I was reading Karen Bennett’s paper on the exclusion argument and I realised half way through that I didn’t really understand some of the concepts that are commonly used in this debate. Here’s the difference I realised I don’t think I understand.

There’s meant to be an important difference between joint causation and overdetermination. Here’s a couple of simple cases to bring out the difference.

A and B shoot at V, each hitting him in the heart at the same time, and each in a way that would be sufficient to kill him instantly. This is overdetermination (I take it!).

A and B throw rocks at V, each of which hits V at the same time and punctures one of V’s lungs. V dies of aphysixiation (sp?). I take it this is a case of joint causation – the two throws kill V, though neither would be sufficient to kill him separately.

(Digression. The intuitions about this case differ a bit when we make the times of the throws different. If A’s throw happens in the morning and B’s in the afternoon, then I think B’s throw is the sole cause. End of Digression)

OK, so we’ve got the distinction, now let’s get to applying it.

Two rockets are fired at planet V. Planet V has a missile defense system that has one virtue and one vice. The virtue is that whenever a solo rocket comes in, then it will intercept the rocket and destroy the threat. The vice is that whenever two rockets come in, the defence system gets confused and fires an interceptor totally the wrong way. So both rockets hit the planet, explode as intended, and destroy the planet. (They are VERY BIG ROCKETS.)

Let F1 be the firing of one of the rocket, and F2 the firing of the other rocket. Let E1 be the explosion of the first rocket’s payload and the E2 the explosion of the second rocket’s payload. The payload explosion happens after the rockets are through where the intercept system would have done its work.

I think that F1 and F2 are joint causes of the destruction of the planet, since neither alone is sufficient to destroy the planet. But E1 and E2 are each causes, perhaps overdetermining causes, of the destruction. This is odd, I think, but perhaps not the worst result ever.

Change the case a little to allow for a third rocket. Call its firing F3. Now are the firings joint causes, or are they each overdetermining causes? Here’s where things get tough.

Karen Bennett’s paper suggests that the following two conditions are necessary for us to have a real case of overdetermination.

(O1) If c1 had occurred and c2 had not, e would (still) have occurred.
(O2) If c2 had occurred and c1 had not, e would (still) have occurred.

How do we extend this to where we have three putative causes. Here’s one triple of counterfactuals that we might think indicate overdetermination.

(O1a) If c1 and c2 had occurred and c3 had not, e would (still) have occurred.
(O2a) If c1 and c3 had occurred and c2 had not, e would (still) have occurred.
(O3a) If c2 and c3 had occurred and c1 had not, e would (still) have occurred.

These are all true. But maybe we should generalise (O1) and (O2) in this direction.

(O1b) If c1 had occurred and c2 and c3 had not, e would (still) have occurred.
(O2b) If c2 had occurred and c1 and c3 had not, e would (still) have occurred.
(O3b) If c3 had occurred and c1 and c2 had not, e would (still) have occurred.

These are all false. So overdetermination or joint causation? I have no idea really, and that makes me wonder whether I really understood the two concepts.

By the way, if (O1) and (O2) are necessary for overdetermination, then we can argue quite easily for compatibilism between causation by parts and causation by wholes. Here’s a homely example to end with.

Invasions cause deaths. In particular they often cause deaths of the invaders. As an example, the Achean invasion of Troy caused Hector’s death. (I’ll just take for granted that Homer’s tale is true, though of course this is doubtful.) It also seems to be the case that Achilles’s charge caused Hector’s death. Now the charge is not identical to the invasion, though it is a part of it. Let c1 be the invasion, and c2 be the charge. Then (O1) is clearly false. Had the invasion occured without this action of Achilles, then Hector wouldn’t have died, for none of the other Acheans could have killed Hector. So here we have a case of two non-identical synchronous causes not amounting to overdetermination. (Does this mean that (O1) is not necessary for overdetermination? Not sure. It might mean it isn’t necessary for bad overdetermination.)