Does everything in time change?

Over the last two days, I’ve been thinking critically about Aquinas’ First Way. Central to my thinking, and especially yesterday’s post, was the idea that you could have an unmoved mover who is in time but isn’t pure act and who isn’t God. Such an unmoved mover constantly and unchangingly exercises—perhaps mentally—one and the same causal power to make something else move.

But I now wonder if this is possible. Suppose a demiurge that exists in time and has the power to make Bob rotate, and constantly exercises this power. Could this demiurge be unchanging? After all, at noon the demiurge is actively rotating Bob at noon, and at 1 pm the demiurge is actively rotating Bob at 1 pm. We can easily and coherently suppose that the demiurge engages in qualitatively the same activity at 1 pm as at noon. That was the intuition that was driving my thinking about this. But can we coherently add that it is the numerically same activity? For if it’s not numerically the same activity at 1 pm as at noon, then the demiurge has undergone a change, from engaging in activity a₁₂ to engaging in activity a₁₃, even if the two activities are exactly alike.

I am not sure, but I feel a pull to thinking that rotating Bob at 1 pm is a different thing from rotating Bob at noon, assuming that the agent is in time. I don’t just mean that it has different effects—which it does, since spinning-at-noon is a different effect from spinning-at-one—but that the activity of causing rotation is itself different. Maybe the pull comes from this thought. Perdurantists think that substances exist at different times by having different temporal parts at them. Perdurantism is likely false for substances. But whether or not it is true for substanes, it seems very plausible for events and activities. What made World War II exist on each day between September 1, 1939 and September 2, 1945 is that there were hostilities on each day, hostilities that are a part of World War II. Even if on two successive days the hostilities happened to be exactly alike, they would have been numerically different hostilities. If this is right in general, then the activity of rotating Bob at 1 pm is numerically different from that of rotating Bob at noon.

Furthermore, I think existence is a kind of activity. This is most obvious in the case of living things, given the Aristotelian idea that life is the existence of the living and life is an activity, but I think is true in general. Thus a thing that exists in time over a lifetime engages in a sequence of numerically different activities—existing at t₁, existing at t₂, and so on. And hence it changes. And intrinsically so. If so, then everything that exists in time must always change.

If the suggestion that there are no unchanging activities that last over time, then we can escape my worry yesterday that perhaps the sequence of moved movers in the First Way leads to a mover that is unchanging with respect to the activity of moving the next mover in the sequence but is still changing in some other coincidental respect. For the activity of moving the next mover in the sequence would have to change over time, and so the mover would be changing in respect of of its moving the next item in the sequence.

But perhaps not. For we might admit that in all the cases we are familiar with, activity only perdures over time, and there is always something numerically different happening at different times, but say that we could still imagine a being where the numerically same activity is temporally multilocated. And such a being could everlastingly rotate Bob with the activity of spinning Bob being genuinely unchanging.

I don’t know.

Gale's criticism of Stump and Kretzmann's ET-simultaneity

Stump and Kretzmann give three main concepts of simultaneity in their famous paper:

• T-simultaneity between items in time

• E-simultaneity between items in eternity

• ET-simultaneity between items in time and items in eternity.

Stump and Kretzmann observe that ET-simultaneity is not reflexive: a temporal item is not ET-simultaneous with a temporal item and an eternal item is not ET-simultaneous with an eternal item. My mentor Richard Gale in his book on God argues that this is a serious problem: a relation that is’t reflexive just doesn’t have a hope of counting as a simultaneity relation.

But Gale is wrong. For T-simultaneity and E-simultaneity are clearly simultaneity relations, but neither of them is reflexive either! For an eternal item is not T-simultaneous with itself and a temporal item is not E-simultaneous with itself.

Now, granted, when we talk of reflexivity of a relation, it’s within a relevant domain. Thus, we say that being the same color is reflexive, even though St Michael the Archangel is not the same color as himself, because the relevant domain for sameness of color is things that have color, not immaterial intellects.

So we might say that T-simultaneity and E-simultaneity are reflexive because their respective domains are temporal and eternal things, and they are each reflexive in their domains.

