14.2 Types of Explanation
Explanations are used to support the premises of an argument, in an attempt to establish why something is the case. Learn the different kinds of explanation and how to evaluate causal explanations.
Table of Contents
- 14.2 Types of Explanation
14.2.1 What is an Explanation?
What does an explanation do?
Explanations and Arguments
We have spent most of this class studying arguments. An argument attempts to establish that something is the case (its conclusion). An argument is not the same thing as an explanation. An explanation attempts to establish why something is the case (the explanandum, the thing explained). Explanations are still very important in sound reasoning, however. For instance, one of the argument forms we studied earlier, “Inference to the Best Explanation”, argues that a conclusion is true because it would best explain some of the information in the premises. So, we will spend this module studying explanations.
Matthew Van Cleve (2016) presents the following contrast between an argument and an explanation:
“Many times the goal of giving an argument is simply to establish that the conclusion is true. For example, when I am trying to convince someone that obesity rates are rising in the U.S. I may cite evidence such as studies from the Center for Disease Control (CDC) and the National Institute of Health (NIH). The studies I cite would function as premises for the conclusion that obesity rates are rising…
“However, sometimes we already know that a statement or claim is true and we are trying to establish why it is true rather than that it is true. An argument that attempts to show why its conclusion is true is an explanation. Contrast the previous example with the following:
‘The reason that the rate of obesity is on the rise in the U.S. is that the foods we most often consume over the past four decades have increasingly contained high levels of sugar and low levels of dietary fiber. Since eating foods high in sugar and low in fiber triggers the insulin system to start storing those calories as fat, it follows that people who consume foods high in sugar and low in fiber will tend to store more of the calories consumed as fat.’
“This passage gives an explanation for why obesity is on the rise in the U.S. Unlike the earlier example, here it is taken for granted that obesity is on the rise in the U.S. That is the claim whose truth we are trying to explain…
“In an explanation we assume that what we are trying to explain (i.e., the conclusion) is true. In this case, the premises are supposed to show why we should expect or predict that the conclusion is true. Explanations often give us an understanding of why the conclusion is true.” (pp. 8-9)
Four Types of Reasons Why
The word “reason” as we’ve been using it so far typically means a reason to believe something is true, “evidence” or “justification”. There is another way to use the word “reason”, however, which has to do with a reason why something is the case: what makes something true, as opposed to why we believe it to be true. For instance, a jury might conclude that somebody committed a murder because of their fingerprints found on the trigger of the murder weapon. What justifies the jury in believing this are the fingerprints on the murder weapon. What makes it true that the person committed the murder (assuming they did), however, is not that their fingerprints were found on the murder weapon. Instead, it is that they actually pulled the trigger with the intention to kill.
Aristotle, in his books Physics and Metaphysics, classified reasons why something is the case into four types, which using his terminology he called the “four causes”. The traditional terminology (“causes”) is confusing, because only one of them involves anything like what we would call causation; it would be better to translate it as the “four becauses”. They are as follows:
- definitional explanations (“formal becauses”) of what makes something what it is.
- functional explanations (“final becauses”) of what something is for, it’s purpose.
- compositional explanations (“material becauses”) of what something is made out of.
- causal explanations (“efficient becauses”) of what makes things happen.
Although Aristotle’s system is no longer used in most of modern physics or metaphysics, it does still provide a useful system of categories when we are studying the ways in which we intuitively explain why something is the case. We will spend time looking at each category.
14.2.2 Definitional Explanations
A dictionary explains what a dictionary is.
Definitional Explanations
Definitional explanations attempt to explain something in terms of what it is to be the kind of thing that it is. Imagine you are attempting to explain what a concept or thing is to somebody entirely unfamiliar with it, like trying to explain automobiles for a person living in the 18th century, or trying to explain the internet to somebody who lives in isolation from technology. The first kind of explanation you’re going to have to give is simply a definition: here is what an automobile is, here is what the internet is. You have to clarify those concepts before you can do anything else.
