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Handbook of the History and Philosophy of Mathematical Practice

Author: Bharath Sriraman

Publisher:

Published: 2020

Total Pages: 985

ISBN-13: 9783030190712

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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.

Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman

Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by . This book was released on 2020 with total page 985 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Bharath Sriraman

Publisher: Springer Nature

Published:

Total Pages: 3221

ISBN-13: 3031408462

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Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman

Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author: Paolo Mancosu

Publisher: Oxford University Press, USA

Published: 1999

Total Pages: 290

ISBN-13: 0195132440

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1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.

Book Synopsis Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century by : Paolo Mancosu

Download or read book Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century written by Paolo Mancosu and published by Oxford University Press, USA. This book was released on 1999 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.

The Philosophy of Mathematical Practice

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

Published: 2008-06-19

Total Pages: 460

ISBN-13: 0199296456

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There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

Book Synopsis The Philosophy of Mathematical Practice by : Paolo Mancosu

Download or read book The Philosophy of Mathematical Practice written by Paolo Mancosu and published by Oxford University Press on Demand. This book was released on 2008-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

Making and Breaking Mathematical Sense

Author: Roi Wagner

Publisher: Princeton University Press

Published: 2017-01-10

Total Pages: 250

ISBN-13: 0691171718

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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.

Book Synopsis Making and Breaking Mathematical Sense by : Roi Wagner

Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Model Theory and the Philosophy of Mathematical Practice

Author: John T. Baldwin

Publisher: Cambridge University Press

Published: 2018-01-25

Total Pages: 365

ISBN-13: 1107189217

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Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Book Synopsis Model Theory and the Philosophy of Mathematical Practice by : John T. Baldwin

Download or read book Model Theory and the Philosophy of Mathematical Practice written by John T. Baldwin and published by Cambridge University Press. This book was released on 2018-01-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

The Oxford Handbook of The History of Analytic Philosophy

Author: Michael Beaney

Publisher: OUP Oxford

Published: 2013-06-20

Total Pages: 1184

ISBN-13: 0191662666

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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.

Book Synopsis The Oxford Handbook of The History of Analytic Philosophy by : Michael Beaney

Download or read book The Oxford Handbook of The History of Analytic Philosophy written by Michael Beaney and published by OUP Oxford. This book was released on 2013-06-20 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Oxford Handbook of the History of Mathematics

Author: Eleanor Robson

Publisher: Oxford University Press on Demand

Published: 2009

Total Pages: 927

ISBN-13: 0199213127

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This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

Book Synopsis The Oxford Handbook of the History of Mathematics by : Eleanor Robson

Download or read book The Oxford Handbook of the History of Mathematics written by Eleanor Robson and published by Oxford University Press on Demand. This book was released on 2009 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

New Perspectives on Mathematical Practices

Author: Bart Van Kerkhove

Publisher: World Scientific

Published: 2009

Total Pages: 248

ISBN-13: 9812812237

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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.

Book Synopsis New Perspectives on Mathematical Practices by : Bart Van Kerkhove

Download or read book New Perspectives on Mathematical Practices written by Bart Van Kerkhove and published by World Scientific. This book was released on 2009 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

International Handbook of Research in History, Philosophy and Science Teaching

Author: Michael R. Matthews

Publisher: Springer

Published: 2014-07-03

Total Pages: 2487

ISBN-13: 9400776543

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This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects. There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. Science educators will be grateful for this unique, encyclopaedic handbook, Gerald Holton, Physics Department, Harvard University This handbook gathers the fruits of over thirty years’ research by a growing international and cosmopolitan community Fabio Bevilacqua, Physics Department, University of Pavia

Book Synopsis International Handbook of Research in History, Philosophy and Science Teaching by : Michael R. Matthews

Download or read book International Handbook of Research in History, Philosophy and Science Teaching written by Michael R. Matthews and published by Springer. This book was released on 2014-07-03 with total page 2487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects. There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. Science educators will be grateful for this unique, encyclopaedic handbook, Gerald Holton, Physics Department, Harvard University This handbook gathers the fruits of over thirty years’ research by a growing international and cosmopolitan community Fabio Bevilacqua, Physics Department, University of Pavia