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.

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.

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).

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.

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.

Presentism and B-theory

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

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

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.

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.

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.

Losing track of time

Suppose that the full saturated truthbearers are tensed propositions (which I think is essentially what the A-theory of time comes to). Now consider an atom with a half-life of a week. I observe the atom exactly at noon on Monday, and it hasn’t decayed yet. I thereby acquire the belief that the atom has not decayed yet. Now suppose that for the next week I stop changing in any relevant respect, and maintain belief in the same truthbearers, and the atom doesn’t decay. In particular I continue to have the tensed belief that the atom hasn’t decayed yet.

But an odd thing happens. While my belief is reliable enough for knowledge initially—it has a probability 0.9999 of remaining true for the first minute after observation—eventually the reliability goes down. After a day, the probability of truth is down to 0.91, after two days it’s 0.82, and after a week, of course, it’s 0.5. So gradually I lose reliability, and (assuming I had it) knowledge, even though nothing relevant has changed in the world in me or around me.

Well, that’s not quite true. For something seems to have changed: my observation has “gotten older”. But it’s still kind of odd—the time slice of the world is relevantly the same right after the observation as a week after.

Should the A-theorist talk of tensed worlds?

For this post, suppose that an A-theory of time is true, so there is an absolute present. If we think of possible worlds as fully encoding how things can be so that:

1. A proposition p is possible if and only if p holds at some world,

then we live in different possible worlds at different times. For today a Friday is absolutely present and tomorrow a Saturday is absolutely present, and so how things are is different between today and tomorrow (or, in terms of propositions, that it’s Saturday is false but possible, so there must be a world where it’s true). In other words, given (1), the A-theorist is forced to think of worlds as tensed, as centered on a time.

But there is something a little counterintuitive about us living in different worlds at different times.

However, the A-theorist can avoid the counterintuitive conclusion by limiting truth at worlds to propositions that cannot change their truth value. The most straightforward way of doing that is to say:

2. Only propositions whose truth value cannot change hold at worlds

and restrict (1) to such propositions.

This, however, requires the rejection of the following plausible claim:

3. If (p or q) is true at a world w then p is true at w or q is true at w.

For the disjunction that it’s Friday or it’s not Friday is true at some world, since it’s a proposition that can’t change truth value, but neither disjunct can be true at a world by (2).

Alternately, we might limit the propositions true at a world to those expressible in B-language. But if our A-theorist is a presentist, then this still leads to a rejection of (3). For on presentism, the fundamental quantifiers quantify over present things, and the quantifiers of B-language are defined in terms of them. In particular, the B-language statement “There exist (tenselessly) dinosaurs” is to be understood as the disjunction “There existed, exist or will exist dinosaurs.” But if we have (3), then worlds will have to be tensed, because different disjuncts of “There existed, exist or will exist dinosaurs” will hold at different times. A similar issue comes up for growing block.

So on the most popular A-theories (presentism and growing block), we have to either allow that we inhabit different worlds at different times or deny (3). I think the better move is to allow that we inhabit different worlds at different times.

Backwards causation, the A-theory and God

Suppose:

1. There are tensed facts.

2. If F is a contingent fact solely about physical reality that does not depend on creaturely free choice, then God can effectually will an exact duplicate of F.

Assumption (1) is a central claim of the A-theory of time, in fact form. Assumption (2) is a hedged consequence of omnipotence, formulated to take into account the possibility of uncreatable Platonic entities and the essentiality of origins.

Add:

3. Backwards causation is impossible.

We now have a problem. Let B be the tensed fact that the Big Bang occurred billions of years ago. This is a contingent fact solely about physical reality that does not depend on creaturely free choice. So, by (2), God can effectually will an exact duplicate of B. But an exact duplicate of B would still be a tensed fact about what happened billions of years ago. And to will such a fact about the past would be backwards causation, contrary to (3).

Note how the problem disappears if we don’t have tensed facts. For then all we have is an untensed fact such as that the Big Bang occurs at t₀, and God can will that without backwards causation, whether God is in time (e.g., he can then will it at t₀) or outside time.

I personally don’t have a problem with backwards causation. But a lot of A-theorists do.

I suppose what the A-theorist should do is to replace (2) with:

4. If F is a contingent fact solely about physical reality that does not depend on creaturely free choice, then God can effectually will a perhaps re-tensed exact duplicate of F.

The A-theory and a countably infinite fair lottery

Let’s suppose that the universe has a beginning and the tensed theory of propositions (which is accepted by most A-theorists) is true. Then consider for each n the proposition d_n that n days have elapsed from the beginning of the universe. This proposition is contingent on a tensed theory of propositions. Exactly one of the propositions d_n is true. No one of the propositions d_n is more likely to be true than any other. So, it seems, we have a countably infinite fair lottery. But such are, arguably, impossible. See Chapter 4 of my infinity book. (E.g., it’s fun to note that on the tensed theory of time we should be incredibly surprised that it’s only 13 billion years since the beginning of the universe.)