The word “definition” doesn’t mean dictionary definition. Dictionary definitions are guidelines for how to properly use words. Instead, the idea is that there are criteria for actually being a certain thing, not set by the dictionary, but set by the kinds of things there are, and we want to explain what those criteria are. For instance, a table with wheels is not an automobile, because part of the definition of an automobile is that it is designed for moving from one place to another without being pushed by an outside force, and while we might move a table with wheels, we’d have to push it from the outside in order to do so. Similarly, a paperback book full of crossword puzzles is not the internet, even though it contains information, because part of being the internet is connecting information in different places over great distances. On the other hand, a broken down automobile being pushed around is still an automobile, even though it doesn’t currently move from one place to another on its own, because it was intended or designed to do so. Likewise, the internet in 1990 was still the internet, even though it was very slow and had far less information than the internet has now.
The criteria used in formulating a definition are called necessary and sufficient conditions:
A is a necessary condition of B if and only if every possible B is an A.
A is a sufficient condition of B if and only if every possible A is a B.
For instance, being an unmarried-but-eligible male is a sufficient condition for being a bachelor, because every possible unmarried-but-eligible male is a bachelor. It is also a necessary condition for being a bachelor, because every possible bachelor is an unmarried-but-eligible male. On the other hand, being male, by itself, is a necessary but not sufficient condition for being a bachelor, because every possible bachelor is male, but not every male is a bachelor.
Recognizing Non-Sufficient Conditions
It is difficult to give sufficient conditions for most things, or to give “complete” definitions. Practically speaking, it is a more useful skill to be able to identify why certain things are not sufficient conditions than it is to try to actually give sufficient conditions. Through identifying why a definition isn’t sufficient and gradually adding to it, we can start to approximate more complete definitions. A is not a sufficient condition for B when it is possible to be A without being B. For instance, “killing” is not a sufficient condition for “murder”, because some killings are not murders, like killing in war or self-defense. “Unjustified killing” is still not a sufficient condition for “murder”, because the killing might have been unintentional or an accident. “Intentional unjustified killing” is still not a sufficient condition for “murder”, because killing plants is not murder. “Intentional unjustified killing of a person” probably comes much closer to being a sufficient condition for “murder”. Can you think of any exceptions?
Recognizing Necessary and Non-Necessary Conditions
On the other hand, it is not difficult to give necessary conditions for most things. Killing is certainly a necessary condition for being a murder, since there can’t be a murder if nothing is killed. Being an animal is a necessary (but not sufficient) condition for being a cat, and being unmarried is a necessary (but not sufficient) condition for being a bachelor.
What’s very tricky is not accidentally mistaking something for a necessary condition which is not a necessary condition. For example, it is not a necessary condition for being a murder that the killer had evil intentions. Somebody suffering from delusions might mistakenly believe they are justified in killing when they are not. It is not a necessary condition of being an automobile that the vehicle run on gasoline, since there are electric cars, and it is not a necessary condition of being a cat that something have a tail and four legs, since there are cats without tails and cats missing legs. Being interested in the opposite sex is not a necessary condition for being a bachelor, and being easily searchable through a search engine is not a necessary condition for being the internet. A table is still a table even if it doesn’t have multiple legs. A very common fallacy is mistaking something which is commonly associated with a thing for part of the definition of that thing. For instance, the majority of college students are between the ages of 18-24, but it is highly problematic when people or institutions assume that this is a necessary condition for being a college student, or use the phrase “college student” as though it meant “18-24 year old”, since a large number of students are 25 or older.
The Genetic Fallacy
The genetic fallacy occurs when one argues (or, more commonly, implies) that the cause or origin of something (e.g., a theory, idea, policy, etc.) is a reason for rejecting (or accepting) it. It involves confusing the cause of something with its definition or nature.
For example, suppose that Jack is arguing that we should allow physician assisted suicide and Jill responds that that idea first was used in Nazi Germany. Jill has just committed a genetic fallacy because she is implying that because the idea is associated with Nazi Germany, there must be something wrong with the idea itself. What she should have done instead is explain what, exactly, is wrong with the idea rather than simply assuming that there must be something wrong with it since it has a negative origin. The origin of an idea has nothing inherently to do with its truth or plausibility. Suppose that Hitler constructed a mathematical proof in his early adulthood (he didn’t, but just suppose). The validity of that mathematical proof stands on its own; the fact that Hitler was a horrible person has nothing to do with whether the proof is good. Likewise with any other idea: ideas must be assessed on their own merits and the origin of an idea is neither a merit nor demerit of the idea and does not tell us about its nature.
