Distinguishing eternalism and growing block at the end of time

Imagine that Alice lives in a classic growing block world, while Twin Alice lives in an eternalist world. Otherwise, the two worlds are exactly alike at all times. Moreover, in both worlds time started at noon, and ends at midnight.

Now let’s consider things from the point of view of both Alices right at the last moment of time, namely midnight.

In both cases, reality is a four-dimensional block, twelve hours long along the temporal axis. In both cases, there is a past but no future. However, the following would be true as asserted by Alice, but not as asserted by Twin Alice:

1. An hour ago, the block of reality was eleven hours long.

Question: What grounds the fact that (1) is true for Alice but not for Twin Alice? In other words, what grounds the fact that Alice inhabited a growing block world rather than an eternalist world?

This seems quite mysterious to me. And this seems to me to weaken the main arguments for why growing block is preferred to presentism and moving spotlight, namely that growing block gives you a better account of the grounds of claims about the past. But not in the case of (1). It seems that the growing blocker needs to ground (1) in one of the ways in which the presentist grounds claims about the past, say by positing a past-tensed fact at midnight of the block of reality having been eleven hours long an hour ago, or a past-tensed property, etc. And even so we have a puzzle.

My puzzle looks different depending on whether the eternalist world has A-eternalism or B-eternalism. If it has A-eternalism, then we can distinguish the two worlds as follows: the growing block world at the last moment of time does not have a spotlight anywhere, while the A-eternalist world does have a spotlight shining on midnight. But if that’s the answer we take, then there is a cost: there seems to be no difference between the growing block world at midnight and the B-eternalist world at midnight, and yet (1) is true in the growing block world and false in the B-eternalist world.

What did I mean by a classic growing block world? Well, in response to Merricks-style arguments that growing blockers can’t know that their thoughts are happening now, some have opted or a faded growing block, on which the past is missing some properties, like consciousness. On such a modified growing block theory, we have some hope of grounding the difference at the last moment of time between growing block and B-eternalism, because the B-eternalist world does not have a faded past. But now we can modify the story: suppose the B-eternalist world literally had a faded past (a past with no consciousness, say).

I think that if I was a growing blocker, I would be inclined to say something like this. The growing block theory is necessarily true in any world with time. What grounds the difference between being in a growing block world and an eternalist world is that an eternalist world doesn’t have time—it just has a fourth spatial dimension that enters differently into the laws of nature from the other three. Moreover, it is a necessary truth that at time t, time t is at leading edge of reality. This necessary truth does not need further grounding, but itself grounds (1) when combined with the fact that currently reality is twelve hours long.

I don’t like this invocation of an ungrounded necessary truth here. I wonder if it is much better than a Merricks-style presentism where truths about past facts are ungrounded (though admittedly contingent).

More on minimal diachronic fusions and temporal parts

This is yet another attempt to answer the question of the conditions under which in an atomic world with classical mereology we have unrestricted minimal diachronic fusions, with neater assumptions (and in particular without atomism).

Say that an object is instantaneous provided that it exists at exactly one time.

Assumptions:

1. Classical (atemporal) Mereology.

2. Parthood-at-t is reflexive and transitive, and x is a part at t of y only if x and y both exist at t.

3. SO: If x and y exist at t, but x is not a part of y at t, then x has some part at t that does not overlap y at t.

4. I-Parthood Bridge: If x is instantaneous, then x is a part of y if and only if x is a part of y at the time at which x exists.

5. I-Temporality: Every part of an instantaneous object exists at a time.

Say that a function is admissible provided that it is a non-empty function from times to sets of objects such that all the objects in f(t) exist at t. Define minimal diachronic fusions as in Sider’s paper. Say that a t-temporal part of x is a minimal diachronic fusion of the function f(t′) = x defined only for t′ = t.

Theorem: Given Assumptions 1-5, the following are equivalent:

1. Every admissible function f has a minimal diachronic fusion.

2. For every object x and every time t at which x exists, x has a t-temporal part.

3. For every object x and every time t at which x exists, there is an instantaneous part y of x that exists at t.

Notes: Since Sider in his paper explicitly accepts 1–3. I don’t love 3. It’s hard to deny 4.

I am actually a bit worried about 5, because I am worried about the possibility of objects that have both a temporal and atemporal mode of existence, and such an object could be instantaneous (i.e., its temporal mode of existence could be at only one time) while yet having a part that is atemporal. I think I might be able to handle the case of objects with a temporal and atemporal mode of existence by strengthening the concept of a minimal diachronic fusion and a temporal part to forbid the object from having an atemporal mode of existence.

In any case, the result shows that in Sider’s setting, the crucial question is whether every object has an instantaneous part at every time at which it exists.

