John Stuart Mill
He is best known as a utilitarian moral philosopher; but his book on logic (1843) contains views on induction, scientific or causal explanation, and the methodology of social sciences. Although he had no experience in natural science, he reorganized materials drawn from empiricist philosophy and scientists such as John Herschel, and made up a rather influential view. His disputes with Whewell are also interesting, touching upon many issues of scientific methodology.
See Mill's five canons of induction