This is a new, fully updated, thoroughly revised, and substantially enlarged edition of Howson and Urbach's much-acclaimed account of scientific method from the Bayesian standpoint. Scientific Reasoning is both an introduction to probability theory and a philosophical commentary on the problems of scientific inference. The second edition includes chapter exercises, and extended material on such topics as regression analysis, distributions and densities, randomization, and conditionalization. Confronting the controversial issues in induction and the confirmation of scientific theories, Howson and Urbach reject the "objectivist ideal" and the fashionable non-probabilistic standards of scientific worth, associated with such writers as Neyman and Pearson, Fisher, Popper, and Lakatos. Howson and Urbach contend that "scientific reasoning is reasoning in accordance with the calculus of probabilities", and (assuming little more advanced than elementary algebra) they give a concise introduction to this calculus. The authors examine the way in which scientists actually appeal to probability arguments, and expound the 'classical' model of statistical inference, which they demonstrate to be full of flaws. They then present the Bayesian approach, showing that it avoids the difficulties of the classical system. Finally, they reply to all the major criticisms levelled against the Bayesian method, especially the charge that it is 'too subjective'.