Proof of Theorem: Clearly (A) implies (B).

Assume (B). Let y be a t-temporal part of x. This exists at t and only at t, so it’s instantaneous. It is, further, a fusion-at-t of x itself. If we can show that y is a part of x at t, then by I-Parthood Bridge, we will have y a part of x, and thus we will have (C). Suppose y is not a part of x at t. Then by SO there is a z at t that is a part of y and does not overlap x. But this contradicts fusion-at-t.

It remains to show that (C) implies (B). Assume (C). Let S be the set of all x for which there is a t and a y in f(t) such that x is an instantaneous part of y existing at t. Let z be the (atemporal) fusion of S. We need to prove that z is a minimal diachronic fusion of f.

This requires us to show that for any time t in the domain of f, z is a fusion-at-t of f(t), and that z exists ony at the times in the domain of f.

Suppose y ∈ f(t). We must show that y is a part of z at t. Suppose it’s not. Then by SO, y has a part x at t that does not overlap z at t. By (C), let u be an instantaneous part of x that exists at t. Then u ∈ S, and so u is a part of z. By I-Parthood Bridge, u is a part of z at t and u is a part of x at t. Hence x overlaps z at t, a contradiction.

Next, we must show that everything that overlaps z at t also overlaps some y ∈ f(t) at t. Suppose x overlaps z at t. Let u be a part at t of both x and z. Let v be an instantaneous part of u that exists at t. Then v is a part of u at t by I-Parthood Bridge. Thus, v is a part of z at t by transitivity. Hence, v is a part of z by I-Parthood Bridge.

So, v overlaps some w ∈ S. Let s be a common instantaneous part of v and w (the existence of s follows from (C) and I-Temporality). By I-Parthood Bridge (using the fact that a part at a time exists at that time), s exists at t, since v exists only at t. Thus s is an instantaneous part, existing at t, of some y ∈ f(t) (since s is a part of w, and w is a part of such a y). Hence s is a part of y at t by I-Parthood Bridge. Moreover, s is a part of v at t by I-Parthood Bridge, and hence by transitivity it is a part of u at t, and likewise of x at t. Thus, z overlaps y at t.

We have shown that z is a fusion-at-t of f(t).

It remains to show that z exists only at times in the domain of f. Suppose z exists at a time t. Let x be an instaneous part of z existing at t by (C). Then x overlaps some member y of S. Any member y of S is an instantaneous object existing at some time t′ in the domain of f. Now, x and y will have to have a common instantaneous part (again using (C) and I-Temporality). That instaneous part must exist at precisely t as well as at precisely t′ by I-Parthood Bridge. Thus, t = t′, and so t is in the domain of f.

If time is necessary, it's discrete

Say that a total order is locally finite provided that between any two elements there are at most finitely many elements. A locally finite total order is discrete: each non-extreme element has an immediate predecessor and successor.

Here’s a valid argument:

1. If time is necessary, the order structure of time cannot be problematically arbitrary.

2. The only possible order structures for time that are not problematically arbitrary are locally finite.

3. Thus, if time is necessary, it has to be locally finite, and in particular discrete.

Premise (1) is motivated by my and Josh Rasmussen’s research project on which fundamental and necessary things cannot be problematically arbitrary. But if time is necessary, it is very likely to be fundamental.

Why accept (2)? I am thinking like this. Suppose there are two times between which there are infinitely many times. The size of that infinity of times is arbitrary—is it countable, is it the continuum, is it something in between (if there is anything in between), is it something even bigger?

So, if time is necessary, the order of time is locally finite.

Up to isomorphism, the following are the only possible locally finite total orders:

1. ...,  − 3,  − 2,  − 1, 0, 1, 2, 3, ...: no beginning or end

2. ...,  − 3,  − 2,  − 1, 0: end but no beginning

3. 0, 1, 2, 3...: beginning but no end

4. 0, 1, 2, 3, ..., n (for some finite n): beginning and end.

Now a complex thesis:

4. If time is necessary, then either (i) necessarily time has structure A or B, or (ii) necessarily time has structure C or D.

Here’s why. If there were possible worlds where time has structure A or B and other possible worlds where time has structure C or D, it would be problematically arbitrary whether time starts off with an infinite past or a finite past.

Can we go further? Maybe, but I get less confident. Still, it seems like it would be weird that time could end at some point, but had to have started. Thus:

5. If time does not have to go on endlessly, there need not have been time at all.

It follows that:

6. If time is necessary, then it necessarily has structure A or it necessarily has structure C.

In other words, if time is necessary, it must be like the integers (option A) or like the natural numbers (option C).

Can we narrow it down further? Well, causal finitism suggests but does not prove that options with no beginning are problematic. That would get one down to option C. But this is a weak argument. Option A also has the disadvantage that it leaves unexplained why events in time didn’t all happen a day earlier than they did.

