I think that time travel is logically possible, but I think that even if it were physically possible no time traveler would be able to go back in time and kill her baby self. My argument has two premises:
- Premise1: A person can do something (is able to do that thing) only if it isn't always true that: if he tried to do it, he would fail.
- Premise 2: It is always true of Suzy, the time traveller, that if she tried to kill the baby who is her younger self, she would fail.
In this post I'm going to defend the first premise. That premise isn't specific to time travelers. It asserts a quite general link between our beliefs about what a person can do and the truth of certain counterfactuals. That is why (1) is worth thinking about quite apart from worries about time travel: it captures an essential feature of what we mean when we say that people are able to do things even if they don't do them. It partly defines how we understand 'can' when we make choices: that is, when we choose to do one thing from among the other things we can do.
Think of 'narrow' abilities as those abilities you have in virtue of what's beneath your skin; think of your 'wide' abilities as those abilities you have in virtue of what's beneath your skin and also your surroundings. To have a wide ability to do something is to have the narrow ability to do it, but not vice versa. When we say that someone has the narrow ability to do something – ride a bike, for instance – we mean that she 'has what it takes' to ride a bike. She's got bike-riding skills (she's learned how to ride a bike and she hasn't forgotten) and she's got the relevant physical capacities -- her legs and arms aren't broken. No doubt other things are required as well – e.g. the absence of a pathological fear of bike-riding. But what's not required, for the narrow ability to ride a bike, is proximity to a bike or the absence of external impediments to bike-riding. The prisoner in shackles may retain the narrow ability to ride a bike.
Since the facts relevant to the existence of a narrow ability are facts about what is beneath someone's skin, it seems reasonable to suppose that narrow abilities obey a principle I'm going to call the Intrinsicness principle.
Intrinsicness principle: If two persons governed by the same laws are intrinsic duplicates, then they have the same narrow abilities.
Two persons with the same narrow abilities need not share the same wide abilities. The shackled prisoner retains the narrow ability to ride a bike, but he no longer has the wide ability; he's got 'what it takes', but his surroundings are not favorable. An unshackled bicyclist without a bike, or a broken bike, also lacks the wide ability to ride a bike, as does the person whose attempts to ride a bike will be systematically prevented by a sinister figure lurking in the background.
We've got a number of different ways to express the claim that someone has the wide ability to do something. We might say: "she's got the ability, the means, and the opportunity", or "she's got what it takes and she's in the right place at the right time", or "she's got the ability and there's nothing that would stop her from acting on her ability". But we might also say something like: "she's able to do it", "it's in her power to do it"; "it's one of her options", "it's one of her alternatives", or "it's one of her choices", or, simply, "she can do it".
To avoid any confusion, I will always say "narrow ability" when I am referrring to narrow abilities. When context makes it clear that I mean 'wide ability', I will say 'has the ability' or 'is able to' or 'can'.
Since narrow abilities obey the Intrinsicness principle, and since we have wide abilities by having narrow abilities together with some further facts about our environment, it's tempting to conclude that wide abilities are governed by a principle I will call 'Snapshot':
Snapshot Principle: If two persons governed by the same laws are intrinsic duplicates in qualitatively identical surroundings, then they have the same wide abilities.
And, indeed, Snapshot, or some approximation of it, is a principle that we use in our actual reasoning about what we are able to do. (I will be arguing that Snapshot is false at time travel worlds, but I haven't argued that yet.)
Note that there are limits to what Snapshot tells us. It tells us when people have the same wide abilities, but it doesn't tell us what wide abilities anyone has. Snapshot leaves incompatibilists free to argue that at deterministic worlds no one ever has the wide ability to do anything other than what she actually does. (The surroundings are always unfavorable, the incompatibilist might argue.)
Snapshot isn't the only principle that we use in reasoning about our wide abilities. We also accept, and I think we should accept, a principle that links wide abilities to counterfactuals. There are different ways of framing such a principle, but for the purposes of my argument, all I need is a very weak principle.
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.
