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.

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).

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.

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.

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.

Why isn't a timeless being evanescent?

I think God is timeless. For a long time I’ve been vaguely worried by the thought that on a B-theory of time, a timeless being is like a being that exists at only one instant of time. But the latter being is really evanescent, while a timeless being is the opposite of evanescent. What’s the difference?

We can say: well, a being that exists at only one instant will cease to be when a new instant comes, but a timeless being won’t cease to be. But now imagine a being that exists at only one instant, but that instant is the very last instant of time. It’s no longer true that that being will cease to be, because to cease to be there has to be a future time at which one does not exist, and at the last instant of time there is no future at all. Yet the being that exists at the last instant of time is still evanescent.

If one believes in a “flow of time”, one can say that a timeless being is like a being at an instant of “time” in a “time” sequence that doesn’t flow (so it’s not really time, but only “time”). But a “flow of time” is hard to make sense of.

Here are two alternative stories. First, we might suppose that instants of time can have a “duration weight”. Thus, while one might think that the duration of n instants of time is always (in the most natural units) precisely n, one might think that instants have a duration which measures how long they endure. It’s not that they are exactly intervals. It’s still going to be the case that no change is possible during an instant. But perhaps duration is possible. Then on a discrete theory of time, a sequence of instants has a duration equal to the sum of the durations of the instants. And on a continuous theory of time, the temporal length of a segment of intervals is equal to the integral of the durations.

We can then say that a timeless being is like one that exists on an instant of infinite duration, an instant that has nothing before it or after it. On a discrete theory, this is straightforwardly just an infinite duration. On a continuous theory, it would be like a Dirac delta.

Second, we might hypothesize that what yields the subjective experience of “moving on” from one instant to another is the poverty of our experiences contained in the instant. But mystics talks of being caught up to eternity in their experiences of the infinite: time appears to slow down for them. But the experiences of mystics do not, after all, comprehend the infinite. However, perhaps, an experience that did comprehend the infinite would slow one down to the point that an instant would literally last subjectively for eternity. And this subjective time could then be an accurate reflection of the internal time of the being. If so, then only a being that comprehends the infinite, like an infinite God contemplating himself, could be timeless.

(Note that there may be some difficulty in fitting the above to the common observation that time flies when you’re having fun. But it has been hypothesized that the latter is due to the fact that when you’re having fun, you fail to notice every tick of your internal clock. Thus the fact that time flies when you’re having fun isn’t merely due to the richness of the experience when you’re having fun. It may be that what we have is a kind of phenomenon where modest finite fun makes subjective time go by faster, but then once we transcend fun into a mystical experience, the opposite happens.)

The Incarnation and timelessness

Consider the standard argument against the Incarnation:

1. Everything that is God is F (omnipotent, omniscient, impassible, etc.).

2. Everything that is human is non-F.

3. Christ is God and human.

4. So, Christ is F and non-F.

5. Contradiction!

But it is only a contradiction to be F and non-F at the same time: we’ve known this since Aristotle.
Thus the kenotic theologian gets out of the argument by holding that Christ was F prior to the Incarnation and wasn’t F after the Incarnation. (A difficult question for the kenoticist: is he now F?) But that’s contrary to the teaching of the Councils.

However, the “at the same time” observation does not need to lead to kenoticism. In fact, the Christian who is a classical theist should deny that Christ is F and non-F at the same time. For it is strictly false to say that Christ is F at t for any divine attribute F and any time time t, since God has the divine attributes timelessly rather than at a time.

This is not kenoticism. Rather, the view is that Christ is F timelessly eternally and non-F at t (for any t after the beginning of the Incarnation). Kenoticism on this view is metaphysically absurd, because God cannot cease to be F: one can only cease to be something that one used to be, and there is no “used to be” where there is no temporality.

But we sometimes say things like:

• While he was suffering on the cross, Christ was upholding the existence of the universe.

I think there are two ways of make sense of such statements. First, maybe, things that happen timelessly count honorifically as holding at all times. (Compare David Lewis’s idea that abstract objects count as existing in all his worlds.) Second, the statement can be understood as follows:

• While he was suffering on the cross, the following proposition was true: Christ is upholding the existence of the universe.

So, orthodox Christians do not actually need to talk of natures to get out of (1)-(5). Of course, if we want to allow—as I think we should—for the logical possibility of multiple simultaneous incarnations, then the temporal qualification way out won’t help. (Nor will the kenotic solution help in that case, either.)

Note, by the way, that once we realize that there can be timelessly eternal existence, we need to modify Aristotle’s temporal qualification to the law of non-contradiction:

• it is impossible to be F and non-F in the same respect at the same time or both eternally.

God and the B-theory of time

1. All reality is such that it can be known perfectly from the point of view of God.

2. The point of view of God is eternal and timeless.

3. Thus, all reality is such that it can be known perfectly from an eternal and timeless point of view.

4. If all reality is such that it can be known perfectly from an eternal and timeless point of view, then the B-theory of time is true.

5. So, the B-theory of time is true.

I am not sure of premise (4), however.

Presentism and classical theism

1. If presentism is true, then everything that exists, exists presently.

2. Anything that exists presently is temporal.

3. God exists.

4. So, if presentism is true, then God is temporal.

5. But God is not temporal.

6. So, presentism is not true.

Some presentists will be happy to embrace the thesis that God is temporal. But what about presentist classical theists? I suppose they will have to deny (1). Maybe they can replace it with:

7. If presentism is true, then everything temporal that exists, exists presently.

Presentism is now longer an elegant thesis about the nature of existence, though.

Maybe a better move for the presentist is to deny (2)? There is some reason to do that. God while not being spatial is everywhere. Similarly God is everywhen, and hence he is in the present, too. But I am not sure if being in the present is the same as existing presently.

Presentism and the contingency of time

1. (Premise) If presentism is correct, it is impossible that something has a timeless existence.
2. (Premise) Possibly, there is no time.
3. (Premise) Necessarily, something exists.
4. (Premise) Necessarily, if there is no time, everything has a timeless existence.
5. There is a world w where there is no time and yet something exists. (2 and 3)
6. In w, something has a timeless existence. (4 and 5)
7. Presentism is not correct.

Premise 3 is pretty plausible. It's accepted by theists (who think God necessarily exists), Platonists (who think abstracta do) and by Bergsonians who think it is a necessary truth that there is at least one contingent being. Presentists thus have to deny 1 or 2 or both.

Here is an intuition in favor of 1. A timeless mode of being is an intrinsic characteristic of a being. Now it should be possible to combine beings with all sorts of possible intrinsic characteristics. Thus, if a timeless mode of being is possible, then it should be possible to have a world much like ours but where there is also a timeless being. But that would be a world where presentism is false, since then existence of timeless beings is incompatible with presentism, as presentness would no longer be coextensive with existence. Now, we make this move: as soon as it is admitted that such a world is possible, what reason do we have to think it's not actual? We are in no position to know there aren't any such timeless beings, given that they could coexist with beings like us. And now, while presentism could be true, we have little reason to think it is. So presentists should accept 1.

Maybe, though, presentists should make this move: Timelessness is just presentness in the absence of anything past or future. In that case, 1 may be false. Timelessness is no longer an intrinsic characteristic of a being, and there could be worlds where all there is is a present. However, it seems to me that it is essential to a present to be evanescent. But timelessness is opposed to evanescence. On this analysis of timelessness, some instantaneous event would be timeless if nothing came before it and after it. But surely that would make it no less evanescent.

So, perhaps, presentists should deny 2. But, the following seems quite possible: there is a time than which there is no earlier. It is also imaginable that there is a time than which there is no later. And there is no reason why you shouldn't be able to combine the two, and have a time than which there is no earlier or later. In such a world, there would still be a time—a single present—but there would be no past or future, no flow of time. Everything in such a world would be maximally evanescent, if there were no timeless beings. But, plausibly, neither God nor Platonic abstracta could be maximally evanescent.

Talking of God brings us to another argument, or, actually, a pair of arguments (it's up to you which version you find more plausible):

8. (Premise) Possibly, time has a beginning (respectively, an ending).
9. (Premise) God can have no beginning (an ending).
10. (Premise) God exists necessarily.
11. (Premise) If presentism is true in a world, everything in that world is a temporal being.
12. (Premise) If there is a world where time has a beginning (ending) and if presentism is actually true, there is a world where time has a beginning (ending) and presentism is true.
13. (Premise) In a world where time has a beginning (an ending), every temporal being has a beginning (an ending).
14. If presentism is true, possibly God has a beginning (an ending). (8, 10, 11, 12)
15. Presentism is not true. (9, 14)