The Changing the Past Objection and the Freedom Contradiction Objection
My critics and I agree about many things. We agree that time travel is logically and metaphysically possible and we regard it as an empirically open question whether time travel is possible, given the actual laws and space-time of our universe. We agree that David Lewis and other defenders of time travel have given satisfactory answers to the standard objections to the possibility of time travel. Most of us agree about the metaphysics of time -- the 4D view -- and some of us agree that the best way to think about identity through time is to think of ourselves as four-dimensional objects, stretching across time in the way that a highway stretches across space. But even if we disagree about some of the details, we all agree that the standard objections to the logical and metaphysical possibility of time travel can be answered. We part company only on the question of what the time traveler is able to do. I say that the time traveler cannot kill the baby who is her younger self; my critics say that she can. But this is where things get complicated, since some of my critics think that my inability claim is not compatible with my claim about the possibility of time travel. So before I explain and defend my inability argument, I need to clarify my position concerning the possibility of time travel. 
There are two different objections to time travel that are not always distinguished (or not distinguished carefully enough). I call these objections the 'Changing the Past' objection and the 'Freedom Contradiction' objection. If you don't distinguish these objections, you might be led to think, as Ted Sider does, that "there is nothing special about auto-infanticide"; it is simply "an especially vivid example" of the problems that arise:
"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."
Sider is mistaken, and his mistake is due at least partly to his failure to distinguish these two different objections.
The more simple-minded objection is the Changing the Past objection. It says that time travel is impossible because it entails changing the one and only actual past, which is impossible. Lincoln already gave the Gettysburg address, so you can't travel back in time and stop him from doing it. (Contradictions would be true if Lincoln both gave and did not give the Gettysburg address, and contradictions can't be true.) Your next door neighbor lived to be an adult, so you can't travel back and kill him when he was still a baby. (Contradictions would be true if your next door neighbor was both killed as a baby and not killed as a baby.) And you lived to be an adult, so you can't travel back and kill yourself when you were still a baby. (Same reason; note that it doesn't matter who does the killing.)
Auto-infanticide can, indeed, be understood as an especially vivid example of the "Changing the Past" objection. But it is important to see that this objection has nothing to do with freedom or ability (or any alleged contradictions concerning the time traveler's freedom or ability). The 'Changing the Past" objection arises even if we assign a Guardian of the Past to every time traveler, to ensure that he will not (because he cannot) do anything that contradicts any of the known historical facts. The objection arises the moment the shackled and guarded time traveler arrives in the past. John Hospers puts the objection in a particularly clear way:
"Many centuries BC, the pyramids were built, and when all this happened you were not there – you weren't even born. It all happened long before you were born, and it all happened without your assistance or even your observation. This is an unchangeable fact: you can't change the past. That is the crucial point: the past is what has happened, and you can't make what has happened not have happened…for this is a logical impossibility. When you say that it is logically possible for you (literally) to go back to 3000 BC and help build the pyramids, you are faced with the question: did you help them build the pyramids or did you not? The first time it happened, you did not; you weren't there, you weren't even born, it was all over before you came on the scene. All you could say, then, would be that the second time it happened, you were there – and there was at least a difference between the first time and the second time: the first time you weren't there, and the second time you were there."
Defenders of time travel call this 'the Second Time Around' mistake; the cure for the mistake is to think of time the 4D way and to think of the time traveler as a four-dimensional object. The time traveler who is about to embark on a journey to the past has already been in the past; the historical record already includes his footprints in the sand, his labor on the pyramids, and so on. He doesn't remember any of this because it lies in what Lewis calls his "personal future". But it has already happened, so the past is safe from being changed, and logic safe from contradiction. If the time traveler is about to travel to the past to be in the audience to hear the Gettysburg address, then it is already true that he was there, and already true that he did exactly those things that, from his present temporal perspective, he is about to do.
The second objection, which is more subtle, is sometimes called "the Grandfather problem" or, more recently, "the auto-infanticide problem" and I think that there is a reason why the objection is always introduced by telling stories about failed attempts to kill grandfathers or baby selves. But insofar as the problem counts as as objection to the logical possibility of time travel, it is an objection that can be raised concerning any case where it seems that we are committed to contradictory claims about the time traveler's freedom or ability.
The alleged contradiction lies, not in anything a time traveler actually does, but in the things she doesn't do, but, in some ordinary sense of 'can', can do. The time traveler at the Gettysburg address won't cause a disruption that prevents Lincoln from giving the address (because he didn't). But, it seems, he can. After all, he is in the audience; and, we can easily amend our story so he is carrying a gun and nothing, it seems, stops him from firing it. And that appears to be all it would take to prevent the address from being given -- at least on that day. Actual murder or even physical injury is surely not required. The threat of death or serious harm to Lincoln would have been enough to prevent Lincoln from giving the address (that day). So it seems that our time traveler can prevent the Gettysburg address. On the other hand... Well, on the other hand, what?
The Freedom Contradiction objection is based on the claim that a time traveler both can do something that he didn't actually do and also that he can't do that very thing, and this, it is alleged, is a contradiction. Since there is no possible world where contradictions are true, it follows that time travel is impossible.
