The Paradox of Time-Travelling

Consider Tim. He detests his grandfather, whose suc-

cess in the munitions trade built the family fortune that

paid for Tim’s time machine. Tim would like nothing so

much as to kill Grandfather, but alas he is too late.

Grandfather died in his bed in 1957, while Tim was a

young boy. But when Tim has built his time machine and

traveled to 1920, suddenly he realizes that he is not too

late after all. He buys a rifle; he spends long hours in

target practice; he shadows Grandfather to learn the

route of his daily walk to the munitions works; he rents

a room along the route; and there he lurks, one winter

day in 1921, rifle loaded, hate in his heart, as Grandfather

walks closer, closer,. . . .

Tim can kill Grandfather. He has what it takes. Con-

ditions are perfect in every way: the best rifle money

could buy, Grandfather an easy target only twenty yards

away, not a breeze, door securely locked against intrud-

ers. Tim a good shot to begin with and now at the peak

of training, and so on. What’s to stop him? The forces

of logic will not stay his hand! No powerful chaperone

stands by to defend the past from interference. (To imag-

ine such a chaperone, as some authors do, is a boring

evasion, not needed to make Tim’s story consistent.) In

short, Tim is as much able to kill Grandfather as anyone

ever is to kill anyone. Suppose that down the street an-

other sniper, Tom, lurks waiting for another victim,

Grandfather’s partner. Tom is not a time traveler, but oth-

erwise he is just like Tim: same make of rifle, same mur-

derous intent, same everything. We can even suppose

that Tom, like Tim, believes himself to be a time traveler.

Someone has gone to a lot of trouble to deceive Tom into

thinking so. There’s no doubt that Tom can kill his vic-

tim; and Tim has everything going for him that Tom does. By any ordinary standards of ability, Tim can kill

Grandfather.

Tim cannot kill Grandfather. Grandfather lived, so to kill

him would be to change the past. But the events of a past

moment are not subdivisible into temporal parts and there-

fore cannot change. Either the events of 1921 timelessly

do include Tim’s killing of Grandfather, or else they

timelessly don’t. We may be tempted to speak of the

“original” 1921 that lies in Tim’s personal past, many

years before his birth, in which Grandfather lived; and

of the “new” 1921 in which Tim now finds himself wait-

ing in ambush to kill Grandfather. But if we do speak

so, we merely confer two names on one thing. The events

of 1921 are doubly located in Tim’s (extended) personal

time, like the trestle on the railway, but the “original” 1921

and the “new” 1921 are one and the same. If Tim did not

kill Grandfather in the “original” 1921, then if he does kill

Grandfather in the “new” 1921, he must both kill and not

kill Grandfather in 1921—in the one and only 1921, which

is both the “new” and the “original” 1921. It is logically

impossible that Tim should change the past by killing

Grandfather in 1921. So Tim cannot kill Grandfather.

Not that past moments are special; no more can any-

one change the present or the future. Present and future

momentary events no more have temporal parts than

past ones do. You cannot change a present or future

event from what it was originally to what it is after you

change it. What you can do is to change the present or

the future from the unactualized way they would have

been without some action of yours to the way they ac-

tually are. But that is not an actual change: not a differ-

ence between two successive actualities. And Tim can

certainly do as much; he changes the past from the un-

actualized way it would have been without him to the

one and only way it actually is. To “change” the past in

this way, Tim need not do anything momentous; it is

enough just to be there, however unobtrusively.

You know, of course, roughly how the story of Tim

must go on if it is to be consistent: he somehow fails.

Since Tim didn’t kill Grandfather in the “original” 1921,

consistency demands that neither does he kill Grandfa-

ther in the “new” 1921. Why not? For some common-

place reason. Perhaps some noise distracts him at the last

moment, perhaps he misses despite all his target practice,

perhaps his nerve fails, perhaps he even feels a pang of

unaccustomed mercy. His failure by no means proves

that he was not really able to kill Grandfather. We often

try and fail to do what we are able to do. Success at

some tasks requires not only ability but also luck, and

lack of luck is not a temporary lack of ability. Suppose

our other sniper, Tom, fails to kill Grandfather’s partner

for the same reason, whatever it is, that Tim fails to kill

Grandfather. It does not follow that Tom was unable to.

No more does it follow in Tim’s case that he was unable

to do what he did not succeed in doing.

