A System of Logic was first published in 1843 and immediately enjoyed a wide circulation, going through numerous editions. Mill himself made substantial changes in the third edition, published in 1850, and the eighth edition, published in 1872, a year before his death. This book is Mill’s most comprehensive and systematic philosophical work, elaborating his inductive method, which helped to free the empirical sciences from the rigidity of analysis by way of syllogisms. Syllogisms are arguments grounded in general principles, in which two premises are used to deduce a third premise, or conclusion. In A System of Logic, Mill breaks away from this age-old practice and instead proposes the use of a form of logic derived from the principles of the natural sciences. He uses his method to address questions of language and logic, induction, the relativity of knowledge, the structure of the scientific method, the structure of arithmetic and geometry, and the principles of the moral sciences. In effect, Mill provides a solid, scientific methodology for reasoning and for philosophy, derived from science and mathematics.
The introduction discusses the role and purpose of logic in human understanding. Logic is the art and science of reasoning, a means for the pursuit of truth. However, logic is only concerned with making inferences from observed phenomena, not with intuitive truths. Logic does not produce new evidence, but it can determine whether something offered as evidence is valid. Logic judges but does not observe, invent, or discover. Logic serves a purpose in some larger project of inquiry that gives it meaning. Fundamentally, logic is a method of evaluating evidence.
Book I defines logic as a method of proof. Proof always involves an assertion or proposition that must be proven. A proposition is a discourse that either affirms or denies something about some other thing. Thus, a proposition is a belief that depends on the ability to attach a name to something. When two names are joined together by a copula (“the sun is bright”), they form the proposition. Mill proceeds to examine the nature of predicates, which are properties that can be said to be possessed by substances. Predicates include such things as joy, fear, sound, smell, taste, pain, pleasure, thought, judgment, and conception. Mill suggests that feelings or states of consciousness are realities; that is, they are neither substances nor attributes. Mill proceeds to examine volition and action, substance and attribute, body, mind, quality, relation, resemblance, quantity, states of consciousness, and attributes of mind.
Book II discusses the place of logic within the field of knowledge, specifically denying that logic is related to metaphysics and stating that preconceived notions and speculative thought are foreign to the workings of logic, since they suggest that logic be reduced to consistency rather than truth. In book II, Mill opens up logic to include the various fields of science and knowledge and denies logic any kind of restrictive structure.
Book III introduces Mill’s inductive method. An inductive inquiry begins with the analysis of things according to their elements. The first step in induction is the separation of a thing into its various elements through a process of experimentation and observation. Mill proceeds to examine the relationship between cause and effect and concludes that one effect may have several causes. Mill distinguishes between complex and compound effects, which brings him to examine the nature of generalizations and probable evidence, operations which, he says, are more useful in life than in science.
Book IV discusses the need for a philosophical language that would further the practice of induction by helping us to accurately observe, record, and communicate. Such a language must have a steady and determinate meaning for every general name, since names often have unclear connotations. Book V deals with various fallacies that must be resolved before logic can be firmly grounded. These include the fallacies of confusion; of ambiguous words; and the petitio principii, which states that the premise either appears to be the same as the conclusion or is proved from the conclusion. Mill concludes that this argument is a fallacy because it is nothing more than a circular argument, since the attempt is to prove two propositions reciprocally from one another leads nowhere.