In any case, there is another move we can make at this point. It follows from 6 that:

7. If time is necessary, all the specifics of the order structure of time are necessary.

I am personally inclined to add:

8. The specifics of the order structure of time are not necessary.

9. So, time is not necessary.

But my intuitions for 8 aren’t that strong, so I don’t think this is a very strong argument for the contingency of time.

Evanescence

Compare two worlds:

• Evanescent World (EW): There is a rich three-dimensional reality that exists for only one moment of time.

• Timeless World (TW): There is a rich timeless three-dimensional reality.

Intuitively, EW is, well, evanescent, while TW is “permanent”.

On a B-theory of time, it is difficult to make sense of any such difference in evanescence between EW and TW. But a staunch B-theorist will say that this is a feature, not a bug.

However, an A-theorist will, I think, want to distinguish EW from TW. But it is difficult to do so.

Start with a moving spotlight theory. The difference between TW and EW seems to be that in EW we have time’s spotlight, and in Timeless we don’t. But time’s spotlight in EW is always (i.e., at all times, of which there is only one) lighting all of the three-dimensional reality. The spotlight is no more evanescent than the rest of the reality, and so adding the spotlight does not seem to make the Evanescent world be really evanescent.

Now, consider any of the three major A-theories: moving spotlight, presentism and growing block. At the one and only moment of time in EW, one could say (if one could speak in one moment):

1. It is not the case that there will be anything

2. It is not the case that there was anything.

But one could say the very same thing in TW (if one could speak timelessly, which is no harder than speaking in one moment). And in neither EW nor in TW can one say things like:

3. Reality will vanish.

For “will” cannot reach beyond time.

What can the A-theorist do? I think they can do only thing: They can say that EW is evanescent precisely because:

4. In EW there is exactly one moment of time.

But this is something that the B-theorist can say as well. In other words, the alleged dynamism of time on the A-theory does not seem to do anything to help explain why EW is evanescent.

So what? Well, if the A-theory explains anything better than the B-theory does, it better explains more ordinary evanescence, such as the evanescence of our lives—things flow out of existence with time, or something like that. But now take the limit case of ordinary evanescence: an entity that exists for only one moment, in a world like ours which begins long before the entity and ends long after it. And notice that the entity that exists for one moment of time in a world like ours is no more evanescent than every entity in EW. Thus there is something wrong with an A-theoretic explanation for evanescence that applies to the entity in a world like ours but not to all the entities of EW—it fails to really get at what evanescence is.

But if the A-theory really doesn’t explain evanescence better than the B-theory does, then I suspect it fails to be the better alternative.

Myth of passage

Donald Williams in his famous “The Myth of Passage” argued that time cannot flow, because if it did, then it would require either a meta-time to flow in or would flow at a rate of 1 (i.e., one second per second = one hour per hour = etc.) I’ve always been puzzled by what’s supposed to be wrong with the second option. Is it that if something flows at some rate, then it could have flowed at a different rate? But light appears to be a counterexample to that—it cannot flow but at c.

Here’s another take on what’s wrong with time flowing at a rate of 1. The flow of time is supposed to be intrinsically directional. But there is nothing intrinsically directional with a flow at a rate of one. Imagine that, somehow, our universe is divided into two halves, and in one of them time flows in one direction and in the other in the other direction. In our half, from 1 to 3 pm, it flows at a rate of 2 hrs / 2 hrs = 1. In the other half, from their 3 pm to their 1 pm it flows at a rate of  −2 hrs / −2 hrs = 1. So regardless of the direction that time flows, the rate is 1: it is never −1, say. And that makes the flow of time as measured against time itself a kind of triviality that cannot capture the myth of passage.

It seems that only when we measure the flow against a meta-time do we have a non-trivial flow. That said, perhaps Williams is wrong that we need a regress of meta-times. Maybe time’s flow can be measured against a meta-time that itself does not flow.

Existing for all times is still puzzling

Let’s assume causal finitism is false, and that the past can be infinite.

If an object pops into existence ex nihilo at a specific time t, that feels objectionably arbitrary, since we want to know why did it pop into existence then rather than earlier or later (or if it couldn’t have done that, for essentiality of origins reasons, why didn’t something just like it do that).

But if the object has existed for infinite time, that does not feel arbitrary, and some people have the intuition that the object does not call out for an explanation even if it is metaphysically contingent.

This failure to be puzzled is I think based on a mistake. For even if the object existed for an infinite time, we can ask why it didn’t exist for a longer infinite time. That question makes sense. After all, if the object existed on days ...,  − 3,  − 2,  − 1, 0, where 0 is today, then we can ask why before all those days it didn’t exist on an earlier day, one which we might denote  − ω, where ω is the first infinite ordinal.