We might, but we shouldn’t. Stump and Kretzmann’s investigation is of a domain of items that may or may not be simultaneous in different senses, a domain that includes both eternal and temporal things. And in that domain, none of the relations they consider are reflexive. And that’s OK.

Punishment and presentism

This seems a bit plausible:

1. It is unjust to punish someone for a feature that is not intrinsic to them.

2. If presentism is true, then having done A is not an intrinsic feature of the agent.

3. Thus, if presentism is true, then punishment for past actions is always unjust.

The presentist may well question (2), insisting that presently having a past-tensed feature that was intrinsic when it was presently had counts as intrinsic. I am a bit unsure of this. It’s a question someone should investigate.

Here is a reason to think that presently having a past-tensed feature should not count as intrinsic. Suppose I am facing a free choice, with the possibilities of doing B and not doing B. Then it seems that no present intrinsic feature of me entails what I will do. But suppose that in fact I will do B. Then just as I have past-tensed properties like having done A, I presently have future-tensed properties like being about to do B. And it seems that if one is intrinsic, so is the other. Thus, if my being about to do B is not a present intrinsic feature of me, my having done A is not a present intrinsic feature of me.

The presentist might respond by embracing an open future and denying that it can be true in the case of a free choice that I will do B. But if this is right, then it seems that in order to defend the justice of punishment for past deeds, the presentist has to do something very controversial—accept an open future. Moreover, this means that a classical Jew, Christian and Muslim can’t be a presentist, since classical monotheists are committed to comprehensive foreknowledge, and hence to the denial of an open future, and the justice of retrospective punishment.

Of course, one might question (1). Here’s how one might start. We can punish Alice for punching Bob. But that’s not an intrinsic feature of Alice. We might respond by saying that Alice is punished for her internal act of will, but that doesn’t seem quite right. Probably a better move is to replace (1) by saying that there must be an intrinsic component to the feature one punishes someone for—say, Alice’s act of will. And the presentist now has trouble with this intrinsic component.

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.

Persons and temporal parts

On perdurantism, we are four-dimensional beings made of temporal parts, and our actions are fundamentally those of the temporal parts.

This is troubling. Imagine a person with a large number of brains, only one of which is active at any one time, and every millisecond a new brain gets activated. There would be something troubling about the fact that we are always interacting with a different brain person, and only interacting with the person as a whole by virtue of interacting with ever different brains. And this is pretty much what happens on perdurantism.

Maybe it’s not so bad if each brain’s data comes from the previous brain, so that by learning about the new brain we also learn about the old one. And, granted, on any view over time we interact to some degree with different parts of the person—most cells swap out, and we would be untroubled if this turned out to hold for neurons as well. But it seems to me that it is a more attractive picture of interpersonal interactions if there is a fundamental core of the person with which we interact that is numerically the same core in all the interactions, so that the changing cells are just expressions of that same core.

This is not really much of an argument, just an expression of a feeling.

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.

Three fixity principles

In debates about free will and foreknowledge as well as about compatibility and incompatibilism, fixity-of-history theses come up. Here is such a thesis:

1. If a decision is causally or logically necessitated by the history behind the decision, then one could not have decided otherwise.

But now we have a crucial question as to what is meant by “the history behind the decision”. There are at least two takes on this. On the temporal version, the history behind the decision is the sum total of what happened temporally prior to the decision. On the causal version, the history is the sum total of what happend causally prior to the decision.

This is not just a nitpicking question. Linda Zagzebski for instance nicely shows that if we go for the causal-history version of (1), then the main argument for the incompatibility of free will and foreknowledge does not get off the ground assuming God’s forebelief is not causally prior to the action. On the other hand, if we go the temporal-history version, then we have a prima facie argument for such incompatibility (though I think it’s blockable).

I am pretty confident that we should go for the causal-history version, and this has to do with the fact that the temporal-history version is not strong enough to capture our fixity intuitions. Suppose that we live in a world with simultaneous causation—say, a Newtonian world with rigid objects such that if you push object A and A pushes B, then B begins to move at exactly the same time as you start pushing (rather than with a delay caused by then need for a compression wave traveling through nonrigid materials at less than the speed of light). Then we could imagine cases where someone’s decision is causally necessitated by something outside the agent that is simultaneous with the decision. Such causal necessitation would just much make it true that one could not have decided otherwise as would causal necessitation by something in the past.

Furthermore, if backwards causation is possible, then a neurosurgeon in the future who used a backwards-causing machine to determine your decision would clearly prevent you from deciding otherwise, even though the neurosurgeon’s action was not in the temporal history. We may not believe backwards causation is possible, but it is clear that if it were possible, then deterministic backwards causation would be just as threatening for free decisions as deterministic forwards causation. This shows that causal determination is indeed a threat.

Of course, my above argument only shows that if we need to choose between the causal and temporal history versions of (1), we should definitely go for the causal one. But perhaps we don’t need to choose. We could accept both versions. But if we think we accept both versions, I think what we really should accept is an even stronger principle, where “history” is causal-cum-temporal (cct). On that stronger principle, event A counts as in the cct history of event E provided that it is either temporally or causally prior to E. The resulting fixity principle is pretty strong principle, but also a bit gerrymandered. And I think accepting this principle not that plausible, because the much simpler causal version captures our intuitions about all the ordinary cases (not involving God, or backwards or simultaneous causation), since in all ordinary cases causal and temporal history coincide, and we should not go for a more complex principle without pretty good reason.

God's forebeliefs are soft facts

The most commonly discussed argument against the compatibility of foreknowledge and free will is based on the “fixity of the past”—that nothing you can do can affect how things were, and hence nothing you can do can affect what God had believed.

However, everyone except the logical fatalist agrees that the “fixity of the past” does not apply to so-called “soft facts”. An example of a soft fact (an expansion of an example of Richard Gale) is to suppose that Alice drank a cup of poison, but hasn’t died yet. Alice would survive if Bob calls 911, but he’s not going to. Then it’s a fact that Alice drank a fatal cup, but this is a soft fact, and there is no difficulty in saying that Bob can make this fact not to have obtained. It is only the hard facts about the past that are supposed to be fixed.

Thus, much of the discussion has focused on the question of whether God’s past forebeliefs could be soft facts. In this post, I want to note that classical theists have very good reason to think that God’s past forebeliefs are soft facts.

Start with the following plausible principle:

1. If a fact F expressed by a past-tense statement is partly grounded in a fact G about the present or future, then F is a soft fact.

Of course, defining a fact “about the present or future” is just as difficult as defining a soft fact, but I am not trying to give a definition of a soft fact, just giving a sufficient condition for being one.

Now, on classical theism, God is simple and hence has no intrinsic accidental features. God’s beliefs about contingent realities then have to be partly constituted by those contingent realities (this is the extrinsic constitution model, and it is unavoidable). Such partial extrinsic constitution is a type of grounding. Thus, God’s belief in a fact is partly grounded in that fact.

Hence, God’s having believed in a fact about the present or future is partly grounded in that fact, and thus by (1) is a soft fact. And everyone except the logical fatalist agrees that soft facts are not subject to the fixity of the past, and hence soft facts about God’s forebeliefs do not threaten free will.

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.

Could a being in time be eternal in Boethius' sense?

Famously, Boethius says that an eternal being, unlike a merely temporally everlasting being, embraces all of its infinite life at once, “possess[ing] the whole fulness of unending life at once”. What’s that mean?

Our life is strung out across time. Sitting right now I as I am I do not embrace the past and future portions of my life where I am lying down or standing up. If I fully and vividly knew my past and my future, I would be a little closer to being eternal, but it would still not be true that I possess the fullness of that life at once. For it would still be true that I now only possess the property of being seated and not the property of lying down or of standing up. So I think epistemic things are not enough for eternity. And this seems intuitively right—eternity is not an epistemic matter. (Could you have an eternal being that isn’t minded? I don’t see why not.) A necessary condition for being eternal is being unchanging.

But being unchanging is not sufficient. Suppose I were everlastingly frozen sitting in front of my laptop. It would still be true that in addition to the present part of my life there is the future part and the past part, and further subdivisions of these, even if they happen to be boringly all alike. The life of an eternal being does not have temporal divisions, even boring ones. It is all at once.

