Time Travel, Coincidences and Counterfactuals

Time Travel, Coincidences and Counterfactuals

Theodore Sider

1. Failures in autoinfanticide

Imagine you had a time machine. Nothing would stop you, it would seem, from using the time machine to go back in time and kill yourself as an infant, before you ever entered the time machine. Then a contradiction would be true: you would never have entered any time machine (since you were killed before doing so^[1]), and yet you would have entered a time machine (in order to travel back in time to kill yourself). Some conclude that time travel is impossible, since it would lead to a contradiction.

There is nothing particularly special about autoinfanticide. The same sort of problem arises whenever a time traveler resolves to go back in time and do something that did not in fact occur. A time traveler who remembers owning a 1974 Plymouth Gold Duster could, it would seem, go back into the past and prevent herself from ever owning such a fine automobile; a time traveler could, it would seem, go back and prevent Lincoln from giving the Gettysburg address, and so on. But autoinfanticide is a particularly vivid example.

As it stands, this argument is very weak. All it shows is that autoinfanticide is impossible (as are related scenarios, such as one in which an address is given, but in which someone travels back in time and prevents that address from being given.) But the impossibility of a certain kind of time-travel scenario does not impugn the possibility of time travel in general, any more than the existence of an impossible story about an empty box containing a figurine impugns the possibility of boxes.

We have admitted the possibility of time travel, though not the possibility of autoinfanticide. But these possible time travelers who do not kill their earlier selves: some have the desire as well as the means. What stops them?

No one thing. Some have a sudden change of heart. Some fear awful forces that would be unleashed by a violation of the laws of logic. Some attempt the deed but fail for various reasons: non-lethal wounds, slipping on banana peels, and the like. Others succeed in committing a murder, only to find they killed the wrong person. And, I suppose, there are possible worlds in which time travelers are shackled by gods or by other means that prevent them from doing mischief, though surely this is not required for time travel to occur.

But focus now on cases in which time travelers are not shackled in ways we do not take ourselves to be shackled. These time travelers would then have the ability to do the sorts of things we could do, in their circumstances. If I had a gun, had the evil desire to kill, and were suitably positioned in front of an unprotected victim, I would have the ability to kill that victim. So the time traveler, too, could kill her victim. But the time traveler’s victim is her earlier self, and surely the time traveler cannot kill her earlier self, since if she were to do that, contradictions would be true. Thus, this argument concludes, unless time travelers are strangely shackled by gods or whatnot, time travel is impossible. A time traveler both would have and would lack the ability to kill her earlier self.

Paul Horwich (1975) and David Lewis (1976) have defended time travel against this argument by objecting to the claim that the time traveler would not be able to kill her earlier self. Forget time travel for a moment and focus on ordinary cases of action. My having the ability to do A in a world, w, does not require that my doing A is consistent with every other fact about w. If I in fact will not do A, it is a fact about w that I will not do A (let us set aside philosophies of time according to which the future is “open”), but no one other than a fatalist thinks this undermines my ability to do A. For Lewis, one has the ability to do A in w if one’s doing A is consistent with the relevant facts about w (where what facts count as relevant varies according to the context of the speaker^[2]); the fact that the time traveler’s victim is in fact the time traveler herself is (typically) not a contextually relevant fact.

We have arrived at the following (familiar) position in the dialectical tree: despite the impossibility of autoinfanticide, time travel is possible. Moreover, though time travelers do not kill their earlier selves, they typically have the ability to do so. The goal of this paper is to present and then answer a challenge to this position. In an interesting thought experiment due to Horwich (1987, chapter 7; 1995), time travelers repeatedly go back in time with the goal of killing their former selves. Imagine a futuristic Institute for Autoinfanticide sending out legions of assassins. (Perhaps these assassins have been emboldened by the failures of repeated attempts on their lives in their childhoods and fear nothing, not even the rumored cataclysmic destruction of the world that would result from a violation of the laws of logic.) Since autoinfanticide is impossible, each assassin will fail. Presumably, some would have a change of heart, others would slip and fall on banana peels, yet others would kill the wrong target, and so on. But surely there is something odd about the idea that such “coincidences” would be guaranteed to happen, again and again!

There are, in fact, a few different arguments in the vicinity. But none, I think, succeeds in undermining the possibility or likelihood of time travel. The goal of this paper is to present and then rebut these arguments.

