REASONING ABOUT CAUSATION
In the last chapter we discussed Mill’s methods and their limitations. Here are some further issues to consider about causation. In many situations, causes are correlated with their effects. An event C is said to be positively correlated with E when the presence of C increases the probability that E will also occur. C is said to be negatively correlated with E when C decreases the probability of E. If C has no effect on the probability of E, then C is not correlated with E, or C is independent of E. So for example, the appearance of lightning is positively correlated with thunder, negatively correlated with a clear sky, and presumably not at all correlated with the day of the week.
Correlation is about how often two things are associated with each other, so it is a matter of degree. Lightning is inevitably followed by thunder,1 and there is no thunder without lightning. This is 100% or a perfect correlation. Smoking is positively correlated with lung cancer, but obviously not all smokers will get cancer. Indeed, a low correlation between two types of events does not rule out causation in particular instances. A hunter might fail to shoot his prey most of the time, but when he succeeds his shot will be the cause of the animal’s death. Similarly, most people are fine after taking aspirin, and there is only a low positive correlation between aspirin and allergic reactions. But aspirin does cause allergic reactions in about 1% of the population. ...