Humanizing Mathematics And Its Philosophy

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Humanizing Mathematics and its Philosophy

Author : Bharath Sriraman
Publisher : Birkhäuser
ISBN 13 : 331961231X
Total Pages : 363 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Humanizing Mathematics and its Philosophy by : Bharath Sriraman

Download or read book Humanizing Mathematics and its Philosophy written by Bharath Sriraman and published by Birkhäuser. This book was released on 2017-11-07 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

Handbook of the History and Philosophy of Mathematical Practice

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.0/5 (314 download)

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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:

The Making of Mathematics

Author : Carlo Cellucci
Publisher : Springer Nature
ISBN 13 : 3030897311
Total Pages : 457 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis The Making of Mathematics by : Carlo Cellucci

Download or read book The Making of Mathematics written by Carlo Cellucci and published by Springer Nature. This book was released on 2022-03-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.

Handbook of the History and Philosophy of Mathematical Practice

Author : Bharath Sriraman
Publisher :
ISBN 13 : 9783030190712
Total Pages : 985 pages
Book Rating : 4.1/5 (97 download)

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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 . 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.

The Best Writing on Mathematics 2019

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 0691197946
Total Pages : 304 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Best Writing on Mathematics 2019 by : Mircea Pitici

Download or read book The Best Writing on Mathematics 2019 written by Mircea Pitici and published by Princeton University Press. This book was released on 2019-11-05 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year's finest mathematical writing from around the world This annual 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 2019 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 essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today's hottest mathematical debates. In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more. In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.

Imagination and Art: Explorations in Contemporary Theory

Author : Keith Moser
Publisher : BRILL
ISBN 13 : 9004436359
Total Pages : 810 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis Imagination and Art: Explorations in Contemporary Theory by : Keith Moser

Download or read book Imagination and Art: Explorations in Contemporary Theory written by Keith Moser and published by BRILL. This book was released on 2020-07-27 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This transdisciplinary project represents the most comprehensive study of imagination to date. The eclectic group of international scholars who comprise Imagination and Art propose bold and innovative theoretical frameworks for (re-) conceptualizing imagination in all of its divergent forms.

Rethinking Knowledge

Author : Carlo Cellucci
Publisher : Springer
ISBN 13 : 3319532375
Total Pages : 427 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Rethinking Knowledge by : Carlo Cellucci

Download or read book Rethinking Knowledge written by Carlo Cellucci and published by Springer. This book was released on 2017-03-29 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Abductive Cognition

Author : Lorenzo Magnani
Publisher : Springer Nature
ISBN 13 : 3031101359
Total Pages : 1921 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Handbook of Abductive Cognition by : Lorenzo Magnani

Download or read book Handbook of Abductive Cognition written by Lorenzo Magnani and published by Springer Nature. This book was released on 2023-03-31 with total page 1921 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group of internationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.

International Handbook of Research in History, Philosophy and Science Teaching

Author : Michael R. Matthews
Publisher : Springer
ISBN 13 : 9400776543
Total Pages : 2532 pages
Book Rating : 4.4/5 (7 download)

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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 2532 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

The Map and the Territory

Author : Shyam Wuppuluri
Publisher : Springer
ISBN 13 : 3319724789
Total Pages : 641 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Map and the Territory by : Shyam Wuppuluri

Download or read book The Map and the Territory written by Shyam Wuppuluri and published by Springer. This book was released on 2018-02-13 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction between the former and the latter is lost. This error that has its roots in the pedagogy often generates a plethora of paradoxes/confusions which hinder the proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map (theory/representation)? Or do they actually belong to the territory (Reality)? Researcher, like a cartographer, clothes (or creates?) the reality by stitching multitudes of maps that simultaneously co-exist. A simple apple, for example, can be analyzed from several viewpoints beginning with evolution and biology, all the way down its microscopic quantum mechanical components. Is there a reality (or a real apple) out there apart from these maps? How do these various maps interact/intermingle with each other to produce a coherent reality that we interact with? Or do they not? Does our brain uses its own internal maps to facilitate “physicist/mathematician” in us to construct the maps about the external territories in turn? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But the question is, to what extent? Is there a way out of the metaphorical Platonic cave erected around us by the nature? While “Map is not the territory” as Alfred Korzybski remarked, join us in this journey to know more, while we inquire on the nature and the reality of the maps which try to map the reality out there. The book also includes a foreword by Sir Roger Penrose and an afterword by Dagfinn Follesdal.

Attributing Knowledge

Author : Jody Azzouni
Publisher : Oxford University Press
ISBN 13 : 0197508820
Total Pages : 352 pages
Book Rating : 4.1/5 (975 download)

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Book Synopsis Attributing Knowledge by : Jody Azzouni

