A System of Logic, Book III: Of Induction

Summary

A System of Logic, Ratiocinative and Inductive, was published in London in 1843 in two volumes and went through eight editions in John Stuart Mill's lifetime, the last revised in 1872. Of its six books, the third, Of Induction, is the longest and the most influential; the library text gives that book alone, from an 1882 American printing of the eighth edition. Mill's aim is to explain how we can reason legitimately from observed facts to general truths, and so to give the empirical sciences a logic as rigorous as the syllogism had been for deduction. The book has twenty-five chapters. After preliminary remarks, Chapter II separates true induction from operations that only resemble it, and here Mill disputes William Whewell's account of Kepler: the ellipse, he insists, was in the facts before Kepler recognized it. Chapter III states the ground of induction. We infer not from past to future as such, but from the known to the unknown, and the warrant for every such inference is the uniformity of the course of nature, which Mill holds is itself the last and widest of our inductions. The chapter closes by asking why a single instance sometimes suffices for a universal conclusion while countless agreeing instances, such as the white swans Europeans had seen before Australia was explored, sometimes do not. Chapters IV and V treat laws of nature and the law of universal causation. Mill defines the cause of an event, philosophically speaking, as the sum total of its conditions, positive and negative, and argues that causation is invariable and unconditional sequence. After chapters on the composition of causes and on observation and experiment, Chapter VIII sets out the five canons for which the book is best known: the Methods of Agreement, Difference, the Joint Method, Residues and Concomitant Variations. Chapter IX illustrates them with Liebig's work on metallic poisons, Wells's theory of dew and other examples. The remaining chapters show the limits of these methods. Where many causes combine, as in medicine, physiology and society, direct experiment is weak, and Mill's example is the difficulty of learning whether mercury cures a disease; science must then rely on the deductive method, reasoning from known laws and verifying the conclusions. He goes on to explanation, hypotheses, empirical laws, chance and the calculation of probabilities, analogy, and approximate generalizations. The final chapter, on the grounds of disbelief, takes up Hume's argument on miracles and concludes that a miracle is not a breach of causation but a new effect ascribed to a new cause, so that the question turns on prior belief in such a cause. The Logic became a standard text at British universities, and Mill's methods remain the usual starting point for discussions of causal inference.

Top Lessons

• From the known to the unknown

  Mill argues that induction is not a matter of trusting that the future will resemble the past; we reason in the same way about the unobserved present and the unobserved past. Every such inference rests on the uniformity of nature, yet that uniformity is itself learned by experience. He leaves students with a hard question: why one careful experiment sometimes proves a law while a thousand agreeing observations, like the white swans, may not.

• The cause is the whole set of conditions

  In ordinary speech we name one condition as the cause of an event, but Mill insists that, philosophically speaking, the cause is the sum of all the conditions, positive and negative, on which the effect follows. A man who catches cold after taking mercury and going out of doors needed both conditions.

• Eliminate what cannot be the cause

  The five canons of Chapter VIII all work by comparison and elimination. The Method of Difference, which compares a case where the effect occurs with one where it does not and which differ in only one circumstance, is the logic of the controlled experiment.

• Why medicine is hard to prove

  Chapter X uses the question whether mercury cures a disease to show how many causes mingle in the body. Simple observation gives only vague impressions, and experiment is weakened by the many conditions of age, constitution and stage of illness. A few specifics, such as quinine, are strong enough to be proved directly; otherwise, Mill argues, medicine must combine known laws with careful verification.

Verified Quotes

Medical Lens

Book III is a key text in the history of therapeutic reasoning. Chapter X uses the question whether mercury cures a disease to show why simple observation of recoveries proves little and why the many conditions of age, constitution and stage of illness defeat crude experiment; Mill concludes that only strong specifics such as quinine, colchicum, lime-juice and cod-liver oil are proved by direct trial. His Method of Difference states the logic later embodied in controlled comparison, and his account of the plurality and intermixture of causes anticipates the problem of confounding in clinical and epidemiological inference. Chapter IX discusses Liebig's explanation of metallic poisoning, and Chapter VII the poison urali (curare) as an example of reasoning from effect to cause. Mill also treats the relation of volition to nerves and muscles and the limits of experiment in mental philosophy. Readers should take these as illustrations within a logic, not as clinical guidance of his day or ours.

• Book III, Ch. X, §§ 6–8

  The extended example of testing mercury as a remedy, comparing the deductive, experimental and observational methods, and the remark on specifics such as quinine.

• Book III, Ch. IX, § 1

  Liebig's account of how arsenious acid and salts of lead, copper and mercury destroy life by combining with animal tissue, used to illustrate the first two methods.

• Book III, Ch. VII, § 4

  The poison urali, known from the arrows of Guiana, as an example of discovering an effect by experiment or a cause by observation.

• Book III, Ch. V, § 3

  The man who takes mercury, goes out of doors and catches cold, used to show that the cause is the whole set of conditions.

• Book III, Ch. V

  Discussion of volition, nerves and muscles in the production of bodily motion, and of the continuance of effects such as brain-fever after sunstroke.