I. Grattan-Guinness's Books

The Rainbow of Mathematics

A History of the Mathematical Sciences

By: Ivor Grattan-Guinness,I. Grattan-Guinness

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The Rainbow of Mathematics

A History of the Mathematical Sciences

By: Ivor Grattan-Guinness,I. Grattan-Guinness

For Ivor Grattan-Guinness . . . the story of how numbers were invented and harnessed is a passionate, physical saga."--"The New Yorker." The author charts the growth of mathematics through the centuries and describes the evolution of arithmetic and geometry, trigonometry, and other disciplines.

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Page Count

836

Publisher

W. W. Norton & Company

Published Date

ISBN 10

0393320308

ISBN 13

9780393320305

The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel

By: I. Grattan-Guinness

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The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel

By: I. Grattan-Guinness

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.

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Page Count

690

Published Date

ISBN 10

0691058571

ISBN 13

9780691058573

The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

By: Ivor Grattan-Guinness

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The Search for Mathematical Roots, 1870-1940

Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

By: Ivor Grattan-Guinness

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.

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Page Count

705

Publisher

Princeton University Press

Published Date

ISBN 10

1400824044

ISBN 13

9781400824045

Corroborations and Criticisms

Forays with the Philosophy of Karl Popper

By: Ivor Grattan-Guinness

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Corroborations and Criticisms

Forays with the Philosophy of Karl Popper

By: Ivor Grattan-Guinness

This book contains around of a score of essays that examine or use Popperis fallibilist philosophy of science from various points of view. The opening sextet includes a new solution of the problem of induction, the status of corroboration, and the place of truth-values and logic(s). Then follow a trio of studies of relationships with some other philosophies, especially Bertrand Russellis. Next come five essays on the history and historiography of science and mathematics, and of mathematics education. They are followed by a quintet of speculations relating to aspects of psychology, especially psychical research, coincidences and the formation of languages in humans. Finally come two new items: one on the philosophy of mathematics, the other a public acknowledgement of the influence of Popper in August 2009 when the International Commission on the History of Mathematics awarded Grattan-Guinness the Kenneth O. May Medal and Prize in the History of Mathematics. I. Grattan-Guinness is Emeritus Professor of the History of Mathematics and Logic at Middlesex University, England, and also a Visiting Research Associate in the Centre for Philosophy of Natural and Social Science at the London School of Economics.

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Page Count

342

Published Date

ISBN 10

184890004X

ISBN 13

9781848900042

Book's by I. Grattan-Guinness

The Rainbow of Mathematics

The Rainbow of Mathematics

The Search for Mathematical Roots, 1870-1940

The Search for Mathematical Roots, 1870-1940

The Search for Mathematical Roots, 1870-1940

The Search for Mathematical Roots, 1870-1940

Corroborations and Criticisms

Corroborations and Criticisms

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