In "The Paradoxes of Time Travel," 1 David Lewis defends the possibility of time travel against some of the apparent paradoxes that time travel stories seem to generate. The most serious of these is the grandfather paradox.
Consider Tim. He detests his grandfather, whose success in the munitions business 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, . . . . (141)
Lewis maintains that Tim can kill Grandfather, for Tim "has what it takes": Tim's rifle is in working condition, Tim has good aim, and Grandfather is an easy target. Furthermore, Lewis maintains, because of the way the word 'can' works, no paradox arises. I shall argue that nevertheless Tim cannot kill Grandfather in any ordinary sense of 'can': not because Tim cannot alter the past, for I concede that he can do that; but because there are certain essential facts about Tim that cannot be changed. To be more precise, I shall argue that if a doctrine I shall call "origins essentialism" is correct, then either time travelers can do the impossible, or there are certain deeds that a time traveler cannot succeed in performing that could be performed by one in similar circumstances but who is not a time traveler. Since I think that origins essentialism is correct, and I also think that no one can do the impossible (although I shall argue for neither of these doctrines), I conclude that there are things a time traveler cannot do that could be performed by one in similar circumstances who is not a time traveler. As we shall see, this does not bode well for the possibility of time travel more than a certain "distance" into the past.
The first point to note is that Lewis is concerned with the possibility of time travel in a "classical" world with one-dimensional, linear time, not in a world with branching time or a number of parallel time lines that the time traveler may travel between, such as that described by David Deutch and Michael Lockwood in a recent Scientific American article. 2 In a classical world, either Grandfather is killed in 1921 or he is not. We already know that he survives until 1957, so (unless he is miraculously resurrected somehow 3) we also know that he is not killed in 1921 by Tim. It is as if we have "read the end of the story first," and thereby know what is going to happen (or not going to happen) in the middle chapters. Tim will somehow miss despite all his training, or will have a last minute change of heart. The apparent paradox is not that Tim kills Grandfather in 1921 and Grandfather survives until 1957: this is a genuine contradiction, and is of course impossible. The apparent paradox is that Tim can kill Grandfather, for he "has what it takes," viz. a loaded rifle and skill; but we also want to say, intuitively, that Tim cannot kill Grandfather.
It is also important to note that Lewis insists that this paradox is resolvable without resort to any "metaphysical chaperon," something waiting in the wings to make sure that Tim doesn't unduly interfere with history. No magical shield would spring up to protect Grandfather to protect him if Tim were to fire the rifle; the guardians of history wouldn't whisk Tim away just before he pulls the trigger. For if there were such a metaphysical chaperon, it would not be true to say that Tim can kill Grandfather. In such a case, Tim would not have "what it takes."
What is our motivation for our saying that Tim cannot kill Grandfather? It cannot be merely our knowledge that Tim will not shoot Grandfather, for knowledge that S will do A does not entail that S cannot refrain from doing A. I know that I will get up before noon tomorrow, and so do many people who are acquainted with me, for I have an excessive amount of work to do tomorrow, and I don't sleep late when I have work to do. It doesn't follow from this knowledge, my own or that of others, that I cannot refrain from getting up tomorrow morning. The reasoning, rather, seems to be the following; if Tim were to kill Grandfather, then Father would not be born; if Father were not born, then Tim would not be born; and if Tim were not born, then Tim would not travel back in time and kill Grandfather. Or: if Tim were to shoot Grandfather, then there would be no family fortune; if there were no family fortune, there would be no time machine; if there were no time machine, then Tim would not travel back in time and kill Grandfather. Either route seems to take us to the conclusion that if Tim were to kill Grandfather, then Tim would not kill Grandfather, a seeming reductio ad absurdum of the proposition that Tim can shoot Grandfather. For whenever we say that a person can do something, we must be able to describe the counter-factual situation in which she does do it. And if this line of reasoning is correct, then we cannot describe this situation without contradicting ourselves.
The hypothetical syllogism used to arrive at the seeming _reductio_ , however, is not a valid form for arguments involving counterfactual conditionals. Consider the following example, due to Robert Stalnaker: if Hoover had been a Communist, he would have been a traitor; if Hoover had been a Russian, he would have been a Communist; therefore, if Hoover had been a Russian, he would have been a traitor. Both of the premises of this hypothetical syllogism are true, but the conclusion is false: if Hoover had been a Russian, he would have been a patriotic Soviet citizen, no doubt, and probably the head of the KGB. Since the premises are true, but the conclusion false, this cannot be a valid argument. Similarly with the above arguments to the conclusion that if Tim were to kill Grandfather, then Tim would not kill Grandfather. Since it is not a valid argument, Lewis is free to grant the premisses but deny the conclusion. What would be the case if Tim were to kill Grandfather? "Perhaps Tim might have been the time-traveling grandson of someone else. . . ." Perhaps he might not have been a time traveler at all, but rather someone created out of nothing in 1920 equipped false memories of a personal past that never was" (146). Neither of these situations is contradictory, so it seems that the reductio has been defused.
Perhaps, however, the reasoning to the conclusion that Tim cannot kill Grandfather is much simpler than that. There is no possible world in which Tim kills Grandfather (permanently, before he has any offspring) and in which Tim is Grandfather's grandson. We might say that Tim's killing Grandfather is not compossible with Tim's being Grandfather's grandson. So given that Tim is Grandfather's grandson, Tim cannot kill Grandfather. Lewis is perfectly willing to grant this, as it is stated: "Given that. . . ." Given that Tim is Grandfather's grandson, Tim cannot kill Grandfather. But it is also true to say that Tim can kill Grandfather, when we are "given" only that Tim has a loaded rifle, has a good aim, and an intent to kill.
Lewis resolves this apparent paradox by pointing out the contextual dependence of statements involving ability, e.g. ones involving the word 'can'. Lewis gives the following example to illustrate this (143). Monkeys can't speak any human language, e.g. Finnish, for their vocal apparatus and cognitive development do not allow them to do so. But Lewis is a human being, so he can speak Finnish. But it would be useless to take Lewis along as an interpreter on a trip to Helsinki, because Lewis can't speak Finnish. It appears both that Lewis can speak Finnish, and he cannot speak Finnish. The apparent contradiction is resolved when one notes that the two statements, 'Lewis can speak Finnish' and 'Lewis cannot speak Finnish' are true in different contexts. When we have in mind only facts about the vocal apparatus and cognitive abilities of human beings, it is true to say that Lewis can speak Finnish. When we take into account facts about Lewis's educational background, it is true to say that Lewis cannot speak Finnish. "To say that something can happen is to say that its happening is compossible with certain facts. Which facts? That is determined, but sometimes not well enough, by context." (143)
A similar resolution applies to the case of Tim's killing Grandfather. When we are considering only Tim's state of being in 1921, his holding a loaded rifle, his skill, and his murderous intent, it is correct to say that he can kill Grandfather. When we "smuggle in" facts about the future, including the fact that Tim is descended from Grandfather, we tend to say that Tim cannot kill Grandfather. Lewis notes that the argument from 'Tim's killing Grandfather is not compossible with his being Grandfather's grandson' to 'Tim cannot kill Grandfather' is the same sort of move used in the fallacious arguments for fatalism. "Either you will be kill yourself tomorrow or you won't," the fatalist begins. "If it is true that you will kill yourself tomorrow, then it is not compossible with this fact that you will not kill yourself. Therefore, if you will kill yourself, you cannot refrain from doing so. If it is true that you will not kill yourself, then it is not compossible with this fact that you do so; therefore, you cannot kill yourself. Whatever you kill yourself or not, this is not a course of action from which you can refrain." This reasoning is clearly invalid in the fatalism argument, but we are likely to be misled by it in the argument that Tim cannot kill Grandfather. Normally, we discount certain future facts as irrelevant to the determination of the truth of ability statements. But in Tim's case, these future facts, such as the fact that Grandfather lives until 1957, come disguised as statements about Tim's personal past. Nevertheless, they are irrelevant to ordinary determinations of Tim's abilities, just as true statements about what I will do tomorrow are relevant to the determination of what I can do tomorrow.
Lewis is surely right that certain facts about the future (Tim's personal past) are irrelevant to the determination of Tim's abilities. Suppose that Tim also hates Grandfather's business partner, Jones, whom Tim met as a child, and suppose that Jones always accompanies Grandfather on his daily walk to the munitions works. Tim's killing Jones is not compossible with Tim's having met him as a child, but it does not follow that Tim cannot kill Jones, for he can: Tim "has what it takes." What does follow is that Tim does not kill Jones, and that if he had killed Jones, he would not have met him as a child. Tim can kill Jones, but, I maintain, he cannot kill Grandfather, for this would involve an impossibility.
In light of Saul Kripke's Naming and Necessity, 4 many philosophers have come back around to essentialism, the view that at least some entities have essential properties of a non-trivial sort. 5 A property F is an essential property of an entity x if and only if x could not cease to have F and continue to exist, and any entity y (in any possible world) not having F is not identical to x. 6 Descartes, for example, held that persons are essentially thinking things. According to Descartes, a person S cannot cease to think and yet continue to exist, and there is no possible situation in which S is not a thinking thing. Another sort of property commonly held to be an essential for some entities are "substantial properties," properties of being composed of a certain sort of stuff (Kripke, 113-115). If this coin is made of gold, then it is essentially made of gold. There is no entity x in any possible world such that x is identical with (or is a counterpart of) this coin and is not made of gold. And a third sort of property commonly held to be an essential for some entities are properties having to do with the thing's origin. For a person, the essential property having to do with her origin is having such and such parents.
