Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
Part IV. About the author -- An amusing elementary example -- Annotated research bibliography -- Curriculum vitae -- List of articles -- Index -- Back Cover
This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.
This edited volume of 13 new essays aims to turn past discussions of natural kinds on their head. Instead of presenting a metaphysical view of kinds based largely on an unempirical vantage point, it pursues questions of kindedness which take the use of kinds and activities of kinding in practice as significant in the articulation of them as kinds. The book brings philosophical study of current and historical episodes and case studies from various scientific disciplines to bear on natural kinds as traditionally conceived of within metaphysics. Focusing on these practices reveals the different knowledge-producing activities of kinding and processes involved in natural kind use, generation, and discovery. Specialists in their field, the esteemed group of contributors use diverse empirically responsive approaches to explore the nature of kindhood. This groundbreaking volume presents detailed case studies that exemplify kinding in use. Newly written for this volume, each chapter engages with the activities of kinding across a variety of disciplines. Chapter topics include the nature of kinds, kindhood, kinding, and kind-making in linguistics, chemical classification, neuroscience, gene and protein classification, colour theory in applied mathematics, homology in comparative biology, sex and gender identity theory, memory research, race, extended cognition, symbolic algebra, cartography, and geographic information science. The volume seeks to open up an as-yet unexplored area within the emerging field of philosophy of science in practice, and constitutes a valuable addition to the disciplines of philosophy and history of science, technology, engineering, and mathematics.
The year's finest writing on mathematics from around the world This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations. The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.
This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality.
