PHIL 3330
Metaphysics

Smart et al. on Four-Dimensionalism

J. J. C. Smart, like Bertrand Russell and many other philosophers, defends an overall view of time that is sometimes called "four-dimensionalism" or the "4D" view of time. Let's explore some of the main features of this view.

1. Tense, Nowness, etc. Are Perspectival (Part of Appearance, Not Reality)

Science (and metaphysics) is largely about trying to distinguish, in our conception of the world, what is objective and what is just due to our perspective. For example, it appears from our perspective that the sun moves around the earth, but in fact it doesn't; what we're observing is really due to the earth's rotation instead.

Smart's view is that all of the "motion" aspects of time are due to our perspective, and not part of objective reality.

In McTaggart's terms, we could say that the B-series contains all the facts about time that are objective. What the A-series adds to the B-series is just our own subjective perspective, not any additional facts about the world. (Of course, McTaggart himself can't accept this conclusion, because he thinks that the B-series is impossible without the A-series.)

2. All the Objective Facts about Time Can Be Expressed Tenselessly

According to Smart, all the objective facts about time can be expressed without using "now," "past," "present," "future," or tensed verbs. All we need is tenseless verbs, the relations "earlier" and "later," and the ability to refer to particular (token) utterances or thoughts. His translations are similar to the Russellian translations discussed by van Inwagen. Let's follow Smart's suggestion, and take italicized verbs to be tenseless. (I've also boldfaced them to make them easier to spot.) For example:

tensed discourse translation
I am (present tense) in San Antonio. I am (tenseless) in San Antonio at the time of this utterance.
I was in San Antonio. I am in San Antonio at a time earlier than the time of this utterance.
I will be in San Antonio. I am in San Antonio at a time later than the time of this utterance.
World War II is in the past. World War II is earlier than the time of this utterance.
Thank goodness my midterm is over. Thank goodness my midterm is earlier than the time of this utterance. [Prior doesn't like this translation!]
This event was future, is present, and will be past. Smart says untranslatable, and good riddance. But why not: "This event is later than times earlier than this utterance, at the same time as this utterance, and earlier than times after this utterance"?

By the way, a bit of a side issue, but the "token-reflexive" analysis of temporal discourse does face some problems. "Now" can't quite mean "at the time of this utterance." For consider: "If I had made this utterance earlier, I wouldn't have made it now." Proposed translation: "If I had made this utterance earlier, I wouldn't have made it at the time of this utterance." That doesn't seem right! It's better to treat "now" as an indexical expression. "Now" refers to a specific time only relative to a context, and with respect to any context, "now" refers to the time of that context. But this is a relatively minor technical issue.

3. We Can Represent the World as a Four-Dimensional Object

Unfortunately it's hard to draw 4D pictures. But if we imagine space squished down to two dimensions (so that everything's flat), then 3D diagrams can illustrate regions of space-time.

Rudy Rucker has some nice illustrations along these lines in his book The Fourth Dimension. For example:

The idea is that we are looking at the history of a world with only two spatial dimensions. The vertical dimension represents time. The square is A. Square, the equilateral triangle is his father, the line segment with an eye on the end is Una. Moving up the time dimension, we see A. Square have a liaison with Una, which the hexagon spies on. Later, A. Square has a confrontation with his father. Then he goes to sleep, after which his timeline stays vertical, showing that he is not moving. At the top of the cube, A. Square is still asleep, and is being protected by his father from the threatening Hexagon and Isosceles, while Una looks on from a distance.

4. Arguments for the 4D Conception: (1) Incoherence of Passage

McTaggart has one version of an argument that the A-series (i.e. the idea that facts about past, present, and future add something substantial to the idea of time as a mere dimension) is incoherent. It's a sort of baffling argument. Here's one way of thinking about the main idea. Let's pick on the idea of an event being past. Either this is a one-place property or a two-place predicate (or, put differently, either it's a property or it's a relation).

Suppose it's a relation: that is, E is in the past relative to some times but not others. So we can think of "Past" as a two-place predicate: Past(E, t) saying that an event E is in the past relative to a time t. Let's let t(E) mean the time of E, i.e. the time in which E occurs. Then Past(E, t) iff Earlier(T(E), t). But in that case we can completely account for past, present, and future in terms of the B series, without anything like motion through time. Every event is present relative to its own time, past relative to later times, and future relative to earlier times. No flow!

So it seems as though, to account for the idea that time moves or flows, we must take nowness to be an actual property: there is an absolute fact about which time is present, not just a relative one. But that just doesn't seem to make sense. 1985 was present in 1985, but it isn't any more. If we insist that presentness is absolute, then we seem to be led straight into McTaggart's contradiction, since pastness, presentness, and futureness all apply to the same events.

5. Arguments for the 4D Conception: (2) Relativity of Simultaneity

Smart mentions this argument. According to relativity theory, whether two events are simultaneous or not depends on your frame of reference. But this seems to show that we can't think of "now" as a plane moving through the block that is the history of the universe. Why not? Because "now" is a different plane for different frames of reference.

Smart mentions "rotation of axes." The idea is basically this. Space-time is a big 4-dimensional whole. But how the axes are oriented depends on the frame of reference. If you're in motion relative to someone else, then the time axis points in a slightly different direction for you. This is really just a different way to say that simultaneity is relative, not absolute. Here's an illustration from Brian Greene's book, The Fabric of the Cosmos, chapter 3, p. 59. For an extended critique of the idea of passage from the standpoint of relativity theory, see his chapter 5, "The Frozen River: Does Time Flow?"

Prior objects to this. But he doesn't seem to have any argument. He just says that it seems perfectly clear to him that there's an objective fact about which of two events came first. But lots of things that aren't true have seemed obvious to people! Relativity theory is extremely well confirmed, and according to it, there's no such thing as absolute simultaneity. (There would be if there were absolute locations, and therefore absolute facts about who's in motion and who's at rest. But relativity theory rejects these ideas completely: there is only relative motion, not absolute motion. [Acceleration is absolute, but not motion at a constant speed.])

6. A Puzzle: Then Where Does the Feeling of Passage Come From?

Hinkfuss points out that the 4D view does not seem to offer any explanation of the feeling that time moves or flows. (Van Inwagen stresses the same point.) Hinkfuss does this in a fairly nifty way, by pointing out that even if our spatial terms systematically mirrored our temporal ones, we wouldn't have a similar temptation to say that space moved.

The experience of flow seems to be closely related to one of the main differences between space and time, namely that time has a "direction" -- that is, that the way things change from past to future is very different from the way they "change" from future to past. (For one thing, entropy increases as you go from past to future, and decreases in the other direction.)

In particular, we remember past events but not future ones. This makes my experience at any moment seem a natural continuation of my experience at earlier moments. I think it's what makes us think of time as moving.

Here's a thought experiment: if someone remembered future things and anticipated past ones (Like Merlin in The Once and Future King, or the main character in Martin Amis's Time's Arrow), wouldn't it seem to them that time flowed in the opposite direction?



Last update: September 14, 2007
Curtis Brown | Metaphysics | Philosophy Department | Trinity University
cbrown@trinity.edu