Mill's methods of causal reasoning: QCE Philosophy and Reason
“Explain and apply Mill's methods of causal reasoning, including agreement, difference, joint method, residues and concomitant variation”
Mill's methods are five inductive patterns for inferring causes. Agreement: the single factor common to all cases of the effect is the probable cause. Difference: when a positive and a negative case differ in just one factor, that factor is the probable cause, which is the logic of the controlled experiment and usually the strongest. The joint method combines both. Residues: subtract known causes and assign the remainder to the remaining antecedent. Concomitant variation: factors that vary together are probably causally linked. All are inductive and fallible, and none on its own settles correlation versus causation, since links may be reversed, due to a common cause, or coincidental.
Jump to a section
What this dot point is asking
QCAA wants you to understand how reasoning moves from observed patterns to causes. The set tools are Mill's methods, five patterns set out by John Stuart Mill in A System of Logic (1843) for discovering the causes of phenomena. You need to explain each method, apply it to a case, and recognise that causal inference is inductive and fallible, including the gap between correlation and causation.
The answer
Why causal reasoning needs method
We constantly ask what causes what: why a patient recovered, why crops failed, why an experiment worked. Mill systematised the everyday logic of isolating a cause by comparing cases where the effect occurs with cases where it does not, then looking for the factor that tracks the effect. All five methods are inductive: they yield a probable cause, not a proof.
Method of agreement
If two or more cases of the effect share only one common antecedent circumstance, that circumstance is probably the cause. Several diners fall ill; the only food they all ate was the oysters; the oysters are the probable cause. Weakness: the cases may share more than one factor you have not noticed.
Method of difference
If a case where the effect occurs and a case where it does not are alike in every circumstance except one, that one difference is probably the cause (or part of it). Two identical plants are grown together; one is given a nutrient, the other not; only the fed plant flourishes; the nutrient is the probable cause. This is the logic of the controlled experiment and is generally the strongest of the methods.
Joint method of agreement and difference
Combining the two: positive cases all share factor X (agreement) and the negative cases all lack X (difference). The joint method strengthens the inference because it checks both that X is present when the effect appears and absent when it does not. Most epidemiological reasoning uses this double pattern.
Method of residues
Subtract from a phenomenon the parts already known to be the effects of known causes; the remaining part of the phenomenon is the effect of the remaining antecedents. Astronomers used this when wobbles in a planet's orbit could not be explained by known bodies, inferring an unknown planet as the residual cause, which led to the discovery of Neptune.
Method of concomitant variation
If one factor varies whenever another factor varies, in a regular way, the two are probably causally connected. As atmospheric pressure falls, the mercury in a barometer falls in step, indicating a causal link. This method handles causes that are always present in some degree (you cannot remove them entirely), so you study how the effect changes as the suspected cause changes.
Correlation is not causation
A standing warning across all the methods: a regular association between two things does not by itself establish that one causes the other. The relationship may be reversed (the effect causes the apparent cause), or both may be effects of a common cause (ice-cream sales and drownings both rise with summer heat), or the link may be coincidence. Mill's methods help, but they assume the real cause is among the factors being considered, which is not guaranteed.
Holding everything constant except one factor and seeing whether the effect appears is exactly what a controlled experiment does, which is why the method of difference is usually the strongest of Mill's five. Its power depends on the two cases truly being alike in every other relevant respect.
Where Mill's methods sit in science
Mill's methods formalise the inductive side of scientific discovery, complementing the hypothetico-deductive method in which hypotheses are tested by deducing and checking predictions. They remain the backbone of how we design experiments and read epidemiological data. But because they are inductive, their conclusions are always open to revision, linking back to Hume's problem of induction.
A teacher notices some students score much higher on a test. Find the probable cause.
Step 1: Record the positive cases and their antecedents
List the high scorers and everything that might matter: sleep, breakfast, study hours, a new revision app. Suppose all high scorers used the revision app and had varied sleep, breakfast and study hours.
Step 2: Apply the method of agreement
The single antecedent common to every high scorer is the revision app; the other factors vary across them. Agreement points to the app as the probable cause.
Step 3: Apply the method of difference using the negative cases
Examine the low scorers. If they are similar in sleep, breakfast and study hours but did not use the app, then the cases that produce the effect and those that do not differ in just that one factor. Agreement plus difference is the joint method, which is stronger than either alone.
Step 4: Confirm with a controlled test and note the limits
Run a controlled trial varying only app use (method of difference). If app users still outperform, causation is well supported, though the inference stays inductive and assumes the true cause was among the recorded factors.
- Treating any method as proof
- Mill's methods are inductive and give a probable cause, not certainty.
- Inferring causation from correlation
- Concomitant variation suggests a link but does not rule out reverse causation, a common cause, or coincidence.
- Assuming the cause is on your list
- The methods only test the factors you considered; the true cause may be one you never recorded.
- Confusing agreement and difference
- Agreement looks for the shared factor across positive cases; difference compares a positive and a negative case alike in all but one respect.
Try this
Q1. Explain the method of difference and why it underlies controlled experiments. [4 marks]
- Cue. Two cases alike in all factors but one; the differing factor is the probable cause, just as an experiment varies a single variable.
Q2. Distinguish the method of agreement from concomitant variation. [3 marks]
- Cue. Agreement finds a shared factor across cases; concomitant variation tracks how the effect changes as a factor changes in degree.
Q3. Give one reason a strong correlation may not show causation. [2 marks]
- Cue. Both factors may be effects of a common cause, for example summer heat raising both ice-cream sales and drownings.
Exam-style questions
Questions in the style of QCAA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
Practice6 marksSeveral guests at a function became ill. Using Mill's methods, explain how you would reason to the probable cause, and identify which method a controlled follow-up test would use.Show worked answer →
A 6 mark response applies the methods and names the relevant ones.
Method of agreement. List what the ill guests have in common. If the only food or drink every ill guest consumed was the prawns, agreement points to the prawns as the probable cause (the single shared antecedent).
Joint method. Strengthen it by checking the guests who did not fall ill: if they all avoided the prawns, you have agreement among the ill and difference from the well, which is the joint method of agreement and difference.
Controlled follow-up. A deliberate test, holding everything constant and varying only exposure to the suspected prawns, uses the method of difference, the logic of the controlled experiment and usually the strongest method.
Caveat. The inference is inductive and probable; the true cause must actually be among the factors recorded.
Markers reward correct use of agreement, the joint method, and naming the method of difference for the controlled test.
Practice4 marksExplain the method of concomitant variation and why correlation established by it does not by itself prove causation.Show worked answer →
A 4 mark response defines the method and gives the correlation caveat.
Method. Concomitant variation infers a causal link when one factor varies regularly whenever another varies (for example mercury in a barometer falling as atmospheric pressure falls). It is used for causes that are always present in some degree and cannot be removed entirely.
Why not proof of causation. A regular co-variation may be due to reverse causation, a common cause driving both (ice-cream sales and drownings both rise with summer heat), or coincidence. So concomitant variation establishes a probable link to investigate, not a proven cause.
Markers reward an accurate account of the method and at least one reason correlation need not be causation.