9780691058580

The Search for Mathematical Roots, 1870-1940

Grattan-Guinness, I.

ISBN 10: 069105858X / 0-691-05858-X
ISBN 13: 9780691058580
Publisher: Princeton University Press
Publication Date: 2000
Binding: Softcover
Editorial Reviews:
Synopsis:

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.


Review:

"I know of no comparably comprehensive treatment of the history of this important period in modern logic. There is a large body of historical literature that is in need of just the kind of synthesis and masterly overview that this work provides. Though most people recognize mathematics as a principal motivating force behind the development of modern logic, the influences on and from mathematics have been largely ignored or minimized. The Search for Mathematical Roots acts as a guide through that challenging mathematical thicket."--Albert C. Lewis, chief editor of The History of Mathematics from Antiquity to the Present

"Ivor Grattan-Guinness provides a marvelous, comprehensive overview of the history of efforts to come to an understanding of mathematical logic and its relation to mathematics in the period 1870-1940. Given its rich detail and inclusion of under-appreciated figures who deserve to be better known, this is an especially important and useful book."--Joseph Dauben, author of George Cantor: His Mathematics and Philosophy of the Infinite

From the Back Cover

Review:

"I know of no comparably comprehensive treatment of the history of this important period in modern logic. There is a large body of historical literature that is in need of just the kind of synthesis and masterly overview that this work provides. Though most people recognize mathematics as a principal motivating force behind the development of modern logic, the influences on and from mathematics have been largely ignored or minimized. The Search for Mathematical Roots acts as a guide through that challenging mathematical thicket."--Albert C. Lewis, chief editor of The History of Mathematics from Antiquity to the Present

"Ivor Grattan-Guinness provides a marvelous, comprehensive overview of the history of efforts to come to an understanding of mathematical logic and its relation to mathematics in the period 1870-1940. Given its rich detail and inclusion of under-appreciated figures who deserve to be better known, this is an especially important and useful book."--Joseph Dauben, author of George Cantor: His Mathematics and Philosophy of the Infinite

From the Inside Flap

 

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The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Godel (Paperback) (ISBN: 9780691058580)
Grattan-Guinness, I.
ISBN 10: 069105858X
ISBN 13: 9780691058580
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Book Description: Princeton University Press, United States, 2000. Paperback. Book Condition: New. 234 x 156 mm. Brand New Book ***** Print on Demand *****.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, Schrder, 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 Gdel. 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 GdeI. 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. Bookseller Inventory # AAV9780691058580

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2.
The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Godel (Paperback) (ISBN: 9780691058580)
Grattan-Guinness, I.
ISBN 10: 069105858X
ISBN 13: 9780691058580
Bookseller: The Book Depository US (Gloucester, ., United Kingdom)
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Book Description: Princeton University Press, United States, 2000. Paperback. Book Condition: New. 229 x 152 mm. Brand New Book ***** Print on Demand *****. 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, Schroder, 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 Godel. 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 GodeI. 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. Bookseller Inventory # AAV9780691058580

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Book Description: Princeton University Press, New Jersey, 2000. Book Condition: New. Language: english. Presents the history of a critical period in mathematics that includes accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. This work provides surveys of many related topics and figures of the late nineteenth century. Bookseller Inventory # 2780588

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