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?

This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

The world is full of people who are very certain--in politics, in religion, in all manner of things. In addition, political, religious, and social organizations are marketing certainty as a cure all to all life's problems. But is such certainty possible? Or even good? The Certainty of Uncertainty explores the question of certainty by looking at the reasons human beings crave certainty and the religious responses we frequently fashion to help meet that need. The book takes an in-depth view of religion, language, our senses, our science, and our world to explore the inescapable uncertainties they reveal. We find that the certainty we crave does not exist. As we reflect on the unavoidable uncertainties in our world, we come to understand that letting go of certainty is not only necessary, it's beneficial. For, in embracing doubt and uncertainty, we find a more meaningful and courageous religious faith, a deeper encounter with mystery, and a way to build strong relationships across religious and philosophical lines. In The Certainty of Uncertainty, we see that embracing our belief systems with humility and uncertainty can be transformative for ourselves and for our world.

The world is full of people who are very certain—in politics, in religion, in all manner of things. In addition, political, religious, and social organizations are marketing certainty as a cure all to all life’s problems. But is such certainty possible? Or even good? The Certainty of Uncertainty explores the question of certainty by looking at the reasons human beings crave certainty and the religious responses we frequently fashion to help meet that need. The book takes an in-depth view of religion, language, our senses, our science, and our world to explore the inescapable uncertainties they reveal. We find that the certainty we crave does not exist. As we reflect on the unavoidable uncertainties in our world, we come to understand that letting go of certainty is not only necessary, it’s beneficial. For, in embracing doubt and uncertainty, we find a more meaningful and courageous religious faith, a deeper encounter with mystery, and a way to build strong relationships across religious and philosophical lines. In The Certainty of Uncertainty, we see that embracing our belief systems with humility and uncertainty can be transformative for ourselves and for our world.

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.

Kierkegaard said that faith without doubt is simply credulity, the will to believe too readily, especially without adequate evidence, and that "in Doubt can Faith begin." All people involved in spiritual practice, of whatever persuasion, must confront doubt at one time or another, and find a way beyond it to belief, however temporary. But "faith is not equivalent to mere belief. Faith is the condition of ultimate confidence that we have the capacity to follow the path of doubt to its end. And courage." In this engaging spiritual memoir, Stephen Batchelor describes his own training, first as a Tibetan Buddhist and then as a Zen practitioner, and his own direct struggles along his path. "It is most uncanny that we are able to ask questions, for to question means to acknowledge that we do not know something. But it is more than an acknowledgement: it includes a yearning to confront an unknown and illuminate it through understanding. Questioning is a quest." Batchelor is a contemporary Buddhist teacher and writer, best known for his secular or agnostic approach to Buddhism. He considers Buddhism to be a constantly evolving culture of awakening rather than a religious system based on immutable dogmas and beliefs. Buddhism has survived for the past 2,500 years because of its capacity to reinvent itself in accord with the needs of the different Asian societies with which it has creatively interacted throughout its history. As Buddhism encounters modernity, it enters a vital new phase of its development. Through his writings, translations and teaching, Stephen engages in a critical exploration of Buddhism's role in the modern world, which has earned him both condemnation as a heretic and praise as a reformer.

"Lane's stimulating analysis asks whether acknowledging how science, religion, and society have produced a growing chasm between faith and doubt, and even destroyed belief, can offer a way forward."Keith Thomson, author of Before Darwin and The Young Charles Darwin --Book Jacket.