Handbook Of The History And Philosophy Of Mathematical Practice
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Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher:
Release Date : 2020
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with History categories.
The philosophy of mathematics can be traced back in time to the dawn of mathematics itself. The axiomatization of Euclid in "The Elements" did not hinder innovations in mathematical practice to develop outside the realm of the deductive method. In fact the history of mathematics shows a rich tapestry of practice that include visual, algorithmic, experimental, probabilistic and computational approaches. However the philosophy of mathematics as argued by Imre Lakatos suggests that the innovations and impasses in mathematical practice have remained more or less unacknowledged in philosophy. For instance mathematical argumentation was primarily the domain of theologians and medieval and postmedieval scholastics for over 1700 years after Aristotle. Similarly the study of logic became the purview of mathematical philosophy criticized by Reuben Hersh as "Quinean ping-pong". In two prior Springer books 18 Unconventional Essays on the Nature of Mathematics (Hersh,2006) and Humanizing Mathematics and its Philosophy (Sriraman, 2017), it is sufficiently clear that the philosophy of mathematics is no longer centered around it origins in theology and logic, but influences and is influenced by other domains. Today the philosophy of mathematics can be informed by computer scientists, historians, logicians, linguists, educators, physicists, psychologists, neuroscientists, statisticians and last but not least mathematicians. At the dawn of the 21st century we still have a cadre of scholars influenced first-hand by the likes of Quine and Brouwer, as well as those who were influenced by Imre Lakatos' seminal work Proofs and Refutations (in the 1970s) that espouse the views of practicing mathematicians. Pluralism is the avant-garde term in vogue today suggesting a "post- modern" view of mathematics that would have been frowned upon a century ago. The purpose of this unique Handbook is to unfold the transformation of the philosophy of mathematics from its origins in the history of mathem atical practice. In order to do so, chapters will describe different mathematical practices in different time periods of history and contrast it with the development of philosophy. The contributions will include scholars from other disciplines who have contributed to the richness of perspectives that abound the study of philosophy today. The Handbook aims to synthesize what is known, and what has unfolded but also offer directions in which the study of philosophy of mathematics as evident in increasingly diverse mathematical practices is headed. Different sections of the Handbook will offer insights into the origins, debates, methodologies and newer perspectives that characterize the discipline today. This Handbook is curated by an editorial advisory board consisting of leading scholars from the disciplines of mathematics, history and philosophy. Editorial Advisory Board Andrew Aberdein Jody Azzouni William Byers Carlo Cellucci Chandler Davis Paul Ernest Michele Friend Reuben Hersh Yuri Manin Athanase Papadopoulos Ulf Persson Kim Plofker John Stillwell David Tall.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date :
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Oxford Handbook Of The History Of Mathematics
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Author : Eleanor Robson
language : en
Publisher: OUP Oxford
Release Date : 2008-12-18
The Oxford Handbook Of The History Of Mathematics written by Eleanor Robson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Mathematics categories.
This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
Making And Breaking Mathematical Sense
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Author : Roi Wagner
language : en
Publisher: Princeton University Press
Release Date : 2017-01-10
Making And Breaking Mathematical Sense written by Roi Wagner and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-10 with Mathematics categories.
In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
The Oxford Handbook Of The History Of Analytic Philosophy
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Author : Michael Beaney
language : en
Publisher: OUP Oxford
Release Date : 2013-06-20
The Oxford Handbook Of The History Of Analytic Philosophy written by Michael Beaney and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Philosophy categories.
During the course of the twentieth century, analytic philosophy developed into the dominant philosophical tradition in the English-speaking world. In the last two decades, it has become increasingly influential in the rest of the world, from continental Europe to Latin America and Asia. At the same time there has been deepening interest in the origins and history of analytic philosophy, as analytic philosophers examine the foundations of their tradition and question many of the assumptions of their predecessors. This has led to greater historical self-consciousness among analytic philosophers and more scholarly work on the historical contexts in which analytic philosophy developed. This historical turn in analytic philosophy has been gathering pace since the 1990s, and the present volume is the most comprehensive collection of essays to date on the history of analytic philosophy. It contains state-of-the-art contributions from many of the leading scholars in the field, all of the contributions specially commissioned. The introductory essays discuss the nature and historiography of analytic philosophy, accompanied by a detailed chronology and bibliography. Part One elucidates the origins of analytic philosophy, with special emphasis on the work of Frege, Russell, Moore, and Wittgenstein. Part Two explains the development of analytic philosophy, from Oxford realism and logical positivism to the most recent work in analytic philosophy, and includes essays on ethics, aesthetics, and political philosophy as well as on the areas usually seen as central to analytic philosophy, such as philosophy of language and mind. Part Three explores certain key themes in the history of analytic philosophy.