Since the universe does have a beginning (and even if it does not, we can still run the argument relative to some other event than the beginning of the universe), it seems we should reject the tensed theory of propositions.

Digital and analog states, consciousness and clock skew

In a computer, we have multiple layers of abstraction. There is an underlying analog hardware level (which itself may be an approximation to a discrete quantum world, for all we know)—all our electronic hardware is, technically, analog hardware. Then there is a digital hardware level which abstracts from the analog hardware level, by counting voltages above a certain threshold as a one, below another—lower—threshold as a zero. And then there are higher layers defined by the software. But it is interesting that there is already semantics present at the digital level: three volts (say) means a one while half a volt (say) means a zero.

At the (single-threaded) software level, we think of the computer as being in a sequence of well-defined discrete states. This sequence unfolds in time. However, it is interesting to note that the time with respect to which this sequence unfolds is not actually real physical time. One reason is this. At the analog hardware level, during state transitions there will be times when the voltage levels are in an area that does not define a digital state. For instance, in 3.3V TTL logic, a voltage below 0.8V is considered a zero, a voltage above 2.0V is considered a one, but in between what we have is “undefined and results in an invalid state”. Since physical changes at the analog hardware level are continuous, whenever there is a change between a zero and a one, there will be a period of physical time at which the voltage is in the “undefined” range.

It seems then that the well-defined software state thus can only occur at a proper subset of the physical times. Between these physical times are physical times at which the digital states, and hence the software states that are abstractions from them, are undefined. This is interesting to think about in connection with the hypothesis of a conscious computer. Would a conscious computer be conscious “all the time” or only during the times when software states are well defined?

But things are more complicated than that. The technical means by which undefined states are dealt with is the system clock, which sends a periodic signal to the various parts of the processor. The system is normally so designed that when the clock signal reaches a component of the processor (say, a flip-flop), that component’s electrical states have a well-defined digital value (i.e., are not in the undefined range). There is thus an official time at which a given component’s digital values are defined. But at the analog hardware level, that official time is slightly different for different components, because of “clock skew”, the physical phenomenon that clock signals reach different components at different times. Thus, when we say that component A is in state 1 and component B is in state 0 at the same time, the “at the same time” is not technically defined by a single physical time, but rather by the (normally) different times at which the same clock signal reaches A and B.

In other words, it may not be technically correct to say that the well-defined software state occurs at a proper subset of the physical times. For the software state is defined by the digital state of multiple components, and the physical times at which these digital state “count” is going to be different for different components because of clock skew. In fact, I assume that the following can and does sometimes happen: component B is designed so that the clock signal reaches it after it has reached component A, and by the time component B is reached by the clock signal, component A has started processing new data and no longer has a well-defined digital state. Thus at least in principle (and I don’t know enough about the engineering to know if this happens in practice) it could be that there is no single physical time at which all the digital states that correspond to a software state are defined.

If this is right, then when we go back to our thought experiment of conscious computer, we should say this: The times of the flow of consciousness in that computer are not even a subset of the physical times. They are, rather, an abstraction, what we might call “software time”. If this is right, the question of whether the computer is presently conscious will be literally nonsense. The computer’s software time, which its consciousness is strung out along, has a rather complex relationship to real time.

So what?

I don’t know exactly. But I think there are a few directions one could take this line of thought:

1. Consciousness has to be strung out in a well-defined way along real time, and so computers cannot be conscious.

2. It is likely that similar phenomena occur in our brains, and so either our consciousness is not based on our brains or else it is not strung out along real time. The latter makes the A-theory of time less plausible, because the main motive for the A-theory is to do justice to our experience of temporality. But if our experience of temporality is tied to an abstracted software time rather than real time, then doing justice to our experience of temporality is unlikely to reach the truth about real time. This in turn suggests to me the conditional: If the A-theory of time is true, then some sort of dualism is true.

3. The problem that transitions between meaningful states (say, the ones and zeros of the digital hardware level) involve non-meaningful states between them is likely to afflict any plausible theory on which our mental functioning supervenes on a physical system. In digital computers, the way a sequence of meaningful states is reconstructed is by means of a clock signal. This leads to an empirical prediction: If the mental supervenes on the physical, then our brains have something analogous to a clock signal. Otherwise, the well-defined unity of our consciousness cannot be saved.

Simultaneity, A-Theory and Relativity

Here is a standard story about Special Relativity and the A-theory of time:

• There is an objective metaphysical simultaneity, but

• this metaphysical simultaneity does not affect physical events and is unobservable.

Let’s assume the A-theory is correct and this story is also correct.

Now, when people talk about this metaphysical simultaneity, they normally think they it aligns with the frame-relative simultaneity of Special Relativity for some privileged reference frame. This seems reasonable. But it is an interesting question to ask for an explanation of this alignment.

Causation may put some constraints on metaphysical simultaneity. For instance, perhaps, there shouldn’t be any possibility of future to past causation. But a metaphysical simultaneity relation can satisfy such constraints without coinciding with any frame-relative simultaneity.

