New Trends In The History And Philosophy Of Mathematics

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New Trends in the History and Philosophy of Mathematics

Author : Tinne Hoff Kjeldsen
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis New Trends in the History and Philosophy of Mathematics by : Tinne Hoff Kjeldsen

Download or read book New Trends in the History and Philosophy of Mathematics written by Tinne Hoff Kjeldsen and published by . This book was released on 2004 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998. The purpose of the meeting was to present some of the new ideas on the study of mathematics, its character and the nature of its development. During the last decades work in history and philosophy of mathematics has led to several new original views on mathematics. Both new methods and angles of study have been introduced, and old views of, say, the nature of mathematical theories and proofs have been challenged. For instance, disciplines as etnohistorical studies of mathematics and the sociology of mathematics have resulted in several new insights, and classical historians of mathematics are also experimenting with new perspectives. In a similar way philosophy of mathematics has witnessed rather deep changes. Classical foundational studies have been challenged by new broader perspectives. The aim was to provide a forum within which historians of mathematics, philosophers, and mathematicians could exchange ideas and discuss different new approaches in the history and philosophy of mathematics. The book includes papers by Joan Richards, Henk J. M. Bos, Donald MacKenzie, Arthur Jaffe, Jody Azzouni and Paulus Gerdes. It also includes an extended introduction.

New Waves in Philosophy of Mathematics

Author : O. Bueno
Publisher : Springer
ISBN 13 : 0230245196
Total Pages : 330 pages
Book Rating : 4.2/5 (32 download)

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Book Synopsis New Waves in Philosophy of Mathematics by : O. Bueno

Download or read book New Waves in Philosophy of Mathematics written by O. Bueno and published by Springer. This book was released on 2009-09-29 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.

An Historical Introduction to the Philosophy of Mathematics: A Reader

Author : Russell Marcus
Publisher : Bloomsbury Publishing
ISBN 13 : 1472525345
Total Pages : 849 pages
Book Rating : 4.4/5 (725 download)

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Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus

Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the first comprehensive collection of historical readings in the philosophy of mathematics, this much-needed introduction reveals the rich history of the subject. Focusing on the philosophy of mathematics before the 20th-century, An Historical Introduction to the Philosophy of Mathematics: A Readerbrings together an impressive collection of primary sources from ancient, medieval and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with modern thinkers. While a selection of recent texts offering insights the current state of the discipline, clearly illustrate the development of the subject. Presenting historical background essential to understanding contemporary trends, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates studying the philosophy of mathematics.

History and Philosophy of Modern Mathematics

Author : William Aspray
Publisher : U of Minnesota Press
ISBN 13 : 0816615675
Total Pages : 396 pages
Book Rating : 4.8/5 (166 download)

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Book Synopsis History and Philosophy of Modern Mathematics by : William Aspray

Download or read book History and Philosophy of Modern Mathematics written by William Aspray and published by U of Minnesota Press. This book was released on 1988 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Mathematics: A Concise History and Philosophy

Author : W.S. Anglin
Publisher : Springer Science & Business Media
ISBN 13 : 0387942807
Total Pages : 282 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Mathematics: A Concise History and Philosophy by : W.S. Anglin

Download or read book Mathematics: A Concise History and Philosophy written by W.S. Anglin and published by Springer Science & Business Media. This book was released on 1994 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise introduction explores the key mathematical and philosophical aspects of the history of mathematics. Detailed explanations of mathematical procedures used by famous mathematicians give readers a greater opportunity to learn the history and philosophy through problem solving. 23 illustrations.

