A Treatise on Probability

Abstract

John Maynard Keynes's A Treatise on Probability is a foundational work of 20th-century philosophy, presenting a groundbreaking logical-relation theory of probability. Moving beyond purely mathematical or frequency-based interpretations, Keynes argues that probability represents a rational degree of belief—a logical relation between a set of premisses (evidence) and a conclusion. The treatise is structured in five comprehensive parts, beginning with the "Fundamental Ideas," where Keynes defines probability and its deep relationship to human knowledge. Part II, "Fundamental Theorems," lays out the mathematical calculus, covering traditional topics like addition, multiplication, and inverse probability (Bayes's theorem). The philosophical core of the book resides in Part III, "Induction and Analogy," where Keynes unconventionally grounds the validity of inductive reasoning—the cornerstone of scientific method—in the principles of probability. He argues that scientific inference is not a matter of certainty but of establishing high probabilities through the accumulation of positive and negative analogies. The final sections, "Some Philosophical Applications of Probability" (Part IV) and "The Foundations of Statistical Inference" (Part V), extend this framework to analyze the logic of scientific hypothesis, the probability of causes, and the meaning of statistical laws like the Law of Great Numbers. The book remains a profound exploration of how we justify our knowledge in an uncertain world.