# Methods of Induction

John Stuart Mill is famed for his discourse on Induction. He gives us a system of discovering causes.

## Types of Causes

There are two general kinds of causes. A cause can be a sufficient condition or a necessary condition.

A brick is a sufficient condition to break a window - not a necessary one, because other objects may break a window.

A disruptive force is a necessary condition - it can be caused by a brick, or another heavy object, or pressure, or even vibration.

## The Methods of Induction

Here now, are the various methods. Notice one more significant difference between logical methods and inductive methods - the following methodologies depend upon experimentation, rather than (solely) logical argument.

### Direct Method of Agreement

This is a method of identifying a necessary cause. You examine all cases in which a given effect is present and try to find some factor, or putative cause, that is present in ALL of these cases. You eliminate all factors not present in these cases as possible causes. Any factor that remains is a candidate for necessary condition for the effect.

### Inverse Method of Agreement

A method for identifying sufficient causes. Examine all cases in which a given effect, E, is absent and try to find some F that is also absent. Any factor that remains will be such that its nonpresence may be a necessary condition for the nonpresence of E.

### Double Method

Combination of the two above methods.

Shows both necessary and sufficient conditions.

### Method of Difference

Examine two cases - one which exhibits the effect E, and one which does not. Try to find a single factor, F, that is present in the cases where E is present, and absent when E is not. This F is a candidate for a sufficient cause.

### Joint Method of Agreement and Difference

Guess what this entails? A combination of the direct method (the first one listed) with the previous method, the method of difference. The factor revealed will be a strong candidate for a sufficient and necessary condition.

### Method of Residues

Tough one to explain. In this one, you subtract known causal connections from other more complex (and known) casual relations, leaving as a candidate for a causal connection the remaining relation. If there is a causal connection between a complex or conjunctive event, called A and another event, called B, and if event a is an isolatable part of event A, and b is a likewise isolatable part of event B, and if there is a known causal relationship between a and b, then I can be concluded that there is a probable causal connection between the residue Aa and the residue Bb. It is difficult to assess from this point whether this is a sufficient or necessary cause.

### Method of Concomitant Variation

Identify a functional relationship between a factor that admits of quantity or degree and an effect, E, that admits of quantity or degree, such that variations of F correspond (correlate) with variations in E. This may be a direct, or inverse relationship. Since this is a correlation, causality is only probabilistic - i.e. correlational data cannot link causality.

## References

• Hurely, P. J. (2000) A Concise Introduction to Logic - 7th Edition