People often make this argument with the etymology of a word. The etymology of a word is the cause or origin of the word, what it originally meant historically to people long ago: for instance, the word “window” derives from a root meeting “wind-eye”. This does not mean you should consult an optometrist about your broken windows. The current meaning of a word is often not the same as its etymology. The meaning of a word is determined by how it is currently used by the community of people who use it. The genetic fallacy occurs with somebody infers that the history of something determines its current definition
14.2.3 Functional Explanations
Wings are for flying.
Functional Explanations
One of the most basic kinds of explanation that even young children understand is what something is for, its purpose or function. Chairs are for sitting on, can openers are for opening cans, and forks are for eating with. Cars are for transportation, the wings of a bird are for flying, eyes are for seeing, hearts are for pumping blood, and boots are made for walking. Not all things have clear purposes (what is the function of dust?), but most things we encounter both in the natural world and in the world of human artifacts do. Flowers and leaves on plants have functions, and so do plastic bags and cups of coffee. Within a particular social role, people have functions: the role of a firefighter is to fight fires.
Functions can shift and change. The internet was not originally designed for e-commerce. Things can be put to new uses: trees are not naturally for windbreaks, but trees can be planted to serve as windbreaks. The social function of a thing might be different from its original function: watches are for telling time, but socially an expensive watch may begin to function as a sign of wealth or status. The plasticity of the brain means that other parts of the brain ordinarily for one purpose can come to take over the functions of the parts of the brain which were damaged. In evolutionary theory, there are “spandrels” which originally arise as a byproduct of other adaptations, rather than things which were originally adapted for a certain purpose, but these spandrels then go on to become adaptive or beneficial in some other way. The fact that functions can shift and change does not mean they are merely “in the eye of the beholder”, however.
Intentions
What something is for is not always the same as what it was designed or intended to do. Incandescent light bulbs may be designed to burn out quickly so that you have to buy new ones from the manufacturer, and certain parts of a car may be designed to break down in order to keep the car parts company in business, but car parts are not for breaking down, and light bulbs are for lighting up, not for burning out.
At the same time, the way somebody represents the function of something they do or make, their intention, is usually evidence of the true function of what they have done or made. When you install a program on your computer or an app on your phone, it’s common to read the description first of what it was intended it to do. Most actions people take have some intended function, and it’s important to living in society that we be aware of and attentive to the intentions of the actions of others. For instance, when the driver in front of you turns on their right turn signal, it’s important to slow down, because you interpret the intended function of their action as signaling that they are about to turn left.
Malfunctions
Having a function does not mean achieving that function. A bad can opener is still for opening cans, and a broken down car is still for transportation. Kidneys are for filtering the blood and ears are for hearing even when they do not perform those functions. Many apps or programs are worthless and terrible at doing what they were intended to do. The fact that something can fail, break down, or otherwise malfunction is evidence that it had a function to begin with, and studying the ways things malfunction can inform us about what their functions are. The ways people complain about governments tells us about what they believe the function of governments to be, for instance.
Misattributing Intentions
Functional explanations are very intuitive for humans, and very useful for us, since we constantly use tools of various sorts with different roles and functions and we live social lives in which we constantly have to guess at the intentions of other people. When faced with a choice between attributing an intended function and assuming something has no function, we tend to err on the side of attributing intentions or functions.
For instance, imagine yourself walking through the woods, when you hear the leaves rustle behind you. Should you believe that the leaves were rustled by some animal or person sneaking up behind you, and look behind you to see what is there, or should you think it is just the wind? If you believe you are being stalked, but you aren’t, the worst that happens is you are delayed a moment to look behind you. If you believe it is just the wind, but you are being stalked, on the other hand, failing to look behind you could be deadly. So, it is safer to assume events around you are the result of intentions even when they aren’t, than to assume they aren’t even when they are. In the social world, suppose that you receive an email from a person you haven’t heard from in many years inviting you to lunch. It’s possible they just miss you and want to catch up. But it is also possible that they have some other intentions: they want you to join their multi-level marketing program, or they want to ask for your help finding a job, or they want to sell you life insurance. It is often safer to read intentions into other people which aren’t there.
This tendency can become a problem, however, because often the intentions we attribute to other people aren’t there. We interpret other peoples’ blank stares as judgment or criticism, or we interpret their silence as rejection. We look at a photograph of somebody, and read into the expression they happened to have when the photo was taken all sorts of assumptions about their intentions and character.
