they imply that you will perish, but at the last moment of time there is no “will”. You need awkward wide-scope negations like: “It is not the case that you will continue to exist.”

But I think the philosophical puzzles go beyond the choice of words.

Thing about a world where time begins and ends with t₁, where there is only one moment. That’s a world with no flux or flow or dynamism or change. It seems, then, that that’s a world where essentially temporal attitudes, like fear of ceasing to exist, are inappropriate. It doesn’t, it seems, to be a world where it’s right for you to feel the terror of facing nothingness. Indeed, it doesn’t seem like anything in this world is fleeting or lasting.

But the difference between the only-one-moment and last-moment scenarios is just with regard to the past. Now in the last-moment scenario you would have a reasonable (pace Epicurus) terror of impending nonexistence and a vivid feeling of the fleetingness of existence.

But taking away the past, and hence moving to the only-on-moment scenario, shouldn’t change any of that! It doesn’t make your existence last any longer. It makes you no more eternal. We have to be able to say that somehow in the only-one-moment world our existence would be tenuous and fleeting (indeed, it seems, maximally so).

This pulls us to a very deep conclusion here:

1. The phenomenon of fleetingness does not require the flow of time.

For in the only-one-moment world we have fleetingness but no flow.

So if we are to look at what grounds the fleetingness of our existence, it seems we must look away from the distinctive resources of the A-theory of time, and towards the B-theory.

One obvious thing to say is that there is an incompleteness to our existence when restricted to any finite compass. Eighty years is not enough for the kind of being we are, and a moment is much less. This is something an eternalist can say, whether or not they accept the A-theory or the B-theory of time. Though it’s not quite so clear that a presentist or Growing Blocker can say it, since on their views our future life is not a part of reality anyway, no matter whether it is finite or infinite.

But perhaps there is a resource available for the A-theorist, even the presentist. Instead of thinking that it is the present moment that is present, we can suppose that what is present is an interval between two succeeding times in a discrete account of time. If so, then neither the only-one-moment and last-moment scenarios work. Instead, one has only-one-interval and last-interval scenarios. And these are not so problematic. Even if there is only one interval of time, that’s enough for change and flow—things move from one state to another over an interval. The impending doom has to do with the fact that the later end of the present interval borders nothingness. And over that interval, we can say (if we have a flowy theory of time) that we are flowing—but not for long!

Of course, there are technical issues with the suggestion that what is present is an interval between two successive times. If there is flow during that interval, it sees can always ask: “How long before the interval is finished?” But any clear answer to that subdivides the interval and places us at a moment within it. So we must refuse to countenance any answer beyond: “I am flowing from t_n to t_n + 1.” (We might then say: We’re between 0 and t_n + 1 − t_n units of time before the next interval begins.)

I started thinking about an A-theory on which what is present is an interval just as an exercise in wacky theories of time. I am now thinking that perhaps this is the best version of presentism.

In defense of a changing beatific vision

It is widely taken in the Thomistic tradition that:

1. Different people in heaven have the beatific vision to different degrees, corresponding to the saints’ different levels of holiness.

2. The beatific vision does not change with time for a given individual.

I think there is a tension between these two claims which is best resolved by dropping the no-change thesis (2). Dropping the difference thesis (1) is not an option for Catholics at least, since it’s a dogma taught by the Council of Florence.

To see the tension, note that the fact that different saints have holiness to different degrees implies that those saints who have a lesser holiness have not maxed out what human nature makes possible. And holiness is attractive to the holy, and infectious. If one saint is less holy than another, it seems likely that given a sufficient amount of time, we would expect the second saint’s greater holiness to inspire the first to even greater holiness. And then we would expect the beatific vision to increase.

We also have one New Testament case where it seems likely that a person’s level of beatific vision has increased. In 2 Corinthians, Paul writes of knowing someone who, fourteen years ago, was caught up to the third heaven. It is common to take that to be a modest reference to Paul himself, and the “third heaven” to be a reference to the beatific vision. Now, eventually Paul died and experienced the beatific vision again. It seems very implausible to think that the significant number of years between Paul’s first experience of heaven and his final experience of heaven did not result in Christian maturation and growth in virtue. Thus, it seems quite plausible that Paul had greater holiness when he died than when he was first caught up to heaven, and hence by the correspondence thesis (1), he had a greater degree of beatific vision at death than at the earlier incident.