One might answer: “Well, it didn’t exist on day  − ω, because time does not include day  − ω.” But that doesn’t solve the puzzle. After all, imagine that on day  − 18 an object popped into existence, and when we are puzzled by this, we are told: “Well, day  − 18 is the first day of time. The object couldn’t have existed on day  − 19 because there was no such day.” But now we want to know: Why did time itself begin on day  − 18 rather than on day  −19 or day −10⁹⁴? And similarly, we should want to know why time extends only to the dates ...,  − 3,  − 2,  − 1, 0 and not to day  − ω, or day  − ω − 1, or day  − 2^ω₉₄.

In fact, there is a sense in which the first of the following questions might be less puzzling than the second:

• Why did time begin on day  − 18 rather than day  − 10⁹⁴?

• Why did time extend only to days ...,  − 3,  − 2,  − 1, 0 rather than beginning with day  − ω, inclusive?

For if time is relational, then there might be no real metaphysical difference between time beginning on day  − 18 and time beginning on day  − 10⁹⁴, but even so there is a metaphysical difference between time extending only to days ...,  − 3,  − 2,  − 1, 0 and its starting on  − ω. If time extends only to days ...,  − 3,  − 2,  − 1, 0, then it has no first day, but if it starts on day  − ω, then it has a first day, namely  − ω.

In fact, there are infinities of different possible temporal orders, all of them linear (i.e., reflexive, transitive and total). Why is time one of these rather than another? If times are representable as real numbers (as classical physics assumes), why? Why not merely as rational numbers? Or, more expansively, why not as hyperreals? Or why not as an order that looks like the real numbers with zero removed?

Whatever is the time sequence occupied by an object, even if the object fills the time sequence, it calls out for an explanation why the time sequence that it fills is this one rather than another one.

Restricting the PSR to things with a finite past

A correspondent asked me why not to simply believe in a restricted Principle of Sufficient Reason (PSR) that says that everything contingent that has a beginning in time has an explanation. (Graham Oppy has once proposed such an idea.)

One of the reasons for accepting the PSR is that without it we fall into skepticism. If violations of the PSR are possible, they have no meaningful probabilities, and in particular cannot be said to be unlikely. E.g., without the PSR, we have to say it is not unlikely that we just popped into existence five minutes ago for no reason at all, and so we cannot say that skeptical hypotheses about the past are improbable.

There are two types of skepticism. On weak skepticism about X, we conclude we can’t know about X. On strong skepticism about X, we conclude that we can’t have a reasonable belief about X. Weak skepticism is not a big deal. Strong skepticism is. This is strong skepticism about the past.

The specific case of the five minute past doesn’t survive if we have the PSR restricted to things with a beginning. But another argument does. Suppose the full PSR is false but the restricted PSR is true. Now consider the scenario where reality consists of a large number of persons who for an infinite amount of time have been caught in an endless five minute loop of experiences just like mine. Violations of the PSR have no meaningful probabilities, so we cannot say that this hypothesis is unlikely. So, we get skepticism. Of the strong kind.

The antisymmetry of temporary parthood

Sider suggests this four-dimensionalist characterization of “temporary parthood” in terms of temporal parts:

1. Necessarily, x is part of y at t iff x and y each exist at t, and x’s temporal part at t is part of y’s temporal part at t.

Somehow I never noticed something that is probably pretty obvious to people who work on this: temporary parthood defined thus is not antisymmetric (where a relation R is antisymmetric provided that xRy and yRx implies x = y). For consider myself, x, and my temporal part, x_t, at t. Then x_t ≠ x, but x_t is a part of x and x is a part of x_t, assuming plausibly that the temporal part of x_t at t is x_t (otherwise, we get a weird infinite regress where each temporal part at t has a distinct temporal part at t).

Is this a problem? I think so. We do after all seem to have an ordinary notion of parthood at a time, and that notion is antisymmetric: two distinct objects can’t be mutually parts of each other at the same time. If you are a part of a club at t, the club isn’t a part of you at t, even if you are the only member at that time.

We can avoid the above temporal part counterexample to asymmetry by modifying (1) to be:

2. Necessarily, x is part of y at t iff x and y each exist at t, and x’s temporal part at t is part of y’s temporal part at t, and y is not a proper part of x.

But that’s not good enough. For consider non-instantaneous temporal parts, such as myself from time a to time b (both inclusive): x_[a,b]. Then x_[0,3] and x_[1,4] have the same temporal part at t, and so by (2) they are still mutually parts of each other at t, since neither is a proper part of the other simpliciter.