2. Why bother?

But before expending too much energy on the topic, it is worth thinking a bit about its point. Beyond the (perfectly legitimate) desire to set the record straight, is there any reason to care about time travel?

There is indeed. The most straightforward reason to care is that today’s physics community shows a substantial interest in time travel. Whether the actual laws of nature permit time travel is a live debate in contemporary physics journals (see Earman 1995). And whatever else metaphysicians must do, surely they must be prepared to at least try to make metaphysical sense out of what the physicists take seriously.

Secondly, time travel is tied up with larger issues in metaphysics and philosophy of science concerning the direction of time, causation, and so on. If time travel is indeed impossible, this limits the space of acceptable theories in these areas.

Finally, time travel is connected with important issues in the philosophy of persistence. I have argued elsewhere (forthcoming, chapter 4) that the possibility of time travel undermines “three-dimensionalism”, the view that objects persist over time by being “wholly present” or “enduring”, rather than by “perduring”, i.e., persisting by means of temporal parts.

3. The improbability of coincidences

Having resolved to care about time travel, let us consider various arguments that might be based on Horwich’s thought experiment. There is first the argument that Horwich himself advances (1987, chapter 7). Repeated attempts at autoinfanticide would lead to repeated “coincidental” failures — repeated slips on banana peels, failures of nerve, etc. But we have empirical reason to think that such repeated coincidences do not occur. We do notice the odd slip on a banana peel en route to a murder, but such slips are rare indeed. Surely we have strong inductive evidence against the existence of a rash of coincidences of this sort. So we have reason to think that time travel into the recent past does not occur.

At best, the argument establishes that we have defeasible reason to believe that time travel into the recent past does not actually occur. The argument concerns only the actual world because the evidence against coincidences is contingent; clearly strings of coincidences might have occurred. The argument provides only defeasible evidence because the evidence is inductive: the future existence of strings of coincidences is logically compatible with our present evidence. The argument does not even establish that we have reason to think that time travel is prohibited by the actual laws of nature; at any rate, a rash of coincidences would apparently not violate the laws of physics. Thus, the argument has little impact on the philosophical interest in time travel. For even if time travel is unlikely to occur in the actual world, if time travel is nevertheless possible — even, perhaps, physically possible — we have no right to ignore it while theorizing about the nature of persistence, time, causation, and so on. (This is no criticism of Horwich, who is not trying to undermine the possibility of time travel. Indeed, Horwich himself defends the possibility of time travel.^[3])

Moreover, the argument does not show that time travel per se is unlikely, for time travel might well occur without the formation of an Institute for Autoinfanticide. Large numbers of attempts at autoinfanticide and the like would result in large numbers of “coincidences”; but for all the argument shows, there might well be thousands of time travelers among us today, avoiding the banana peels and annoying pricks of conscience simply because they have no interest in “changing the past”. Alternatively, perhaps the advent of time travel is so far in the future that time travelers consider us ancient history not worth bothering with.

Moreover, the kinds of coincidences envisioned here seem to require persons traveling back in time with the intention of doing things inconsistent with what actually happened in the past (or at least persons directing large quantities of objects to travel back in time). Quantities of unthinking time-traveling particles from the future going about their random business would not be particularly likely to exhibit “coincidental” patterns noticeable to us. The more cynical might accept the conditional “if time travel will one day be possible then there now exist numerous time-traveling assassins hunting down their ancestors”. But an analogous conditional for electrons is implausible. Thus, Horwich’s argument at best concerns the likelihood of future persons traveling back in time.

Horwich acknowledges some of these limitations of his argument, but there is another limitation he does not acknowledge. I doubt our present evidence makes it unlikely that in the future we will encounter time travelers with attendant strings of “coincidences”, since the present absence of coincidences does not seem to be projectible.^[4] Suppose for the sake of argument that the actual laws of nature permit time travel. Then the lack of coincidences we have experienced so far would seem not to issue from any law of nature, but rather simply from the fact that no legion of assassins has descended upon the present time (either because time travel will never be discovered, or because no future Institute for Autoinfanticide has directed its attention upon our time.) Our current observation of an absence of coincidences does not warrant our postulating a law prohibiting them; it only requires our postulating a particular matter of fact, namely the absence of a legion of assassins descending upon the present time. But there is no reason to expect such a particular matter of fact to continue to obtain (absent independent evidence against the existence of time machines).

