
Mill's Methods of Induction 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
Mill's Methods of Induction First Canon: The Method of Agreement
We observe the following two sets of conditions:
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
We observe the following two sets of conditions:
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
We observe the following sets of conditions:
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
We observe the following three sets of conditions:
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
We observe the following two sets of conditions:
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.

