The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable'. Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us (...) understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness. The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. (shrink)

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been revived for (...) a new generation of readers. (shrink)

... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It is (...) shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

Public and professional debates have come to rely heavily on a special type of reasoning: the argument-from-ignorance, in which conclusions depend on the _lack_ of compelling information. "I win my argument," says the skillful advocate, "unless you can prove that I am wrong." This extraordinary gambit has been largely ignored in modern rhetorical and philosophical studies. Yet its broad force can be demonstrated by analogy with the modern legal system, where courts have long manipulated burdens of proof with skill and (...) subtlety. This legal, philosophical, and rhetorical study by Richard H. Gaskins provides the first systematic treatment of arguments-from-ignorance across a wide range of modern discourse—from constitutional law, scientific inquiry, and moral philosophy to organizational behavior, computer operation, and personal interaction. Gaskins reviews the historic shifts in constitutional proof burdens that have shaped public debate on fundamental rights and, by analogy, on the fundamental status of intellectual and cultural authority. He shows how similar shifts have dominated polemical battles between scientific and ethical modes of authority, affecting both academic and popular discussion. Finally, he discovers the philosophical roots of default reasoning strategies in the arguments of Kant and nineteenth-century Kantian schools. Concluding that shifting proof burdens are inescapable in a world of scientific and moral uncertainty, Gaskins emphasizes the common strategic ground shared by dogmatic and skeptical reasoning. Using Hegelian strategies, he describes a more pluralistic temper that can move critical thinking beyond polemics and strengthen our capacities for common discourse. (shrink)