Mill's Methods

# Mill's Methods

Discussion

Encyclopedia
Mill's Methods are five methods of induction
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...

described by philosopher John Stuart Mill
John Stuart Mill
John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

in his 1843 book A System of Logic
A System of Logic
A System of Logic, Ratiocinative and Inductive is an 1843 book by English philosopher John Stuart Mill. In this work, he formulated the five principles of inductive reasoning that are known as Mill's methods.-References:...

. They are intended to illuminate issues of causation
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....

.

## Direct method of agreement

"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."

For a property to be a necessary
Necessary and sufficient conditions
In logic, the words necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true.-Definitions:A necessary condition...

condition it must always be present if the effect is present. Since this is so, then we are interested in looking at cases where the effect is present and taking note of which properties, among those considered to be 'possible necessary conditions' are present and which are absent. Obviously, any properties which are absent when the effect is present cannot be necessary conditions for the effect.

Symbolically, the method of agreement can be represented as:
A B C D occur together with w x y z
A E F G occur together with w t u v
——————————————————
Therefore A is the cause of w.

## Method of difference

“If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.”

A B C D occur together with w x y z

B C D occur together with x y z

——————————————————

Therefore A is the cause, or the effect, or a part of the cause of w.

## Joint method of agreement and difference

"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."

Also called simply the "joint method," this principle simply represents the application of the methods of agreement and difference.

Symbolically, the Joint method of agreement and difference can be represented as:
A B C occur together with x y z
A D E occur together with x v w also B C occur with y z
——————————————————
Therefore A is the cause, or the effect, or a part of the cause of x.

## Method of Residue

"Deduct 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."

If a range of factors are believed to cause a range of phenomena, and we have matched all the factors, except one, with all the phenomena, except one, then the remaining phenomenon can be attributed to the remaining factor.

Symbolically, the Method of Residue can be represented as:
A B C occur together with x y z
B is known to be the cause of y
C is known to be the cause of z
——————————————————
Therefore A is the cause or effect of x.

## Method of concomitant variations

"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."

If across a range of circumstances leading to a phenomenon, some property of the phenomenon varies in tandem with some factor existing in the circumstances, then the phenomenon can be attributed to that factor. For instance, suppose that various samples of water, each containing both salt
Salt
In chemistry, salts are ionic compounds that result from the neutralization reaction of an acid and a base. They are composed of cations and anions so that the product is electrically neutral...

Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

, were found to be toxic. If the level of toxicity varied in tandem with the level of lead, one could attribute the toxicity to the presence of lead.

Symbolically, the method of concomitant variation can be represented as (with ± representing a shift):
A B C occur together with x y z
A± B C results in x± y z.
—————————————————————
Therefore A and x are causally connected

Unlike the preceding four inductive methods, the method of concomitant variation doesn't involve the elimination of any circumstance
Process of elimination
Process of elimination is a method to identify an entity of interest among several ones by excluding all other entities.-In education testing:...

. Changing the magnitude of one factor results in the change in the magnitude of another factor.