For all we have learned from the probabilistic argument, time travel might yet occur in our world. But let us leave the actual world to the physicists (for it is surely their province anyway), and return to the question of whether there are conceptual or metaphysical challenges to the very possibility of time travel. As noted, the probabilistic argument provides no such challenge. But further interesting challenges to time travel may be based on Horwich’s thought experiment.

4. Counterfactuals of coincidence

Imagine that time travel is indeed possible, and that The Corporate Board is contemplating the formation of an Institute for Autoinfanticide. In fact they decide against its formation. But what would have happened had the Institute been formed? It would seem that there would have been an incredible series of coincidences. Had the institute been formed, there would have been a long string of slips on banana peels, serendipitous changes of heart, and so on. We are all familiar with might-conditionals of this sort: if I had gotten up from the couch today, I might have tripped on a banana peel. But few of us think that in normal cases, would-conditionals of this sort are ever true. Unless one’s couch is surrounded by banana peels, garden rakes and hanging cymbals, counterfactuals of this sort seem false:

If I had gotten up from the couch, I would have encountered some “coincidental” disaster

All that is true is:

If I had gotten up from the couch, I might have encountered some “coincidental” disaster

One does has the feeling that “something funny is going on” after hearing time travel defended in the face of Horwich’s thought experiment. The following argument against the possibility of time travel makes precise one worry in the vicinity. If time travel were possible, then counterfactuals like the following would be true:

If many, many time travelers went back in time intending to kill their earlier selves, equipped with deadly weapons, hardened hearts and excellent information about their targets, there would be a long string of coincidences: slips on banana peels, sudden attacks of remorse, mistaken identities and so on.

But these “would-counterfactuals of coincidence” are never true. At best, “might-counterfactuals of coincidence” are true. Coincidences are not things that would happen; they are things that might happen. Therefore, time travel is impossible.

5. Counterfactuals of coincidence and freedom

Rather than basing an argument against time travel on the claim that would-counterfactuals of coincidence are never true, one might instead use those counterfactuals to undermine the alleged ability or freedom of the time traveler to kill her infant self.^[5] Kadri Vihvelin (1996) in effect does just this. She argues that if S has the ability to do A, then it must be the case that if S were to try to do A, S would or at least might succeed. If it is the case that S would fail — repeatedly! — if S were to try to do A, then S does not in fact have the ability to do A. Given Vihvelin’s principle, would-counterfactuals of coincidence would undermine the freedom of time travelers to kill their former selves, for if those time travelers attempted autoinfanticide, they would fail.

One might press the argument further, as an argument against the possibility of time travel, at least in cases where the time traveler has no strange shackles that restrict her activity. For surely, one might argue, absent any such strange shackles, a time-traveler with the means and inclination could kill her former self; what would be stopping her? Thus, such a time traveler both could and could not kill her former self. The only escape from this contradiction, so the argument runs, is to reject the possibility of time travel, or to argue that time travel essentially requires strange shackles on the time traveler. Vihvelin herself does not draw this conclusion, but it is hard to see why. Once the inability of the time traveler to kill her former self is admitted, one faces the question: what is preventing her from doing so?

6. Coincidences and freedom

A final argument would be that the repeated slips on banana peels are too predictable and regular to be coincidences. It must be that the slips are caused in some way by the fact that the would-be assassins are time travelers. But if that’s so, then again we have a challenge to the freedom of the time-travelers. Of course, this is no threat to the possibility of time travel itself, for one can always spin a time-travel yarn with a convenient guardian of logic, who is ready to cause slips on banana peels when inconsistency threatens. But the argument nevertheless threatens those of us who think that time travel is possible without such shackles on time travelers. It moreover threatens the possibility of time travel in worlds like our own, in which any time travelers would presumably be unshackled.

7. A closer look at counterfactuals of coincidence

In fact, each of these arguments may be rebutted. I begin with the argument of section 4, that would-counterfactuals of coincidence are never true. Let us leave time travel for the moment and consider a more mundane case. Suppose I were to attempt to throw a heavy stone at a fragile window. Since I have good aim and a strong arm, the window would break. It is possible, I suppose, that I might slip on a banana peel, or that the rock might hit a bird passing by, or that a great gust of wind might divert the stone, or that my many years of training in stone-throwing might suddenly fail me. But at the very least, it surely is not the case that one of these strange coincidences would happen. The would-counterfactual of coincidence:

If I were to try to throw the stone at the window, I would slip on a banana peel or the rock would hit a passing bird or . . .

is false.

