# Are Short-Circuits Causes?

The other day I wrote about Ned Hall’s recent theory of causation. I should have mentioned the reference for the paper. It’s “Structrural Equations and Causation”, Philosophical Studies 132: 109-136. What I was really interested in in that paper was what Ned says about ‘short-circuits’. This is his name for causal structures like the following.

We have a causal pathway leading from A that will, if unchecked, result in E. C launches two causal pathways. The first of these, T, is a Threat to E. If unchecked it will cause D, and that will prevent E. In the examples to follow, E is the survival of Victim sometime after the events described, and D is (or would be if it occured) a particular death of Victim’s. Victim is merely the victim of misfortune in these stories; he always however survives. That’s because C also causes P, which Protects Victim from the threat, and Prevents D from happening.

Question: Does C cause E?

Answer 1 (Lewis): Yes. Causation is the ancestral of counterfactual dependence. And E is counterfactually dependent on P, which in turn is counterfactually dependent on C.

Answer 2 (Structural Equations Theory): Yes. It is sufficient for C to cause E that there is a related model in which E is counterfactually dependent on C. The model where we determine exogenously that T occurs is a model where E is counterfactually dependent on C, and is related in the right way to the actual model. So C causes E.

Answer 3 (Hall): No. C never produces a real threat to E, because it cancels itself out. So C does not cause E.

My answer: We just haven’t been given enough information. Some cases with this structure are cases where C causes E, and some are not. So everyone is wrong. Figuring out what separates the causal cases from the non-causal cases, or figuring out which features of a case and its presentation make us judge a case as causal or not, is really a very hard puzzle. Below the fold I’ll work through some hypotheses and theories.

First a case that I think pretty clearly supports Ned’s take on matters.

Arrested Assassin
Enemy hires Assassin1 to kill Victim. (This is C.) Assassin1 starts planning the kill. (This is T.) Happily, Agent has a wire inside Enemy’s building, and hears of the plan. Assassin1’s accepting the contract to kill Victim is obviously a criminal offence, so this leads Agent to arrest Assassin1, thus preventing Assassin1 carrying out his mission. (This is P.) As always, D is Victim’s death (which doesn’t happen) and E is Victim’s Survival (which does).

Here is seems just bizarre to say that C caused E. Perhaps I could be talked into accepting this – in philosophy we often have to accept bizarre claims. But let me just say that my intuition that C does not cause E in this case is stronger than my intuition that Gettier cases are not cases of knowledge. So this makes it look like Hall is right. But we should look at some more cases before we are so sure.

Bomb Detector
Victim is now a little nervous. He is particularly worried about bombs on his car. So he hires Mechanic to install a bomb detector on his car, one that blows up the car when a bomb is detected, as long as it detects no one is actually in the car. Let C be the installation of the detector. Assassin2 sees Mechanic installing the detector. Assassin2 doesn’t want to kill Victim; he wants to kill Bill Clinton. Unfortunately, Assassin2 believes that only Bill Clinton would be having this kind of bomb detector installed, so this is the car he should attack. Fortunately, Assassin2 always assassinates with car bombs, bombs that he (mistakenly) believes can’t be detected by bomb detectors. So Assassin2 puts a bomb on Victim’s car. (This is T.) The bomb detector is programmed to regularly scan the car for bombs. As T is happening, one of the regularly scheduled scans starts. (This is P.) The scan detects the bomb, and blows up the car. Victim is safely inside his house, so D does not occur.

I imagine people will have differing reactions to this case, but I have both an intuition that C causes E, and a small argument that C causes E. The argument is that in the case Mechanic saves Victim’s life. At least if I were Victim, I would feel that Mechanic had saved my life. But you can’t save someone’s life without causing their continued survival. And there’s nothing that Mechanic does other than install the bomb detector to save Victim’s life, so it must be C that causes E.

This suggests that there is something in the fine details of the case that distinguishes between various ‘short-circuits’. Some short-circuits are causes and some are not. What might separate the two?

My first hypothesis turns on a suggestion that Christopher Hitchcock and Ned Hall have made. They have both argued recently that we should distinguish between ‘default’ and ‘deviant’ states of affairs. The distinction is meant to be somewhat intuitive, and I won’t try to say much to explicate it here.

Now all of the events (except D) in the above diagram are deviant happenings. But C doesn’t produce T and P all by itself. There are background conditions at play as well. Let’s put these in to the diagram and see what happens. So let T and P be ‘recalcitrant’ neurons that only fire if doubly stimulated. (That’s what we represent in the diagram by giving them a thick border.) And let BT and BP be ‘background’ events that combined with C are sufficient for T and P respectively.

