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.

God's timelessness, the A-theory of time, and two kinds of Cambridge change

Classical theism holds that God is timeless and knows all objective truths. According to A-theories of time, objective truths change (e.g., what exists simpliciter changes on presentism, and on other A-theories at least what time is objectively present changes). There is a prima facie conflict here, which leads some classical theists to reject the A-theory of time.

But there is also a widely accepted reply. Classical theism also holds that God is simple. One of the consequences of divine simplicity is that if God had created a different world, he wouldn’t have been any different intrinsically—and yet he would know something different, namely that he created that world rather than this one. Seemingly the only good solution to this problem is to suppose that God’s knowledge is in part extrinsically constituted—that facts about what God knows about contingent things are partly constituted by these contingent things.

But the same move seems to save timelessness and the A-theory. For if God’s knowledge is partly extrinsically constituted, then as the created world objectively changes, as the A-theory holds, God’s knowledge can change without any intrinsic change in God. Basically, the change of God’s knowledge is only a Cambridge change in God—a purely relational change.

I have always been pulled two ways here. Since I accepted divine simplicity, the response seemed right. But it also seemed right to think there is a tension between God’s timelessness and the A-theory of time, thereby yielding an argument against the A-theory.

I haven’t settled this entirely to my satisfaction, but I now think there may well be an argument from classical theism against the A-theory.

First, note that the extrinsic constitution move is aimed not specifically at a tension between God’s timelessness and the A-theory, but at a tension between God’s immutability and the A-theory. The move shows how an immutable being could have changing knowledge, because of extrinsic constitution. But while any timeless being is immutable, the other implication need not hold: timelessness is a stronger condition than immutability, and hence there could be a tension between divine timelessness and the A-theory even if there isn’t a tension between immutability and the A-theory.

Here is why I see a tension. The crucial concept here is of a merely relational change, a Cambridge change. The most common example of a Cambridge change is something like:

1. Bob became shorter than his daughter Alice.

Here, we’re not supposed to think that Bob changed intrinsically, but simply that Alice got taller!

But there is another kind of change that I used to lump in with (1):

2. Dinosaurs became beloved of children around the world.

Both are, I suppose, Cambridge changes. But they are crucially different. The difference comes from the fact that in (1), the change is between the slightly younger Bob being taller than Alice was then and the slightly older bob being sorter than Alice was then. While the change was due to Alice’s growth, rather than Bob’s shrinkage, nonetheless it is crucial to this kind of Cambridge change that we be comparing the subject at t₁, considered relationally, with the subject at t₂, again considered relationally. It is, say, the 2018 Bob who is taller than Alice, while it is the 2023 Bob who is shorter than Alice. I will call this kind of thing strong Cambridge change.

But when dinosaurs become beloved of children around the world, as they did over the course of the 20th century, this wasn’t a change between earlier and later dinosaurs. Indeed, the dinosaurs were no longer around when this Cambridge change happened. I will call this kind of thing weak Cambridge change.

Strong Cambridge change requires an object to at least persist through time: to be one way (relationally) at one time and another way (again, relationally) at another. Weak Cambridge change does not require even that. One can have weak Cambridge change of an object that exists only for an instant (think of an instantaneous event that becomes notorious).

A timeless being can “undergo” weak Cambridge change, but not strong Cambridge change. And I suspect that change in knowledge, even when the knowledge is extrinsically constituted, is strong Cambridge change.

Here is a piece of evidence for this thesis. Knowledge for us is partly extrinsically constituted—if only because (I am grateful to Christopher Tomaszewski for this decisive point) what we know has to be true, and truths is typically extrinsic to us! But now suppose that I have a case where the only thing lacking to knowledge is truth—I have a belief that is justified in the right way, but it just happens not to be true. Now suppose that at noon the thing I believe comes to be true (here we are assuming the A-theory). If we set up the case right, I come to know the thing at noon, though the change is a strong Cambridge change. But suppose that at noon I also cease to exist. Then I don’t come to know the thing! To come to know something, I would have to persist from not knowing to knowing. Prior to noon I was such that if the thing were true, I’d know it, but the thing isn’t true. After noon, I don’t know the thing, even though it isn’t true, because I don’t exist after noon. Change in extrinsically constituted knowledge seems to be at least strong Cambridge change.

Further, think about this. When God knows p in one world and not-p in another, this transworld difference is a difference between how God is in the one world and how God is in the other world, even if it is a relational difference. Similarly, we would expect that if God changes from knowing p at t₁ to knowing not-p at t₂, God exists at t₁ and also at t₂. And this does not seem to fit with God’s timelessness. (But don’t classical theists say God is omnipresent, and shouldn’t that include omnitemporal presence? Yes, but omnitemporal presence is not omnitemporal existence.)

In other words, I think for God to change in knowledge in lockstep with the objective facts changing, God has to exist in lockstep with these objective facts. To change from knowing to not knowing some fact due to the change in these facts, one needs to be a contemporary of these changing facts. And a timeless being is not (except should there be an Incarnation) a contemporary of anything.

In summary: A timeless being can only undergo weak Cambridge change, while it is strong Cambridge change that would be needed to maintain knowledge through a change in objective truths, even if that change is extrinsically constituted. One can uphold the A-theory with a changeless God, but not, I think, a timeless God.

Or so I suspect, but I am far from sure, because the distinction between weak and strong Cambridge change is still a bit vague for me.

And even if my specific arguments about God aren't right, I think the weak/strong Cambridge change distinction is worth thinking about.

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.