But there doesn't seem to be a contradiction in the case of the time traveler who attends the Gettysburg address. Granted, he won't do anything that prevents the address from being given. (Because he didn't.) But he seems to be in as good a position as anyone in the audience that day to cause a disruption that would have prevented the address. Of course, if he (or anyone else) had caused such a disruption, the subsequent course of events would have been different, and the historical record (from our perspective) would also have been different. But this is unproblematic; if any historical event had happened differently, or failed to happen, this would have had ramifications for the rest of history.
So the Freedom Contradiction objection does not arise in this case. (Or, at least, it does not arise if we understand the correct response to the 'Changing the Past' objection.) The time traveler won't cause a disruption, preventing the address, but there is no reason to say that he can't.
If we consider other cases, it seems even more clear that the Freedom Contradiction objection doesn't arise. Suppose the time traveler travels back to the year 500 and finds herself on a deserted island, near a beach. She doesn't go for a walk on the beach, but there is no reason to think she can't. Or suppose that the time traveler travels back to her own past and walks right past the house where she lived as a baby. She pauses for a moment, contemplating whether to ring the doorbell, but in the end decides not to. Again, there is no particular reason to think that she could not have rung the doorbell.
The Freedom Contradiction objection, unlike the Changing the Past objection, does not automatically arise with respect to every case of time travel to the past, nor does it arise with respect to every claim about the time traveler's freedom. The objection, if there is one, arises for a restricted set of cases, of which auto-infanticide is the most compelling example. Whether it is correct or not, almost everyone's intuitive response is that the time traveler cannot kill the baby who is her younger self. The time traveler's very existence depends -- causally, counterfactually, nomologically -- on the survival of the baby. In trying to kill the baby, she is trying to prevent her own present existence. Of course, that's bound to fail. Or so it seems.
On the other hand, if we saw only an adult and a baby, without knowing that one is a time traveler and the other is the time traveler's baby self, we would say: "Of course, that adult can kill that baby." She's got what we would ordinarily call the ability (the skills and physical capacity), and she has what we would ordinarily call the means and opportunity. (She's got a gun, and is right beside the unprotected baby.) She's got what it takes and she's in the right place at the right time. Even if her first attempt fails, that's just bad luck. She is able to kill that baby.
So there is definitely a puzzle here, a puzzle that I will be addressing in these posts. But does this case count as an objection to the possibility of time travel?
It counts as an objection only if we are committed, as the Freedom Contradiction objection alleges, to the claim that it is both true that the time traveller can kill the baby who is her younger self and also false that she can kill that baby.
I deny that we are committed to any such contradiction. My argument will show that it is false that the time traveler can kill the baby who is her younger self, given what we ordinarily mean by 'can'. If we are tempted to think otherwise, it is because we are relying on an assumption about ability to which we are not entitled at time travel worlds.
I also deny that there is any other case in which we are committed to inconsistent claims about what the time traveler can do. Either it will be true, given what we ordinarily mean by 'can', that she can do something, or it will be false. In no case will it be both true and false that the time traveler can do something. The Freedom Contradiction objection to the possibility of time travel fails . 
Before I move on, I need to say something about David Lewis's well-known reply to the Freedom Contradiction objection.
According to Lewis, "can" always means " compossible with some set of facts F", with intentions of speaker and context fixing the relevant facts F. In order to avoid equivocation, we must be careful to specify the relevant facts. Just as we don't contradict ourselves, but only equivocate, when we say that a baby elephant is both big (for an animal) and small (for an elephant), we don't contradict ourselves, but only equivocate, when we say that the time traveler both can and can't kill his baby self. Given the way we ordinarily use 'can'; the time traveler can kill his baby self; his doing so is compossible with facts about his shooting skills, the proximity of the unprotected baby, and other intrinsic facts about himself and his surroundings at the time of the contemplated killing. Given the way the fatalist uses 'can', the time traveler cannot kill his baby self; his doing so is not compossible with the fact that the baby will grow up to be him. So there is no contradiction, and if you think there is, you have been taken in by fatalist trickery.
Almost every philosopher who defends the possibility of time travel assumes that David Lewis gave the correct response to the Freedom Contradiction objection; indeed, Lewis's reply is so widely accepted it has become known as "the Standard Reply". Some philosophers even think that you must accept Lewis's reply in order to defend the possibility of time travel. These defenders of time travel think it important to claim that time travel doesn't cramp our style in any way, and to argue that anyone who thinks that it does is guilty of some fatalist mistake.
(Here there is a striking contrast with the literature on the free will/determinism problem where it is routinely claimed that determinism or a Frankfurt-style "counterfactual intervener" would deprive us of all "alternative possibilities" and hardly anyone worries about fatalist trickery. But I digress.)
I think that the defenders of the Standard Reply are mistaken. You don't need Lewis's account of 'can' to respond to the Freedom Contradiction objection; there are other ways of responding, as I just suggested. And while it's true that the Freedom Contradiction objection is often fueled by fatalist confusions, it's not true that anyone who thinks that time travel makes a difference to our freedom is guilty of the fatalist's collapse of "will not" and "cannot". My argument, at least, is based on no such mistake. My claim, once again, is that the time traveler cannot kill the baby who is her younger self, given what we ordinarily mean by 'can'.