Here is a distinction between our two cases. In Arrested Assassin, BT is basically Assassin1’s disposition to accept contracts and ability to carry them out. That’s a relatively stable state of affairs, and we can think of it as happening by default. In Bomb Detector, BT is that Assassin2 is watching Mechanic’s shop, and has formed the belief that only Bill Clinton would be having a bomb detector installed. That is not the way the world is by default. Here then is a hypothesis.

Hypothesis 1: C causes E in a short-circuit case iff BT is a deviant state of affairs.

This covers a lot of cases, but I think it makes it too easy for C to cause E in cases like the following.

Meat Pie
Victim goes to the shop and orders a Steak and Vegemite Pie. (This is C.) Around this moment, Assassin3 decides that he is going to kill the next person who orders a Steak and Vegemite Pie. Hearing Victim order this, he starts trailing Victim looking for a good time to kill him. (This is T.) Psychic has had a vision that someone who orders a Steak and Vegemite Pie will be in danger. On hearing Victim order the pie, he decides that Victim needs assistance. So he starts trailing Victim as well, watching out for threats. (This is P.) Because Psychic is also trailing Victim, Assassin3 has to pass up several opportunities that would otherwise have been perfect chances to kill Victim without any observers. Eventually Assassin3 tires of this and leaves without killing Victim, so Victim survives.

Here it still seems odd to say that C caused E. C put Victim’s life at risk, and only the lucky intervention of Psychic saved the day. So C did not cause E. What seems distinctive about this case is that both BT and BP are deviant states of affairs. Normally there aren’t assassins waiting to kill the next person who orders a certain kind of pie, or psychics waiting to protect such pie-buyers. This suggests a refined version of Hypothesis 1.

Hypothesis 2: C causes E in a short-circuit case iff BT is a deviant state of affairs, but BP is a default state of affairs.

This has some plausibility I think. If C is the kind of thing that, by default, protects against threats like T, and a threat like T arises, then arguably C is a cause of E, even if C plays some role, in conjunction with a very odd state of affairs, in bringing about the threat. I have some sympathy for this conclusion, but I’m worried that it leads to mistakes in cases like the following.

Volvo Driver
Friend advises Victim to buy a Volvo because they have so many safety features. (This is C.) Victim does go on to buy a Volvo on Friend’s advice. The next day the Aliens invade. As everyone knows, what the Aliens really hate are Volvo drivers, so they go about throwing large boulders at all cars, including Victim’s car while Victim is driving it. (This is T.) Happily, the airbags that Friend was so stressing do their job when the boulder hits, launching and protecting Victim from the attacks. (This is P.) So Victim survives.

I’m a little torn about the case, but I think here C does not cause E. That is despite the fact that BP consists entirely of pretty default states of affairs (like that airbags work) and BT consists of pretty deviant states of affairs (like that Volvo-hating Aliens invade). So I don’t think Hypothesis 2 gets to the heart of the matter.

My preferred solution is rather more radical, but stating it requires some set-up. We all know that there is a distinction between Phi-ing and causing something to be Phi-ed. If I say something that offends my guests and they storm out, I cause my front door to be opened (and slammed), but I don’t open (or slam) my front door. In some places a new meaning for ‘direct’ is stipulated so that one opens a door iff only directly (in this proprietary sense) causes the door to open. It has to be a special sense because, as Lewis pointed out, we can open a door using arbitrarily complicated devices. (Lewis’s way of putting this was to refer to Rube Goldberg machines, but that reference might be too old for youngsters like, er, me!) But I think we can make sense of this idea that some causal chains are more apt to be the truthmakers for causatives like open, and we’ll call these causal chains more direct. This lets us state my preferred view.

Hypothesis 3: C causes E in a short-circuit case iff the chain running from C to P is (much) more direct than the chain running from C to T.

Roughly, C causes E iff C protects Victim from threats like T (as opposed to merely causing Victim to be protected) and doesn’t threaten Victim (as opposed to causing Victim to be threatened).

I think this does get the cases right. In particular in Volvo Driver it links up with a rather delicate intuition I have about a more realistic case. If my friend advises me to buy a car with airbags, and I do so, then the friend has caused me to be protected from various threats. But my friend hasn’t protected me from those threats. On the other hand, if the friend actually installs the airbags, then she has protected me from the threats. It is the inapplicability of causatives in advice cases like this that leads to the inapplicability of ‘cause’ in Volvo Driver.