The Fundamental Attribution Error
The fundamental attribution error is the fallacy of explaining the actions or behavior of other people as resulting from some intended, planned, fixed, stable part of their personality or character, rather than explaining them in terms of chance or whim. For example, when a cashier is rude to you as you are checking out (or when a customer is rude, if you are the cashier), the fundamental attribution error is the mistake of concluding that the cashier or customer is generally rude, that they are an uncourteous person, and that their behavior is intentionally directed against you. This is a form of the fallacy of hasty generalization, discussed earlier in the class. The actions we observe of strangers are a snapshot of how they act in a particular context, and not necessarily a sign of who they are or what they are like generally.
To guard against the fundamental attribution error, try to keep in mind the possible contexts in which another person might be reacting. The rude cashier might be upset by the rudeness of the previous customer they had to deal with, or the rude customer might be upset because they didn’t sleep well, they feel sick, and are running late for work. The driver who is tailgating you might be a habitual tailgater, but they might also normally be a good driver who just happens to be in an unusual hurry to get to the hospital. The protestors with the giant sign yelling the slogan at the top of their lungs along with the rest of the crowd might be very upset at the moment, but they probably don’t act that way at work.
Thinking in terms of functions and intentions is extremely useful, but it is important to also be aware that it is easy to over-extend these concepts.
14.2.4 Compositional Explanations
Concrete is made from sand, water, and cement.
Taking Things Apart
Some children go through a stage during which their goal becomes disassembling everything in the house, from emptying the kitchen cupboards to taking apart their toys and trying to put them back together again. In fact, an important way in which we humans come to understand and explain things is through taking them apart. This is how compositional explanations work: we understand the whole through understanding the parts which compose it. For instance, a chemist will explain why chemical reactions happen in terms of the molecular properties of each chemical, or a biologist will explain how a disease progresses in terms of the behaviors of cells. Explaining a company to a newly hired employee means explaining each of the divisions and departments of the company to them. If you want to understand what you are eating, you read the list of ingredients printed on the label.
The composition of a thing is not always a part of its definition or a necessary condition of it. A sculptor can make the same image out of bronze, lead, clay, or glass. The people who make up a company can completely change over the course of five years, but the company continues to exist. So, compositional explanations are not the same as definitional explanations. How well or poorly a thing fulfills its function depends on its composition: nails made out of cheap metals are less effective at holding things together than those made out of steel. But the composition of a thing is not what it is for, and compositional explanations are not functional ones.
While compositional explanations are very important, and without them scientists and engineers would have nothing to work with, in a logic class we have to pay attention to the ways in which they sometimes go wrong. These are the whole-parts fallacies, known as the fallacy of composition and the fallacy of division.
The Fallacy of Composition
Consider the following argument:
1. Each member on the gymnastics team weighs less than 110 lbs.
C. The whole gymnastics team weighs less than 110 lbs.
This argument commits the composition fallacy. In the composition fallacy, one argues that since each part of the whole has a certain feature, it follows that the whole has that same feature.
However, you cannot generally identify any argument that moves from statements about parts to statements about wholes as committing the composition fallacy because whether or not there is a fallacy depends on what features we are attributing to the parts and wholes. Here is an example of an argument that moves from claims about the parts possessing a feature to a claim about the whole possessing that same feature, but doesn’t commit the composition fallacy:
1. Every part of the car is made of plastic.
C. The whole car is made of plastic.
This conclusion does follow from the premises; there is no fallacy here. The difference between this argument and the preceding argument (about the gymnastics team) isn’t their form. In fact both arguments have the same form:
1. Every part of X has the feature f.
C. The whole X has the feature f.
And yet one of the arguments is clearly fallacious, while the other isn’t. The difference between the two arguments is not their form, but their content. That is, the difference is what feature is being attributed to the parts and wholes. Some features (like weighing a certain amount) are such that if they belong to each part, then it does not follow that they belong to the whole. Other features (such as being made of plastic) are such that if they belong to each part, it follows that they belong to the whole.
