Scholar, ecclesiastic, teacher and poet of the eighth century, Alcuin was a person of deep Christian faith, tenacious in his loyalty to orthodox Catholic theology. He had a seminal influence upon his own generation and those that came after him. Althoughhe remained a Northumbrian Christian at heart, the part of his life about which most is known was spent on the Continent. He never lost contact with his homeland; but his most significant and lasting work was evidently accomplished in Europe and his influence on the early medieval Western Church was an abiding one. This book examines his life and career in England and on the continent; it also considers his legacy as a churchman and a leading political figure. This volume prefigures a forthcoming work onAlcuin's intellectual legacy, 'Alcuin : A Study of his Theology' (due for release, April 2013). This rich study is intended for the general reader as well as for those studying, teaching or researching this period of early medieval history and theology in schools and universities.

Propositiones ad acuendos juvenes (“Problems to Sharpen the Young”) is a ninth-century book written by medieval teacher and scholar Alcuin of York. Today, it has become one of the foundational texts in what is commonly called recreational mathematics. The book has been translated in many languages and analysed from various mathematical angles and perspectives, from contemporary arithmetic and geometry to the nature of sequences. It is not only a collection of ingenious and challenging puzzles, but the core ideas collected in this book have become major themes and branches of mathematics. Here, Marcel Danesi revisits all fifty-three problems in Alcuin's original text, providing detailed solutions and analyses. Alcuin's Recreational Mathematics examines the problems in the Propositiones in easy-to-follow language, extracting from them the notions and techniques that today constitute basic mathematics. Each chapter discusses Alcuin's problems more broadly, and ends with ten exploratory puzzles based on Alcuin's original problems and related themes. Answers and detailed solutions are included at the back. Alcuin's Recreational Mathematics demonstrates how Alcuin's Propositiones puts basic mathematical thinking on display via ingenious problems that often require outside-of-the-box thinking, constituting an original and imaginative investigation of mathematics in its essence.

Scholar, ecclesiastic, teacher and poet of the eighth century, Alcuin was a person of deep Christian faith, tenacious in his loyalty to orthodox Catholic theology. He had a seminal influence upon his own generation and those that came after him. Althoughhe remained a Northumbrian Christian at heart, the part of his life about which most is known was spent on the Continent. He never lost contact with his homeland; but his most significant and lasting work was evidently accomplished in Europe and his influence on the early medieval Western Church was an abiding one. This book examines his life and career in England and on the continent; it also considers his legacy as a churchman and a leading political figure. This volume prefigures a forthcoming work onAlcuin's intellectual legacy, 'Alcuin : A Study of his Theology' (due for release, April 2013). This rich study is intended for the general reader as well as for those studying, teaching or researching this period of early medieval history and theology in schools and universities.

An intellectual biography of Alcuin, the most prominent Anglo-Saxon scholar at the court of Charlemagne. It examines his early years in Northumbria and his time at the Carolingian court, reassessing the chronology of Alcuin's career and writings, and the significance of his large output.

Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-19th century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the 11th and 16th centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to inquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece.Mediaeval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.- Provides detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic