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Mill's Methods of Induction: Decision Rules for Causal Inference

 

Mill's Methods of Induction

Title page of Mill's "A System of Logic"John Stuart Mill's "methods of induction" are five basic rules for making inductive causal inferences. The rules were first described in the 1848 edition of Mill's classic A System of Logic and were retained through all subsequent editions. In A System of Logic, Mill expanded and modernized Francis Bacon's views of inductive science as expressed in his Novum Organon and other works, with the added benefit of numerous examples and detailed explanations. Murray Sidman's Tactics of Scientific Research, in which Sidman discusses the application of inductive methods to research in the experimental analysis of behavior, can be seen to be an conceptual descendant of Mill's work. Although Mill's System of Logic is now difficult to read due to its expansive 19th century writing style, reading it is still worth the effort.

Mill's methods, here taken from chapter VIII of the 1859 edition of A System of Logic, describe the basic methods of causal determination that, although not without limits, continue to form the basis of inferences of causality throughout science. Although a functional analysis of behavior is a hybrid of inductive and deductive methods, a behavior analyst will see Mill's rules as comprising the basic methodology for discovering functional relations in behavior.

The limitations of these kinds of inferences will be seen to lie in the completeness of the cataloging of events. It is possible arrive at incorrect conclusions if all the possible causal events have not been identified. Thus, these methods become increasingly effective as the analysis of the situation becomes more thorough. The examples below show minimum conditions. As more combinations of events are added, irrelevant conditions can be excluded, and methods of analysis are combined, the inferences become stronger. For instance, if we see that two events always occur together, we can determine which causes the other, or if they are both caused by a third unknown event, by presenting each exclusion, and observing the effect. Further analysis of this type will further narrow possible causes.

While these rules might seem like "common sense," it is to be remembered that such logic was not always clear in the history of science. The application of these rules in complex cases is not necessarily as straightforward as it would seem in the kinds of examples we provide below. The fact that so many seem to fail to apply these rules in everyday and scientific decision making also suggests that "common sense" is not as common as it should be.

References

  • Bacon, F. (1620/1860). The novum organon, or a true guide to the interpretation of nature [trans. G.W. Kitchen].Oxford: Oxford University Press. (PDF)
  • Mill, J.S. (1859). A system of logic, ratioclinative and inductive; being a connected view of the principles of evidence and the methods of scientific investigation. New York: Harper Brothers. (PDF)

Mill's Methods of Induction

First Canon: The Method of Agreement

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 effect) of the given phenomenon. (Mill, 1859, p. 224)

We observe the following two sets of conditions:

  • A B C D a b c d
  • A E F G a h i j

We concluded that "A" is related to "a" because they are the only events in common. We are looking for what the two sets of events have in common.

If cookies are stolen only when Johnny is present in a group of children, we would suspect Johnny as the thief. If another child were also always present we could use this method only to narrow the suspects down to those two.

Second Canon: 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 save one in common, that one occurring only in the former ; the circumstance tn which alone the two instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon. (Mill, 1859, p. 225)

We observe the following two sets of conditions:

  • A B C D a b c d
  • A B C D a b c d

We conclude that "A" is related to "a" because when "A" is absent "a" does not occur.

Cookies are always missing from the cookie jar except on days when Johnny is gone. We suspect Johnny is the thief because the cookies remain safe when Johnny is not there. Freddy, a clever thief, could use our method of analysis to "frame" Johnny by stealing cookies only when Johnny is present. A more thorough analysis might be needed to discover the real culprit.

Third Canon: The Joint Method of Agreement and Difference

If two or more instances in which the phenomenon occur 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. (Mill, 1859, p. 229)

We observe the following sets of conditions:

  • A B C a b c
  • A D E a b c
  • A B C a b c
We conclude that "A" is related to "a" because "a" only occurs when "A" occurs, and never occurs when "A" is a absent.

Cookies are always missing from the cookie jar whenever Johnny is in a group of children, and never when Johnny is missing from one or more of those same groups. This does not apply to any other child. We therefore suspect Johnny as the thief.

Fourth Canon: The Method of Residues

Subduct from any phenomenon such part at it known by previous inductions to be the eject of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. (Mill, 1859, p. 230)

We observe the following three sets of conditions:

  • A B C a b c
  • B is known to be the cause of b by prior analysis
  • C is known to be the cause of c by prior analysis

We conclude that "A" is related to "a" because we know that "B" is not related to "a," but related to "b," and "C" is not related "a" but is related to "c."

New cookies appear in jar one day shortly after Mary, Sally, and Sue arrive for work. We know that Mary only brought potato chips and Sally only brought juice. Therefore, we suspect that Sue has brought the cookies.

Fifth Canon: The Method of Concomitant Variations

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 it connected with it through some fact of causation. (Mill, 1859, p. 233)

We observe the following two sets of conditions:

  • A B C a b c
  • Both A and a change in magnitude, with no change in any other event.

We conclude that "A" is related to "a" because changes in the value of "A" are only accompanied by changes in "a."

The number of cookies missing from the jar in the morning is proportional to the number of crumbs on Johnny's shirt. Similar corresponding variations are not observed in any other child. We therefore suspect that Johnny is the thief.