PHIL 3330

Time Travel and the 4D View of Time
Notes on Heinlein, "By His Bootstraps," and Lewis, "The Paradoxes of Time Travel"

Heinlein's story raises a number of philosophical issues that Lewis explores in more detail. I will focus on a few puzzles that arise in the story, and what Lewis has to say about them.

1. Closed Causal Loops

Examples: (1) notebook in Heinlein's story; (2) Lewis's conversation: as a young man, you meet an older stranger who tells you how to build a time machine.  It takes you twenty years to do it, but you manage it. then you get inside, travel twenty years into the past, and tell yourself how to build a time machine . . . (3) Heinlein's story of the person who's both of his own parents ("--All You Zombies--").

The problem: Although every event in the loop is caused, there is no outside cause: the whole thing is closed off, so to speak.

However, although this is very strange, it does not seem to be impossible or incoherent.

Compare the cosmological argument for God's existence: the universe cannot be causeless, so God must exist to provide everything with a first cause. But then of course the whole problem reappears for God. It seems that no matter how many causes we add, there will be one missing. So it seems inevitable that some things (well, at least one thing) will lack a causal explanation. So, the lack of a causal explanation doesn't show that something is impossible or incoherent.

Lewis also mentions that modern physics is indeterministic: according to the best story we currently have, there are many events that do not have (complete) causal explanations. Example: decay of a radioactive atom.

2. Multiple Locations

Puzzle: Nothing can be in two places at the same time. But here's Bob Wilson at three or four places at the same time! Isn't that impossible?

Let's start by refining the principle that nothing can be in two places at the same time. I am simultaneously near the floor and several feet above it (since my feet are on the floor while my head is quite a bit higher). There is no problem about having different parts of the same thing in different locations at the same time. It's just that all of an object cannot be in different locations at the same time.

(Do the parts of an object have to be continuous, i.e. all connected to each other, for it to be a single thing? No. (1) For one thing, everything is made up of atoms with empty space in between. (2) Also, if I take my watch to the jeweler, he or she may dismantle it in order to repair it, putting it back together again when finished. But it's still my watch, even when the parts are separated.)

So a more accurate statement of the principle would be: All of an object cannot be in two places at the same time.

Now, Lewis's lovely move is to suggest that me-yesterday and me-today are both different parts of me, in much the same way that my hand and my foot are different parts of me. In addition to spatial parts, I have temporal parts, stages or slices. If we consider the whole four-dimensional me, my baby-stage is just a part of me, as is my adolescent stage, my college-going stage, etc.

If we think about objects in this way, then the multiple Bob Wilsons in Heinlein's story are just different parts of the entire Bob Wilson, so there's no problem about how they can be in different places at the same time.

3. Multiple Centers of Consciousness

Puzzle: if that's me over there, why can't I see things from that point of view? (And: why can't I lift that arm, etc.) Short answer: I can, just not at this moment of my personal time.

What's "personal time"? We begin by considering a person as consisting of many stages or slices, as in the previous section.

Notice the relationship between this view and the view that time moves: now, instead of thinking of all of me as moving through time, we are thinking of a lot of parts of me -- me-at-t1, me-at-t2, etc. -- which timelessly exist, just as it is timelessly true that Columbus sailed in 1492. (As Lewis says, I move through time in the same sense that a fence moves across a field, namely by having different parts at the different times.)

Lewis distinguishes between external or objective time, on the one hand, and personal time, on the other. (In some ways it's an unfortunate choice of terminology: as Lewis himself stresses, "personal time" is not actually time.) Objective, external time is just plain old time, the order in which events occur in the world. "Personal time," on the other hand, is a way of ordering person-stages or person-slices. Given a bunch of person-slices of the same person, personal time is the ordering of those stages that makes a normal life out of them: the stages show signs of aging from earlier to later; later ones remember things that happened to the earlier ones; and so on.

Of course, under normal circumstances, personal time and objective time coincide exactly: the personal-time ordering of my stages, and the objective time ordering of those stages, are exactly the same. In time travel, however, this coincidence breaks down.