But perhaps we can argue that temporary parthood is not antisymmetric. Consider this story:

• t₁: you have a lump of unbaked clay

• t₂: the clay has been formed into a statue

• t₃: the statue has just been gilded

• t₄: the gilding has just been removed

• t₅: a piece of the clay has been pinched off in order to improve the appearance of the statue’s nose.

Consider the cloud of molecules of the original lump of clay. This cloud persists through the whole story. Initially, it does not form a statue, and at the end it forms more than the statue (since the pinched off bit is a part of the cloud but not the statue then). It seems clear that:

1. The cloud is a part of the statue at t₃, with the gold being the other part at t₃

But the cloud did not become a temporary part of the statue when it was gilded. Thus:

2. The cloud is already a part of the statue at t₂.

Conversely:

3. The statue is a part of the cloud at t₅.

But the statue does not become a temporary part of the cloud when a bit is pinched off. Thus:

4. The statue is a part of the cloud at t₄.

But there is surely no difference in the temporary relationships between the statue and the cloud at t₂ and t₄, so:

22. The statue is a part of the cloud at t₂.

But since the statue is not the cloud, (ii) and (v) imply that parthood at t₂ is not antisymmetric.

If we have a strong intuition that temporary parthood should be antisymmetric, the above example suggests that we should have a restricted view of composition, one on which at least one of the cloud and the statue does not exist.

An argument against 4D unrestricted composition

1. How many objects exist at t is not even partly grounded in facts about how things are at times later than t in worlds without backwards causation.

2. If standard four-dimensional unrestricted composition is true, then how many objects exists at t is partly grounded in fact about how things are at times other than t.

3. Standard four-dimensional unrestricted composition is false.

I think (1) is very plausible. What about (2)? Bracket God. Consider a world w₂ without backwards causation whose timeline consists of two moments, t₁ and t₂, and where there is a simple a existining only at t₁ aand a different simple b existing only at t₂. On standard four-dimensional unrestricted composition, there are three objects in existence in w₂: a, b and a + b. Of these, two objects, namely a and a + b, exist at t₁. Now consider a world w₁ just like w₂ but without b, and hence without anything at t₂. There is only one object, namely a, at t₁ in w₁.

What grounds the difference between the number of objects at t₁ in the worlds is whether b exists at t₂, contrary to (1).

The best escape from this argument is to suppose what I call five-dimensional unrestricted composition, where all modal profiles are filled. On that view, in both worlds there are infinitely many objects—probably beyond cardinality—at t₁. But that has other plausibility problems.

Subjective time and self-locating probability

Suppose I am sluggish mentally in the morning and function fast mentally in the afternoons. I find myself in a dark room with no information about what time it is. Consider the two hypotheses MORN, that it is between 7am and 8am and AFT, that it is between 1pm and 2pm. Which is more likely, or are they equally likely?

It seems obvious that if I function mentally the same way in the morning and afternoon, MORN and AFT should be equally likely.

But now suppose I live in a world where every morning all processes in the solar system slow down by a factor of two, returning to the normal speed in the afternoon. Then, surely, for all practical purposes, the period from 7am to 8am is half an hour long! And so it seems right to say P(MORN) = (1/2)P(AFT). But the case of my own mental sluggishness seems to be just a more localized version of the solar system slowing down. Thus, in my original story we should say that likewise P(MORN) < P(AFT).

Here is one way to imagine mental functioning slowing down: my thinking is divided into discrete moments (like a computer’s internal clock, where basic operations take a clock cycle), and in the morning there are fewer of these discrete moments of thinking. If so, then it seems reasonable to say that the probability that the current time is between x and y is proportional to the number of discrete moments of thought between x and y, and hence P(MORN) < P(AFT), there being fewer moments of thought in the morning.

But I have a hard time getting good intuitions about the continuous case.

An Aristotelian argument for Causal Finitism

The Aristotelian account of individuation for beings in the same species proceeds by matter. But to fill out this account, we may need to talk about the times at which the matter is different.

One reason for talking about this is the possibility on some versions of Aristotelianism that a chunk of matter can survive substantial change, and hence can compose different substances—albeit at different times. If one wolf kills and eats another, there is in principle no reason why eventually the cannibal wolf’s matter might not entirely be the same as the matter of the victim, then.

So, perhaps, we may want to say that what distinguishes members x and y of the same material species is that they have different matter at the same time. But that’s not quite right. For it could be that x and y don’t ever exist at the same time! We might thus want to say that what grounds the distinction between x and y is:

1. at some time t, either x exists and y doesn’t or x doesn’t exist and y does or x and y both exist and have different matter.

This has at least two problems. First, if I travel backwards in time to a time when I already existed, then I will have different matter from my past self at the same time (since I’ve changed some cells in the meanwhile).