Note, too, that a Catholic cannot say that the level of holiness is fixed at the time of death, since then purgatory wouldn’t make sense. And, intuitively, we would expect heaven to be inspiring of growth in holiness!

Now, one could insist that the level of holiness is fixed at the time of entry to heaven. But if so, then we couldn’t really say that the death of a saint is always something to rejoice at. Imagine that Paul had died at the time of his first experience of the beatific vision. Then on the no-change view of the beatific vision, he would eternally have had a lesser beatific vision than in actual world where he continued to grow in holiness for over decades more.

A picture of continual growth in holiness and the beatific vision fits better with our temporality. One may worry, however, that it takes away from the picture of resting in God. However, rest is compatible with change. One of the best ways to rest is to read a good book. But as one reads the book, one grows in knowledge of its content. And if one worries that the thought that one will come to have a greater happiness should induce in one a present sorrow of longing, I think it is plausible that with perfect virtue one would no more find the expectation of greater future happiness to be a source of sorrow than a lesser saint would find the observation of greater saints a source of envy. And, coming back to the book analogy, when one reads a good book, there need be no unhappiness at the fact that there is more of the book yet to come—on the contrary, one can rejoice that there is more to come. (In some cases, there may be a weak negative emotion as one longs for the author to reveal something—say, the solution of a mystery. But not every genre will generate that.)

Furthermore, there is good reason to think that change is not incompatible with rest. Since we will have bodies in heaven, and we will flourish in body and soul, while bodily flourishing involves change, heavenly rest must be compatible with change. And plausibly some of the bodily activities we will engage in will involve a variation in the level of happiness at least in some respects. Thus, eating is an episodic joy, and music, I take it, involves much in the way of anticipation and change.

Change without a plurality of times

Assume presentism. Then Aristotle’s definition of change as the actuality of a potentiality seems to have a serious logical problem. For consider a precise statement of that definition:

1. There is change just in case there is a potentiality P and an actuality A and A is the actuality of P.

Given presentism, quantification has to be over present items. Thus, the potentiality P and the actuality A are both present items (presumably, accidents of some substance). But if the actuality and potentiality can be simultaneous, then Aristotle’s definition of change does not logically require multiple times: one can have a moment t at which there is an actuality A of a potentiality P, and t could be the only time at which the underlying substance exists. But it seems obvious that if something changes, it exists at more than one time.

One way out of this problem is to deny presentism. I would like that, but Aristotle was probably a presentist.

A second way out is to be careful with tensing:

2. There is change just in case there was a potentiality P and there is an actuality A and A is the actuality of P.

This makes being the actuality of a cross-time relation. Cross-time relations are awkward for a presentist, but probably unavoidable anyway, so this isn’t so terrible. However, there are other problems with (2). First, it seems that tense depends on time, and for Aristotle, time depends on change, so (2) becomes circular. Second, if we can help ourselves to tense, we can just define change as being in a state in which one previously was not.

I want to suggest a more radical way out of the problem for (1). This more radical way starts by embracing the idea that a substance can change even if it exists only at one time. One way to motivate that is to think of Newtonian physics. Suppose that the universe consists of a number of particles that come into existence at time t₀. We may further suppose the state of the Newtonian universe at times after t₀ is deterministically caused by the state at t₀ (barring things like Norton’s dome). But this is only true if the state of the universe at t₀ includes the momenta of the particles, some of which we can assume to be initially non-zero. In other words, the fact about what the momenta are has to be a fact about what the universe is like at t₀, in the sense that even if God annihilated the universe right after t₀, it would still be true that the particles had the momenta at t₀ that they do. Thus, having a non-zero momentum at a time does not require existing at other times. But if one has non-zero momentum, then one is in motion. Hence, being in motion does not require existing at more than one time.

This sounds quite paradoxical, but I think it makes sense if we think of motion as that which explains the succession of states rather than as that which arises from the succession of states.

Next, let’s slightly tweak the English translation of Aristotle’s definition of change:

3. Change is the actualizing of potentiality.

One can be actualizing a potentiality without ever being in a state of having actualized it. Imagine a substance that is falling, and thus on Aristotle’s account in the process of actualizing the potentiality for being in the center of the universe, and yet which never reaches the center of the universe. At every moment of its existence, that substance is striving to be in the center. That striving, that actualizing of its potential, is what makes it be in motion. It would be in motion even if it only existed for an instant.

