Causal reasoning

​Suppose a bunch of people get upset stomachs after a dinner party. Here are the details of what the various people at the dinner party ate:

Foods eaten by people who got sick

• Person A: ham, potato salad, coleslaw
• Person B: ham, rice salad, lettuce salad
• Person C: ham, pasta salad, carrot salad.

Foods eaten by people who didn’t get sick

• Person D: chicken, rice salad, coleslaw
• Person E: sausages, pasta salad, lettuce salad
• Person F: bean salad, potato salad, carrot salad

Probably, the ham caused the illness.

Why?

• All those who got sick ate ham
• All those who didn’t get sick didn’t eat ham
• There’s nothing else that was eaten by all and only those who got sick
• Eating bad ham is the kind of thing that we expect to causes upset stomachs – we know roughly how this happens (unlike, for example, something else that the people who got sick might have had in common such as all wearing red shirts).  

Note that it could have been true that the ham caused the illness even if it wasn’t true that all and only the ham-eaters got sick – eating ham might have raised the probability of someone’s getting sick without guaranteeing that they would get sick (some people have cast-iron constitutions).

Causal statements are sentences which say that one thing causes, or doesn’t cause, another thing.  For example, smoking causes lung cancer, drinking coffee after dinner makes me stay awake, reading logic textbooks after dinner puts me to sleep.

Causal statements are made all the time, both in everyday conversation and in the context of scientific research. We need to know what kinds of effects our actions and other people’s actions are likely to have, so that we can decide what we should do in any given situation. Doctors often need to know the causes of diseases in order to know how to treat them. Airlines need to know what caused a particular plane-crash so that they can ensure that the same thing won’t cause another one.

Causal arguments consist of a causal claim plus the reasons we have for believing that claim.  Suppose that American Airlines claims that their plane hit a mountain because the altimeter wasn’t working properly and visibility was extremely poor because of low cloud. Their reasons for believing this claim might include records which show that the altimeter was reading fifteen thousand feet just before the plane hit the mountain, when the mountain is nothing like that tall; a tape recording of the pilot’s exclamation as he saw the mountain emerge from the fog in front of him, and so on. If you list these reasons as premises and the causal claim as a conclusion, you have a causal argument.

Causal arguments are non-deductive. In the plane case, for example, you can list all the evidence you want and it will still not be 100% certain that you’re right about what caused the crash. But it can still be a very good argument.

Consider a more general causal claim: Attending St Peter’s Cambridge causes people to get better NCEA results. Suppose we do the stats and it turns out that indeed, the average marks of students at St Peter’s are higher than the average mark for the country at large. Does that provide good reason to believe the causal claim?

No, not on its own. Correlation is not proof of causation. There are other possibilities that you should consider before accepting a causal argument like this one.

1. Coincidence. Might it be pure chance that students at St Peter’s did better?
2. Common cause. Perhaps there is some underlying factor which both makes it likely that students will go to St Peter’s and makes it likely that they will get good marks: having wealthy parents, perhaps, or having parents who care about their children’s education and therefore are likely to both send them to a school with a good reputation and to make sure they do their homework.If you wanted to rule out those alternatives, you should conduct a more complex study. Take a group of students which are the same as your group of St Peter’s students in all relevant respects except for which school they go to. Then see if the St Peter’s students do better than this control group. If they do, and you’ve really thought of all other relevant factors, you then have much better reason than before to think your causal claim – going to that school causes you to get better marks – is justified.
3. Opposite direction of causation. I don’t think this applies in this case, but sometimes when people infer causation from correlation, they mistake the cause for the effect. Here is an example. New Hebrides Islanders used to believe that lice caused good health. Why? All the healthy islanders were infested with lice, while sick islanders weren’t. In fact, it turned out, the causal connection went the other way. Lice would jump ship when their hosts got a fever, because they don’t like high temperatures – so getting sick caused the absence of lice, rather than the absence of lice causing you to get sick. Just from the correlation between health and the presence of lice, you can’t infer that the lice cause good health: in this case, the causing went in the other direction.How was the truth about this discovered? I don’t know. But it might have been discovered by paying close attention to the order of events. If X doesn’t come before Y, then X can’t cause Y.  (But if X does come before Y, that doesn’t necessarily mean X causes Y, of course.)

Having a theory to explain how the causal process in question works is also important.  If you discover on independent grounds that lice don’t like high temperatures, that gives extra reason to think that illness causes lack of lice rather lack of lice causing illness.

Here is a causal argument:

P. Most people who take mega-doses of Vitamin C when they have a cold recover from their cold within a week.
                                              
C. Mega-doses of Vitamin C cure colds. 

We are only justified in believing this conclusion on the basis of this premise if we have considered and ruled out the likely alternatives. 

It might be that people naturally recover from colds within a week with or without Vitamin C. This would be easily tested by collected data about the recovery speed of people who don’t take megadoses of Vitamin C.

Or perhaps the people who take Vitamin C are people who care about their health and are inclined, when they have a cold, to eat chicken soup and go to bed early, and perhaps those are the factors that cause them to recover quickly, rather than the Vitamin C. The way to test this would be to observe a control group who are exactly like your test group in all relevant respects (diet, sleeping habits, etc) except that they don’t take Vitamin C, and compare the two groups.