Featured Review:; Probability Theory: The Logic of Science

Abstract

SIAM Review, Volume 68, Issue 2, Page 459-462, June 2026.
Probability Theory: The Logic of Science by E. T. Jaynes is a highly ambitious, unusual, and personal book. Its goal is no less than to lay the foundation for how to reason under uncertainty, not only in science, but generally. Inspired by Polya’s Mathematics and Plausible Reasoning, throughout his career Jaynes pursued a program of understanding the rules of plausible reasoning that would be broadly applicable across domains. Starting not from axioms, but from the “desiderata,” or desirable properties, that one would like to have in a quantitative system of reasoning, Jaynes arrives at the traditional rules of probability theory, namely, the sum and product rules. In so doing, he argues that probability theory is not constrained to any discipline, but constitutes a widely applicable extension of traditional logical systems, wherein statements have truth values that have a quantifiable uncertainty. Jaynes viewed probability theory as a kind of “theory of everything” for reasoning. The book contains an extensive and impressive collection of examples and discussions aimed at underlining this idea and showing the ways in which it aligns or not with traditional views.