Book: A System of Logic, Ratiocinative and Inductive

Purpose and Structure
Mill presents logic as the general science of evidence, uniting ratiocinative (deductive) and inductive reasoning under a single account of how knowledge is established and expanded. Against purely formal or intuitive traditions, he grounds justification in experience, arguing that valid inference ultimately depends on observed regularities in nature. Deduction has a vital role in organizing and extending what induction supplies, but it cannot create new knowledge ex nihilo. The book unfolds from language and propositions, through syllogistic and scientific reasoning, to a methodology for the moral and social sciences.

Language, Meaning, and Classification
Logic begins with how statements bear on reality. Mill distinguishes denotation (what a name applies to) from connotation (the attributes it signifies). Predication asserts attributes of subjects; definitions state the connotation of names rather than reveal essences of things. Good classification groups objects by shared, causally connected properties, aiming at natural kinds whose features travel together. This semantic groundwork disciplines generalization: to reason well, one must be clear about what a proposition claims and what evidence could bear on it.

Deduction and the Syllogism
The syllogism does not generate truth; it makes explicit what is already contained in general propositions. Its worth lies in organizing reasoning and transmitting the warrant earned elsewhere. Every deductive step tacitly relies on the major premise that the properties affirmed of a class belong to its members, authority the premise gains by prior induction. Hence the “ratiocinative” part of logic is an instrument for drawing out consequences from established laws and for checking consistency and relevance, not an independent source of first principles.

Induction, Causation, and the Methods
Induction discovers laws through experience. Mill treats causation as invariable and unconditional sequence: the cause is the totality of conditions sufficient for the effect. Because complex conditions obscure regularities, inquiry proceeds by elimination and control. He formulates five “Methods of Experimental Inquiry”: Agreement, Difference, Joint Method, Residues, and Concomitant Variations. Properly applied, they isolate causal connections, distinguish mere coexistence from dependence, and guide investigation where direct experimentation is limited. Empirical laws of coexistence can be useful, but causal laws, once found, support powerful deductive prediction when combined with initial conditions.

Mathematics, Necessity, and Probability
Mill extends empiricism to mathematics and necessary truths. Arithmetical and geometrical propositions are, on his view, highly confirmed generalizations from experience, their apparent necessity arising from firm habits of association and the uniformity of nature. He denies that they rest on innate intuition. Probability enters as a measure of the strength of evidence when causes are not fully known; chance denotes ignorance of causes, not their absence. He analyzes common fallacies as failures of relevance, ambiguity, or unwarranted generalization, often traceable to neglect of connotation or to hasty induction.

The Deductive Method of Science
Mature sciences advance by a hypothetico-deductive pattern: infer consequences from known laws, then test them against observation, revising either the laws or the auxiliary assumptions as needed. This “deductive method” is indispensable in domains where direct isolation of causes is impossible. Mill distinguishes “geometrical” cases where effects add linearly from “chemical” cases where interactions yield new properties; the latter demand cautious decomposition of conditions and iterative verification.

Logic of the Moral and Social Sciences
Human affairs pose special challenges: multiple, interacting causes and limited experimental control. Mill proposes an “inverse deductive method,” beginning from laws of mind and motivation, elaborated into “ethology” (the science of character formation), and then confronting historical and statistical evidence. Sound social explanation combines theoretical derivation with careful verification, avoiding naive readings of historical sequences as causal without mediating laws.

Significance
The treatise codifies a systematic empirical logic that shaped scientific method across the nineteenth century, articulates the classic canons of causal inference, and offers an ambitious program for the moral sciences. Its bold reduction of necessity to strong induction and its semantics of connotation and denotation were influential and controversial, spurring later refinements in logic, philosophy of science, and the foundations of mathematics.