Here is another example:
1. Every member of the team has been to Paris.
C. The team has been to Paris.
The conclusion of this argument does not follow. Just because each member of the team has been to Paris, it doesn’t follow that the whole team has been to Paris, since it may not have been the case that each individual was there at the same time and was there in their capacity as a member of the team. Thus, even though it is plausible to say that the team is composed of every member of the team, it doesn’t follow that since every member of the team has been to Paris, the whole team has been to Paris. Contrast that example with this one:
1. Every member of the team was on the plane.
C. The whole team was on the plane.
This argument, in contrast to the last one, contains no fallacy. It is true that if every member is on the plane then the whole team is on the plane. And yet, these two arguments have almost exactly the same form. The only difference is that the first argument is talking about the property, having been to Paris, whereas the second argument is talking about the property, being on the plane. The only reason we are able to identify the first argument as committing the composition fallacy and the second argument as not committing a fallacy is that we understand the relationship between the concepts involved. In the first case, we understand that it is possible that every member could have been to Paris without the team ever having been; in the second case we understand that as long as every member of the team is on the plane, it has to be true that the whole team is on the plane. The take home point here is that in order to identify whether an argument has committed the composition fallacy, one must understand the concepts involved in the argument.
The Fallacy of Division
The division fallacy is like the composition fallacy and they are easy to confuse. The difference is that the division fallacy argues that since the whole has some feature, each part must also have that feature. The composition fallacy, as we have just seen, goes in the opposite direction: since each part has some feature, the whole must have that same feature. Here is an example of a division fallacy:
1. The house costs 1 million dollars.
C. Each part of the house costs 1 million dollars.
This is clearly a fallacy. Just because the whole house costs 1 million dollars, it doesn’t follow that each part of the house costs 1 million dollars. However, here is an argument that has the same form, but that doesn’t commit the division fallacy:
1. The whole team died in a plane crash.
C. Each individual on the team died in a plane crash.
In this example, since we seem to be referring to one plane crash in which all the members of the team died (“the” plane crash), it follows that if the whole team died in the crash, then every individual on the team died in the crash. So this argument does not commit the division fallacy. In contrast, the following argument has exactly the same form, but does commit the division fallacy:
1. The team played its worst game ever tonight.
C. Each individual on the team played their worst game ever tonight.
It can be true that the whole team played its worst game ever even if it is true that no individual on the team played their worst game ever. Thus, this argument does commit the fallacy of division even though it has the same form as the previous argument, which doesn’t commit the fallacy of division. This shows (again) that we must rely on our understanding of the concepts involved in the argument. Some concepts (like “team” and “dying in a plane crash”) are such that if they apply to the whole, they also apply to all the parts. Other concepts (like “team” and “worst game played”) are such that they can apply to the whole even if they do not apply to all the parts, and these can lead our compositional explanations to turn into fallacies.
14.2.5 Causal Explanations
Striking one billiard ball causes the others to move also.
Causal Explanations
The kind of explanation we use most often is causal explanation, when some event in the past explains why some effect happened after it. For instance, eating legumes in the past causes the effect of excess gas, working in the summer sun causes the effect of sweat, and a past failure to bathe causes the future effect of foul body odor. Engine failure might cause an airplane accident, a lack of oversight might cause election fraud, and a corporation’s bad behavior might cause a consumer boycott.
Causal explanations are unlike other forms of explanation, because the explanation (cause) is always before the thing it explains (the effect). For instance, consider a table. The wood which composes the table occurs at the same time as the table, and the function of the table for eating or writing upon can only occur after the table exists. On the other hand, the making of the table in a workshop must occur before the table exists. So the making of the table is a cause of the table.
Complexity and Context
Causal explanations can get complicated quickly. For example, 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 a 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. So, which of these conditions is actually the cause?
In some sense, all of them are causes or causal influences on the effect. Which one of the causes we choose to focus on and call “the cause” will depend 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, and our knowledge of what background conditions tend to be the case is called “background knowledge”.
Necessary and Sufficient Causal 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 (as was the fate of Steve Buscemi’s character in the movie Fargo).
Causal Generalizations
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 any x, if x has the feature(s) F, then x has the feature G
For example:
- For any human, if that human has been fed through an operating wood chipper, then that human is dead.
- For any engine, if that engine has no fuel, then that engine will not operate.
- For any object near the surface of the earth, if that object is unsupported and not impeded by some contrary force, then that object will fall towards the earth at 9.8 m/s2.