We have this seeming contradiction: “Tim doesn’t, but

can, because he has what it takes” versus “Tim doesn’t, and can’t, because it’s logically impossible to change the past.” I

reply that there is no contradiction. Both conclusions are

true, and for the reasons given. They are compatible be-

cause “can” is equivocal.

To say that something can happen means that its hap-

pening is compossible with certain facts. Which facts?

That is determined, but sometimes not determined well

enough, by context. An ape can’t speak a human lan-

guage—say, Finnish—but I can. Facts about the anatomy

and operation of the ape’s larynx and nervous system

are not compossible with his speaking Finnish. The cor-

responding facts about my larynx and nervous system

are compossible with my speaking Finnish. But don’t

take me along to Helsinki as your interpreter: I can’t

speak Finnish. My speaking Finnish is compossible with

the facts considered so far, but not with further facts

about my lack of training. What I can do, relative to one

set of facts, I cannot do, relative to another, more inclu-

sive, set. Whenever the context leaves it open which facts

are to count as relevant, it is possible to equivocate about

whether I can speak Finnish. It is likewise possible to

equivocate about whether it is possible for me to speak

Finnish, or whether I am able to, or whether I have the

ability or capacity or power or potentiality to. Our many

words for much the same thing are little help since they

do not seem to correspond to different fixed delineations

of the relevant facts.

Tim’s killing Grandfather that day in 1921 is compos-

sible with a fairly rich set of facts: the facts about his

rifle, his skill and training, the unobstructed line of fire,

the locked door and the absence of any chaperone to

defend the past, and so on. Indeed it is compossible with

all the facts of the sorts we would ordinarily count as

relevant is saying what someone can do. It is compossi-

ble with all the facts corresponding to those we deem

relevant in Tom’s case. Relative to these facts, Tim can

kill Grandfather. But his killing Grandfather is not com-

possible with another, more inclusive set of facts. There

is the simple fact that Grandfather was not killed. Also

there are various other facts about Grandfather’s doings

after 1921 and their effects: Grandfather begat Father in

1922 and Father begat Tim in 1949. Relative to these facts,

Tim cannot kill Grandfather. He can and he can’t, but

under different delineations of the relevant facts. You

can reasonably choose the narrower delineation, and

say that he can; or the wider delineation, and say that

he can’t. But choose. What you mustn’t do is waver,

say in the same breath that he both can and can’t, and

then claim that this contradiction proves that time

travel is impossible.

Exactly the same goes for Tom’s parallel failure. For

Tom to kill Grandfather’s partner also is compossible

with all facts of the sorts we ordinarily count as relevant,

but not compossible with a larger set including, for in-

stance, the fact that the intended victim lived until 1934.

In Tom’s case we are not puzzled. We say without hesi-

tation that he can do it, because we see at once that the facts that are not compossible with his success are facts

about the future of the time in question and therefore

not the sort of facts we count as relevant in saying what

Tom can do.

In Tim’s case it is harder to keep track of which facts

are relevant. We are accustomed to exclude facts about

the future of the time in question, but to include some

facts about its past. Our standards do not apply un-

equivocally to the crucial facts in this special case: Tim’s

failure, Grandfather’s survival, and his subsequent do-

ings. If we have foremost in mind that they lie in the

external future of that moment in 1921 when Tim is al-

most ready to shoot, then we exclude them just as we

exclude the parallel facts in Tom’s case. But if we have

foremost in mind that they precede that moment in Tim’s

extended personal time, then we tend to include them.

To make the latter be foremost in your mind, I chose to

tell Tim’s story in the order of his personal time, rather

than in the order of external time. The fact of Grandfa-

ther’s survival until 1957 had already been told before I

got to the part of the story about Tim lurking in ambush

to kill him in 1921. We must decide, if we can, whether

to treat these personally past and externally future facts

as if they were straightforwardly past or as if they were

straightforwardly future.

Fatalists—the best of them—are philosophers who

take facts we count as irrelevant in saying what someone

can do, disguise them somehow as facts of a different

sort that we count as relevant, and thereby argue that

we can do less than we think—indeed, that there is noth-

ing at all that we don’t do but can. I am not going to

vote Republican next fall. The fatalist argues that, strange

to say, I not only won’t but can’t; for my voting Repub-

lican is not compossible with the fact that it was true

already in the year 1548 that I was not going to vote

Republican 428 years later. My rejoinder is that this is

a fact, sure enough; however, it is an irrelevant fact

about the future masquerading as a relevant fact about

the past, and so should be left out of account in saying

what, in any ordinary sense, I can do. We are unlikely

to be fooled by the fatalist’s methods of disguise in

this case, or other ordinary cases. But in cases of time

travel, precognition, or the like, we’re on less familiar

ground, so it may take less of a disguise to fool us.