But the second is probably the more serious. According to the story in (1), past, present and future differences in matter all ground the distinction between x and y. But it is implausible that future differences in matter be relevant to my present distinction from you. So we should minimally restrict (1) to talking of past and present times t. But if we do that, then what grounds our difference changes over time, and does so pointlessly, because as soon as our distinction has once been established, that’s surely all we need. In fact, the last point is particularly important given the soul’s survival past death: what makes your soul past death different from mine is presumably the past difference in matter. This suggests that if we want to get at what truly grounds our distinction, we have to go back in time as far as we can, to the very beginnings of our existence, and say:

2. either x and y differ in the time at which they began to exist, or x and y began at the same time with different matter.

There is another reason to prefer (2) to (1). We not only want an account of the distinction of substances within a world, but between possible worlds. But there are many possible worlds where I exist but where my current matter is different from the matter I now have in the actual world (namely, because my diet was different). Thus, (1) has no hope of being extended to an account of transworld distinction. But (2) has some hope of such an extension. At the very least, it gives a sufficient condition for distinctness in the transworld case, while (1) does not even do that.

But now here is an interesting thing. If (2) is the true story about the distinction between material substances of the same species, it follows that:

3. It is impossible for there to be two material substances of the same species that have no beginning in time.

But if Causal Finitism (the doctrine that one effect cannot have infinitely many causes) is false, it seems like it should be possible to have an organism that has lived for an infinite amount of time, and likewise possible to have two such organisms in one species. So (2) gives us a new reason to accept Causal Finitism.

However, personally, I don’t like the Aristotelian account of distinctions between substances.

Value supervenes on being

Consider this thesis, which both Augustine and Aquinas would accept:

1. Value supervenes on being (VSB): How valuable reality is is determined by what entities exist.

However:

2. It is good to have a true belief and bad to have a false belief.

We now have an argument against presentism (only present things exist) and growing block (only present and past things exist). Among our beliefs, we have beliefs about contingent future events. Some of these beliefs are contingently true and others are contingently false. (I am assuming a bivalent temporal logic.) The value of these beliefs is determined by what entities exist. But present and past entities are insufficient to determine whether the beliefs are true, and hence what the value of the beliefs is. Thus, contrary to presentism and growing block, there must be future things.

A four-dimensional model of Eucharistic presence

In yesterday’s post, I discussed the Real Presence in the context of relativistic time. There, I made the assumption that when Christ is really present in the Eucharist, it is Christ at a specific time of life (intuitively, the current time, but that notion is tricky given Relativity). It is, in particular, an adult glorified Christ and not the toddler Christ who is present in the Eucharist.

But after discussion with my Aquinas seminar grad students, I think there is something rather appealing about denying that assumption. What if instead we say that the whole of the four-dimensional Christ is present in the Eucharist? Aquinas apparently thinks that the whole Christ is present in every potential “part” of the consecrated host. This suggests (but does not entail) the idea of a three-dimensional entity present at a single point in space. Why, then, can’t a four-dimensional entity be present at a single point of spacetime? This would require a distinction between internal and external time. During an instant of external time there would be a positive (indeed, infinite, in the case of a being that lives forever) length of internal time. This is just as the whole-presence of a three-dimensionally Christ in the Eucharist requires a distinction between internal and external space: there may be five feet (say) of internal space between Christ’s head and Christ’s toes, but both are present in the external space of two inches—or much less if Aquinas is right that Christ is present in every potential part.

Is there any point to such a supposition? Yes.

First, the Tradition holds that Christ is wholly present in the Eucharist. Given four-dimensionalism, a literal metaphysical reading of that requires the whole of the four-dimensional extent of Christ to be present. Granted, I think this is an overreading of the Tradition: even if four-dimensionalism is true, it is plausible that the doctrinal pronouncements on this only refer to the whole three-dimensional extent of Christ. But, still, supposing the four-dimensionalism, it is certainly in the spirit of the teaching on Christ being wholly present, even if not required by it, to suppose the whole four-dimensional extent of Christ to be present.

Second, in Q73.A4, Aquinas has a beautiful discussion of the threefold temporal signification of the Eucharist. With respect to the past, it commemorates Christ’s passion. With respect to the present, it brings all the members of the Church together. With respect to the future, it prefigures the enjoyment of God in heaven. If we think that we are united with Christ in his full four-dimensional extent, this deepens and underscores this threefold signification.

Third, the Catholic tradition holds that the Mass is a re-presentation of the sacrifice of Calvary. This is a mysterious doctrine, and a four-dimensional whole-presence model of the Eucharist gives us a precise account of that doctrine as well: Christ as hanging on the Cross is present in the Eucharist.

