91. Inductive Methods. -- Following Mill's terminology, these are the methods of agreement, of difference, of concomitant variations, of remainders, and the composite method. The first three are the principal ones.

(1) Method of agreement: When the phenomenon, the nature of which is to be determined, has occurred in several different cases, and these different cases have a single circumstance in common, this common circumstance is probably the sufficient reason of the phenomenon.

(2) Method of difference: Two cases are observed: in one the phenomenon occurs, in the other, it does not; all the circumstances of the two cases are identical except one, which is present in the first case and absent in the second. It may be inferred that this one circumstance is the whole or partial sufficient reason of the observed phenomenon.

(3) Method of remainders, a composite method, produced by a modification of the methods of agreement and of difference: When the part known to result from certain antecedents, already determined by previous inductions, is eliminated from the phenomenon, then what is left of the phenomenon is caused by the remaining antecedents.

(4) Method of concomitant variations: When the degrees of variation of a phenomenon correspond with the degrees of variation of a given antecedent, it is to be presumed that there is between the two a relation of causality, immediate or mediate. This method, Mill observes, is particularly demanded when in all the cases the preceding methods are inapplicable, as happens when the cause of the phenomenon cannot be completely isolated.

(5) The composite method is the cumulative employment of all the preceding.