In the problem of the heap the distinction is indeed arbitrary, and the consequences of drawing the line in the wrong part are semantic only. If we came to a different conclusion, it would only mean we have different definitions of heap. But with who caused death, the question is of ethics. The line between ethical an unethical isn't arbitrary. It can be hard to pin down, but that's not the same thing.
If the distinction between scenario's where B causes the circumstances of C's death, and where he doesn't is arbitrary, then it cannot be a factor in the morality of what B did. So I disagree that this is "a causal problem primarily and an ethical problem only in a derivative way". Cause must be defined in a way that is relevant to ethics, so it is an ethical problem primarily, and causal only because ethics, according to you, depends on who actually killed C.
Therefore there are two possibilities: either cause is irrelevant to ethics, or the distinguishing line of who caused C's death is not arbitrary. Now I have posited the former, but in fairness I have not actually disproved the latter.
Ok, I see the problem! Look at the OP again. There are actually two questions asked; 'Who killed C?' and 'Who is guilty?'. We have been trying to answer different questions, which is why I have been taking it as a primarily causal problem and you have been preoccupied with questions of ethics; of moral responsibility.
Your argument, as I take it, is this; in individuating deaths we must make an arbitrary, even if justified, distinction somewhere. There can be
no arbitrarinness in ethics. Or, at least, something so important as the
moral responsibility -the guilt- for an act of wrongdoing as great as murder cannot swing on anything arbitrary. Hence, the question 'who is guilty' cannot swing on how we individuate deaths. And that's fine.
But, so I have argued, the question of who is
causally responsible for C's death must be solved by individuating deaths in the way I have explained. I haven't quite explained why this is absolutely necessary, but there are all sorts of problems formally similar to this one that make it so.
I'll explain this if you want; in general the problem is that unless we do this for any event E with multiple sufficient causes we can not say any of those causes 'caused' E. I'll give one example. Suppose A and B each throw bricks at a window. A's brick hits the window first, and smashes it. B's sails right through (because the window is smashed). Both throwings would be sufficient to cause the window smashing. But it was A's which actually caused it. Why is this so? Because A's caused the particular smashing that actually happened, and B's did not.
So it looks very much like causal questions need to be solved in this way. And the question 'Who Killed C?' is a causal question. It is asking us who caused C's death. And, as we have established, in individuating deaths (and, for that matter, smashings) we must make an arbitrary distinction somewhere.
The problem arises then, if and only if we accept that 'cause must be defined in a way that is relevant to ethics'. This is a problem because, if causation depends on an arbitrary distinction, and ethics never depends on such a distinction (at least, in such big issues), we have a paradox. We must either drop our account of causation, drop the non-arbitrariness of ethics or drop the link between the two.
You yourself posit the latter; you say that 'cause is irrelevant to (the big issues) in ethics'. And this is definitely the right way to go. I certainly haven't said anything that should have lead you to believe we disagree here. It is the right way to go because it means that we can say -in cases like this- that it was B who killed C, but that both are roughly equally guilty (of wrongdoing - not necessarily C's death). Consequently, an agents guilt does not depend on the exact things they caused. And this seems right; someone who killed successfully out of good) luck is no less guilty then someone who failed to kill due to bad luck. In these cases, cause doesn't depend on ethics.
So that seems like it resolves our problem. There are two notions of responsibility at work in this debate; causal responsibility and moral responsibility. Causal responsibility depends on arbitrarily individuated events. But moral responsibility can't depend on such individuation. Consequently, moral responsibility does not depend on causal responsibility.
(Note that on this strategy we are likely going to have to say something like the 'guilt' is not for a particular killing, but for a great wrongdoing. But I don't see any problem here).
