This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Perceptively explores the shifting intersections between algorithmic systems and human practices in the modern era. How have algorithmic systems and human practices developed in tandem since 1800? This volume of Osiris deftly addresses the question, dispelling along the way the traditional notion of algorithmic “code” and human “craft” as natural opposites. Instead, algorithms and humans have always acted in concert, depending on each other to advance new knowledge and produce social consequences. By shining light on alternative computational imaginaries, Beyond Craft and Code opens fresh space in which to understand algorithmic diversity, its governance, and even its conservation. The volume contains essays by experts in fields extending from early modern arithmetic to contemporary robotics. Traversing a range of cases and arguments that connect politics, historical epistemology, aesthetics, and artificial intelligence, the contributors collectively propose a novel vocabulary of concepts with which to think about how the history of science can contribute to understanding today’s world. Ultimately, Beyond Craft and Code reconfigures the historiography of science and technology to suggest a new way to approach the questions posed by an algorithmic culture—not only improving our understanding of algorithmic pasts and futures but also unlocking our ability to better govern our present.
The Oxford Handbook of Indian Philosophy tells the story of philosophy in India through a series of exceptional individual acts of philosophical virtuosity. It brings together forty leading international scholars to record the diverse figures, movements, and approaches that constitute philosophy in the geographical region of the Indian subcontinent, a region sometimes nowadays designated South Asia. The volume aims to be ecumenical, drawing from different locales, languages, and literary cultures, inclusive of dissenters, heretics and sceptics, of philosophical ideas in thinkers not themselves primarily philosophers, and reflecting India's north-western borders with the Persianate and Arabic worlds, its north-eastern boundaries with Tibet, Nepal, Ladakh and China, as well as the southern and eastern shores that afford maritime links with the lands of Theravda Buddhism. Indian Philosophy has been written in many languages, including Pali, Prakrit, Sanskrit, Malayalam, Urdu, Gujarati, Tamil, Telugu, Bengali, Marathi, Persian, Kannada, Punjabi, Hindi, Tibetan, Arabic and Assamese. From the time of the British colonial occupation, it has also been written in English. It spans philosophy of law, logic, politics, environment and society, but is most strongly associated with wide-ranging discussions in the philosophy of mind and language, epistemology and metaphysics (how we know and what is there to be known), ethics, metaethics and aesthetics, and metaphilosophy. The reach of Indian ideas has been vast, both historically and geographically, and it has been and continues to be a major influence in world philosophy. In the breadth as well as the depth of its philosophical investigation, in the sheer bulk of surviving texts and in the diffusion of its ideas, the philosophical heritage of India easily stands comparison with that of China, Greece, the Latin west, or the Islamic world.
Mesopotamian Commentaries on the Diagnostic Handbook Sa-gig is intended for specialists in cuneiform studies, and includes a cuneiform edition, English translation, and notes on medical lexicography for thirty Sa-gig commentary tablets and fragments, as well as a study on technical notations recurring in these commentaries. Within the Cuneiform Monographs series, this book represents a companion volume to Knowledge and Rhetoric in Medical Commentary (Brill, 2019).
A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection.
Handbook of Hinduism in Europe portrays and analyses how Hindu traditions have expanded across the continent, and presents the main Hindu communities, religious groups, forms, practices and teachings. The Handbook does this in two parts, Part One covers historical and thematic topics which are of importance for understanding Hinduism in Europe as a whole and Part Two has chapters on Hindu traditions in every country in Europe. Hindu traditions have a long history of interaction with Europe, but the developments during the last fifty years represent a new phase. Globalization and increased ease of communication have led to the presence of a great plurality of Hindu traditions. Hinduism has become one of the major religions in Europe and is present in every country of the continent.
This book is a companion to logical thought and logical thinking in China with a comparative and interdisciplinary perspective. It introduces the basic ideas and theories of Chinese thought in a comprehensive and analytical way. It covers thoughts in ancient, pre-modern and modern China from a historical point of view. It deals with topics in logical (including logico-philosophical) concepts and theories rooted in China, Indian and Western Logic transplanted to China, and the development of logical studies in contemporary China and other Chinese communities. The term “philosophy of logic” or “logico-philosophical thought” is used in this book to represent “logical thought” in a broad sense which includes thinking on logical concepts, modes of reasoning, and linguistic ideas related to logic and philosophical logic. Unique in its approach, the book uses Western logical theories and philosophy of language, Chinese philology, and history of ideas to deal with the basic ideas and major problems in logical thought and logical thinking in China. In doing so, it advances the understanding of the lost tradition in Chinese philosophical studies.
As of yet, the remarkable and highly influential textual form of Euclidean mathematics has not been considered from a literary-aesthetic perspective. By its extreme standardization and seeming non-literariness it appears to defy such an approach. This book nonetheless attempts precisely a literary-aesthetic study of the language and style of Euclid’s Elements, focusing on book I. It aims to find out what is literary about the form and what motivates this form as form. In doing so, it employs the concept of clarity, asking: How is the textual form related to logical and communicative clarity? That is, how far is the omnipresent standardization necessary for the accomplishment and successful communication of the proofs? Based on a close analysis of the standardization at all levels of the text (lexicon, grammar, structure, and especially diagram), it argues that the textual form of the Elements is standardized beyond logical-communicative purposes, and that it is in this sense ‘aesthetic’. The book exposes the unexpected literary dimension of Euclid’s Elements, provides a new interpretation of the peculiar form of the work, and offers a model for determining the role of clarity (not only) in Greek theoretical mathematics.
