The central theme running throughout this outstanding new survey is the nature of the philosophical debate created by modern science's foundation in experimental and mathematical method. Key chapters critically discuss * Galileo's demonstrative method, Bacon's inductive method, and Newton's rules of reasoning * the rise of probabilistic Bayesian' methods in the eighteenth century * the method of hypotheses through the work of Herschel, Mill and Whewell * the conventionalist views of Poincare and Duhem * the inductivism of Peirce, Russell and Keynes * Popper's falsification compared with Reichenbach's enumerative induction * Carnap's scientific method as Bayesian reasoning