One cannot, I take it, have actualized a potentiality while still having the potentiality. But one can be actualizing it while still having it. One is actualing it until one has actualized it, and once one has actualized it, one is no longer actualizing it.

Granted, on this view, change does not entail a plurality of times. It is possible to have a changing universe that exists only for an instant. This complicates the Aristotelian projects of grounding time in change: change is not sufficient for time. Nor does Aristotle say it is. He says that time is a kind of number for change. But a single change may not be enough for number (Aristotle thought that one is not a number: number, for him, requires plurality). Thus, the single-moment universe may have change, but not enough change to have time on Aristotle’s view.

Change and potentiality

Aristotle defines motion or, more generally, change as the actuality of potentiality.

Imagine a helicopter hovering in one location, x. Its being at the same location x at time t₂ as it was at time t₁ is an actualization of its potentiality at t₁: namely, its potentiality to keep itself hovering in the same place by counteracting the force of gravity. Thus, by Aristotle’s definition it seems that the helicopter’s motionless hovering is motion.

Perhaps, though, we need to distinguish between potentiality and power. The helicopter, unlike a rock, has a power to stay in one place in mid-air. But neither the helicopter nor the rock has a potentiality to stay in one place, because a potentiality is necessarily for a state that does not yet obtain.

This suggests a view of potentiality like the following:

1. An object a has a potentiality for a state F just in case the object a has a possibility of being in state F and a is not in state F.

Here, “possibility” is used in the modern sense as not excluding actuality.

The helicopter has a possibility of being at location x in the future, but since it is already at location x, that possibility is not a potentiality.

Now, let’s go back to Aristotle’s definition. When are the actuality and potentiality predicated? Given that, as we saw, a necessary condition for a potentiality is lack of the corresponding actuality, it seems they cannot be predicated at the same time. This suggests that the Aristotelian account is:

2. An object changes provided it has a potentiality at one time and some other time actualizes that potentiality.

But now consider the simple at-at theory of change.

3. An object changes provided that it has a state at one time and lacks it at another.

We might call (2) “Aristotelian change” and (3) “at-at change”.

The following is trivially true:

4. Aristotelian change entails at-at change.

But what is curious is that the converse also seems to be true:

5. At-at change entails Aristotelian change.

For suppose that an object a is in state F at one time and not in state F at another. Swapping F and non-F if needed, we may assume for simplicity it is earlier in state non-F. Let t₁ be the earlier time. Since the object will later in be in state F, at t₁ it has a possibility for being in state F. That possibility is a potentiality by (1). And at t₂ that possibility is realized and hence is actual. Thus, at one time a has a potentiality for F and at another that potentiality is actualized. Hence, we have Aristotelian change.

So:

6. Necessarily, at-at change occurs if and only if Aristotelian change occurs.

So what does the Aristotelian account add?

Perhaps, though, we might say that (1) is too simplistic an account of potentiality. Perhaps not every unrealized possibility is a potentiality, but only an unrealized internally-grounded possibility. For instance, I have an internally-grounded possibility of standing up. But I do not have an internally-grounded possibility of instantly doubling in mass: rather, this possibility is grounded in the power of God.

On this view, however, the Aristotelian account of change appears to be false. For suppose that I have a possibility for a non-actual state F, but that possibility is not internally-grounded. Then if that possibility comes to be realized, clearly I have changed. Thus, if God miraculously doubles my mass, I have grown more massive, that’s a change. But that change isn’t a realization of an internally-grounded possibility.

One can escape this objection by insisting that every possibility for an object has to be internally-grounded. If so, then the Aristotelian account of change applies precisely to the same cases as the at-at account does, once again, but it adds a richer claim that change is always related to an internally-grounded possibility.

Property dualism and relativity theory

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

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

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

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

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

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

Temporary intrinsics and internal time

The main problem the literature presents for eternalist theories is the problem of temporary intrinsics: how an object can have an intrinsic property at one time and lack it at another.

The most common solution is perdurantism: four-dimensional objects have ordinary properties derivatively from their instantaneous temporal parts or slices having them, and since the slices only exist at one time, the properties can be as intrinsic as one likes.

