Suppose I pull a drowning person out of the water, and no one else around would have. Then I save the person's life. Why? The natural thing to say is: he's alive because I pulled him out; and had I not pulled him out, he would have been dead.
In both cases we have explanation and counterfactuals. But one is a case of saving a life and the other is not. One obvious difference is that the trapeze artist wouldn't have leapt had the other not been there to catch. So the life-endangering activity is itself part and parcel of a joint activity that includes the protective action. However, this is not itself sufficient to distinguish the cases. For it is not uncommon to have arrangements where lifeguards are paid to pull people out of the water and the people wouldn't swim were the lifeguard not there. Yet we still say that the lifeguard saves lives.
I sent some thoughts on this to my colleague Trent Dougherty and he told me that he suspected these issues depended on questions of normal background much as in ascriptions of causation.
This made me think. Another kind of a case where normal background comes in and there are ascriptions of causation is where we are interested in the question whether one person killed another. Not every case of counterfactual and explanatory dependence of a death on someone's actions counts as killing. If I work at a car parts store and sell you a car battery that, surprisingly, you use in an ill-advised fatal amateur chemistry accident, I didn't kill you. This is true even if the counterfactual is true that had I refused to sell, you would have changed your mind about the experiment (or there were no other lead acid batteries available in the vicinity).
Thinking about these cases makes me wonder if there isn't a general rule (almost surely with exceptions) that connects saving a life with killing. If the trapeze artist failed to catch (even accidentally), she would have killed her fellow performer. On the other hand, if the lifeguard failed to save (even culpably--maybe he was texting), he wouldn't have killed the swimmer: the relevant cause of the swimmer's death would be the swimmer's weakness, etc. So perhaps, generally speaking, an action is a case of saving a life if and only if omission of that action wouldn't be a case of killing (though it might well be culpable).
Given this correlation, we would expect that we would be more confident that an action is a saving of a life when we are more confident that omission wouldn't be killing, and vice versa. I suspect this is generally the case. The most glaring cases of saving a life are cases of supererogation. The person who leaps before a train to push a child out of the way at the cost of her own life is certainly saving a life, and we are confident that a failure to leap wouldn't be a killing. (But it would be hard to live with the knowledge that one could have leapt but didn't have the courage.) So here we have clarity in both judgments.
But as I said the above correlation is just a general rule. In the car battery case, my selling you the battery isn't a killing. But suppose I have no idea what you want to use the battery for but don't like your eye color. Then my refusal to sell isn't a case of saving a life.
Maybe we can improve on the general rule as follows. To kill or save a life one must have a certain amount of knowledge (or true belief?) that the action is one that can have relevantly life-curtailing or preserving effects. Given this knowledge, we have the general rule: you save iff omission wouldn't be a killing.