Here is a weird thought experiment. Imagine you are an everlasting point-sized being with a rich and changing mental life. Suppose all your life is spent at the one spatial location (x₀,y₀,z₀). But now imagine that you get infinitely multilocated across all time, in such a way that your numerically same life occurs at every x-coordinate. Thus, you live your everlasting and rich mental life (x,y₀,z₀) for every possible value of x, and it’s the very same life. Your life isn’t spatially divided. The life at x-coordinate  − 7.0 is not merely qualitatively but numerically the same life as the one at x-coordinate  + 99.4.

Now, one more step. Your life is within a four-dimensional spacetime. Assume that spacetime is Galilean or Minkowskian. Now imagine rotating your life in the four-dimensional spacetime in such a way that what was previously along the x-axis is along the t-axis and vice versa. So now your rich and temporally varied mental life becomes temporally unchanging, but all the variation is now strung out spatially along the x-axis. Furthermore, whereas previously due to multilocation you had your life wholly at every x-coordinate, now you have your life wholly—and the numerically same life—at every t-coordinate. Thus, you have an infinite life all at once at every time for everlasting time. Your life isn’t temporally divided: tomorrow’s life is not simply just like today’s, but it is the numerically same as today’s, because your life is fully multilocated at all the different times.

Here is an interesting thing to note about this. This “sideways life”, varying along the x-axis, satisfies the Boethian definition of eternity even though the life is found in time—indeed at every time. If this is right, then having an eternal life in the Boethian sense is compatible with being in time!

Of course, God is not like you are in my weird story. In my story, your life includes different instances of consciousness strung out along the x-axis, though not along the t-axis. Still this kind of inner division is contrary to the undividedness of the divine mind. An eternal God would not have such divisions either. Nor would he be spatial. Perhaps an argument can be made that if God possesses Boethian eternity, then he has to be timeless. But I think that’s not going to be an easy argument to make.

If this is right, then I have overcome an obstacle to combining classical theism with the A-theory of time. I am convinced that an omniscient being has to be in time if the A-theory is true. But if a being can be in time and yet eternal in the Boethian sense, then a classical theist may be able to accept the A-theory of time. After all, Boethius is paradigmatically a classical theist.

That said, my own view is that the above argument just shows that Boethius has not given us a fully satisfactory characterization of eternity. And I have other reasons to reject the A-theory besides theistic ones.

From three or four problems of omniscience down to one

The three most influential problems of omniscience are:

1. Boethius’ problem of foreknowledge: What is known is necessarily so, and thus if God knows what you will do, you will necessarily do it.

2. Pike’s problem of foreknowledge: If you can act otherwise, you can thereby make it be that either God didn’t exist or that God wasn’t omniscient or that God had believed otherwise than God actually did, and you just can’t do that.

3. The simplicity and knowledge of contingents problem: If the world had been different, God’s beliefs would have been different, which implies that God’s beliefs are accidents of God, contrary to divine simplicity.

Of these, (1) is fully solved by Boethius/Aquinas by distinguishing between necessity of consequence and necessity of consequent. The problem in (1) is just a simple matter of a fallacy of modal scope ambiguity. It’s a non-problem.

I now want to argue that the most widely accepted solution to (3) also solves (2).

This solution, likely already known to Aquinas, is that God’s belief in contingent facts is partly extrinsically constituted by creatures, and all the contingency is on the created side. For instance, God’s belief that there are zebras is grounded in essential facts about God that do not vary between possible worlds and the actual existence of zebras, which only obtains in some possible worlds.

Suppose we apply this solution to (3). Then God’s belief that you will ϕ at t is partly grounded in your ϕing at t and partly in essential facts about God. At this point it is obvious that:

4. If you were not to ϕ at t, God wouldn’t have believed you would ϕ at t.

For the contingent part of the grounds of God’s believing that you would ϕ at t is your actually ϕing at t, so when you take that away, God’s belief goes away. And if instead you ψ at t, your action thereby constitutes the contingent part of the grounds of God’s believing that you would ψ at t, and so:

5. If you were to ψ at t, God would have believe you would ψ at t.

If God’s past belief is partly constituted by our actions, it is no surprise that there is counterfactual dependence between our actions and God’s past belief. In other words, the classical theist who accepts divine simplicity has a way out of Pike’s argument that is motivated completely independently of considerations of time and freedom, namely by embracing counterfactuals like (4) and (5) that Pike considers absurd.