Download or read book Attributing Knowledge written by Jody Azzouni and published by Oxford University Press. This book was released on 2020-09-21 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Attributing Knowledge, Jody Azzouni challenges philosophical conventions about what it means to know something. He argues that the restrictive conditions philosophers place on knowers only hold in special cases; knowledge can be attributed to babies, sophisticated animals (great apes, orcas), unsophisticated animals (bees), and machinery (drones, driverless cars). Azzouni also gives a fresh defense of fallibilism. Relying on lexical semantics and ordinary usage, he shows that there are no knowledge norms for assertion or action. He examines everyday cases of knowledge challenge and attribution to show many recent and popular epistemological positions are wrong. By providing a long-sought intelligible characterization of knowledge attribution, Azzouni explains why the concept has puzzled philosophers so long, and he solves longstanding and recent puzzles that have perplexed epistemologists--including the dogmatism paradox, Gettier puzzles, and the surprise-exam paradox. "This is a terrific book, full of surprises. For instance, Chapter 9 is full of points that are original, insightful, and useful in helping to resolve stale debates. I especially liked the points that we don't ordinarily describe someone as losing knowledge by gaining defeating evidence, that "knows" is vague and tri-scoped, that vagueness needn't be explained by appeal to precise metasemantic machinery, and that Williamson's anti-luminosity argument founders on the fact that knowledge doesn't require confidence. Bravo!" --Ram Neta, University of North Carolina, Chapel Hill Praise for Jody Azzouni's Ontology without Borders: "Azzouni offers a very strong drink, proposing that we do without central elements of what almost anyone would call logic or ontology. His arguments are serious and wide-ranging. If he's right, the reader will have learned something very important. If he's wrong, then the reader who figures out how he went wrong will also have learned something very important. Not every book has this feature." --Michael Gorman, The Catholic University of America

Great Circles

Author : Emily Rolfe Grosholz
Publisher : Springer
ISBN 13 : 3319982311
Total Pages : 274 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Great Circles by : Emily Rolfe Grosholz

Download or read book Great Circles written by Emily Rolfe Grosholz and published by Springer. This book was released on 2018-11-13 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.

The International Science and Evidence Based Education (ISEE) Assessment

Author : UNESCO MGIEP
Publisher : UNESCO MGIEP
ISBN 13 : 9391756042
Total Pages : 1838 pages
Book Rating : 4.3/5 (917 download)

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Book Synopsis The International Science and Evidence Based Education (ISEE) Assessment by : UNESCO MGIEP

Download or read book The International Science and Evidence Based Education (ISEE) Assessment written by UNESCO MGIEP and published by UNESCO MGIEP. This book was released on 2022-03-22 with total page 1838 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Science and Evidence Based Education (ISEE) Assessment is an initiative of the UNESCO Mahatma Gandhi Institute of Education for Peace and Sustainable Development (MGIEP), and is its contribution to the Futures of Education process launched by UNESCO Paris in September 2019. In order to contribute to re-envisioning the future of education with a science and evidence based report, UNESCO MGIEP embarked on the first-ever large-scale assessment of knowledge of education.

Math in the Time of Corona

Author : Alice Wonders
Publisher : Springer Nature
ISBN 13 : 3030771660
Total Pages : 208 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Math in the Time of Corona by : Alice Wonders

Download or read book Math in the Time of Corona written by Alice Wonders and published by Springer Nature. This book was released on 2021-11-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title of this book, Math in the Time of Corona, has been drawn from the highly acclaimed novel by Gabriel García Márquez, Love in the Time of Cholera. The volume editor, Alice Wonders, holds a fictitious name that represents the mathematics publishing group at Springer Nature. Undeterred by disasters, so many mathematical and scientific discoveries have been made during times of duress or confinement. Unlike most any other subject, mathematics may be researched from anywhere. Covid-19, like Cholera, implementation of vaccinations have been uneven throughout the globe since the beginning of 2021. However, there has been a renewed hope for a return to normalcy though the timing will no doubt vary worldwide. Essays in this volume vary in topic and are written by members of the greater mathematics community, hence the use of “Math” in the book title. They recount or describe significant or noteworthy discoveries, musings, award winnings, eureka moments, challenges, solutions, inspirations, etc. that have resulted from, or have occurred during, an unprecedented global pandemic. Several of the authors have been involved in starting new research and devising new methodologies related to society’s response to the outbreak and its ability to self-organize during a dramatic and complex situation. Some contributions describe how mathematical models and the management of big data have proved to be fundamental tools for the interpretation of epidemic activity and development of coping mechanisms.

18 Unconventional Essays on the Nature of Mathematics

Author : Reuben Hersh
Publisher : Springer Science & Business Media
ISBN 13 : 0387298312
Total Pages : 346 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis 18 Unconventional Essays on the Nature of Mathematics by : Reuben Hersh

Download or read book 18 Unconventional Essays on the Nature of Mathematics written by Reuben Hersh and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Technologies in a Multilingual Environment

Author : Daria Bylieva
Publisher : Springer Nature
ISBN 13 : 3031267834
Total Pages : 550 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Technologies in a Multilingual Environment by : Daria Bylieva

Download or read book Technologies in a Multilingual Environment written by Daria Bylieva and published by Springer Nature. This book was released on 2023-02-18 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses the challenge of living in a multilingual world from three perspectives: socio-linguistics and the study of multilingualism in contrast, philosophy of technology with its emphasis on the world as a technosphere—how it is made, how it is experienced, and how it can be managed, and then pedagogy and the question of teaching and learning to competently negotiate multilingual environments. In today‘s multicultural and multilingual world, technologies provide a common ground. The story of the technosphere as a multilingual environment offers new perspective, namely that of learning to cooperate and coordinate.

Geometry in History

Author : S. G. Dani
Publisher : Springer Nature
ISBN 13 : 3030136094
Total Pages : 759 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Geometry in History by : S. G. Dani

Download or read book Geometry in History written by S. G. Dani and published by Springer Nature. This book was released on 2019-10-18 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.