How could a person originating from different parents, from a totally different sperm and egg, be this very woman [Queen Elizabeth II]? One can imagine, given the woman, that various things in her life could have been changed: that she should have become a pauper, that her royal blood should have become unknown, and so on. . . . But what is harder to imagine is her being born of different parents. It seems to me that anything coming from a different origin would not be this object. (Kripke, 113) The thesis that sometimes properties having to with the origin of a thing are essential properties of the thing I call "origins essentialism."Now consider again what would be the case, according to Lewis, if Tim had killed Grandfather. "Perhaps Tim might have been the time-traveling grandson of someone else. . . . Perhaps he might not have been a time traveler at all, but rather someone created out of nothing in 1920 equipped false memories of a personal past that never was" (146). This situations do not involve any contradiction, but if origins essentialism is correct, they involve another sort of impossibility, viz. an entity not having an essential property of that entity. According to origins essentialism, Tim is essentially the son of Father, and Father essentially the son of Grandfather. 7 There is no possible situation in which Tim exists but is not the son of Father, and no possible situation in which Father exists but is not the son of Grandfather. It follows that there is no possible situation in which Tim is not the grandson of Grandfather. But this is just the sort of situation Lewis says would be the case if Tim had killed Grandfather. And that which counterfactually implies an impossibility is itself an impossibility. Therefore it is impossible for Tim to kill Grandfather. And since no one can do the impossible, Tim cannot kill Grandfather.
One might perhaps balk at the origins essentialist thesis that Tim is essentially the grandson of Grandfather. Far less controversial, however, is the thesis that if someone is human, that person is essentially human. This weaker thesis can generate the same sorts of problems for time travel. Suppose that Anne is human, and a misanthrope who holds the human race is a scourge on the planet, and that the world would be a better place if there were no human beings. She has managed to raise enough funds to build a time machine and a few small nuclear weapons. Anne travels along with the nuclear weapons, back in time several million years to the savannas of eastern Africa, so that by judicious placement of a few nuclear explosions, Anne may wipe out the early hominids from whom humanity evolved. Lewis would say that Anne can wipe out the hominids from whom humanity evolved. (We know already that she won't, due to a change of heart or her becoming a meal for some Pliocene predator, but that is beside the point.) And if Anne had wiped out those early hominids, Anne would not have been descended from them. But one is human only if one is a descendent of those early hominids: the inhabitants of Twin Earth, for example, are not human, despite their striking similarity to human beings. So if Anne had wiped out those early hominids, Anne would not have been human. 8 But this is an impossibility, since Anne is essentially human. Therefore Anne cannot wipe out those early hominids.
I have argued that if origins essentialism is correct, then Tim cannot go back in time and kill Grandfather, and Anne cannot go back in time and destroy her hominid ancestors. But it is clear from the story that the person who appears in 1920, looking just like Tim and sharing Tim's hatred, can kill Grandfather: for he has what it takes, and there is no metaphysical chaperon there to stop him. And the person who looks like Anne who appears in 5 million BCE and who shares Anne's misanthropy quite clearly can wipe out those early hominids. It follows from Leibniz' Law that the person who appears in 1920 is not Tim, and the person who appears in 5 million BCE is not Anne. Time travel into the future remains unproblematic, but one cannot travel back in time to a situation in which one could alter one's essential origin. (Similar problems arise for one traveling back to a time after one's birth, I think, but I shall not discuss these problems here.) So if survival matters to you, be sure to check and see when and where you're supposedly going before you step into a time machine: it may not be you that steps out the other side.
2. "The Quantum Physics of Time Travel," Scientific American 270 no. 3 (March 1994), 68-74.
3. I'll assume that this cannot happen. If this is considered a relevant possibility, read 'kill' as 'kill permanently'. In any case, the truth of 'If Tim were to kill Grandfather, then Grandfather would be miraculously resurrected' would require a "metaphysical chaperon."
4. Cambridge: Harvard University Press, 1980.
5. A trivial essential property is one that is necessarily had by all objects, such as being self-identical.
6. Or, for those who do not accept genuine trans-world identity, no entity y not having F is a counterpart of x.
7. Perhaps Neither Tim nor Father are essentially male. If so, then Tim is essentially the child of Father, and Father essentially the child of Grandfather.
8. No doubt she would have been a descendant of the Golgafrinchans. See Douglas Adams' The Restaurant at the End of the Universe. New York: Pocket Books, 1980.
Back to Brock's Philosophy Page