Why "again"? To rule out cases in which a person tries and fails to do something that she has the narrow ability to do. We want to say that her failure doesn't automatically rule out her wide ability to do that thing yet on the standard semantics for counterfactuals the fact that she actually tried and failed entails the truth of the counterfactual < she had tried, she would have failed>. However, if the person's failure, on that occasion, was due to bad luck rather than lack of wide ability, we believe that it's false that if she had tried again to do X, she would have failed.
Why do I say we accept the Counterfactual Principle for wide ability? Well, think about how you deliberate when you decide what to do. You choose among possible course of actions that you believe are your options. You wouldn't waste time deliberating about whether to do one thing or another if you didn't believe that you can – in the wide sense – do each of these things. Compatibilists and incompatibilists disagree about what, exactly, this belief entails. But everyone agrees that a course of action is an option for you (something you have the wide ability to do) only if you would have some reasonable chance of doing it, if you tried, then and there, to do it. If the things you deliberate about are all things such that if you tried to do them, you would fail, you are wasting your time. (The classic example is the person falling off a bridge; we think that it is pointless for her to deliberate about her downward descent because we all agree that it would continue even if she tried to stop it.) And everyone also agrees that determinism doesn't entail fatalism, where fatalism is understood as the thesis that whatever happens will happen regardless of your intentions and efforts; that is, as the thesis that your intentions and efforts are always causally and counterfactually impotent.
One more distinction. Someone might have the wide ability to do something without having the wide ability to do it with respect to a particular object. Consider Sally, who is a serious bike-rider who owns two bikes, which are usually in perfect working order. On most days, it's true not only that Sally has the narrow ability to ride a bike, and that she can (wide) ride a bike; it's also true, of each of her bikes, that she can ride that bike. But today one of the bikes – her favorite, as it happens – is broken. Sally has the ability (narrow) to ride a bike, and it's still true that she can (wide) ride one of her bikes – the unbroken one. But she cannot (wide) ride the bike she likes best. For if she tried to ride that bike, she would fail.
Let's change the story a bit and suppose that Sally has two bikes that are exact intrinsic duplicates of each other. Neither is broken; each is in perfect working order. Sally has the narrow ability to ride a bike, an ability that she exercises nearly every day by riding one of her bikes -- let's call it 'bike A'. But her other bike -- call it 'bike B' -- is such that her attempts to ride it never succeed. Something always goes wrong -- the bike suddenly breaks, banana peels appear out of nowhere, Sally's legs go limp and cease working properly, and so on, for a wide variety of different intrinsic and extrinsic preventers of bike-riding. We might write off these events as mere co-incidences and 'bad luck' and insist that Sally's clearly demonstrated (narrow and wide) ability to ride bike A is proof that she also has the (narrow and wide) ability to ride bike B. But if we say this, then I think it is because we don't believe that it is true, on every occasion, that:
Would Fail: If Sally had tried (again) to ride bike B, she would have failed.
On the other hand if we somehow came to believe that Would Fail is always true, we would give up our belief that Sally is able to ride bike B. (We would stop advising her to ride it; stop blaming her for never riding it, and so on.)
With this background in place, I can now explain and defend my first premise. My first premise should be understood as a premise about wide ability. It says that Suzy -- our time traveler -- has the wide ability to kill the particular baby who is her younger self only if it isn't always true, on every single occasion, that if she tried (again) to kill that baby, she would fail (once again).
My claim is that the time traveler may find herself in the position that Sally is in. Suppose that a time traveler had a twin sister who was tragically killed in infancy. The time traveler travels back in time and stands in a room in front of two unprotected babies -- her younger self and her twin sister's younger self. The time traveler has the (narrow) ability to kill babies, an ability that includes babies that are intrinsic duplicates of the babies she now confronts. She is in circumstances suitable for baby-killing; she's got the means and opportunity to kill a baby. She can kill a baby; she has the wide ability to do so. Indeed, for all I've said so far, it may have been true – all along – that the time traveler was the mysterious stranger who killed her twin sister. What I deny is that the time traveler can kill the other baby – the one who is her younger self.
Which brings us to premise (2) of my argument…