Causal reasoning (Dr. Van Cleave)

By Matthew Van Cleave

When I strike a match, it will produce a flame.  It is natural to take the striking of the match as the cause that produces the effect of a flame.  But what if the matchbook is wet?  Or what if I happen to be in a vacuum in which there is no oxygen (such as in outer space)?  If either of those things is the case, then the striking of the match will not produce a flame.  So it isn’t simply the striking of the match that produces the flame, but a combination of the striking of the match together with a number of other conditions that must be in place in order for the striking of the match to create a flame.  Which of those conditions we call the “cause” depends in part on the context.  Suppose that I’m in outer space striking a match (suppose I’m wearing a space suit that supplies me with oxygen but that I’m striking the match in space, where there is no oxygen).  I continuously strike it but no flame appears (of course).  But then someone (also in a space suit) brings out a can of compressed oxygen that they spray on the match while I strike it.  All of a sudden a flame is produced.  In this context, it looks like it is the spraying of oxygen that causes flame, not the striking of the match.  Just as in the case of the striking of the match, any cause is more complex than just a simple event that produces some other event.  Rather, there are always multiple conditions that must be in place for any cause to occur.  These conditions are called background conditions.  That said, we often take for granted the background conditions in normal contexts and just refer to one particular event as the cause.  Thus, we call the striking of the match the cause of the flame.  We don’t go on to specify all the other conditions that conspired to create the flame (such as the presence of oxygen and the absence of water).  But this is more for convenience than correctness.  For just about any cause, there are a number of conditions that must be in place in order for the effect to occur.  These are called necessary conditions.  For example, a necessary condition of the match lighting is that there is oxygen present.  A necessary condition of a car running is that there is gas in the tank.  We can use necessary conditions to diagnose what has gone wrong in cases of malfunction.  That is, we can consider each condition in turn in order to determine what caused the malfunction.  For example, if the match doesn’t light, we can check to see whether the matches are wet.  If we find that the matches are wet then we can explain the lack of the flame by saying something like, “dropping the matches in the water caused the matches not to light.”  In contrast, a sufficient condition is one which, if present, will always bring about the effect.  For example, a person being fed through an operating wood chipper is sufficient for causing that person’s death. 

Because the natural world functions in accordance with natural laws (such as the laws of physics), causes can be generalized.  For example, any object near the surface of the earth will fall towards the earth at 9.8 m/s² unless impeded by some contrary force (such as the propulsion of a rocket).  This generalization applies to apples, rocks, people, wood chippers and every other object.  Such causal generalizations are often parts of explanations.  For example, we can explain why the airplane crashed to the ground by citing the causal generalization that all unsupported objects fall to the ground and by noting that the airplane had lost any method of propelling itself because the engines had died.  So we invoke the causal generalization in explaining why the airplane crashed.  Causal generalizations have a particular form:

For example:

Being able to determine when causal generalizations are true is an important part of becoming a critical thinker.  Since in both scientific and every day contexts we rely on causal generalizations in explaining and understanding our world, the ability to assess when a causal generalization is true is an important skill. 

For example, suppose we are trying to figure out whether CO₂ (carbon dioxide) is a contributing cause to higher global temperatures. If we see that as CO₂ levels rise, global temperatures also rise, then this is evidence that CO₂ and higher temperatures are positively correlated.  When two things are positively correlated, as one increases, the other also increases at a similar rate (or as one decreases, the other decreases at a similar rate).  In contrast, when two things are negatively correlated, as one increases, the other decreases at similar rate (or vice versa).  For example, if as a police department increased the number of police officers on the street, the number of crimes reported decreases, then number of police on the street and number of crimes reported would be negatively correlated.  In each of these examples, we may think we can directly infer the cause from the correlation—the rising CO₂ levels are causing the rising global temperatures and the increasing number of police on the street is causing the crime rate to drop.  However, we cannot directly infer causation from correlation.  Correlation is not causation.  If A and B are positively correlated, then there are four distinct possibilities regarding what the cause is:

In order to infer what causes what in a correlation, we must rely on our general background knowledge (i.e., things we know to be true about the world), our scientific knowledge, and possibly further scientific testing.  For example, in the global warming case, there is no scientific theory that explains how rising global temperatures could cause rising levels of CO₂ but there is a scientific theory that enables us to understand how rising levels of CO₂ could increase average global temperatures.  This knowledge makes it plausible to infer that the rising CO₂ levels are causing (or contributing to) the rising average global temperatures.  In the police/crime case, drawing on our background knowledge we can easily come up with an inference to the best explanation argument for why increased police presence on the streets would lower the crime rate—the more police on the street, the harder it is for criminals to get away with crimes because there are fewer places where those crimes could take place without the criminal being caught.  Since criminals don’t want to risk getting caught when they commit a crime, seeing more police around will make them less likely to commit a crime.  In contrast, there is no good explanation for why decreased crime would cause there to be more police on the street.  In fact, it would seem to be just the opposite: if the crime rate is low, the city should cut back, or at least remain stable, on the number of police officers and put those resources somewhere else.  This makes it plausible to infer that it is the increased police officers on the street that is causing the decrease in crime. 

Sometimes two things can be correlated without either one causing the other.  Rather, some third thing is causing them both.  For example, suppose that Bob discovers a correlation between waking up with all his clothes on and waking up with a headache.  Bob might try to infer that sleeping with all his clothes on causes headaches, but there is probably a better explanation than that.  It is more likely that Bob’s drinking too much the night before caused him to pass out in his bed with all his clothes on, as well as his headache.  In this scenario, Bob’s inebriation is the common cause of both his headache and his clothes being on in bed.

Sometimes correlations are merely accidental, meaning that there is no causal relationship between them at all.  For example, Tyler Vigen² reports that the per capita consumption of cheese in the U.S. correlates with the number of people who die by becoming entangled in their bedsheets:

And the number of Mexican lemons imported to the U.S. correlates with the number of traffic fatalities³:

Clearly neither of these correlations are causally related at all—they are accidental correlations.  What makes them accidental is that we have no theory that would make sense of how they could be causally related.  This just goes to show that it isn’t simply the correlation that allows us to infer a cause, but, rather, some additional background theory, scientific theory, or other evidence that establishes one thing as causing another.  We can explain the relationship between correlation and causation using the concepts of necessary and sufficient conditions: correlation is a necessary condition for causation, but it is not a sufficient condition for causation.

Our discussion of causes has shown that we cannot say that just because A precedes B or is correlated with B, that A caused B.  To claim that since A precedes or correlates with B, A must therefore be the cause of B is to commit what is called the false cause fallacy.  The false cause fallacy is sometimes called the “post hoc” fallacy.  “Post hoc” is short for the Latin phrase, “post hoc ergo propter hoc,” which means “after this therefore because of this.”  As we’ve seen, false cause fallacies occur any time someone assumes that two events that are correlated must be in a causal relationship, or that since one event precedes another, it must cause the other.  To avoid the false cause fallacy, one must look more carefully into the relationship between A and B to determine whether there is a true cause or just a common cause or accidental correlation.  Common causes and accidental correlations are more common than one might think.

Do Quiz 5a before moving further in the course.