This book is concerned with the mathematical analysis of the concept of formal proof in classical logic, and records - in substance - a longer exercise in applied λ-calculus. Following colloquialisms going back to L. E. J. Brouwer, the objects of study in this enterprise are called witnesses. A witness is meant to represent the logical proof of a classically valid formula, in a given proof-context. The formalisms used to express witnesses and their equational behaviour are extensions of the pure `typed' λ-calculus, considered as equational theories. Formally, a witness is generated from decorated - or `typed' - witness variables, representing assumptions, and witness operators, representing logical rules of inference. The equational specifications serve to define the witness operators. In general, this can be done by ignoring the `typing', i.e., the logic formulas themselves. Model-theoretically, the witnesses are objects of an extensional Scott λ-model. The approach - called, generically, `witness theory' - is inspired from work of N. G. de Bruijn, on a mathematical theory of proving, done during the late 1960s and the early 1970s, at the University of Eindhoven (The Netherlands), and is similar to the approach behind the Curry-Howard Correspondence, familiar from intuitionistic logic. For the classical case, the decorations - oft called `types' - are classical logic formulas. At quantifier-free level, the equational theory of concern is the λ-calculus with `surjective pairing' and some subsystens thereof, appropriately decorated. The extension to propositional, first- and second-order quantifiers is straightforward. The book consists of a collection of notes and papers written and circulated during the last ten years, as a continuation of previous research done by the author during the nineteen eighties. Among other things, it includes a survey of the origins of modern proof theory - Frege to Gentzen - from a witness-theoretical point of view, as well as a characteristic application of witness theory to a practical logic problem concerning axiomatisability.

WINNER OF THE NATIONAL JEWISH BOOK AWARD--BIOGRAPHY Elie Wiesel was a towering presence on the world stage--a Nobel laureate, activist, adviser to world leaders, and the author of more than forty books, including the Oprah's Book Club selection Night. But when asked, Wiesel always said, "I am a teacher first." In fact, he taught at Boston University for nearly four decades, and with this book, Ariel Burger--devoted prot g , apprentice, and friend--takes us into the sacred space of Wiesel's classroom. There, Wiesel challenged his students to explore moral complexity and to resist the dangerous lure of absolutes. In bringing together never-before-recounted moments between Wiesel and his students, Witness serves as a moral education in and of itself--a primer on educating against indifference, on the urgency of memory and individual responsibility, and on the role of literature, music, and art in making the world a more compassionate place. Burger first met Wiesel at age fifteen; he became his student in his twenties, and his teaching assistant in his thirties. In this profoundly thought-provoking and inspiring book, Burger gives us a front-row seat to Wiesel's remarkable exchanges in and out of the classroom, and chronicles the intimate conversations between these two men over the decades as Burger sought counsel on matters of intellect, spirituality, and faith, while navigating his own personal journey from boyhood to manhood, from student and assistant, to rabbi and, in time, teacher. "Listening to a witness makes you a witness," said Wiesel. Ariel Burger's book is an invitation to every reader to become Wiesel's student, and witness.

The Model Rules of Professional Conduct provides an up-to-date resource for information on legal ethics. Federal, state and local courts in all jurisdictions look to the Rules for guidance in solving lawyer malpractice cases, disciplinary actions, disqualification issues, sanctions questions and much more. In this volume, black-letter Rules of Professional Conduct are followed by numbered Comments that explain each Rule's purpose and provide suggestions for its practical application. The Rules will help you identify proper conduct in a variety of given situations, review those instances where discretionary action is possible, and define the nature of the relationship between you and your clients, colleagues and the courts.

Today more than ever before, the historical witness is now a “museum objectâ€_x009d_ in the form of video interviews with individuals remembering events of historical importance. Such video testimonies now not only are part of the collections and research activities of museums, but become deeply intertwined with narrative and exhibit design. With a focus on Holocaust museums, this study scrutinizes for the first time this new global process of “musealisationâ€_x009d_ of testimony, exploring the processes, prerequisites, and consequences of the transformation of video testimonies into exhibits.