How did John Stuart Mill connect empiricism with scientific reasoning?

In his A System of Logic (1843), John Stuart Mill connected empiricism with scientific reasoning by developing a thoroughly empiricist theory of knowledge that treated even logic and mathematics as empirical sciences. He argued that all genuine knowledge is inductive and empirical, viewing deduction as a sterile process that should be supplemented rather than superseded by inductive logic.123

To formalize this, Mill distinguished five methods of experimental reasoning to identify causal connections between factors and effects:4

• Method of Agreement: Identifies factors present on all occasions when an effect occurs.
• Method of Difference: Identifies factors present when an effect occurs but absent when it does not, under otherwise similar circumstances.
• Joint Method of Agreement and Difference: A combination of the two previous methods.
• Method of Residues: Attributes the remaining part of an effect to the remaining circumstances after other factors are accounted for.
• Method of Concomitant Variation: Infers a causal connection if variations in a factor are correlated with variations in the effect.4

By applying these methods, Mill sought to provide an unimpeachable method of proof for the human and social sciences.3