There is though one kind of case that I’m worried about. It is widely known that the application of causatives depends on the intention of the causal agent. I’ve been in various offices where, if the door was opened, opening the window would cause the door to slam shut. (Often quite violently, which was a little unpleasant.) Now in general in such a case my opening the window would cause the door to close, but wouldn’t be a way that I’d close the door. There is one exception. Say that I wanted the door closed, but I was nearer the window than the door, and opened the window with the intent of causing the door to close, and as a result the door became closed. In such a case I would have closed the door, not merely caused it to close. That is to say, intention matters to directness. But, I worry, it doesn’t matter to short-circuits. So consider one last case.

Door Stopper
Victim is in Friend’s office. Friend opens the window of his office. (This is C.) The wind that comes in causes Friend’s door to slam shut. (This is P.) Assassin4 is waiting outside Friend’s office, hoping to kill Victim. When Friend moves the window (open, as it turns out) Assassin4 sees Victim’s reflection and thinks he can kill Victim. So he fires. (This is T.) Unhappily, the bullet is headed straight for Victim. Happily, the door, which is a big thick steel door, closes shut just in time to prevent the bullet getting to Victim. So Victim lives.

I’m (tentatively) inclined to say that this is a case where C causes E. More importantly, I’m worried that whether Friend intended the door to close makes a lot of difference to whether the chain from C to P is direct, but makes no difference to whether C caused E. That is to say, whether we fill out Door Stopper to say that Friend intended the door to close, or was surprised by its closing, seems to make no difference to whether C causes E. But Hypothesis 3 suggests that it should make some difference.

This is a problem for Hypothesis 3, but I think it can be, to some extent, parried. Even if Friend didn’t close the door, there is still a good sense in which the C-P causal chain is much more direct than the C-T causal chain. Opening a window was not a way that Friend threatened Victim’s life, or even I’d say endangered Victim, though it did cause Victim to be in some danger. So Hypothesis 3 predicts that in both variants of Door Stopper, C causes E.

If Hypothesis 3 is right, a rather radical conclusion follows. To know whether cause applies in a particular case, we have to not just know the causal relationships between various subsidiary events, but know whether causatives are applicable to those subsidiary events. That means that any analysis of causatives that uses the concept of causation will be circular, since in some cases whether cause is applicable depends on whether causatives are applicable.

That’s to say that our concept of causation can’t be conceptually prior to our causative concepts like open and protect. And that, if right, is I think quite a striking conclusion.

## 6 Replies to “Are Short-Circuits Causes?”

1. That’s a remarkably number of hypotheses and counterexamples!

Anyway, I think the arrows pointing in to D on both diagrams have the wrong sort of heads. Unless I’ve got one too many preventions going on the way I interpreted things.

2. Oops, you’re right. I got the excite and inhibit arrows the wrong way around. Sadly the software for doing the diagrams lives only in the office. I’ll try to fix it tomorrow.

3. wo says:

Just for the record, I share your intuitions about Arrested Assassin and Bomb Detector, but in all other cases, I don’t have any clear intuitions either way.

I agree that the deviant/default distinction alone cannot explain these intuitions. What seems more important about Arrested Assassin vs. Bomb Detector is that in Assassin, C unwittingly causes P but intentionally T, whereas in Detector, it’s the other way round. The intentions really make a difference, I believe. Here are two variations in support of this. (They are a rather artificial because I wanted to revert the intuitions while leaving defaultness/deviance the same.)

Suppose in Arrested Assassin, Enemy and his brother Enemy2 know that Friend is about to hire Assassin1 to kill Victim. They want to prevent this (secretly, to avoid Friend’s revenge). To this end, Enemy2 anonymously sends Friend a lottery ticket, hoping that the ticket will win and Friend will be so delighted that he will completely forget about his plans to kill Victim. Enemy is skeptical about this strategy, and sets up a better plan: he knows about the wire in his building and that Agent will get Assassin1 arrested if he (Enemy) hires Assassin1 to kill Victim. Since there are no other good assassins in town, this will prevent Friend from hiring somebody to kill Victim. (Friend would never do the dirty work himself.) So after double-checking the wire, Enemy hires Assassin1, and as intended, Assassin1 gets arrested by Agent. Surprisingly, in the meantime, Enemy2’s plan has worked out as well: the ticket did win the lottery and Friend completely forgot about Victim. So Victim was doubly saved. Didn’t Enemy take part in causing his survival?

