Bücher von Ivor Grattan-Guinness

He charts the growth of mathematics through its refinement by ancient Greeks and then medieval Arabs, to its systematic development by Europeans from the Middle Ages to the early twentieth century. This book describes the evolution of arithmetic and geometry, trigonometry and algebra; the interplay between mathematics, physics, and mathematical astronomy; and "new" branches such as probability and statistics. Authoritative and comprehensive, The Rainbow of Mathematics is a unique account of the development of the science that is at the heart of so many other sciences. Originally published under the title The Norton History of the Mathematical Sciences.

This book contains around of a score of essays that examine oruse Popperís fallibilist philosophy of science from various pointsof view. The opening sextet includes a new solution of theproblem of induction, the status of corroboration, and the placeof truth-values and logic(s). Then follow a trio of studies ofrelationships with some other philosophies, especially BertrandRussellís. Next come five essays on the history andhistoriography of science and mathematics, and of mathematicseducation. They are followed by a quintet of speculations relatingto aspects of psychology, especially psychical research,coincidences and the formation of languages in humans. Finallycome two new items: one on the philosophy of mathematics,the other a public acknowledgement of the influence of Popperin August 2009 when the International Commission on theHistory of Mathematics awarded Grattan-Guinness theKenneth O. May Medal and Prize in the History of Mathematics.I. Grattan-Guinness is Emeritus Professor of the History ofMathematics and Logic at Middlesex University, England,and also a Visiting Research Associate in the Centre forPhilosophy of Natural and Social Science at the LondonSchool of Economics.

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.