Another solution that has found some purchase is a view on which the properties that we previously thought were intrinsic, such as shape and charge, are in fact fundamentally relational, defined by a relation to a time. Thus, to be square is to be square at some time or other. This results in a more commonsense ontology than perdurantism, but it has the problem of just denying that there are temporary intrinsic properties.

This morning it’s occurred to me that if we say that substances carry with them an internal time sequence that is intrinsic to them, then relationalism can admit temporary intrinsic properties. A property of a substance, after all, can be intrinsic even if the property is relational, as long as the relations that the possession of the property is grounded in are intrinsic to the object, say by being relations between parts or other metaphysical components of that object. After all, shape is seen as the paradigmatic case of an intrinsic property, and yet it is often seen as grounded in the relations between the particles making up an object. But on a view on which substances carry an internal time sequence, the internal times can be taken to be intrinsic aspects of the substance, and then ordinary properties can be seen as relational to the these internal times. Thus, to be square is more fundamentally to be square at some internal time or other.

What kinds of intrinsic aspects of the substance are the internal times? Here, there are multiple options. They could be sui generis aspects of the substance. They could be tropes—for instance, if substances all have beginnings, one could identify a time with the trope of having survived for a temporal duration D.

Internal times could even be time slices of the substance. This last option may seem to take us back to perdurantism, but it does not. For it is one thing to say that I am in pain because my temporal part ARP_t is in pain—it sure seems implausible to say that I am in pain derivatively from something else being in pain—and another to say that my being in pain is constituted by a relation to ARP_t, which part is in no pain at all. (That pain is constituted by a relation between the aspects of a substance is not at all strange and unfamiliar as a view: a materialist may well say that pain is constituted by relations between neuronal activities.)

Note, too, a view on which intrinsics are relational to internal times also solves another problem with views on which ordinary properties are relational to times: if those times are external, then time travel to a time at which one “already” exists is ruled out.

My own preferred view is that a nested trope ontology. I have a trope of being human. That trope then has an infinite number of temporal existence tropes, corresponding to all the different internal times at which I exist. These temporal existence tropes—or maybe even temporal human existence tropes—are then the internal times. And I can even say what the relation that makes a temporary intrinsic obtain at a temporal existence tropes t is: that temporary intrinsic obtains at t provided that it is a trope of t.

A variant of the at-at theory of change

It’s occurred to me that some of the difficulties with the at-at theory of change nicely disappear if the theory is expressed in terms of the internal time of an object: x changes provided that it is F at internal time t₁ and not-F at internal time t₂ such that t₁ < t₂ or t₂ < t₁.

For instance, consider this difficulty: Fred is bilocated and is sitting all day today and he is standing all day today. So at 10 he is not standing (and standing!) and at noon he is standing (and not standing!). On an external-time at-at theory of change, Fred has changed: at one time he is standing and and at another he isn’t. But that doesn’t seem right.

On an internal-time account of bilocation, we need to ask: is an internal time at which Fred is standing earlier or later than an internal time at which Fred is sitting? And what the answer is depends on how the bilocation was arranged. Suppose Fred was sitting all day, and at the end of the day he activated a time machine and went back to the beginning of the day and stood all day. Then he was sitting internally-earlier than he was standing, and so we do have change—just as we should. But suppose that Fred is just leading two parallel bilocated lives, without any time travel involved. Then his internal time splits into two streams when the bilocation begins and rejoins when they reunite. And plauusibly there are no earlier-than or later-than relations between the two parallel streams. And so there is no change.

Mystery and religion

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

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

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

A defense of McTaggart

This argument is valid:

1. An object that really changes from being F to being G first exists at a time at which it is F and then exists at a time at which it is G. (Premise)

2. An object that exists at a time t is present then and not purely past. (Premise)

3. Suppose O changes from being present to being purely past.

4. If O really changes from present to purely past is real, then O first exists and is present and then exists and is purely past. (By 3)

5. O does not exist when it is purely past. (By 2)

6. So, O’s change from being present to being purely past is not real change.

In other words, change from present to (purely) past is Cambridge change. And the same argument goes for change from (purely) future to present. So, nothing really changes with respect to being past, present and future. That much McTaggart was right about.

Reality is strange

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

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

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

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