Mill bases his logical investigations partly on historical and partly on psychological principles.
In matters pertaining to the history of thought, as he openly acknowledged, he was greatly benefited by Whewell's work on the History of the Inductive Sciences. John Herschel's book On the Study of Natural Philosophy (1831) was likewise one of his preparatory studies. Mill's problem consisted in describing the fundamental methods of inductive thought by an analysis of the methods of the empirical sciences as these had been developed during the past three centuries, and then to examine what presuppositions underlie this thought.— He discovers four methods of induction. The method of agreement infers, from a series of cases, in which two circumstances (A and B) always succeed each other, whilst all other circumstances vary, a causal connection between A and B. But this inference is not certain until we can at the same time apply the method of difference because it shows that B does not appear whenever A is excluded, and vice versa. This is the chief inductive method. To this is added the method of residues, in which everything previously explained is eliminated and an inference is then drawn concerning the relation of the remaining circumstances, and the method of proportional variation, in which we have two series of experiences which vary proportionally between each other and infer a causal relation between them. Mill illustrates these methods by striking examples from the history of the sciences. He attempted, by this exposition, to substitute a systematization of inductive logic for the Aristotelian systematization of deductive logic; his logic was a continuation of Bacon's work. He differs from Bacon not only in the wealth and quantity of the examples at his disposal
