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.

Presentism and the mereology of events

According to presentism, non-present events do not exist. Now consider a particular season S of fencing consisting of a dozen fencing meets M₁, M₂, ..., M₁₂ as well as practices and recovery days on other days. Suppose meet M_i occurs on day D_i, and imagine that D₁ is today. Then both M₁ and S exist, and M₁ is a part of S. But according to presentism, the only parts of S that exist are M₁ and its parts. But the mereological axiom of weak supplementation says that:

1. If y is a proper part of x, then x has a proper part that does not overlap y.

Letting x = S and y = M₁, we get a violation of weak supplementation.

Thus:

2. If weak supplementation is true, presentism is false.

Now, I happen to think that weak supplementation is in general false, so I can’t use this argument as it stands. Still, it seems plausible to me that even if it is false in general, weak supplementation is true for the temporal parts of events (where, roughly, a temporal part is a part that can be delimited solely by temporal boundaries), and that’s all we need for the above argument.

Moreover, here is a very plausible weaker version of weak supplementation for events:

3. If event y is a proper part of event x and x has a temporal duration longer than event y, then x has a proper part that does not overlap y.

But in my case above, the fencing season has a temporal duration longer than the first match, so the fencing season needs to have a proper part that does not overlap the first match, which is false on D₁ given presentism. So, (3) requires the rejection of presentism.

Basically, all the problems come from the fact that the presentist has to deny:

4. There is an event that has two non-overlapping temporal parts.

One might object that a presentist will have a version of mereological axioms where the existential quantifier is replaced by “there existed, exists or will exist”. Thus, the weak supplementation axiom might say:

5. If y is a proper part of x, then x had, has or will have a proper part that did not, does not or will not (respectively) overlap y.

I think this is not a move that a presentist will make, as it is a move that in effect makes mereology four-dimensional. For instance, the standard definition of overlap is that x and y overlap if and only if they have a part in common. But the modified version would say that x and y overlap if and only if they had, have or will have a part in common. Now imagine two fir trees, one in Alaska and one in Texas, and suppose that next year the Alaska tree will be transplanted to be right next to the Texan one. And suppose a decade later the two trees grow together in such a way that they have some branch in common. By the tensed version of the definition of overlap, it is now true to say that the tree in Alaska and the tree in Texas overlap. But only a four-dimensionalist will want to say that—that’s exactly the sort of claim the presentist will want to deny.

Moreover, note that (5) doesn’t quite capture the intuitions of weak supplementationist presentists. For it allows for the possibility of an object now having only one proper part, as long as it had another earlier, which is something weak supplementationist presentists will deny.

Perhaps, though, presentists can say that the mereology of events is different from the mereology of objects, and the modification of the axioms is something one only does in the case of events.

Cambridge events and objects

Suppose Joe Shmoe died on February 17, 1982, sadly leaving no relatives or friends behind. Every year, on February 17, the anniversary of Shmoe's death occurs. No one marks it in any way. But it occurs, every year, invariably. It is what one might call a Cambridge event, whose occurrence does not mark any real change in the world.

Similarly, there seem to be Cambridge objects. Just as the anniversary is defined by a certain temporal distance, we can define an object by a certain spatial distance. For instance, let me introduce an object: my visual focus. My visual focus is a moving object a certain distance in front of my eyes--sometimes moving very fast (in principle, a visual focus could move faster than light!). My visual focus is a persisting object, unless I close my eyes (I am not sure whether it persists when I blink or just blinks out of existence). Curiously, my visual focus, while typically having a spatiotemporal location, could also exist outside of spacetime. Imagine that I am focused a meter ahead of my nose, and space has an edge. I walk towards that edge, unblinking and never refocusing, rapt in thought about ontology. Before my nose touches the edge of space, my visual focus will have moved beyond it! We can say that the visual focus is "a meter ahead of my face", but that isn't an actual place. So we cannot identify the visual focus with a whole made up of spacetime locations.

My brief remarks have taught you, I think, a little bit about how to talk about visual foci. You now know roughly when my, or your, visual focus exists. You know something about its persistence conditions. You know a little bit about what predicates apply to it. And there is a vast range of stuff that's as yet underdetermined, and could be determined in more than one way. For instance, how wide is the visual focus? Does it shift very quickly with saccades?

But of course it's also clear that there has to be a sense in which there really are no visual foci. Objects that can leave our spacetime so easily, that can move faster than light, and that are entirely outside us but are entirely grounded in our state just aren't really there. They are Cambridge objects instead of real ones, akin to Cambridge events, Cambridge properties and Cambridge changes.

This post is inspired by John Giannini's dissertation.

Presentism, temporally extended events and Weak Supplementation

Suppose I've been practicing tennis for half an hour, and at this moment I am hitting the ball. Then there are two present events: my practice, P, and my hit, H. Of these events, H is a part of P. But H is distinct from P. After all, P started about half an hour before H. Hence H is a proper part of P. If the Axiom of Weak Supplementation is true, P has to have some proper part K that doesn't overlap H. But H contains all that is present in P. So, K is not present. Thus, there is a non-present event, and hence presentism is false. Assuming, of course, Weak Supplementation, which is the weak point of this argument.

I myself think that Weak Supplementation and Presentism are both false. The argument gets half-way: at least one of the two is false. (There is also the issue that the argument supposes a realism about events.)

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

A simple argument against presentism

1. (Premise) Only an actually existing event can be seen.
2. (Premise) A wholly past event can be seen.
3. Therefore, a wholly past event can be actually existing.
4. (Premise) If presentism is true, a wholly past event cannot actually exist.
5. Therefore, presentism is not true.

A simple example for (2): If the moon were to almost instantaneously change color all over, we could see (without any instruments) the event of this change. But we'd see the event about one second after it happened (only relative to our reference frame, but in any case the presentist has no room for such a relativity).

One might want to make the stronger claim that all the events we perceive are past. I don't know if that's true. Maybe we can have direct perception of the future. Maybe a tennis player's noninferential predictions of future ball positions are like that. Moreover, even if that were true, the presentist only says that no wholly past event is actual. Many of the events we perceive are both past and present—we can only see them because they are in part past, but they are still going, and hence in the future.

Events

Here is a valid argument:

1. (Premise) On the fine-grained view of events, if "A" and "B" are non-synonymous descriptions, then A's shining is distinct from B's shining.
2. (Premise) If A is identical with B, then A's shining is identical with B's shining.
3. (Premise) The morning star is identical with the evening star.
4. (Premise) "Morning star" and "evening star" are non-synonymous descriptions.
5. Therefore, the morning star's shining is identical with the evening star's shining. (2 and 3)
6. Therefore, the fine-grained view of events is false. (1, 4 and 5)

The essential controversial premises are (1) and (2). (If (4) is challenged, the example can be easily changed.)