Mill’s Methods
English philosopher John Stuart Mill described 5 methods of induction from correlation that suggest causality: agreement, difference, joint, residue, and concomitant variations. While helpful, the study required to comprehend Mill’s methods shows that they are not natural mental mechanisms.
For the method of agreement, the commonality among phenomena that have similar effect indicates cause.
If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon. ~ John Stuart Mill
Symbolic example:
A B C D occur with w x y z
A E F G occur with t u v x
Therefore: A is the cause or effect of x.
For the method of difference, the element missing in 1 of 2 entities being compared suggests the factor that may be causal.
If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance save one in common, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or cause, or an necessary part of the cause, of the phenomenon. ~ John Stuart Mill
Symbolically:
A B C D occur with w x y z
B C D occur with w y z
Therefore: A is the cause or effect of x.
The joint method combines the agreement and difference methods.
If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon. ~ John Stuart Mill
Symbolically:
A B C occur with x y z
B D E occur with x v w
B C occur with y z
Therefore: A is the cause or effect of x.
The method of residue helps identify an effect, or possibly a cause, by a process of elimination.
Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. ~ John Stuart Mill
Symbolically:
A B C occur with x y z
B is the known cause of y
C is the known cause of z
Therefore: A is the cause or effect of x.
The method of concomitant variations finds a causal association between variations in an element or factor and a circumstance.
Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. ~ John Stuart Mill
Symbolically:
A B C occur with x y z.
A± B C results in x± y z, where ± represents variance.
Therefore: A and x are casually related.
Water toxicity is exemplary. Various samples of water with both salt and lead are found to be toxic. If the level of toxicity varied in tandem with the level of lead, but not so for salt, toxicity is attributable to lead.
Unlike other methods, concomitant variation is an issue of magnitude, and does not involve induction by elimination.