I am always conscious of only one moment of my personal time. More precisely, every stage of me is directly aware only of that stage. Now, as recently mentioned, I normally have only one center of consciousness at a time. But if there were more than one stage of me at the same external time then, since I'm always conscious of only one moment of personal time, there would be two distinct centers of consciousness, both of them mine!

(This raises an issue we will return to later in the class: the problem of personal identity. Given a bunch of person-stages, what makes them all stages of the same person?)

4. Fatalism, Determinism, Free Will

Heinlein's story seems to pose a problem about free will. It's surprisingly difficult to state just what the problem is, though!

A. Determinism?

Determinism says that the state of the universe at a given time, together with the laws of nature, suffices to determine the state of the universe at every later time. "Determines" how? One way to say it: a complete statement of the particular facts at a time, conjoined with a complete statement of the laws of nature, logically implies a complete statement of the particular facts at every later time. It follows that, in principle, if I knew all the laws of nature and all the particular facts at a time, I could predict what would happen at all future times. (Except that the "in principle" here is rather extreme; making the prediction would require completely absurd memory and processing power.)

This is not the problem with the 4D view and Heinlein's time travel story! The 4D view is entirely compatible with the idea that there is irreducible randomness in nature.

B. Fatalism?

Fatalism is usually described as the view that, since there are already facts about the future, it doesn't make any difference what I do. What will be will be, so there's no point trying to change anything. (Somerset Maugham's "Appointment in Samarra" is a nice illustration of the view.)

We need to distinguish two pieces of this picture. First is the idea that there are facts about the future. Second is the idea that it makes no difference what we do. The second is what makes this view fatalistic, but it doesn't follow from the first. That there are facts about the future is quite compatible with the idea that what makes them facts is (will be) my own actions.

C. Bivalence?

Bivalence is the idea that every proposition is either true or false. A "proposition" here must be a timeless (untensed), B-series style proposition. So consider the sentence "CB comes to Metaphysics class on September 21, 2007." (With tenseless "is".) The idea is that, if the 4D view is correct, this must be timelessly true or false. It can't become true (or false) on September 21, 2007; it just is true (or false).

Does it follow that I can't do anything about whether the proposition is true or false? No! It's true (or false) because of what I will do in two days. It's the future fact that makes the proposition true, not the other way around. So (I claim), the existence of facts about the future does nothing to call my free will into question. That there are facts about the future is compatible with the idea that what makes them facts is what I will freely do.

(Compare: if God is omniscient, and therefore knows what I will do on Friday, does that mean that I'm not free? I say no: among the things an omniscient being would know are the facts about what I will freely do.)

People are sometimes persuaded by a bad argument that if it's a fact that I will be in class on Friday, then it is impossible for me not to come to class. But this is a mistake. Consider:

If it's a fact that I will be in class, then, necessarily, I will be in class
It is a fact that I will be in class
Necessarily, I will be in class

This looks OK, but it's not. The first premise is ambiguous between two readings:

(1) Necessarily (If I will be in class, then I will be in class)


(2) If I will be in class, then Necessarily (I will be in class).

(1) is (trivially!) true, but does not imply that it's necessary that I will be in class. (2) is simply not true. That I could fail to come if I chose is quite compatible with it being a fact that I will come. (The argument above is the kind of thing Lewis calls "fatalist trickery.")

D. Knowledge of the future?

There's an extra layer of weirdness in Bob Wilson's story. Not only are there facts about what Bob will do, but Bob knows some of them. Does it follow that he can't do anything about them?

This is tricky. I want to say: no, it doesn't follow that he can't act differently, only that he won't.

(Notice: we don't think that facts about the past destroy freedom. I went to class on Monday. It hardly follows that I couldn't have failed to go to class on Monday! But then why should we think that facts about the future destroy freedom? Why should the fact that I will go to class on Friday show that I must go to class on Friday?)

Last update: September 19, 2007
Curtis Brown | Metaphysics | Philosophy Department | Trinity University