Two kinds of change

I ran across this old post of mine and it made me think that there is an interesting distinction between two kinds of change which one might label as objectual and factual change. Objectual change is change in objects, including both an object’s acquiring or losing properties and an object’s coming or ceasing to be. Factual change is change in reality itself—the facts of reality themselves change, with future facts coming to be present (and on open future views getting filled out) and present facts coming to be past. We can put this in terms of change of facts, change of truth value of (“fully closed”) propositions, or change of reality as a whole.

When A-theorists accuse B-theorists of having a static picture of the universe and B-theorists respond with the at-at theory of change (change is a thing’s having a property at one time and lacking it at another), they are talking past each other to some degree. The A-theorist is talking of factual change. The B-theorist is talking of objectual change. The A-theorist is simply right that on the B-theory there is no factual change: the facts about reality were, are and will ever be the same. That there is objectual change on the B-theory does not contradict this. But at the same time, the A-theorist’s accusation of static factuality is something the B-theorist should proudly admit as a feature and not a bug: truth does not change.

That there is objectual change is a part of our uncontroversial data about the world. That there is factual change is the A-theory in a nutshell, and hence begs the question against the B-theorist.

At this point it seems we have an impasse. Where should the debate go? I think one thing to figure out is whether one of the kinds of change depends on the other. Suppose it turns out that objectual change would need to depend on factual change. Then the A-theorist has won: the B-theory has no change at all. Note that the at-at theory of change is not a sufficient response to a claim that objectual change depends on factual change. For the at-at theory depends on the concept of time (change is having different properties at different times), and if time itself requires factual change, then the at-at theory itself requires the A-theory. This suggests that if the at-at theory is going to be the B-theorist’s response, the B-theorist owes the A-theorist an account of what makes time be time (McTaggart insisted on the latter point).

What about the other direction? That one is kind of interesting, too. One might think that factual change would need to arise from objectual change. Aristotle apparently did. It’s not clear, however, how one gets the A-theorist’s change of reality, where future facts become present and present facts become past, out of changes in objects. Perhaps one can read McTaggart’s infamous argument against the coherence of the A-theory as an attempt to show that this task can’t be done, at least in the special case where the objects are events.

Can we offer such an argument? Maybe. We aren’t going to be able to get factual change simply from the fact that objects have different ordinary properties at different times, say a light being green at t₁, orange at t₂, and red at t₃. For there is no way to use such facts to ground which of these times are past, present or future. So it seems that if we’re to get factual change from objectual change, we’re going to have go the route McTaggart suggests, and try to ground it in terms of objects’ temporal A-properties, say this light’s being past, present, or future. But that seems problematic. For the change between past, present and future does not happen in the lifetime of the light. During the lifetime of the light, the light is always present—it is only past after its existence and it is only future before its existence! But a change that does not happen during an object’s lifetime is, of course, a Cambridge change, like a horse’s becoming posthumously famous. And Cambridge change must always be relative to something else changing really. But then it is in the latter change that we should be grounding our factual change. And now we are off on a vicious regress, much as McTaggart (perhaps for somewhat different reasons) thought.

This suggests to me that just as the B-theorist denies that objectual change depends on factual change, the A-theorist should deny that factual change arises from objectual change. As more than one philosopher has noted, the A-theorist should respond to McTaggart by taking A-temporality, understood as factual change, as primitive.

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.

A defense of McTaggart

This argument is valid:

1. An object that really changes from being F to being G first exists at a time at which it is F and then exists at a time at which it is G. (Premise)

2. An object that exists at a time t is present then and not purely past. (Premise)

3. Suppose O changes from being present to being purely past.

4. If O really changes from present to purely past is real, then O first exists and is present and then exists and is purely past. (By 3)

5. O does not exist when it is purely past. (By 2)

6. So, O’s change from being present to being purely past is not real change.

In other words, change from present to (purely) past is Cambridge change. And the same argument goes for change from (purely) future to present. So, nothing really changes with respect to being past, present and future. That much McTaggart was right about.

The unreality of time

McTaggart argued that time is unreal. Hence, time is real.

Age and time

Say that an entity E has age T at t if and only if E began to exist exactly at t-T[note 1] Observe that the age of an entity can be positive, zero, or negative. What kind of property of E is the having of a particular age?

Here is the problem. An entity continues to change in respect of age even when it no longer exists. But when an entity does not exist, the only change it can engage in is pure Cambridge change—the sort of "change" that Napoleon "experiences" when he changes from not being thought about by the Duke of Wellington or Bill Clinton to being thought about. I will assume that the age is the same kind of property during a substance's lifetime as afterwards.[note 2]

Now, Cambridge change is in the end grounded in something else undergoing non-Cambridge change. The Duke of Wellington or Bill Clinton change from not thinking to thinking about Napoleon, and thus Napoleon "changes" from being not thought about by them to being thought about by them. So the change in the age of an entity must be grounded in an something else's undergoing a genuine, non-Cambridge change. But what is that something else? And what does that something else change in respect of?

One intuitive thing to say is that "the time changes". E comes to have age T when the time changes from not being equal to t₀+T, where t₀ is the time E first came to exist, to being equal to t₀+T. But what kind of a change is that? Time surely isn't literally some enduring entity that has a succession of temporal properties like "being noon", "being 3pm", etc. Maybe what we want to say is that reality itself or the cosmos changes in respect of time: it changes from being such that it is not t₀+T to its being such that it is t₀+T.

Suppose that our ontology includes moments of time, and that if t is a moment of time, then t exists at t and only at t. We can then say that the age of E changes to T precisely when reality changes so as to include the moment t₀+T. If our ontology does not include moments of time, but, say, is relational, we may need to do some more work, but I do not see any obvious in-principle bar to defining the time.

We now have a seemingly well-defined property of age, defined in terms of reality's inclusion of a particular moment of time. Now, here is an oddity. This property of age can be equally well defined on a B-theory as on an A-theory. Indeed, I alluded to nothing A-theoretical in the account. A first consequence—Dean Zimmerman has a paper that among many other interesting things says something like this—is that it won't do to define the difference between the A- and B-theories in terms of the objective futurity, presentness and pastness of events, since such properties can be defined in terms of age, and both the A- and B-theories can define the property of age, and the definition seems mind-independent. Nor will it do to define the distinction between the A-theory and the B-theory in terms of an A-theorist's being committed to age being a non-Cambridge property. For the above argument shows that age is a Cambridge property (and by the same token, so are futurity, presentness and pastness), so it would be grossly unfair to the A-theorist thus to define the A-theory. A third consequence is that a reductio, like McTaggart's, of the very idea of futurity, presentness and pastness properties is apt to equally attack the B-theory as the A-theory, since both the B-theory and the A-theory can define such properties.

How, then, to define the A-theory, if not in terms of objective futurity, presentness and pastness of events? I see only one way at present: in terms of the idea that propositions change in truth value. The A-theorist, then, is one who gives up on the eternity of truth: p can be true at t₀ but false at t₁. This Aristotelian theory of propositions is, I think, false (on this theory, tomorrow I will no longer believe the same things as I believed today about my actions from today, even in cases where I have not forgotten these actions), but it is not clearly absurd.