But now let us consider a different counterfactual:

(C) If I were to try to throw the stone at the window but the window did not subsequently break, then I would slip on a banana peel or the rock would hit a passing bird or . . .

Here I have built my failure into the antecedent; the counterfactual concerns what would have happened had I tried and failed. Here, I think, our sense is that the counterfactual is now true. Given the background facts, the only way for me to fail to hit the window would be for some strange coincidence to occur. Though most ordinary would-counterfactuals of coincidence are false, some are true, namely those whose antecedents describe circumstances that could only come about by an “unlikely coincidence”. We can think of the antecedents of these conditionals as describing states of affairs that embed a certain “tension”, states of affairs that are “difficult” to make true. To include such a state of affairs, a possible world must include some strange coincidence. (Or something even stranger, for example in the case considered above, a lurking guardian of the window ready to spring out and intercept the rock. Since no such guardian is present in the actual world, surely such a guardian would not exist had I thrown the rock.)

The important point here is that we should all agree that there are true would-counterfactuals of coincidence like (C) whose antecedents “embed tension” in this way. But in fact, the counterfactuals in the time travel case share the same feature. We ask what would have happened if a time traveler had tried to kill her earlier self. If the time traveler is in fact a capable assassin and has the appropriate resolve and information, then making this antecedent true is very “difficult” — it is hard to find a non-coincidental reason why the time traveler would fail. And yet there is no possible world in which the time traveler successfully kills her earlier self. Thus, the would-counterfactual of coincidence:

If a certain time traveler had tried to kill her earlier self, she would have slipped on a banana peel or had a sudden change of heart or . . .

looks a lot like (C). But we admitted that (C) is true. We should say the same thing about this counterfactual. Coincidences would have happened, in the right circumstances.

The same can be said for counterfactuals concerning repeated attempts at auto-infanticide:

These counterfactuals are true as well; their truth is no more remarkable than that of (C). Here the coincidences described in the consequent are even more “unlikely” than those in the case of an individual assassin. But this is what one should expect, since the antecedent here describes a state of affairs that is more difficult to make true than the antecedent in the single-assassin case. This same phenomenon may be observed in uncontroversial cases. If one “loads” the antecedent of (C) thus:

If I were to try to throw the stone at the window and the window did not break as a result, and there existed no banana peels in the entire world, and there existed no birds, and I were the deadliest rock-thrower in the world, then . . .

then to get a true counterfactual, the consequent will need to become even wilder:

. . . then a random quantum-event would have caused the rock to explode or I would have been struck by lightening or . . .

The antecedents of these counterfactuals concerning time travel in a sense “have their difficulty built-in”. The first begins “If a certain time traveler had tried to kill her earlier self”; one can tell just from looking at this sentence that a world in which it is true will contain an odd, “coincidental” event. But we might instead consider counterfactuals like this:

(T) If Tina had tried to kill the little girl standing in front of her at t, she would have slipped on a banana peel or had a sudden change of heart or . . .

where Tina is the time traveler in question, and where the little girl standing in front of her at t is in fact her earlier self. Such counterfactuals are not quite so parallel to those concerning throwing the stone at the window, since the latter also “have their difficulty built-in”. Nevertheless, the truth of (T) may still be explained in the same way. Let us assume the Lewis-Stalnaker theory of counterfactual conditionals, according to which, roughly, “If P had been the case then Q would have been the case” is true at w iff the possible world most similar to w in which P is true is a world in which Q is true.^[6] Here the relevant similarity relation is one determined in part by the conversational context of the speaker, and may weight contextually salient factors more heavily than others. In the context in which (T) seems true, we are holding constant the fact that Tina is a time traveler, and the fact that the little girl standing in front of her at t is in fact Tina herself. So in this context, the counterfactual is a lot like (C), in containing an antecedent that is very “difficult” to make true in worlds similar to the actual world, given that in all those worlds Tina is a time traveler and attempting to kill her earlier self. (T)’s truth is therefore no more surprising than (C)’s.

8. Selective attention

The truth of certain would-counterfactuals of coincidence in cases of time travel has been defended. But what of their connection with freedom? How can the members of the Institute for Autoinfanticide be said to be free of unusual constraints during time travel, when if they were to attempt to kill their former selves they would repeatedly fail?