Causal Counterfactuals
Causal relationships are often expressed through the use of counterfactuals, statements about what would have gone differently if the cause had not been present. For instance, somebody arguing that human carbon emissions are a cause of global warming would want to establish that, were it not for these emissions, not as much warming would occur. Similarly, somebody who wants to argue that discrimination caused them to miss out on a promotion would want to establish that, were it not for the discrimination they faced, they would have received the promotion. More simply, dropping a glass vase causes it to shatter, since were the vase not dropped, it wouldn’t have shattered. The logical form of a counterfactual is:
If it were not for C, then E would not have happened.
It can be tricky trying to determine what would have happened, since so many different things could have happened. It could have happened that the vase wasn’t dropped, but the vase still shattered, because the person holding it smashed it with a hammer. But not everything that could have happened is what would have happened. When determining what would have happened, we need to keep fixed everything else which isn’t part of the relationship between the cause and the effect. If, in the real world, the person holding the vase didn’t have a hammer and wasn’t about to smash the vase, then it’s safe to assume that, were the vase not dropped, it wouldn’t have broken. We have to rely on our background knowledge of the world in order to evaluate what would have happened, in particular our knowledge of what causal generalizations are true. We know that “for any object, if it is fragile, then when it falls to the floor it will break” is a true causal generalization, whereas it is not true that “for any object, if it is held in a person’s arms, then they will hit it with a hammer”.
Correlation and Causation
Two variables are said to be correlated when one tends to occur simultaneously with another. For instance, cold weather and the rate of people wearing warm clothes are correlated, as are warm weather and the rate of people wearing swimsuits. Often, correlations are explained by causal relationships: if A and B are correlated, then often either A causes B, or B causes A. It is the cold weather which causes people to wear warm clothes, and the warm weather which causes people to go swimming. To check which is the cause and which is the effect, the counterfactual test earlier is helpful:
- “Were the weather not cold, people wouldn’t wear warm clothes”, and “Were the weather not hot, then people would not wear swimsuits”, are both true.
- “Were people not to wear warm clothes, the weather wouldn’t be cold”, and “Were people not to wear swimsuits, then the weather would not be warm”, are both false.
Sometimes, however, a correlation between two variables can occur even though one doesn’t cause the other. The fallacy of concluding that every correlation involves causation, the “correlation to causation” fallacy, neglects two possibilities:
- A and B might have a common cause, C. For instance, wearing swimsuits and eating ice cream are correlated, because both result from warmer weather. Were it not for the warmer weather, people would neither wear swimsuits nor eat as much ice cream.
- A and B might be only accidentally correlated. For instance, U. S. margarine sales and divorce rates in Maine are correlated, but there is no plausible common cause here. It is not plausibly the case that, were people to buy less margarine over the whole U. S., marriages of people in Maine would last longer, or vice-versa.
Again, we have to rely on our background knowledge about the world when evaluating whether a correlation is likely to involve causation, or some other relationship.
14.2.6 Mill’s Methods
J. S. Mill (1806 – 1873), author of “A System of Logic”
Mill’s Methods
Philosopher John Stuart Mill devised a set of five careful methods (or canons) by means of which to analyze and interpret our observations for the purpose of drawing conclusions about the causal relationships they exhibit.
In order to see how each of the five methods work, let’s consider their practical application to a specific situation. Suppose that on an otherwise uneventful afternoon, the College Nurse becomes aware that an unusual number of students are suffering from severe indigestion. Ms. Hayes naturally suspects that this symptom results from something the students ate for lunch, and she would like to find out for sure. The Nurse wants to find evidence that will support a conclusion that “Eating X causes indigestion.” Mill’s Methods can help.
Method of Agreement
Suppose that four students come to Ms. Hayes with indigestion, and she questions each about what they had for lunch. The first had pizza, coleslaw, orange juice, and a cookie; the second had a hot dog and french fries, coleslaw, and iced tea; the third ate pizza and coleslaw and drank iced tea; and the fourth ate only french fries, coleslaw, and chocolate cake. Ms. Hayes, of course, concludes that “Eating coleslaw caused the indigestion.”
This is an application of Mill’s Method of Agreement: investigation of the cases in which the effect occurred revealed only one prior circumstance that all of them shared. Our customary notion here is that similar effects are likely to arise from a similar cause, and since everyone who fell ill had eaten coleslaw, it was probably the cause.
