My argument is that a time traveler cannot kill her baby self, even if she travels back in time, heavily armed, and finds her baby self undefended, right in front of her, even if anyone else similarly armed in the same position could kill the baby.
My argument is simply this.
First Premise: If Suzy would fail to kill that baby, no matter how many times or ways she tried to kill it, she cannot kill the baby.
Second Premise: Suzy would fail to kill that baby no matter how many times or ways she tried to kill it.
Suzy cannot kill that baby.
I spent my last post defending the first premise and the connection between abilities and counterfactuals it assumes. In this post I'm going to focus on the second premise.
Both premises of my argument are claims about counterfactuals. Counterfactual conditionals are different from indicative conditionals. If you don't notice this, you will misunderstand my argument.
Indicatives and counterfactuals have different truth conditions. The classic example of this in the literature is this pair of conditionals about Lee Harvey Oswald.
(1) If Oswald did not kill Kennedy, someone else did.
(2) If Oswald had not killed Kennedy, someone else would have.
If we assume that the Warren commision was correct, and Oswald was the only gunman present that day, then (2) -- the counterfactual conditional -- is false. But (1) -- the indicative conditional -- is true.
There is no general agreement, at the present time, about the correct semantics for indicatives (or even whether they have truth conditions), but it is generally agreed that they are sensitive to our subjective probabilities of belief in a way that counterfactuals are not. The so-called 'Ramsay test' for indicatives says that you should add the antecedent to your stock of beliefs, adjust your other beliefs in the most natural, conservative way, and then ask whether you now believe that the consequent is true. Since we are sure that Kennedy was killed that day in Dallas, we preserve this belief when we revise our beliefs by adding "Oswald didn't kill Kennedy" to our beliefs, and we conclude that someone else must have killed him.
Counterfactuals work differently. We evaluate counterfactuals by considering, not what we should believe, upon acquiring new beliefs about the actual world, but, rather, by considering whether the consequent is true at some relevant set of possible worlds where the antecedent is true. Counterfactuals are notoriously vague and context-dependent, but there is a standard or default way of resolving the vagueness of counterfactuals, and it is this standard resolution that we invoke when we say that (2) is false. There are, of course, possible worlds where Oswald was working with a team of back-up assassins, and at these worlds (2) is true; if Oswald had not killed Kennedy, one of the back-up assassins would have done the job. But these worlds are less like the actual world than worlds where Oswald is a sole operator (and where things are otherwise pretty much the way they are at the actual world). And these worlds -- the worlds most similar to ours - are the ones we have in mind when we say that (2) is false.
Counterfactual Principle: S has the wide ability to do X, on some occasion, only if it's not true that if S tried (again) to do X, S would fail.
was so-called because it applies to counterfactuals, not indicative conditionals, and the kind of counterfactuals to which it applies are the counterfactuals that we evaluate by using the similarity metric that we use when we evaluate counterfactuals like the one about Oswald. Given this, we should not assume that whenever an indicative conditional is true of a time traveler, the corresponding counterfactual conditional is true as well.
To see this, suppose that Tim is a time traveler who travels back in time with the intention of preventing the Gettysburg address and killing Baby Hitler.
(a) If Tim tried to prevent the Gettysburg address, he failed.
(b) If Tim had tried to prevent the Gettysburg address, he would have failed.
(c) If Tim tries to kill Baby Hitler, he will fail.
(d) If Tim tried to kill Baby Hitler, he would fail.
The indicative conditionals (a) and (c) are true for the same reasons that the indicative conditional about Oswald is true. But it doesn't follow that (b) and (d) are true, and, depending on the circumstances, both may be false. If Tim took a gun with him, it's easy to imagine a situation in which he would have succeeded in preventing the Gettysburg address, if, contrary to fact, he had tried. And if Tim took a gun, it's also easy to imagine a situation in which he is close to the unprotected baby Hitler, doesn't try to kill him, but in which he would succeed in killing him, if he tried.
This point is a general one. Barring unusual circumstances concerning particular well-protected babies (or particular shackled and guarded time travelers), we are not entitled to infer from the truth of an indicative conditional of the <Tried, Failed> or <Tries, Will Fail> variety to the truth of a counterfactual conditional of the <Tried, Would Fail> or <Tried, Would have Failed> variety.