An Introduction to the Philosophy of Mathematics

Author : Mark Colyvan
Publisher : Cambridge University Press
ISBN 13 : 0521826020
Total Pages : 199 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to the Philosophy of Mathematics by : Mark Colyvan

Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

An Historical Introduction to the Philosophy of Mathematics: A Reader

Author : Russell Marcus
Publisher : Bloomsbury Publishing
ISBN 13 : 1472529480
Total Pages : 849 pages
Book Rating : 4.4/5 (725 download)

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Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus

Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

The Architecture of Modern Mathematics

Author : J. Ferreiros
Publisher : OUP Oxford
ISBN 13 : 0191513792
Total Pages : 456 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Architecture of Modern Mathematics by : J. Ferreiros

Download or read book The Architecture of Modern Mathematics written by J. Ferreiros and published by OUP Oxford. This book was released on 2006-04-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Philosophy of Mathematics

Author : Gerhard Preyer
Publisher : Walter de Gruyter
ISBN 13 : 3110323680
Total Pages : 184 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Philosophy of Mathematics by : Gerhard Preyer

Download or read book Philosophy of Mathematics written by Gerhard Preyer and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

Essays in the Philosophy and History of Logic and Mathematics

Author : Roman Murawski
Publisher : BRILL
ISBN 13 : 9042030917
Total Pages : 327 pages
Book Rating : 4.0/5 (42 download)

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Book Synopsis Essays in the Philosophy and History of Logic and Mathematics by : Roman Murawski

Download or read book Essays in the Philosophy and History of Logic and Mathematics written by Roman Murawski and published by BRILL. This book was released on 2015-06-29 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

New Perspectives on Mathematical Practices

Author : Bart van Kerkhove
Publisher : World Scientific
ISBN 13 : 9812812229
Total Pages : 248 pages
Book Rating : 4.8/5 (128 download)

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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.

Analysis and Synthesis in Mathematics

Author : Michael Otte
Publisher : Springer Science & Business Media
ISBN 13 : 9780792345701
Total Pages : 476 pages
Book Rating : 4.3/5 (457 download)

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Book Synopsis Analysis and Synthesis in Mathematics by : Michael Otte

Download or read book Analysis and Synthesis in Mathematics written by Michael Otte and published by Springer Science & Business Media. This book was released on 1997 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

Why Is There Philosophy of Mathematics At All?

Author : Ian Hacking
Publisher : Cambridge University Press
ISBN 13 : 1107729823
Total Pages : 307 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Why Is There Philosophy of Mathematics At All? by : Ian Hacking

Download or read book Why Is There Philosophy of Mathematics At All? written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

The Oxford Handbook of the History of Mathematics

Author : Eleanor Robson
Publisher : Oxford University Press on Demand
ISBN 13 : 0199213127
Total Pages : 927 pages
Book Rating : 4.1/5 (992 download)

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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.

Before Voltaire

Author : J.B. Shank
Publisher : University of Chicago Press
ISBN 13 : 022650932X
Total Pages : 457 pages
Book Rating : 4.2/5 (265 download)

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Book Synopsis Before Voltaire by : J.B. Shank

Download or read book Before Voltaire written by J.B. Shank and published by University of Chicago Press. This book was released on 2018-06-08 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have grown accustomed to the idea that scientific theories are embedded in their place and time. But in the case of the development of mathematical physics in eighteenth-century France, the relationship was extremely close. In Before Voltaire, J.B. Shank shows that although the publication of Isaac Newton’s Principia in 1687 exerted strong influence, the development of calculus-based physics is better understood as an outcome that grew from French culture in general. Before Voltaire explores how Newton’s ideas made their way not just through the realm of French science, but into the larger world of society and culture of which Principia was an intertwined part. Shank also details a history of the beginnings of calculus-based mathematical physics that integrates it into the larger intellectual currents in France at the time, including the Battle of the Ancients and the Moderns, the emergence of wider audiences for science, and the role of the newly reorganized Royal Academy of Sciences. The resulting book offers an unprecedented cultural history of one the most important and influential elements of Enlightenment science.

From Logic to Practice

Author : Gabriele Lolli
Publisher : Springer
ISBN 13 : 3319104349
Total Pages : 346 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis From Logic to Practice by : Gabriele Lolli

Download or read book From Logic to Practice written by Gabriele Lolli and published by Springer. This book was released on 2014-11-28 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.

The History of Continua

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0192537490
Total Pages : 320 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis The History of Continua by : Stewart Shapiro

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press. This book was released on 2020-12-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.