Monthly Archive: June 2016

Arguing about cause and effect is a difficult enterprise even in the best of circumstances.  Rarely is it as clean, or as boring, as introductory texts on logic make it out to be.  Examples of simple cause and effect – it is raining and therefore the ground is getting wet – are neither controversial nor are they fun.  Most everyone agrees on the matter and that’s that.  But arguments over new things undiscovered or unseen are one of the best things going.  Who isn’t thrilled by the prospect of figuring something out that none else have done?

Interestingly enough, almost all of us use standard methods for arguing from effect to cause.  Most likely, we’ve all learned these methods by first watching others apply them and then by next jumping into the game and trying out the methods ourselves.  As will be discussed in more detail below, these methods worm themselves into almost every aspect of life; often without our notice.  They form the backbone of most editorials, advertisements, and dinner-table arguments.  And despite their anonymity, they do have a name:  Mill’s Methods.

First codified by John Stuart Mill in his book A System of Logic (1843), these methods, which no doubt date back to antiquity, go by the obscure names of:

• Method of Agreement
• Method of Difference
• Joint Method
• Method of Concomitant Variation
• Method of Residues

As unfamiliar as these terms may be to the ear, their use and application is familiar to the thinking of anyone who has ever tried to figure out what food at dinner last night didn’t agree with them or some similar scenario.  Indeed, many of the examples presented in the community deal with food and indigestion.  (In fact, application of Mill’s Methods to epidemiology is the core component of the TV show House).

Not wanting to dwell on food related illness (since it is done to death in the literature), I propose illustrating the methods using a more interesting question faced by parents and teachers across the country:  what factors contribute to good grades.

Consider a group of 10 students from a local school.  After circulating a questionnaire, their teacher compiles a table listing various activities they pursued and the study method they used (written homework or online quizzes).  The teacher wants to see what caused half the students to pass where the other half failed and so he looks for a factor that is both necessary and sufficient to explain why the first group passed.  He suspects that those students who play video games have been poisoned and that students who avoid this digital scourge are the ones that pass.  But being a man of integrity he decides to pursue the answer with an open mind.  To do this he employs Mill’s Methods in succession.

To apply the Method of Agreement, he looks to see what features all the passing students have in common.  He starts by looking at a subset group composed of Amy, Carl and Walter.

He notices that these 3 students have nothing in common in terms of their recreational pursuits, they don’t play the same musical instrument (in fact Amy doesn’t play any), that that they don’t all engage in the same exercise.  But all three of them were taught using the same technique of written homework.  He concludes that there is very likely possibility that written homework is the cause of their success in the class.

To apply the Method of Difference, he then looks for a pair of students, one who has passed and one who has failed, that have almost everything in common.  Any difference between them being a strong indication that it is the cause of success/failure.  He finds such a pair in Ben and Stacey.

Both of them enjoy blogging, play guitar, and exercise by running.  The difference between them seems to be that Stacey was required to do written homework while Ben was required to do online quizzes.  He concludes that there is a very strong possibility that written homework leads to good grades.

The Joint Method marries the two approaches together looking for support that this one factor, the teaching technique, is the primary cause of classroom success.  To this end, our teacher combines all the students into the following table

and he notices that in each case, the only factor that correlates with passing or failing, is written homework or online quizzes, respectively.  Despite his preconception that video games were dangerous he finds that two of the three students (Amy and Vanda) who play actually passed the course.

The final two of Mill’s Methods deal with matters of degree.  They help to answer how much written homework really helps and if there is another factor that might contribute to success.  To this end the teacher modifies the table to list the hours each student spends completing their written homework and their GPA.

In the case of the Method of Concomitant Variation, the teacher notices that in there is a strong correlation between the number of hours of homework each week and the student’s GPA.  Vanda does the least amount of homework each week and she has the lowest GPA.  Carl and Stacey are in the middle in terms of time invested in homework and so is their GPA.  And finally, Amy and Walter have the highest time spent on homework and the highest GPA.  This behavior is a strong indication that requiring students to complete written homework causes students to have high GPAs.

The Method of Residues helps to point towards additional factors that have not been considered but which contribute to the cause and effect relationship.  In the case of the two top performing students, the teacher notices that although Amy spends the greatest amount of time on homework each week she doesn’t have the highest GPA.  Of course, this minor difference between her and Walter might be explained in many ways (e.g. her courses are harder).  But let’s suppose that the table exhaustively lists all the relevant attributes and that Walter and Amy are in the same class in elementary school so that they see all the same material and are assigned the same homework.  Our teacher might be inclined to conclude that either playing a musical instrument or exercising might be the cause of the remaining difference.  This method can also be applied to the situation were the differences are a matter of quality rather than quantity.

One of the most famous examples of the application of the Method of Residues was to the motion of the planet Mercury.  After all the known contributions of Mercury’s orbit had been accounted by astronomers of the late 1800s there was still a remaining 53 arcseconds/century of precession that could be ascribed to any particular cause.  This difference, though small, helped to spur Einstein to create the theory of General Relativity.

While the discussion above was both illustrating and interesting it is hardly the only nor primary application of Mill’s Methods.  As Prof. Dave Beisecker points out on his discussion, Mill’s Methods are used in all sorts of persuasive arguments about products, policies, and the like.  I would encourage the reader to visit his page as some of his examples are both educational and laugh-out-loud funny.  Consider this gem used to illustrate how the Method of Difference is used in advertising

Of course real life is never so clear cut as the contrived examples seem to imply.  But that’s what makes it so fun.  Putting one’s skill to the test to find what causes what can lead to amazing discoveries and brings out the best in us.