But now compare:
(e) If Suzy tried to kill Baby Suzy, she failed.
(f) If Suzy had tried to kill Baby Suzy, she would have failed.
Here things seem different. It's not just that (e) - the indicative conditional -- is true. (f) also seems to be true.
For consider what would have to be the case, for it to be true that Suzy succeeds in killing the baby in front of her. There are, of course, possible worlds where she succeeds. But these are worlds which differ from our world in one of several dramatic ways. Some are worlds where Suzy kills the baby, but the baby is resurrected from the dead and grows up to be the adult Suzy; these are worlds with laws very different from our laws. Others are worlds where Suzy kills the baby and the baby stays dead, but Suzy came into existence ex nihilo shortly before she confronted the baby. Perhaps the laws at such worlds are the same, but this is still a highly improbable event; an event Lewis calls a 'quasi-miracle'. And still others are worlds where Suzy kills the baby, and the baby stays dead but another baby is born 36 years earlier, a baby whose DNA matches Suzy's DNA and who grows to miraculously (or quasi-miraculously) perfectly resemble the adult Suzy as she is just before she pulls the trigger. And some are worlds where the baby stays dead and no extra baby is born, but the DNA and other characteristics of an actually existing baby miraculously (or quasi-miraculously) converge upon the DNA and characteristics of Suzy.
These worlds are all very different from our own, too different, I argued, to count as relevant to the evaluation of counterfactuals about what would have happened had Suzy tried to kill that baby.
The closest worlds where Suzy tries to kill the baby are, I argued, all worlds where some little mundane thing happens -- a bird flies in the path of the bullet, the gun jams, Suzy slips on a banana peel -- and this little mundane thing causes Suzy's attempt to fail in any of a number of different but perfectly ordinary ways.
In my original paper, I assumed very little about counterfactuals. I assumed only that they are variably strict and evaluated by a possible worlds semantics, in the way that Lewis has taught us. I did not appeal to any particular similarity metric, but only to verdicts about counterfactuals that any plausible similarity metric should accommodate. For instance, I assumed that it is uncontroversial that if a person tried to do something she didn't actually do, there would still be no resurrection from dead and there would still be no persons popping into existence ex nihilo. And I assumed that if a person tried to do something she didn't actually do, that person would still be the older self of the baby she once was. And that's all my argument needed.
There is widespread agreement about at least some of the counterfactuals that are true given the standard or default resolution, less agreement about the similarity metric that makes them true. One of the most popular candidates, Lewis's Analysis 1, won't do for time travel worlds because it is temporally asymmetric; it tells us that the closest worlds are worlds with the same past until the occurrence of a small divergence miracle at some time before the time of the antecedent and which conform perfectly to our laws at all times after the divergence miracle. It's not clear whether there is any similarity metric that will give us the right verdicts at time travel worlds, but if there isn't, we are all in trouble, since the defense of time travel requires making sense of the counterfactuals that would be true at time travel worlds.
With these caveats in place, I will now provide additional support for my original argument by sketching two different similarity metrics that support my claim that <Try, Would Fail> is always true.
The first is Lewis's theory, which was explicitly designed as a theory that would not rule out, by stipulation, the possibility of time travel and backwards causation. Lewis provided a temporally neutral similarity metric for counterfactuals, and then argued that, given the contingent facts that obtain at the world as we believe it to be (that is, a world without backwards causation or time travel), this similarity metric picks out the same set of worlds as the simpler (and temporally asymmetric) Analysis 1.
Lewis provides us with a list of the factors that count for determining similarity of worlds. For our purposes, only the first three matter. He says that it's of the first importance to avoid big miracles, of second importance to maximize the spatiotemporal region of exact match of particular fact, and of third importance to avoid little miracles.
Lewis classifies miracles as big or small according to the size of the spatio-temporal region where events fail to happen according to our laws.