Of course the extrinsic constitution of divine beliefs is somewhat hard to swallow, notwithstanding excellent work by people like W. Matthews Grant to make it more plausible (I myself have swallowed it). But once we do that, problem (2) is gone, and problem (1) was never there as it was based on a fallacy.

There is a fourth problem, a more recondite one, which is about the incompatibility between God’s knowledge of what time is objectively present (assuming the A-theory of time) and divine immutability. Probably the most extensive pressing of this problem is in Richard Gale’s On the Nature and Existence of God. But Aquinas (according to the very plausible interpretation by Miriam Pritschet in an excellent paper I heard yesterday at the ACPA) responds to the fourth problem precisely by using the extrinsic constitution of God’s knowledge of continent facts (indeed this is why I said that the solution to the simplicity problem was likely known to Aquinas). So even that fourth problem reduces to the third—or just doesn’t get off the ground if the B-theory of time is true.

Freedom: a problem for presentism and growing block

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

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

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

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

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

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

The good of success is not at the time of success

It’s good for one to succeed, at least if the thing one succeeds in is good. And the good of succeeding at a good task is something over and beyond the good of the task’s good end, since the good end might be good for someone other than the agent, while the good of success is good for the agent.

Here’s a question I’ve wondered about, and now I think I’ve come to a fairly settled view. When does success contribute to one’s well-being? The obvious answer is: when the success happens! But the obvious answer is wrong for multiple reasons, and so we should embrace what seems the main alternative, namely that success is good for us when we are striving for the end.

Before getting to the positive arguments for why the good of success doesn’t apply to us at the time of success, let me say something about one consideration in favor of that view. Obviously, we often celebrate when success happens. However, notice that we also often celebrate when success becomes inevitable. Let’s now move to the positive arguments.

First, success at good tasks would still be good for one even if there were no afterlife. But some important projects have posthumous success—and such success is clearly a part of one’s well-being. And it seems implausible to respond that posthumous success only contributes to our well-being because as a matter of fact we do have an afterlife. Note, too, that in order to locate the good of success at the time of success, we would not just need an afterlife, but an afterlife that begins right at death. For instance, views on which we cease to exist at death and then come back into existence later at the resurrection of the dead (as corruptionist Christians hold) won’t solve the problem, because the success may happen during the gap time. I believe in an afterlife that begins right at death, but it doesn’t seem like I should have to in order to account for the good of success. Furthermore, note that to use the afterlife to save posthumous success, we need a correlation between the timeline the dead are in and the timeline the living are in, and even for those of us who believe in an afterlife right at death, this is unclear.

Second, suppose your project is ensure that some disease does not return before the year 2200. When is your success? Only in 2200. But suppose your project is even more grandiose: the future is infinite and you strive to ensure that the disease never returns. When is your success? Well, “after all of time”. But there is no time after all of time. So although it may be true that you are successful, that success does not happen at any given time. At any given time, there is infinite project-time to go. So if you get the good of success at the time of success, you never get the good of success here. Even an afterlife won’t help here.

Third, consider Special Relativity. You work in mission control on earth to make sure that astronauts on Mars accomplish some task. You are part of the team, but the last part of the team’s work is theirs. But since light can take up to 22 minutes (depending on orbital positions) to travel between Earth and Mars, the question of at what exact you-time the astronauts accomplished their task depends on the reference frame, with a range of variation in the possible answers of up to 22 minutes. But whether you are happy at some moment should not depend on the reference frame. (You might say that it depends on what your reference frame is. But there is no unambiguous such thing as “your” reference frame in general, say if you are shaking your head so your brain is moving in one direction and the rest of your body in another.)

