## Wednesday, November 15, 2017

### A non-reductive eternalist theory of change

It is sometimes said that B-theorists see change as reducible to temporal variation of properties—being non-F at t1 but F at t2 (the “at-at theory of change”)—while A-theorists have a deeper view of change.

But isn’t the A-theorist’s view of change just something like: having been non-F but now being F? But that’s just as reductive as the B-theorist’s at-at theory of change, and it seems just as much to be a matter of temporal variation. Both approaches have this feature: they analyze change in terms of the having and not having of a property. Note, also, that the A-theorist who gives the having-been-but-now-being story about change is committed to the at-at theory being logically sufficient for change from being non-F to being F.

I think there may be something to the intuition that the at-at theory doesn’t wholly capture change. But moving to the A-theory does not by itself solve the problem. In fact, I think the B-theory can do better than the best version of the A-theory.

Let me sketch an Aristotelian story about time. Time is discrete. It has moments. But it is not exhausted by moments. In addition to moments there are intervals between moments. These intervals are in fact undivided, though they might be divisible (Aristotle will think they are). At moments, things are. Between moments, things become. Change is when at one moment t1 something is non-F, at the next moment t2 it is F, and during the interval between t1 and t2 it is changing from non-F to F.

On this story, the at-at theory gives a necessary condition for changing from non-F to F, but perhaps not a sufficient one. For suppose temporally gappy existence is possible, so that an object can cease to exist and come back. Then it is conceivable that an object exist at t1 and at t2, but not during the interval between t1 and t2. Such an object might be brought back into existence at t2 with the property of Fness which it lacked at t1, but it wouldn’t have changed from being non-F to being F.

But there is a serious logical difficulty with the above story: the law of excluded middle. Suppose that a banana turns from non-blue (say, yellow) to blue over the interval I from t1 to t2. What happens during the interval? By excluded middle, the banana is non-blue or blue. But which is it? It cannot be non-blue on a part of the interval I and blue on another part, for that would imply a subdivision of the interval on the Aristotelian view of time. So it must be blue over the whole interval or non-blue over the whole interval. But neither option seems satisfactory. The interval is when it is changing from non-blue to blue; it shouldn’t already be at either endpoint during the interval. Thus, it seems, during I the banana is neither non-blue nor blue, which seems a contradiction.

But the B-theorist has a way of blocking the contradiction. She can take one of the standard B-theoretic solutions to the problem of temporary intrinsics and use that. For instance, she can say that the banana is neither blue-during-I and nor non-blue-during-I. There is no contradiction here, nor any denial of excluded middle.

What the theory denies is temporalized excluded middle:

1. For any period of time u, either s during u or (not s) during u

but it affirms:

1. For any period of time u, either s during u or not (s during u).

A typical presentist is unable to say that. For a typical presentist thinks that if u is present, then s during u if and only if s simpliciter, so that (1) follows from (2), at least if u is present (and then, generalizing, even if it’s not). Such a typical presentism, which identifies present truth with truth simpliciter is I think the best version of the A-theory.

Thinking of time as made up of moments and intervals is, I think, quite fruitful.

Christopher Michael said...

“By excluded middle, the banana is non-blue or blue. But which is it?”

It’s non-blue ex hypothesi, for I is by definition the interval during which the banana is becoming blue, and a thing cannot become what it already is. So a banana that is becoming blue must not be blue.

“So it must be blue over the whole interval or non-blue over the whole interval. But neither option seems satisfactory.”

The latter option is not only satisfactory, but entailed by your claim that the banana is becoming blue during I, for the foregoing reasons.

“The interval is when it is changing from non-blue to blue; it shouldn’t already be at either endpoint during the interval.”

“Non-blue” is said in many ways. It would of course be unreasonable to say that the banana is yellow during the whole interval, but there’s nothing wrong with saying that it is non-blue during the whole interval, so long as you realize that there are many ways of being non-blue, and some are more bluish than others. :-)

And given this, it’s no surprise that the thought experiment also doesn't work if we speak of “yellow” rather than “non-blue,” for we no longer have contradictories at either end of the interval, and therefore no worry about LEM.

Alexander R Pruss said...

Thanks: this helps me think through what I think is going on.

Suppose that the banana comes into existence at t0 and is non-blue, then at t1 it starts to become blue, at t2 it is blue, and at t3 it perishes. Suppose, further, that the interval of time between each of the successive times t0, t1, t2 and t3 is exactly one second, and that the intervals in question are not further subdivided. Then on your account, the banana is non-blue for two seconds and blue for one second. On my account (which I don't endorse yet), the banana is non-blue for one second, neither blue nor non-blue over a one second interval, and blue for one second.

Now reverse the story temporally. Thus, the banana starts off blue at t0, at t1 it starts to become non-blue, at t2 it is blue, and at t3 it perishes. On your account, the banana is blue between t1 and t2, because you need to say that when it is becoming non-blue, it is non-non-blue -- and hence it must be blue. Thus, on your account, in the reversed story, the banana is blue for two seconds and non-blue for one second. On my account, the banana is blue for one second, neither blue nor non-blue over a one second interval, and non-blue for one second.

But when we reverse the story temporally, the total lengths of time that the banana spends in each state should be unchanged. Your account violates this desideratum. Mine preserves it.

Note, too, that my account agrees that "a banana that is becoming blue must not be blue." It just disagrees with the conclusion that the banana that is becoming blue is non-blue. :-)

By the way, if it helps intuitions, think of the in-between state of the banana as somewhat akin to a quantum superposition of the end-states. It's not that, of course, but it's somewhat like that, on this view.

Alexander R Pruss said...

By the way, my post suggests an interesting potential benefit of four-dimensionalism. Four-dimensionalism can accommodate seeming violations of the temporalized law of excluded middle for properties: if x exists at t, then either F(x) at t or non-F(x) at t. It can do this by denying that "F(x)-at-present" and "F(x)" are equivalent.

Christopher Michael said...

Your temporally reversed version of the story is not accurate. If the banana finished becoming blue at t2, then in the temporally reversed version of the story, the banana finishes becoming non-blue at t2 as well. What starts at t2 is not the process of the banana's becoming non-blue per se, but rather the process of the banana's becoming whatever color it was at t1. We can also call that “non-blue,” but there's no absurdity when we say that the banana is non-blue and is becoming non-blue, because we employ two different senses of “non-blue.” “Non-blue” is not a species of colour, and therefore strictly speaking cannot denote the terminus of a change in colour.

Once this is noted, the time distributions are the same.

Alexander R Pruss said...

I don't follow. Are you thinking that colors are continuous, so that if it changes between blue and non-blue, it must go through a series of intermediate colors, or it must change gradually spatially (the blue area growing, etc.)? Is that the force of your earlier remark, which I also couldn't follow, that my argument doesn't work if I say "yellow" instead of "non-blue" because "yellow" and "blue" are not contradictories?

If so, then you are banking too much on the specifics of the example. You can try the thought experiment with something that doesn't vary continuously, like some discrete quantum quantity changing between neighboring values.

Or maybe the force of that earlier remark was that yellow and blue are not exhaustive (with "contradictories" being a typo), so that if there is change between yellow and blue, there is no contradiction in saying that in between the state is neither yellow nor blue. If that's right, then change the case to a person waking up and changing from unconsciousness to consciousness, or a person stubbing his toe and changing from painlessness to pain.

Christopher Michael said...

This would be easily to put using a diagram, but what I am saying is that in the time-reversed scenario, the banana is non-blue on the interval [t1,t2). So we agree about the time distribution. And my saying this doesn't contradict the fact that the banana is becoming "non-blue" on that same interval because the non-blue that the banana is at any point on the interval other than t1 is not the same non-blue that it is at t1.

Alexander R Pruss said...

Is it a different color then? Or is it no color?

Christopher Michael said...

That depends on what story you want to tell about how the change is occurring. But by definition, if the change is not yet complete, then there's more of the change to come, and so the colour of the banana at any point short of t1 can't be the same as at t1. If it were, then t1 would not be the term of the change.