We can divide worlds where Suzy (that adult) succeeds in killing Baby Suzy (that baby) into four classes:
i) worlds where the baby dies but is subsequently resurrected from the dead and grows up to be the adult Suzy; (These are worlds where, in addition to the small divergence miracle that enables Suzy's attempt, there is a big miracle.)
ii) worlds where the baby dies and stays dead, and the adult Suzy is a person who came into existence ex nihilo, either just before she fired her gun, or when she stepped out of the time machine; (These are worlds where, in addition to the small divergence miracle, there is a big miracle.)
iii) worlds where the baby dies and stays dead, but an extra baby is born with DNA that matches Suzy's DNA and this baby grows up to be exactly the way that Suzy actually is at the moment when she stands in front of Baby Suzy; that is, this person has the desire to murder her baby self, and the false belief that Baby Suzy is her baby self; (These are worlds where, in addition to the small divergence miracle and another small miracle that results in the birth of the extra baby, there is a big miracle -- the "convergence miracle" that ensures that the extra baby grows up to be exactly like the adult Suzy.)
iv) worlds where the baby dies and stays dead, but some other baby's DNA miraculously changes so that it matches Suzy's DNA and this baby grows up to be someone who is exactly the way that Suzy actually is at the moment when she stands in front of Baby Suzy; that is, this person has the desire to murder her baby self, and the false belief that Baby Suzy is her baby self. (These are worlds where, in addition to the small divergence miracle, there are two big miracles -- the miracle that secures the change in DNA and the "convergence miracle" that ensures that the other baby grows up to be exactly like the adult Suzy.)
On the other hand, the worlds where Suzy fails to kill the baby can be divided into two classes:
i) worlds where Suzy tries to kill the baby and there is no miracle but some surprising but otherwise mundane event prevents the baby's death. (These are worlds where the only miracle is the small divergence miracle.)
ii) worlds where Suzy tries to kill the baby but a small miracle causes some mundane event (jammed bullet, tremor of hand, etc.) that prevents the baby's death; (These are worlds where, in addition to the small divergence miracle, there is one other small miracle.)
To sum up: The closest worlds where Suzy's attempt to kill the baby succeeds are worlds with one small and one big miracle, whereas the closest worlds where Suzy's attempt fails are worlds with, at most, two small miracles. Since Lewis's theory says that worlds with one or even two small miracles are closer than worlds with one big miracle, his theory says that worlds where Suzy's attempt fails are closer than worlds where her attempt succeeds.
The second similarity metric that supports my claims is a version of a Causal Theory of Counterfactuals. I call it Causal Theory Sophisticated because the theory does not rule out, by stipulation, the possibility of backwards causation.
Causal Theory Sophisticated: The closest antecedent-worlds are worlds which:
i) diverge from our world with respect to the causal history leading up to the antecedent event as far back as is required so that big miracles are avoided and a small miracle secures the divergence from actual causal history;
ii) are exactly like our world with respect to all other facts except for those facts that are the causal upshots of the antecedent event.
The idea is that we consider worlds just different enough for the antecedent to be true in a way that involves a small miracle, rather than a big one, and then we follow the causal arrow traced by the antecedent event, permitting those changes caused by the event, but no other changes.
Causal Theory Sophisticated resembles Lewis's Analysis 1 in its asymmetry, but whereas the asymmetry of Analysis 1 is temporal; the asymmetry of Causal Theory Sophisticated is causal. The theory tells you to causally (not necessarily temporally) backtrack as far as you need to go until you reach the earliest small miracle that allows the antecedent event to occur. In time travel cases, this small miracle can lie in the external future. When we search for the causally closest small miracle that permits the event that is the time traveler's attempt to kill the baby who is her younger self, we must causally backtrack through the time traveler's personal time in a way that ensures that she remains in a position to make the attempt, and the only way to do this while avoiding large miracles (popping into existence ex nihilo, resurrection from the dead, and so on) is by ensuring that she grows up from the child she once was, and the only small miracle that enables this is a jammed bullet or some other mundane event that prevents the time traveler's attempt from succeeding.
My argument consists of two premises. The first premise - the premise that links wide abilities to counterfactuals - says that a time traveler is able to kill the baby who is her younger self only if Would Fail is not always true of that time traveler and that baby. The second premise says that Would Fail is always true, of that time traveler and that baby. I have defended my argument in two main ways: by drawing distinctions between various kinds of ability (narrow, wide, wide ability to do something with respect to a particular thing) and by explaining the relevance of counterfactuals to wide ability. I have also pointed out that it is important to understand the difference between indicative and counterfactual conditionals and to realize that we are not always entitled to infer, from the truth of the indicative <Tried, Failed> to the truth of the counterfactual <Had Tried, Would Have Failed>.