Handbook Of The Mathematics Of The Arts And Sciences
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Author : Bharath Sriraman
language : en
Publisher: Springer
Release Date : 2021-08-15
Handbook Of The Mathematics Of The Arts And Sciences written by Bharath Sriraman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-15 with Mathematics categories.
The goal of this Handbook is to become an authoritative source with chapters that show the origins, unification, and points of similarity between different disciplines and mathematics. Some chapters will also show bifurcations and the development of disciplines which grow to take on a life of their own. Science and Art are used as umbrella terms to encompass the physical, natural and geological sciences, as well as the visual and performing arts. As arts imagine possibilities, science attempts to generate models to test possibilities, mathematics serves as the tool. This handbook is an indispensable collection to understand todays effort to build bridges between disciplines. It answers questions such as: What are the origins of interdisciplinarity in mathematics? What are cross-cultural components of interdisciplinarity linked to mathematics? What are contemporary interdisciplinary trends? Section Editors: Michael J. Ostwald, University of Newcastle (Australia) Kyeong-Hwa Lee, Seoul National University (South Korea) Torsten Lindström, Linnaeus University (Sweden) Gizem Karaali, Pomona College (USA) Ken Valente, Colgate University, (USA) Consulting Editors: Alexandre Borovik, Manchester University (UK) Daina Taimina, Independent Scholar, Cornell University (USA) Nathalie Sinclair, Simon Fraser University (Canada) What do figure skating, invasive species, medieval cathedrals, ropes, poems, wines, metaphors, rhythms, climate change, and origami have in common? Mathematics! The Handbook of the Mathematics of the Arts and Sciences is a stunning compendium of essays on these and scores of other unlikely subjects to which the mathematical imagination has been brought. It is at once a dazzlingly contemporary tour of human success at bringing order to the world, and a throwback to a time before the “unity of knowledge” became a mere slogan. It is a breathtaking work, for its ambitious scope and for its endless stimulation of the reader’s curiosity. - Harry R. Lewis, Gordon McKay Research Professor of Computer Science at Harvard University, editor of Ideas That Created the Future: Classic Papers of Computer Science Mathematics has always enjoyed deep connections with the arts, science, the humanities, philosophy, history, and society in general. However, these links are often overlooked or undervalued. This Handbook makes a massive statement about the extent and importance of the interdisciplinary nature of mathematics, and its relevance to all aspects of human culture. Its articles are scholarly and authoritative, but also highly readable and accessible to non-specialists. A triumph! -Ian Stewart FRS, Emeritus Professor - University of Warwick This handbook will delight anyone who loves the richness of mathematics and its interplay with the arts and humanities. Bharath Sriraman has given us a great gift, a treasure chest of connections to art and architecture, language and literature, philosophy, history, society, you name it. The book is authoritative and charming and instantly establishes itself as a landmark reference for interdisciplinary mathematics. Steven Strogatz - Jacob Gould Schurman Professor of Applied Mathematics at Cornell University.
The Philosophy Of Mathematical Practice
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Author : Paolo Mancosu
language : en
Publisher: OUP Oxford
Release Date : 2008-06-19
The Philosophy Of Mathematical Practice written by Paolo Mancosu and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-19 with Philosophy categories.
Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.
New Perspectives On Mathematical Practices
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Author :
language : en
Publisher:
Release Date :
New Perspectives On Mathematical Practices written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Oxford Handbook Of Generality In Mathematics And The Sciences
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Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016-07-07
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-07 with Mathematics categories.
Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.
New Perspectives On Mathematical Practices
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Author : Bart van Kerkhove
language : en
Publisher: World Scientific
Release Date : 2009
New Perspectives On Mathematical Practices written by Bart van Kerkhove and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.