Here is an interesting corollary of the view: the future is not open (by open, I mean the thesis that there are no facts about how future contingents will go). For if the future is open, often it is only at the time of success that there will be a fact about success, so there won’t be a fact of your having been better off for the success when you were striving earlier for the success. That said, the open-futurist cannot accept the third argument, and is likely to be somewhat dubious of the second.

More on A-theory and divine timelessness

Argument One:

1. If from x’s point of view there is an objective fact about what time it presently is, then x is in time.

2. If x knows an objective fact about something, then from x’s point of view there is an objective fact about it.

3. If the A-theory of time is true, then there is an objective fact about what time it presently is.

4. God knows all objective facts.

5. So, if the A-theory of time is true, then God knows an objective fact about what time it presently is. (3 and 4)

6. So, if the A-theory of time is true, from God’s point of view there is an objective fact about time it presently is. (2 and 5)

7. So, if the A-theory of time is true, God is in time. (1 and 6)

Note that no claim is made that if the A-theory of time is true, God changes.

Argument Two:

1. God is actual.

2. Everything actual is in the actual world.

3. If the A-theory of time is true, the actual world is a temporally-centered world (one where there is a fact as to what time is present).

4. Anything that is in a temporally-centered world is in time.

5. So, if the A-theory of time is true, God is in time.

Many will dispute 3, but if we think of worlds as ways for everything to be, then I think it is hard to dispute 3.

I wonder if a classical theist who is an A-theorist might be able to respond that, yes, God is in time but God is not a temporal being. Compare that by doctrine of omnipresence, God is in space, but God is not a spatial being. Still, I think there is a difference. For as the above arguments show, the claim that God is in time is more limiting than the claim that God is spatially omnipresent—it is a claim that God is at the one objectively present point of time (he was and will be at others, of course).

Spatiality and temporality

Here’s an interesting thing:

1. Learning that our spatiality is an illusion need not radically change the pattern of our rational lives.

2. Learning that our temporality is an illusion would necessarily radically change the pattern of our rational lives.

To see that (1) is true, note that finding out that Berkeley’s idealism is true need not radically change our lives. It would change various things in bioethics, but the basic structure of sociality, planning for the future, and the like could still remain.

On the other hand, if our temporality were an illusion, little of what we think of as rational would make sense.

Thus, temporality is more central to our lives than spatiality, important as the latter is. It is no surprise that one of the great works of philosophy is called Being and Time rather than Being and Space.

Curiously, though, even though temporality is more central to our lives than spatiality, temporality is also much more mysterious!

Divine timelessness and the A-theory of time

1. One can only know a proposition when it is true.

2. One can only know a proposition when one exists.

3. Thus, one can only know a proposition if it ever happens that one exists while it is true. (1 and 2)

4. If the A-theory of time is true, the proposition that it is a Wednesday is true only on Wednesdays.

5. God knows all objectively true propositions.

6. If the A-theory is true, the proposition that it is a Wednesday is objectively true. [I am posting this on a Wednesday.]

7. If the A-theory is true, God knows that it is a Wednesday. (5 and 6)

8. If the A-theory is true, God exists on a Wednesday. (3, 4 and 7)

9. If God exists on Wednesday, God exists in time.

10. So, if the A-theory is true, God exists in time. (8 and 9)

I conclude that the A-theory is false.

The above argument is similar to one that Richard Gale gives in On the Nature and Existence of God, though Gale's purpose is to provide an argument against theism.

Growing Block and a time bias

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

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

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

Two kinds of time bias

In our philosophy of time seminar, we have been thinking about time biases. Humans appear to discount future goods and bads so that a good or bad with value λ at temporal distance T in the future has effective value f(T)λ for some monotonically non-increasing function f. We might call this a relational time bias—the bias is based on the temporal relation between us-now and the goods and bads we are thinking about.

But there are also structural or non-relational time biases. Thus, as is well known, we think that a life of improvement is better to a life of deterioration, even if the total amount of good is the same. In other words, we think it’s better if the goods are rearranged in life to go closer to the end of life. Putting them closer to the end of life is also usually putting them further in the future, but the concern here is purely structural, not about how far or close the goods are to the present as such.

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.