John Wisdom was Professor of Philosophy at Cambridge University through the 1950s and 1960s, holding the chair that had been Wittgenstein's. Later he taught in America, and was elected President of the American Philosophical Association, Pacific Division. This book is based on previously unpublished lectures that Wisdom delivered at the University of Virginia. Its content goes significantly beyond that of his other books. Here he is concerned with how misunderstandings about what it is to prove something or what it is to explain something can infect our thinking in many different fields. Wisdom develops an original and controversial account of what he calls 'case-by-case rocedure,' as he endeavors to dispel those misunderstandings and illuminate the nature of proof and explanation, as these occur in physics, psychology, ethics, and everyday situations. The book includes an introduction by David C. Yalden-Thomson.