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.