The central theme running throughout this 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 18th-century; the method of hypotheses through the work of Herschel, Mill and Whewell; the conventionalist views of Poincare and Suhem; the inductivism of Peirce, Russell and Keynes; Popper's falsification compared with Reichenbach's enumerative induction; and Carnap's scientific method as Bayesian reasoning.