Today’s post on critical thinking concerns the five principles collectively known as Mill’s methods, first presented together in 1843 by the Enlightenment philosopher John Stuart Mill in his book A System of Logic. Each of them is intended to illuminate the flow of causality in a different way, giving us mental tools to link causes and effects. In this post, I’ll highlight past entries in my “Popular Delusions” series, and show how failure to properly use Mill’s methods has duped the practitioners of pseudoscience.

1. The method of agreement. If two or more cases of the event you’re seeking to explain have only one causal factor in common, that factor is probably the cause of the event.

Example: In my post on hauntings, I noted a way in which ghost-hunters conspicuously fail to apply the method of agreement: the vast majority of ghost sightings have nothing in common except that the people involved are in the twilight state on the edge of sleep. These conditions are most suitable for the human neurological state of sleep paralysis, which typically entails hallucination, inability to move, and a strong sense of a looming presence. This is a causal factor in common among these cases which ghost believers generally overlook. Since ghost sightings have little else in common, the method of agreement would suggest that sleep paralysis is the most probable cause of this phenomenon.

2. The method of difference. If there is one case where an event occurs and one case where it doesn’t occur, and all the causal factors except one are the same in both cases, that one factor is probably the cause of why the event happened in one instance and did not happen in another.

Example: Astrology is an excellent example of misapplication of the method of difference. Astrologers claim that the celestial bodies and constellations that are ascendant at the time of a person’s birth determine their subsequent traits of personality and character. This is the sort of claim that could be proven by the method of difference, but most astrologers are steadfastly uninterested in even doing the tests. Those few who have tried, using the method of difference to predict the personality characteristics of strangers based on their birth times, have been dismal failures.

3. The joint method of agreement and difference. If there are some cases where an event occurs and some cases where it does not occur, and all the cases where it does occur have only one causal factor in common, while all the cases where it does not occur lack that causal factor, that factor is probably the cause of the event.

Example: Faith healers are notorious for their ignorance of this method. If sick people who were prayed over frequently experienced otherwise inexplicable remissions, while people lacking such intervention never did, this would be strong evidence in favor of intercessory prayer. But all these conditions, in reality, are absent: sick people who receive prayer experience spontaneous recovery at rates no greater than chance, while spontaneous remission also occurs among people receiving no special theological intervention.

4. The method of residues. When seeking to explain the causes of a set of events, deduct all the causal factors which are known to cause some subset of those events; the remaining causal factors are probably the cause of the remaining members of the set.

Example: The method of residues is routinely ignored by proponents of homeopathy, who believe that a purported remedy can be diluted out of existence and still retain its curative power. A proper application of the method of residues would begin with the application of a chosen homeopathic remedy at full strength, then successively subtract the components of that remedy to observe how the effect diminishes. Homeopaths, however, believe the opposite: that as causes are progressively subtracted, the effects will grow greater in magnitude. This violates not just the laws of physics but the very notion of causality itself.

5. The method of concomitant variation. When two events or circumstances are observed to vary in the same proportions, such that an increase in one always accompanies an increase in the other, one is probably the cause of the other.

Example: This method is abused and misused not once, but twice, by the fanatical anti-vaccine campaigners. When they claim that the preservative chemical thimerosal causes autism in some subset of vaccinated children, they fail to take note of the fact that autism rates have been rising in recent decades even after thimerosal was removed from most vaccines. And in their steadfast denial of vaccines’ efficacy in preventing deadly disease, they steadfastly ignore the declining rates of these infectious diseases, dwindling to near zero in many cases, which accompanied the widespread use of vaccination. And as vaccination declines among the superstitious, these diseases reappear and spread in turn – an unfortunately near-perfect example of the correlation that the method of concomitant variation reminds us not to overlook.