**Author**: I. Grattan-Guinness

**Publisher:** Princeton University Press

**ISBN:** 069105858X

**Category : **Mathematics

**Languages : **en

**Pages : **707

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**Book Description**
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

**Author**: I. Grattan-Guinness

**Publisher:** Princeton University Press

**ISBN:** 069105858X

**Category : **Mathematics

**Languages : **en

**Pages : **707

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**Book Description**
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

**Author**: I. Grattan-Guinness

**Publisher:** Princeton University Press

**ISBN:** 9781400824045

**Category : **Mathematics

**Languages : **en

**Pages : **624

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**Book Description**
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

**Author**: I. Grattan-Guinness

**Publisher:**
**ISBN:** 9780691058573

**Category : **Mathematics

**Languages : **en

**Pages : **690

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**Book Description**
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.

**Author**: Rudolf Seising

**Publisher:** Franz Steiner Verlag

**ISBN:** 9783515085250

**Category : **History

**Languages : **de

**Pages : **952

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**Book Description**
Dieser Band mit 42 aktuellen Arbeiten von 45 Wissenschafts- und Technikwissenschaftlern erscheint aus Anlass des 65. Geburtstages des Muenchner Wissenschaftshistorikers Ivo Schneider. In den einzelnen Beitr�gen der Autoren, von denen die meisten der Wissenschafts- und Technikgeschichte, einige aber auch der Wissenschaftsphilosophie bzw. anderen Wissenschaftsdisziplinen entstammen, werden Arbeiten zur gesamten Wissenschafts- und Technikgeschichte von der Antike bis zum 20. Jahrhundert pr�sentiert. Aus den verschiedenen Kontexten heraus verweisen die Beitr�ge auf die Bedeutung von Form(en) in Mathematik und Philosophie, sie zeigen, dass keine moderne Naturwissenschaft ohne Zahl und Ordnung auskommt, wie auch die (moderne) Mathematik oft mehr mit Ordnung denn mit Zahl zu tun hat. Dem Leser wird in diesem Band das gro�e Spektrum reflektionswissenschaftlicher Forschung ausgebreitet, das in der gegenw�rtigen Wissenschaftslandschaft leider immer weniger beruecksichtigt wird.

**Author**: Ivor Grattan-Guinness

**Publisher:** Elsevier

**ISBN:** 9780080457444

**Category : **Mathematics

**Languages : **en

**Pages : **1040

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**Book Description**
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field

**Author**: Karen Hunger Parshall

**Publisher:** Princeton University Press

**ISBN:** 0691235244

**Category : **History

**Languages : **en

**Pages : **640

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**Book Description**
"The 1920s witnessed the birth of a serious mathematical research community in America. Prior to this, mathematical research was dominated by scholars based in Europe-but World War I had made the importance of scientific and technological development clear to the American research community, resulting in the establishment of new scientific initiatives and infrastructure. Physics and chemistry were the beneficiaries of this renewed scientific focus, but the mathematical community also benefitted, and over time, began to flourish. Over the course of the next two decades, despite significant obstacles, this constellation of mathematical researchers, programs, and government infrastructure would become one of the strongest in the world. In this meticulously-researched book, Karen Parshall documents the uncertain, but ultimately successful, rise of American mathematics during this time. Drawing on research carried out in archives around the country and around the world, as well as on the secondary literature, she reveals how geopolitical circumstances shifted the course of international mathematics. She provides surveys of the mathematical research landscape in the 1920s, 30s, and 40s, introduces the key players and institutions in mathematics at that time, and documents the effect of the Great Depression and the second world war on the international mathematical community. The result is a comprehensive account of the shift of mathematics' "center of gravity" to the American stage"--

**Author**: Roger L. Cooke

**Publisher:** John Wiley & Sons

**ISBN:** 1118030249

**Category : **Mathematics

**Languages : **en

**Pages : **632

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**Book Description**
This new edition brings the fascinating and intriguing historyof mathematics to life The Second Edition of this internationally acclaimed text hasbeen thoroughly revised, updated, and reorganized to give readers afresh perspective on the evolution of mathematics. Written by oneof the world's leading experts on the history of mathematics, thebook details the key historical developments in the field,providing an understanding and appreciation of how mathematicsinfluences today's science, art, music, literature, andsociety. In the first edition, each chapter was devoted to a singleculture. This Second Edition is organized by subject matter: ageneral survey of mathematics in many cultures, arithmetic,geometry, algebra, analysis, and mathematical inference. This neworganization enables students to focus on one complete topic and,at the same time, compare how different cultures approached eachtopic. Many new photographs and diagrams have been added to thisedition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World,including the origin and prehistory of mathematics, culturalsurveys, and women mathematicians Numbers, including counting, calculation, ancient numbertheory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics oncivilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry,post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations andmethods, and modern algebra Analysis, including the calculus, real, and complexanalysis Mathematical Inference, including probability and statistics,and logic and set theory As readers progress through the text, they learn about theevolution of each topic, how different cultures devised their ownsolutions, and how these solutions enabled the cultures to developand progress. In addition, readers will meet some of the greatestmathematicians of the ages, who helped lay the groundwork fortoday's science and technology. The book's lively approach makes it appropriate for anyoneinterested in learning how the field of mathematics came to be whatit is today. It can also serve as a textbook for undergraduate orgraduate-level courses. An Instructor's Manual presenting detailedsolutions to all the problems in the book is available upon requestfrom the Wiley editorial department.

**Author**: David E. Zitarelli

**Publisher:** American Mathematical Soc.

**ISBN:** 1470448297

**Category : **Education

**Languages : **en

**Pages : **474

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**Book Description**
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli is emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he is one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this is his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.

**Author**:

**Publisher:** Elsevier

**ISBN:** 9780080930589

**Category : **Philosophy

**Languages : **en

**Pages : **733

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**Book Description**
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

**Author**: Bart van Kerkhove

**Publisher:** World Scientific

**ISBN:** 9812812229

**Category : **Mathematics

**Languages : **en

**Pages : **248

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**Book Description**
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.