§4 Mill’s Methods of Discovery

While Aristotle provided a broad framework for why things exist, the 19th-century philosopher John Stuart Mill sought a precise, scientific way to isolate the Efficient Cause. In his work A System of Logic (1843), Mill formulated five inductive methods—known as “Mill’s Methods”—designed to identify causal relationships by systematically eliminating alternative explanations.

4.1 The Method of Agreement

If two or more instances of a phenomenon under investigation have only one circumstance in common, that single circumstance is likely the cause (or effect) of the phenomenon.

• The Logical Goal: To identify a Necessary Condition.

• The Process: You look at various cases where the effect occurred and find the one factor they all share.

• Example: Suppose four students get food poisoning after eating at a cafeteria. Student A ate pizza and salad; Student B ate a burger and salad; Student C ate tacos and salad. Since “salad” is the only common factor, the Method of Agreement points to the salad as the cause.

4.2 The Method of Difference

If an instance in which the phenomenon occurs and an instance in which it does not occur have every circumstance in common except one, that one factor is the cause (or an indispensable part of the cause).

• The Logical Goal: To identify a Sufficient Condition.

• The Process: This is the basis of the “Controlled Experiment.” You compare two nearly identical cases, change one variable, and see if the effect changes.

• Example: Two identical twin plants are given the same soil and sunlight. Plant A is given “Super-Grow” fertilizer and doubles in size. Plant B is given no fertilizer and stays small. The “Super-Grow” is identified as the cause of the growth.

4.3 The Joint Method of Agreement and Difference

This method combines the first two to increase inductive strength. You look for a factor that is present in all cases where the effect is present (Agreement) and absent in all cases where the effect is absent (Difference).

• The Process: This provides a double-check, making it much more likely that the identified factor is both a necessary and sufficient part of the cause.

4.4 The Method of Concomitant Variation (Correlation)

This method is used when a factor cannot be entirely removed, but its intensity can be changed. If a change in the strength of a factor is followed by a proportional change in the effect, a causal link is likely.

• The Process: We look for a “sliding scale” of influence.

• Example: As a driver presses the gas pedal harder (increase in factor), the car moves faster (increase in effect). This variation suggests a causal relationship between the pedal and the speed.

4.5 The Method of Residues

If we know that a certain part of a complex phenomenon is caused by specific factors, we can conclude that the remainder of the phenomenon is caused by the remaining factors.

• The Process: “Subtracting” the known causes to find the unknown ones.

• Example: A scale shows a dog in a crate weighs 50 lbs. We know the empty crate weighs 10 lbs. By the Method of Residues, we conclude the dog weighs 40 lbs.

§4 Summary Table: Mill’s Inductive Tools