That said, there are three things that make me uncomfortable about this four-dimensional extension of the doctrine that the whole of Christ is present in the Eucharist. The first is simply that it is a new theological theory (as far as I know), and most new theological theories are heretical.

The second is that it feels important to me that it is the glorified Jesus who is present in the Eucharist. But perhaps I am wrong about this feeling, and in having this feeling I am underplaying the commemorative aspect of the past temporal aspect of the Eucharist. Perhaps a justification for my feeling of discomfort is given by the Church’s emphasis on the Eucharist as an unbloody re-presentation of the sacrifice of Christ—but if Christ’s mangled crucified body is present in the Eucharist, then this the unbloodiness is merely a matter of appearances.

The third is that it is difficult what to make of the period when Christ was dead. Aquinas thinks God was still incarnate in the dead body of Christ, and if the Apostles had celebrated the Eucharist then, a dead body would have come to be present. If Aquinas’s reasons are good ones, which I am not confident of, then on the four-dimensional whole presence model we should say that the dead body of Christ is present. But this doesn’t seem right. I worry both about the apparently unfitting gruesomeness of this, as well as about the idea that there is something in the Eucharist other than Christ’s body, blood, soul and divinity (a dead body is not a body!). That said, I am suspicious of Aquinas’s view of the Incarnation and the dead body of Christ. But even if Aquinas is wrong, we have another problem. If the whole temporal extent of Christ is to be present, the soul of Christ as it was when Christ was dead needs to be present. (Especially if, as I think, survivalism is correct.) But a soul is only present in a spatial location insofar as it is united to a body that is in that location. But the soul of Christ as it was when he was dead was not united to a body, so it seems that there is no way for it to be present in the Eucharist. If this problem cannot be solved, the account may yield the whole four-dimensional extent of Christ being present, but not the whole temporal extent of Christ being present (the soul is temporal but not spatial, and hence not four-dimensional). Thus, the account may not achieve quite as much as it seems to.

One can resolve the second and third problems by supposing a moderate version of the view: Christ’s whole glorified four-dimensional self is present in the Eucharist—namely, Christ in the Eucharist is all of Christ from the time of his resurrection. This loses some of the advantages of the view, and it is not clear that what remains is sufficiently compelling. But, on the other hand, it’s also not clear that there is any serious disadvantage to that view over a three-dimensional-slice view of the Real Presence, except maybe the novelty. And it has the advantage of there not having to be a fact about the exact correlation of times between heaven and earth.

The Real Presence and Relativity Theory

Jesus Christ like all human beings has an internal clock. One can measure that clock in heartbeats or in lower level physical interactions or in some other way. Let’s measure it in “internal years”. If Jesus was born in 4 BC, then in 4 BC, his internal clock was at about a year (he was conceived about 0.75 years before he was born). In 1 BC, it was at 4 years, in 1 AD, it was at 5 years, and in 30 AD, it was at 34 years.

I don’t know what Jesus’s internal clock was at in 100 AD, and it’s not immediately obvious that the question makes sense. For it is not immediately obvious that there is a correlation between time on earth and time in heaven of such a sort it makes sense to ask “What is happening in heaven right now?” After all, according to Relativity Theory, it doesn’t make sense to ask “What is happening right now in the Andromeda Galaxy” without specifying a reference frame for the “right now”, and it’s not immediately clear that there is a common reference frame between heaven and earth.

However, the real presence of Jesus in the Eucharist does provide a temporal correlation between heaven and earth. Around 22:45 UTC today, Jesus will come to be present in our campus parish. Moreover, Jesus will be present as an adult glorified human, not as the three-year-old he was in 1 BC. There thus appears to be a fact of the matter as to what his internal clock will be showing when he comes to be present at 22:45 UTC in Waco today.

Interestingly, this gives a temporal ordering on events scattered across the earth apparently independent of our ordinary relativistic reference frames. For if the Eucharist is celebrated around 22:45 UTC in Waco and around 22:45 UTC in London, there is a fact of the matter whether Christ as present in Waco is older or younger or at the same age (according to his internal clock), and this fact provides a reference-frame independent temporal ordering between these two Eucharistic celebrations.

Indeed, since according to Catholic and Orthodox faith, Christ remains Eucharistically present in the tabernacles across the world, we constantly have a temporal ordering between events scattered spatially across the world. In principle, this defines a theologically privileged reference frame between scattered events—a Eucharistic reference frame. Events at locations z₁ and z₂ in spacetime are Eucharistically simultaneous, we might say, provided that Christ as Eucharistically present at z₁ and at z₂ has the same value of the internal clock.

Of course, some philosophers of time think there is an objective reference frame in the physical world. If they are right, then very likely the theologically privileged frame is the same as the objective one.