Let us again examine an analogous case having nothing to do with time travel.^[7] Suppose we define a permanent bachelor as a person who never gets married. When we survey the class of permanent bachelors across the space of all possible worlds, we find them failing to get married for a variety of reasons. Some never have the inclination, others wish to be married but never find a suitable partner, others slip on banana peels and fatally injure themselves while walking down the aisle, and so on. No anti-nuptial force need be postulated to account for this: by our definition of ‘permanent bachelor’ we selectively attend to a certain class of possible individuals when we ask for the class of permanent bachelors. Many of these permanent bachelors could have gotten married. No force stands in their way; had they gotten married, they would no longer have counted as permanent bachelors.

The example may be brought a step closer to relevance by considering certain counterfactuals.

For all x, if it had been the case that (x is a permanent bachelor who attempts to get married), it would have been the case that: (x would have slipped on a banana peel and died, or had a bad case of cold feet, or . . .)

or even:

For any series of persons, x₁, x₂, . . ., if it had been the case that (x₁, x₂, . . . are all permanent bachelors that attempt to get married), then it would have been the case that (each would have slipped on a banana peel and died, or gotten a bad case of cold feet, or . . .)

Properly filled in, these (universally quantified) would-counterfactuals of coincidence may well be true, since their antecedents are so difficult to make true that the only way they could be true is for some rather odd coincidence, or series of coincidences, to occur.

But now let us ask whether these would-counterfactuals of coincidence undermine the freedom of the permanent bachelors. Clearly, they do not. Their truth simply issues from selective attention on our part. Given our definition of ‘permanent bachelor’, we do not count as a permanent bachelor anyone who succeeds in marrying; we therefore ignore all possible individuals that marry. The class of individuals that remain under our scrutiny then contains a disproportionate number of individuals to whom “coincidental” things occur. But these individuals need not be subject to extraordinary constraints. The “coincidences” that prevent their marriages might be just that — coincidences. And we do not count coincidences of this sort as undermining a person’s freedom. If a person accidentally slips and falls on his way to the pulpit, we do not regard him as incapable of marriage.

Of course, after repeated mishaps, onlookers might begin to doubt that the mishaps are merely coincidental. The person himself might well come to suspect that the obstacles he repeatedly encounters have some common cause, a cause that undermines his freedom to marry. (This hypothesis might suggest itself after, say, the fifteenth lightning bolt eliminates yet another nervous bride.) Such suspicions might even be reasonable. But they would be wrong. Logical space does, after all, contain persons to whom repeated coincidences occur. By defining ‘permanent bachelor’ as we did, we single out these unfortunates for attention. Of course, some permanent bachelors are in the grips of social, psychological, or supernatural pressures rendering them incapable of marriage. Others lack the desire. But those in a third group fail to get married through mishap or coincidence.

In thinking about the freedom of permanent bachelors, we ought to distinguish between two sorts of claim. First, consider a permanent bachelor who decides never to marry. Let this person be a perfectly ordinary, actual, permanent bachelor with no extraordinary social or psychological impediments to marriage. We clearly want to say this person could have gotten married, despite the truth of counterfactuals like: “if this person had been a permanent bachelor, and had tried to get married, he would have slipped on a banana peel or . . .”. The actual freedom to get married is claimed, and his counterfactual failure (under the description ‘permanent bachelor’) is irrelevant to this claim. Contrast this with a claim of counterfactual freedom. One might claim also that, had this person been a permanent bachelor and tried to get married, he would have failed in one of a number of “coincidental ways”, but would nevertheless have been free. Here one is claiming the permanent bachelor has counterfactual freedom, despite counterfactual failure. This claim of freedom would also be true, I think (though it is worth distinguishing from the first claim.) As argued above, cases in which permanent bachelors try and fail to get married include cases of “coincidental failure” of a kind with cases with which we are familiar. Some people really do slip on banana peels on their way to the altar. Such slips involve bad luck, but no failure of freedom. The appearance to the contrary is due to neglecting the role of selective attention in the truth of would-counterfactuals of coincidence.

9. Selective attention and time-travel

The final argument against the possibility of time travel (section 6) was that the numerous mishaps faced by time travelers attempting autoinfanticide just couldn’t be coincidences. They must in some way be causally linked to the fact that the would-be assassins are time travelers. But then, those assassins are shackled in an inexplicable and implausible way.

