Mill's Methods

Mill's Methods
The nineteenth century philosopher John Stuart Mill devised five methods for reasoning about cause and effect. Though they have serious limitations, they are still useful and widely taught today.

1. The Method of Agreement - Mill wrote "If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or the effect) of the given phenomenon." In other words, if there is a single circumstance that is present in all positive instances, then we can conclude that this circumstance was the cause of the phenomenon. Note that in textbooks this is often referred to as the direct the method of agreement and only looks at positive instances of the effect in question.

For example, lets say four students dined together at the cafeteria and two of them became ill with food poisoning. The students were questioned about what they ate which resulted in the following list:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
John             Yes            No           No            Yes             Yes
Tom             Yes            Yes          No            No              No
Mary            No             Yes          Yes           No              No

Based on the above information, we can conclude that it was the beans that gave Carla and John food poisoning as this was the only potential cause that was present in both instances.

Though not listed by Mill, some textbooks also refer to what is called the Inverse Method of Agreement (or Negative Method of Agreement). The Inverse Method of Agreement allows one to conclude that a certain circumstance is the cause of the phenomenon under investigation if this circumstance is the only circumstance (of those considered) that is absent in all negative instances.

Using the above example, the inverse method of agreement would lead us to look at the negative instances of Tom and Mary not getting food poisoning. Here we find the beans to be only potential cause which were absent in both cases and can thus conclude them to be the cause.

2. The Method of Difference - "If an instance in which the phenomenon under investigation occurs and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former, the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon." In other words, if there is a positive and a negative instance where the presence or absence of all possible causes are the same except one cause which is present in the positive instance and absent in the negative instance, then it can be concluded to be the cause of the phenomenon. Note that the method of difference looks at both  positive and negative instances of the effect in question.

Using the food poisoning example above there are two relevant instances where the method of difference can be applied:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
Mary            No             Yes          Yes           No              No

Since the only potential cause in which they differ is present in the positive instance and absent in the negative instance, we can conclude it was the beans that caused the food poisoning.

3. The Joint Method of Agreement & Difference - "if two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon."  There seems to be a fair amount of controversy over this method among those scholars that examine such things. The biggest criticisms seem to be that The joint method/indirect method is not really a combination of the method of agreement and method of difference. Also, the definition above as provided by Mill is restrictive in that it does not allow full achievement of the intended purpose of the joint method. A more usable amended joint method of agreement & difference is provided by Skorupski:

"If two or more instances in which the phenomenon occurs have a circumstance in common, while in two or more instances in which the phenomenon does not occur that circumstance is absent, and if there is no other circumstance or combination of circumstances which is present in all the instances in which the phenomenon occurs, and absent in all the instances in which it does not occur, then the given circumstance is the effect, or the cause, or an indispensable part of the cause, of the phenomenon."

This can be summarized as the circumstance which alone is present in all the positive instances and absent in all the negative instances.

Here is a modified version of the food poisoning example which demonstrates the amended joint method:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
Ann              Yes            Yes          No            Yes            Yes
Doug            Yes            No           No            No              No
Byron           No             Yes          No            No              No

With this example, the method of agreement does not give a unique answer since there are two positive circumstances (fries and beans) present in both positive instances. The method of difference also does not provide an answer since there is not a positive and negative instance where all causes are the same except a single cause which is positive in one instance and negative in the other. However, using the amended joint method we find that the beans are the cause as they are the only circumstance which is present in all positive instances and absent in all negative instances.

4. The Method of Residue - "Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents."

5. The Method of Concomitant Variation - "Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation."