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.

Book VI argues that the “moral sciences,” meaning the study of ethics and human nature, require the same logical structure as the physical sciences. A discussion of the concepts of liberty, causation, and necessity as they apply to human affairs leads Mill to conclude that human nature is governed by scientific principles that logic can lay bare and that can be used to promote happiness. Mill argues that human psychology and behavior are governed by universal laws, as is the formation of each person’s ethical character. However, these laws cannot be studied directly, through experiment and observation, but can only be known deductively. Mill considers various scientific methods and the extent to which they may be applied to the social sciences. Although many of the methods of the natural sciences do not work for the social sciences, the methods of induction may still be applied to understand causes and effects, such as the effects of a given policy or legislative act. The social sciences can also be approached deductively, by starting with a priori laws of human nature and reasoning based on them. Mill divides the social sciences into two branches: those in which the causes and effects of human behavior are studied in a context that is assumed to be stable, and those sciences that examine progress and historical change.

The most innovative aspect of A System of Logic is its rigorous, systematic explanation of induction. This explanation is a particularly impressive accomplishment given how unscientific and unsystematic induction seems to be at first glance, especially in comparison with the certainty of a deduction or syllogism. For example, in the famous syllogism, “All men are mortal. Socrates is a man. Socrates must be mortal,” if you know for certain that all men are mortal and that Socrates is a man, you can be very certain of your conclusion—that Socrates will die at some point. However, if you work in the reverse direction, which induction requires you to do, you get a much less certain answer. Socrates died, and Socrates was a man, so perhaps all men are mortal—but maybe not. The fact that Socrates’ friends Diabetes and Bursitis also died can be offered as further evidence that all men are mortal, but it still doesn’t prove it. Nevertheless, for those who believe that all our ideas come from experience, induction is the source of every general principle that we think we know, so induction is the foundation on which deduction is based.