Before I defend my argument that the Time Traveller cannot kill her baby self I want to explain why it wouldn't matter -- so far as the possibility of time travel is concerned -- if I turned out to be guilty, as charged, of fatalism.
The Logical Fatalist is someone who thinks that there are truths about our future actions, and that these truths entails that we must do whatever we are going to do, that we can never do otherwise. Since you did not kill your baby self, you will not kill her, and thus, according to the fatalist, you cannot kill her. But time travel has nothing to do with it, says the fatalist. We are always in this position – we just don't notice it. The clearheaded fatalist will dismiss the Freedom Contradiction objection to time travel on the grounds that its 'can' premise is false.
The Hard Determinist is someone who thinks that determinism is true and that it follows, from determinism alone, that we are never able to do other than what we actually do. The hard determinist should also be able to defend the logical possibility of time travel. But surely the hard determinist's defense of time travel should not require him to defend the claim that the time traveler has abilities that he thinks we lack.
(After all, time travel worlds are worlds where, in addition to the usual earlier causes, some actions have causes that occur later in time. If you think that deterministic event-causation undermines freedom, you will have more, not fewer, reasons to think that this is so at time travel worlds.)
To summarize: the Freedom Contradiction objection to time travel succeeds only if it is true, without equivocation, that a time traveler both can and can't do something. Lewis's response to the Freedom Contradiction objection is to deny that the 'can' and 'can't' claims are unequivocally true. But the Freedom Contradiction objection can also be answered by denying the 'can' claim. If the time traveler cannot kill her baby self (or grandfather, or baby Hitler, or another baby, or a fly) there is no contradiction. The person who claims that time travelers cannot do things that most of us think he (and we) can do may be mistaken, but this is a separate issue. We should not confuse the defense of the logical or metaphysical possibility of time travel with a defense of the claim that the time traveler can do all the things that commonsense says we can do. Compare: We don't need to defend the claim that determinism is compatible with the ability to do otherwise in order to defend the claim that it is logically or metaphysically possible that determinism is true.
I should quickly add that I am neither a fatalist nor a hard determinist. Like most of the philosophers who defend time travel, I am a compatibilist. I don't say that the time travel is unable to do anything she fails to do. I say that the time traveler is able to kill a fly, to kill other babies. And even – kill baby Hitler. However I still think that the time traveler is not able to kill her baby self.
