What are the main ideas in John Stuart Mill’s A System of Logic?

In his influential work A System of Logic (1843), John Stuart Mill introduced several key concepts that shaped the study of logic and philosophy:

Mill’s Methods

Mill distinguished five methods of experimental reasoning used to determine the causal factors behind a specific effect:
* Method of Agreement: Identifies factors present on all occasions when the effect occurs.1
* Method of Difference: Identifies a factor present when the effect occurs but absent when it does not, under otherwise similar circumstances.1
* Joint Method of Agreement and Difference: A combination of the two previous methods.1
* Method of Residues: Attributes the remaining part of an effect to the remaining circumstances after other parts have been explained by known factors.1
* Method of Concomitant Variation: Infers a causal connection when variations in a factor are correlated with variations in the effect.1

Theory of Connotation

Mill also introduced a significant distinction regarding the meaning of names. He argued that names possess a "connotation" (or sense) that is distinct from their "denotation" (the object they name). While this distinction is foundational, Mill’s treatment is noted for being less comprehensive than later developments by Gottlob Frege, particularly because Mill denied connotation to certain singular names.2