This work breaks new ground by carefully distinguishing the concepts of belief, confirmation, and evidence and then integrating them into a better understanding of personal and scientific epistemologies. It outlines a probabilistic framework in which subjective features of personal knowledge and objective features of public knowledge have their true place. It also discusses the bearings of some statistical theorems on both formal and traditional epistemologies while showing how some of the existing paradoxes in both can be resolved with the help of this framework.This book has two central aims: First, to make precise a distinction between the concepts of confirmation and evidence and to argue that failure to recognize this distinction is the source of certain otherwise intractable epistemological problems. The second goal is to demonstrate to philosophers the fundamental importance of statistical and probabilistic methods, at stake in the uncertain conditions in which for the most part we lead our lives, not simply to inferential practice in science, where they are now standard, but to epistemic inference in other contexts as well. Although the argument is rigorous, it is also accessible. No technical knowledge beyond the rudiments of probability theory, arithmetic, and algebra is presupposed, otherwise unfamiliar terms are always defined and a number of concrete examples are given. At the same time, fresh analyses are offered with a discussion of statistical and epistemic reasoning by philosophers. This book will also be of interest to scientists and statisticians looking for a larger view of their own inferential techniques.The book concludes with a technical appendix which introduces an evidential approach to multi-model inference as an alternative to Bayesian model averaging.

The certainties which once underpinned Christian belief have crumbled in a world where science sets the standard for what is true. A rational case for belief must therefore be constructed out of uncertainties. Probability theory provides the tools for measuring and combining uncertainties and is thus the key to progress. This book examines four much debated topics where the logic of uncertain inference can be brought to bear. These are: miracles, the paranormal, God's existence, and the Bible. Given the great diversity of evidence, it is not surprising that opposite conclusions have been drawn by supposedly rational people. An assessment of the state of argument from a probabilistic perspective is overdue. In this book Professor Bartholomew examines and refutes some of the more extravagent claims, evaluates the weight of some of the quantitive evidence, and provides an answer to the fundamental question: is it rational to be a Christian?

Anti-evolutionists, climate denialists, and anti-vaxxers, among others, question some of the best-established scientific findings by referring to the uncertainties in these areas of research. Uncertainty: How It Makes Science Advance shows that uncertainty is an inherent feature of science that makes it advance by motivating further research.

When in doubt, make belief. For author and news anchor Jeff Bell, these are words to live by. Literally. As someone who has spent much of his life battling severe obsessive compulsive disorder (OCD), Bell has had to overcome crippling uncertainty few people can imagine. In this powerful follow-up to his critically acclaimed memoir, Rewind, Replay, Repeat, Bell expounds on the principles of applied belief that allowed him to make such a remarkable recovery from this “doubting disease” and the lessons he’s learned while traveling the country talking about doubt. With the help of more than a dozen leading experts, Bell offers readers practical techniques for pushing through the discomfort of uncertainty — whether it stems from OCD or just everyday worries — and demonstrates how a shift from decisions based on fear and doubt to ones based on purpose and service can transform any life. Featuring interviews with Sylvia Boorstein, Patty Duke, Dan Millman, Leon Panetta, Tom Sullivan, and others

The Virtue of Uncertainty examines Christianity's origin, its purported revelations, its sacred book, its moral principles, its doctrines, its theology, its history, and its effects on society. The purpose of the book is to show that religious certainty flies in the face of evidence and rational thought, and that doubt ought to be a sine qua non for Christians. The author, Eugene R. Moutoux, spent nine years (1953-1962) preparing for the Catholic priesthood; however, finding it increasingly difficult to believe, and wanting a wife and family, he dropped out of the seminary two months before scheduled ordination. Gene has a Ph.D. in German from the University of California at Santa Barbara. He lives in New Albany, Indiana.

The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.