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Mill's methods of inductive reasoning are, in part, an extension of Bacon's scientific work.  These methods form the backbone of inductive science.  His  methods are essentially simple to understand, but, discovering how these patterns emerge in historical case studies of experimental inquiry can, at times, be quite challenging.

SCIENTIFIC REASONING

MILL'S METHODS OF INDUCTION

• Necessary and Sufficient Conditions
• Causal Laws
• Method of Agreement
• Method of Difference
• Joint Method of Agreement and Difference
• Method of Residues
• Method of Concomitant Variations
• Mill's Methods and Modern Science