Method of Difference
On the other hand, suppose that only two students arrive at the Nurse’s office. The two are roommates who ate together, but one became ill while the other did not. The first had eaten a hot dog, french fries, coleslaw, chocolate cake, and iced tea, while the other had eaten a hot dog, french fries, chocolate cake, and iced tea. Again, Ms. Hayes concludes that the coleslaw is what made the first roommate ill.
This reasoning applies Mill’s Method of Difference: comparison of a case in which the effect occurred and a case in which the effect did not occur revealed that only one prior circumstance was present in the first case but not it the second. In such situations, we commonly suppose that, other things being equal, different effects are likely to arise from different causes, and since only the student who had eaten coleslaw became ill, it was probably the cause.
Joint Method of Agreement and Difference
Now put these two situations together by assuming that eight students come to Ms. Hayes: four of them suffered from indigestion, and with each of these four there is another who did not. Each pair of students had exactly the same lunch, except that everyone in the first group ate coleslaw and no one in the second group did. The Nurse arrives at the same conclusion.
This situation is an example of Mill’s Joint Method of Agreement and Difference: the first four students are evidence that everyone who got ill had eaten coleslaw, and the four matching pairs are evidence that only those who got ill had eaten coleslaw. This is a powerful combination of the first two methods, since it tends to support our notion that genuine causes are necessary and sufficient conditions for their effects.
Method of Concomitant Variation
Change the situation again. Suppose that the Nurse sees five students: the first ate no coleslaw and feels fine; the second had one bite of coleslaw and felt a little queasy; the third had half a dish of coleslaw and is fairly ill; the fourth ate a whole dish of coleslaw and is violently ill; and the fifth ate two servings of coleslaw and had to be rushed to the hospital. The conclusion is again that coleslaw caused the indigestion.
This is an example of Mill’s Method of Concomitant Variation: the evidence appears to show that there is a direct correlation between the degree to which the cause occurred and the degree to which the effect occurred. This conforms to our ordinary supposition that effects are typically proportional to their causes. In effect, this is a sophisticated version of the Joint Method, one in which we notice not just the occurrence or non-occurrence of the causal terms, but the extent to which each of them took place.
Method of Residues
Finally, suppose that Ms. Hayes, during prior investigations of student illness, has already established that pizza tends to produce a rash and iced tea tends to cause headaches. Today, a student arrives at the Nurse’s office complaining of headache, indigestion, and a rash; this student reports having eaten pizza, coleslaw, and iced tea for lunch. Since she can account for most of the student’s symptoms as the effects of known causes, Ms. Hayes concludes that the additional effect of indigestion must be caused by the additional circumstance of eating coleslaw.
This pattern of reasoning exemplifies Mill’s Method of Residues: many elements of a complex effect are shown to result, by reliable causal beliefs, from several elements of a complex cause; whatever remains of the effect must then have been produced by whatever remains of the cause. Notice that if we suppose the truth of all of the causal relationships involved, this method becomes an application of deductive reasoning.
As a general qualification on the reliability of these Methods, notice that the issue of relevance is again crucial. Our Nurse began with the assumption that what students had eaten for lunch was relevant to their digestive health in the afternoon. That’s a reasonable guess, but of course the real cause could have been something else entirely, something about which the Nurse never thought to ask. No matter how much evidence we gather, inductive reasoning cannot achieve perfect certainty.
Discovery, Not Proof
Although Mill’s Methods are an important component of serious investigation of natural phenomena, they have significant limitations. Careful application of these methods succeeds only when every relevant antecedent circumstance is taken into account, and that is impossible to guarantee in advance. Perhaps it is best to regard Mill’s Methods more modestly, as tools we can employ in our efforts to confirm hypotheses about the natural world. If we have already proposed several specific hypotheses about what may be the cause of an observed event, then using the Methods will be helpful, since that will often enable us to eliminate most of the possible causes we have identified, and this tends to confirm the hypothesis that any remaining circumstance is likely to be the genuine cause.
Submodule 14.2 Quiz
Licenses and Attributions
Key Sources:
- Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
- Van Cleave, Matthew (2016), Introduction to Logic and Critical Thinking, under license CC BY-SA 4.0 (Especially §4.1.1-4.1.2, 158-167)
- Kemerling, Garth (2011), “The Philosophy Pages”, under license CC BY-SA 3.0
Next Page: 15.1 Social Freedoms and Responsibilities