Also, new methods of disguise are available, thanks to

the device of personal time.

Here’s another bit of fatalist trickery. Tim, as he lurks,

already knows that he will fail. At least he has the where-

withal to know it if he thinks, he knows it implicitly. For

he remembers that Grandfather was alive when he was

a boy, he knows that those who are killed are thereafter

not alive, he knows (let us suppose) that he is a time

traveler who has reached the same 1921 that lies in his

personal past, and he ought to understand—as we do—

why a time traveler cannot change the past. What is

known cannot be false. So his success is not only not

compossible with facts that belong to the external future and his personal past, but also is not compossible with

the present fact of his knowledge that he will fail. I

reply that the fact of his foreknowledge, at the moment

while he waits to shoot, is not a fact entirely about that

moment. It may be divided into two parts. There is the fact

that he then believes (perhaps only implicitly) that he will

fail; and there is the further fact that his belief is correct,

and correct not at all by accident, and hence qualifies as

an item of knowledge. It is only the latter fact that is not

compossible with his success, but it is only the former

that is entirely about the moment in question. In calling

Tim’s state at that moment knowledge, not just belief,

facts about personally earlier but externally later moments

were smuggled into consideration.

I have argued that Tim’s case and Tom’s are alike, ex-

cept that in Tim’s case we are more tempted than usual—

and with reason—to opt for a semi-fatalist mode of

speech. But perhaps they differ in another way. In Tom’s

case, we can expect a perfectly consistent answer to the

counterfactual question: what if Tom had killed Grand-

father’s partner? Tim’s case is more difficult. If Tim had

killed Grandfather, it seems offhand that contradictions

would have been true. The killing both would and

wouldn’t have occurred. No Grandfather, no Father; no

Father, no Tim; no Tim, no killing. And for good measure:

no Grandfather, no family fortune; no fortune, no time

machine; no time machine, no killing. So the supposition

that Tim killed Grandfather seems impossible in more

than the semi-fatalistic sense already granted.

If you suppose Tim to kill Grandfather and hold all

the rest of his story fixed, of course you get a contradic-

tion. But likewise if you suppose Tom to kill Grandfa-

ther’s partner and hold the rest of his story

fixed—including the part that told of his failure—you

get a contradiction. If you make any counterfactual sup-

position and hold all else fixed you get a contradiction.

The thing to do is rather to make the counterfactual sup-

position and hold all else as close to fixed as you con-

sistently can. That procedure will yield perfectly

consistent answers to the question: what if Tim had not

killed Grandfather? In that case, some of the story I told

would not have been true. Perhaps Tim might have been

the time-traveling grandson of someone else. Perhaps he

might have been the grandson of a man killed in 1921

and miraculously resurrected. Perhaps he might have

been not a time traveler at all, but rather someone cre-

ated out of nothing in 1920 equipped with false memo-

ries of a personal past that never was. It is hard to say

what is the least revision of Tim’s story to make it true

that Tim kills Grandfather, but certainly the contradictory

story in which the killing both does and doesn’t occur

is not the least revision. Hence it is false (according to

the unrevised story) that if Tim had killed Grandfather

then contradictions would have been true.

What difference would it make if Tim travels in

branching time? Suppose that at the possible world of

Tim’s story the space-time manifold branches; the branches are separated not in time, and not in space, but

in some other way. Tim travels not only in time but also

from one branch to another. In one branch Tim is absent

from the events of 1921; Grandfather lives; Tim is born,

grows up, and vanishes in his time machine. The other

branch diverges from the first when Tim turns up in

1920; there Tim kills Grandfather and Grandfather leaves

no descendants and no fortune; the events of the two

branches differ more and more from that time on. Cer-

tainly this is a consistent story; it is a story in which

Grandfather both is and isn’t killed in 1921 (in the dif-

ferent branches); and it is a story in which Tim, by killing

Grandfather, succeeds in preventing his own birth (in

one of the branches). But it is not a story in which Tim’s

killing of Grandfather both does occur and doesn’t: it

simply does, though it is located in one branch and not

the other. And it is not a story in which Tim changes the

past. 1921 and later years contain the events of both

branches, coexisting somehow without interaction. It re-

mains true at all the personal times of Tim’s life, even

after the killing, that Grandfather lives in one branch and

dies in the other.