In light of our remarks on selective attention, the argument loses its force. The many mishaps facing the class of permanent bachelors require no explanation beyond the fact that we delineated the class with our notion of a permanent bachelor. The class of possible worlds containing time travelers who repeatedly attempt autoinfanticide is similar. We have placed two constraints on this class of worlds that are very difficult to jointly satisfy. The first requires the worlds to contain large numbers of persons who want to kill certain other persons, have the means and the desire to do so, and so on. The second constraint is that the first class consists of time travelers and the second class their former selves. This in effect requires that these persons fail in their missions. We thereby selectively attend to a class of worlds that must contain large numbers of “coincidental failures”. This need not be explained by some force compelling failure. We have delineated the class of worlds so that it contains the failures; the failures can still be genuine coincidences. The freedom of the time travelers need not be compromised.

It may help here to remember that logical space contains many worlds with segments that are qualitatively like cases in which time travelers confront their former selves. In some, the murderer succeeds, and in some she fails. Whether a given segment is embedded in a world in which the would-be murderer counts as the later self of the victim determines the inclusion of the segment in the class of worlds to which we have selectively confined our attention, in discussion of time travel and autoinfanticide.

The other argument against the possibility of time travel (section 5) was that the freedom of time travelers is undermined by the truth of would-counterfactuals of coincidence. The argument appealed to Vihvelin’s principle that a person is genuinely free to do a certain thing only if it is true that if she tried to do the thing, she would or at least might succeed. This argument, too, is undermined by the phenomenon of selective attention. The truth of counterfactuals like these:

was argued to undermine neither the freedom of actual permanent bachelors, nor the counterfactual freedom of permanent bachelors in worlds in which they attempt and fail to get married. Likewise, the truth of counterfactuals like:

undermines neither the freedom of time travelers who do not go back in time to kill their earlier selves, nor the freedom of those that do. The slips on banana peels and other mishaps are genuine coincidences; the fact that they would occur, were attempts at autoinfanticide made, is simply due to our selective attention in the antecedent of the counterfactual to a certain class of worlds in which failure has been definitionally guaranteed.

10. Conclusion

So time travel escapes again, unscathed. If many time travelers attempted autoinfanticide, an apparently miraculous series of coincidences would ensue. But this fact is unremarkable, and in no way undermines time travelers’ freedom. As comparison with uncontroversial cases has shown, it is the result of the description “time traveler who attempts autoinfanticide” focusing our attention on a certain class of possible worlds, a class of worlds that is guaranteed, by definition, to include large numbers of what we consider highly improbable coincidences.^[8]

Theodore Sider

Syracuse University

References

Earman, John. 1995. “Recent Work on Time Travel”, in S. Savitt, ed., Time’s Arrows Today: Recent Physical and Philosophical Work on the Direction of Time (Cambridge: Cambridge University Press): pp. 268-324.

Horwich, Paul. 1995. “Closed Causal Chains”, in S. Savitt, ed., Time’s Arrows Today (Cambridge: Cambridge University Press), pp. 259-267.

Horwich, Paul. 1987. Asymmetries in Time: Problems in the Philosophy of Science. (Cambridge, MA: MIT press).

Horwich, Paul. 1975. “On Some Alleged Paradoxes of Time Travel”, Journal of Philosophy 72: 432‑444.

Lewis, David. 1976. “The Paradoxes of Time Travel”, American Philosophical Quarterly 13: 145-152.

Lewis, David. 1973. Counterfactuals. (Cambridge, MA: Harvard University Press).

Sider, Theodore. Forthcoming. Four-Dimensionalism: An Ontology of Persistence and Time. (Oxford: Clarendon Press).

Sider, Theodore. 2000. “Simply Possible”, Philosophy and Phenomenological Research 60: 585-590.

Smith, Nicholas J. J. 1997. “Bananas enough for Time Travel”, British Journal for the Philosophy of Science 48: 363-389.

Stalnaker, Robert. 1968. “A Theory of Conditionals”, in N. Rescher, ed., Studies in Logical Theory (Oxford: Blackwell).

Vihvelin, Kadri. 1996. “What Time Travelers Cannot Do”, Philosophical Studies 81: 315-330.

^[1] Let “killing” be understood throughout as implying permanent death.

^[2] Lewis uses the contextual relativity of ‘can’ to explain why the argument that a time traveler cannot kill her earlier self is so seductive.

^[5] I thank Europa Malynicz for drawing my attention to this argument.

^[7] I put this case to different use in Sider 2000.

^[8] I would like to thank David Braun, Earl Conee, Tamar Szabó Gendler, Europa Malynicz and Brian Weatherson for helpful comments.