If God exists, I guess we might suppose that metaphysical simultaneity coincides with a frame-relative simultaneity because it’s more elegant if it does.

On two knowledge arguments

There is a structural similarity between the main reasons for adopting the A-theory of time and the knowledge argument against physicalism. In both cases, it is claimed that there is some information that we know but which is left out of the reductive theory:

1. I know that Alice is sitting now

and

2. I know what it feels like to be sitting.

The first piece of knowledge cannot be derived from data about tenseless reality and the second cannot be derived from data about physical reality, or so it is claimed.

The similarity between the two arguments suggests that there should be a correlation between dualism and adherence to the A-theory of time: for if one is convinced by one argument, one is more likely to be convinced by the other, and if one is unconvinced by one, one is less likely to be convinced by the other. Speaking for myself, I am a B-theorist dualist, and while I am unconvinced by the time argument, I go back and forth on the mind one.

It is interesting, though, to see if we can go beyond superficial similarity. One way to do that is to see if the best responses to one of the arguments can generate plausible responses to the other.

The best response to the time argument seems to be the Kaplan story that “now” is a mere indexical, and that the content of “Alice is sitting now” is the proposition that Alice sitting is at t₁ (if t₁ is now), though the character or linguistic meaning of “Alice is sitting now” is something different from the character of “Alice is sitting at t₁” (specifically, a character is a function from world-utterance pairs to propositions, and this character assigns to an utterance of “Alice is sitting now” at t in w the proposition that Alice is sitting at t).

Is there a similar story about mind argument? It’s not so clear to me. Perhaps a start would be to say that what makes me it true that I know what it feels like to be sitting is that:

3. I know that sitting feels like this.

The physicalist analogue to the Kaplan story would then be that “Sitting feels like this” expresses the proposition that sitting feels like ϕ where ϕ is some physical state of affairs, but the character or linguistic meaning of “Sitting feels like this” and “Sitting feels like ϕ” are different. I don’t think this works, however. There are two ways of taking this approach:

1. ϕ is a specific neural state that I have when I feel like I’m sitting (say, S-fibers firing)

or

2. ϕ is a complex functional state that anything has when it feels like it’s sitting, a state implemented by different neural or other physical states in different beings.

On (a), we have an analogy to the time case, for we can take the character of “Sitting feels like this” to be a function that assigns to world-utterance pair the proposition that sitting feels like ϕ where ϕ is the physical state that is the feeling for the utterer in that world. But there is also a serious disanalogy: for in the time case, the B-theorist knows (or can claim to know) the character, since the B-theorist knows a priori the specific rule by which a referent is assigned to “now” at a world-utterance pair. But the physicalist does not know a priori the specific functional story which assigns a referent to “like this” at a world-utterance pair.

On (b), we have a disanalogy, since the character is constant: at every world-utterance pair, the same proposition is assigned as the content of “Sitting feels like this.”

Still, maybe there is still a fundamental analogy, in that the time case teaches us (if we accept the Kaplan story) that one proposition can be expressed by two sentences s₁ and s₂ such that it is correct to say “I know s₁” but not correct to say “I know s₂”. Thus, I know that I am sitting now but I don’t know that I am sitting at t₁. And similarly, maybe, I know that sitting feels like this but I don’t know that sitting feels like ϕ.

What if we go the other way around, and see if the best answer to the mind argument helps with the time argument?

I guess what is generally thought to be the best answer to the mind argument is something like this: there is a conceptual difference between the “like this” of the feeling and the physical or functional state ϕ, but ontologically they are the same. And this seems very close to Michelle Beer’s defense of the B-theory.

Another prominent answer to the mind argument is to deny that the knowledge claim expresses factual knowledge, as opposed to something like know-how or imaginative mirroring. It seems to me that a know-how story could be told about the time argument: to know that Alice is sitting now is to have certain kinds of know-how concerning dealing with Alice’s sitting. The “imaginative mirroring” case might be harder.

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.

Is the past changing all the time?

The past is unchangeable. But if the A-theory is true, then past events constantly objectively get older and older. That seems to be a kind of objective change. So, the A-theory is false.

Theories of time and truth-supervenes-on-being

Truth supervenes on being is the thesis that if two worlds have the same entities, they are otherwise the same. I just realized something that should be pretty obvious. One cannot hold on to all three of the following:

• A-theory

• eternalism

• truth supervenes on being.

For according to eternalism, at any two different times, the facts about what exists are the same. So if truth supervenes on being, at any two different times, all facts are the same—and in particular the facts about what time is objectively present will be the same, which contradicts A-theory.

In other words, just as the best version of presentism (that of Trenton Merricks) rejects that truth supervenes on being, so does the best version of the moving spotlight theory. Moreover, closed-future growing blockers—and, in particular, classical theist growing blockers—will also want to reject that truth supervenes on being since substantive truths about the future won’t supervene on being given growing block.

All this suggests that we are left with only two major theories of time available to those who accept that truth supervenes on being:

• B-theoretic eternalism

• growing block with an open future.