All that said, it is not completely clear to me that Christ as Eucharistically present has to have a well-defined value of his internal clock. But I suspect so, because of the intuition that it is the adult and not toddler Jesus who is Eucharistically present.

A method for living forever

Maybe you have a cancer that would kill you in three months.

So, get a powerful rocket.

Accelerate close to the speed of light, and make a one light-year round-trip journey that from your reference frame takes about a month, but takes slightly over a year from the point of view of the earth. If your speed during the first journey was v₁, now repeat the same trip with a speed of v₂ = (3c²+v₁²)^1/2/2. Then repeat with a speed of v₃ = (3c²+v₂²)^1/2/2. And so on, forever.

Fact: Each journey will take a bit more than a year of earth-time but only half of the you-time of the previous. So the total you-time of your journeying will be 1 + 1/2 + 1/4 + 1/8 + ... = 2 months. You’ll never die. At every future time, you will be alive.

But this is pointless. You might as well stay on earth, and then you’ll have three months of you-time. Three months of you-time followed by death is better than two months of you-time with no death.

A Christian argument against eternalism, with some remarks on "finite" and "infinite"

1. We have an infinite future.

2. If eternalism is true, then anything that has an infinite future is infinite.

3. We are finite.

4. So, eternalism is not true.

The crucial premise is 2. One thought behind 2 is that our best version of eternalism holds that we four-dimensional, and if we have an infinite future, that makes us infinite in the fourth dimension.

But I think we can do better than that. Plausibly, part of what we mean by “We have an infinite future” is that we will have infinitely many token future mental states (if not, add that to the premises). On eternalism, all these mental states exist. And they are clearly all ours. So if we have an infinite future, we have an infinite mental life, and that is a way of being infinite.

I am an eternalist, and I want to affirm 1 and 3. What can I do? One move is this. The relevant sense of “finite” in 3 is not a mathematical sense, but something more “metaphysical” like limited. Now, to be limited is to have one or more limits. This is quite compatible with there being respects in which we lack a limit. Thus, the charged infinite rod that sometimes figures in physics homework has limits: not limits of length, but limits of width and height (and others). In the metaphysical sense, then, the rod is finite. Likewise, then, even if we are temporally infinite or infinite in the number of mental states, we are still limited in other ways.

If we go for this move, we have to make a choice what to mean by “infinite”. We could say that something is infinite provided there is some respect in which it is unlimited. If we did that, then one thing could be finite and infinite—as long as it is limited in one way and unlimited in another. The “infinite rod” would then be both finite and infinite. And, if eternalism is true and there is an eternal afterlife, we are finite and infinite. On this take, the argument is invalid, because it is missing the assumption that nothing is both finite and infinite.

A second otion is to make “infinite” mean unlimited in all respects. In that case, we are finite and not infinite. Indeed, only God is infinite then. A set with what the mathematician calls “infinite cardinality” is limited by not having a greater cardinality than the one it has.

A third option would be to take “finite” to mean limited in every way, “infinite” to mean unlimited in all respects, and then allow for the possibility of things that are neither finite or infinite—perhaps us.

Fear of death is not exactly fear of death or being dead

You don’t believe in the afterlife. Your doctor tells you that you will die in a week. You are terrified. A couple of minutes later, the doctor comes back, herself looking terrified. She tells you that she has both good news and bad news. The good news is that she had misdiagnosed you—you are just fine. However, the bad news is that her sister who is a cosmologist has just discovered that the everything—the universe, space and time—is coming to an end in a week. (She begs you not to tell anyone, because that will cause a panic.)

Out of nerdy curiosity, you ask the doctor whether there will be a last moment of time. She says that the same question occurred to her, and there won’t be. The interval of time is open on the upper end: for every time t, there is a later time t′. It’s just that time is literally running out, and all the remaining times are less than about a week from now.

With grim amusement you note that you won’t die. For at every time in the future you will be alive, and there won’t even be a last time which one might want to identify as the “time of death”.

You reflect. It’s a bit of a plus that none of your friends will suffer from your death, but a big minus that they all have only a week left. In any case, there is no relief from fear of death.

I think this case shows that it’s not death or being dead that we fear when we don’t believe in an afterlife. We fear the fact that our future is finite. If this is right, then people like Lucretius who thought that we somehow confusedly imagined ourselves as existing after the end of our existence and that this was what explained the fear of death are likely mistaken.

A nearly equivalent version of the above thought experiment would be one where you find out that you’re going to live for an infinite amount of time, but your life will exponentially slow down. In the next week of life, you will experience half a subjective week. In the week after that, you will only experience a quarter of a subjective week, and then an eighth and so on. Your subjective future will be a week. But you will never die. That’s just as bad as permanently dying.

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.