Bomb Detector is easier. Suppose Mechanic wants to kill Victim. He realises that Assessin2 watches him, and also knows that Assessin2 will probably believe that the car is Bill Clinton’s upon seeing him set up the bomb detector. He also believes (wrongly) that Assessin2 will be smart enough to blow up the car with a remote controlled external bomb that is not detected by the detector. So Mechanic intends to cause Victim’s death by setting up the bomb detector. (One could add that it was him who then persuaded Victim to hire him, or that he would have set up the detector even if Victim hadn’t hire him, or something like that.)
Do you nevertheless want to say that by setting up the detector, he caused Victim’s survival?

I have to say that I’m a little skeptical about all these cases. It is too easy to confuse causing someone’s death with murdering, and causing someone’s survival with saving their life. But these are really different things.

It is also easy to confuse being causally relevant for E with being the cause of E, or being part of the cause of E.

Arrested Assassin looks a lot like accidents causing functioning body parts and rains causing fire. Here, too, it seems quite wrong to say that C causes E, even though C can reasonably be counted as one of the factors causally contributing to E. I think you’re right that our usage of “causing” (and “being a/the cause of”) are related to causative concepts. I also think it often depends on how the cases are described: if you make the absence of oxygen a live possibility (even just by talking about it), the presence of oxygen suddenly can be said to be a cause of my waking up this morning. Causal relevance seems to be less dependent on such matters, and I think this is what Lewis wanted to analyse. (Though he probably didn’t believe there is an interesting distinction between causing and being causally relevant.)

Sorry, this got way too long.

4. ejhall says:

The point about causatives seems really important. Just to see if I’ve got it, does this at least seem right as a general, “causatively-loaded” way of describing the cases—that when C protects against a threat (and happens also to provoke such a threat) it will intuitively count as a cause, but when C itselfs threatens (and happens also to provoke an effective response to that threat) then it won’t? I find my intuitive judgements about the cases lining up nicely with the intuitive appropriateness of using “protects” or “threatens”.

Your point about causatives may extend to switches as well. The engineer flips the switch, sending the train down the left-hand track instead of the right. The tracks reconverge up ahead. Case 1: No funny business; both tracks are in good working order, etc. We find the engineer’s action not to be a cause of the train’s arrival. Case 2: As before, but this time the right-hand track has a gaping hole in it, which would have been hastily fixed, just in time, had the train been sent down that track. Now there’s some pull to the idea that the engineer’s action does count as a cause of the arrival, an intuition that can be reinforced by appropriate use of causatives: In case 2 (but not case 1), it seems intuitively right to say that the engineer’s action protects against a threat.

Not sure what to make of all this…but at any rate, your distinction between short-circuits in which C protects against a kind of threat, an instance of which it also happens to trigger, and ones in which it threatens in a way that it also happens to counteract, is wonderful.

5. Wo,

I agree that intentions make a huge difference to these cases. My guess is still that they make a difference because they make a difference to whether we’d use causatives.

The variant on Bomb Detector is great for these purposes. I’d say in that case that Mechanic threatens the life of Victim, which is not something Mechanic does in the original case.

Having said that, I am worried that our responses here are just tracking facts about killing and saving lives, not facts about causal influence generally. One somewhat heretical thought about this: this could be because causation isn’t that important, at least when it comes apart from causatives.

Ned,

Thanks for the nice comments! The summary in your first paragraph is pretty much what I think. I’m sure there are going to be cases where this doesn’t work, but it seems to cover a lot.

I hadn’t thought about switching cases, but I suspect that what you say is going to be correct. We’re going to count switches as causes when, and only when, we can use causatives like ‘protect’. If we say that ‘mere causing’ is causing where a causative is inapplicable, then I think it’s true that switches (like short-circuits) will never be mere causes.

One last thought about how this stuff about causatives all links up with the work on default conditions, which is where the impetus for this post (and to some extent the previous post on Ned’s paper) came from.

I’d say it is hard, perhaps impossible, for genuinely default conditions to ever be the subject of a causative. The presence of oxygen in this room is a cause of my continued survival, as are the walls holding the higher floors up, but neither is saving my life as we speak. Similarly we can’t be killed by an event that happens by default. We can be killed by events (e.g. earthquakes) that are caused in regular ways by default events (e.g. the presence of a fault line) but the killing events are not default events.

6. wo says:

Don’t we sometimes say that the gravitational force exerted by the earth causes the plate to fall when dropped, or that the presence of the air bag in the car saved the driver’s life, or things like that?