Ivor Grattan-Guinness - Böcker

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.

* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century* 176 articles contributed by authors of 18 nationalities* Chronological table of main events in the development of mathematics* Fully integrated index of people, events and topics* Annotated bibliographies of both classic and contemporary sources* Unique coverage of Ancient and non-Western traditions of mathematics

* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century* 176 articles contributed by authors of 18 nationalities* Chronological table of main events in the development of mathematics* Fully integrated index of people, events and topics* Annotated bibliographies of both classic and contemporary sources* Unique coverage of Ancient and non-Western traditions of mathematics

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

From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Moller-Pedersen.

This seminal collection gathers together many general writings of one of the world's leading historians of mathematics. Organized thematically, these essays ponder the intellectual underpinnings of the field, examine the major topics in the history of mathematics, and recount the bizarre history of pseudomath. Ivor Grattan-Guinness explores how people understand mathematics-the routes of learning they take as they make important discoveries and study mathematical concepts and theories. The essays in the first part of the book discuss the history of mathematics as a field and its central philosophical issues. Those in the next part address the history of mathematics education and its importance to current modes of teaching. In the last section Grattan-Guinness investigates various understudied aspects of math, including numerology, Masonic symbols in classical music, and the links between mathematics and Christianity. This collection includes several essays that are difficult to find anywhere else. All historians of mathematics and students of the field will want a copy of this remarkable resource on their bookshelves.

This seminal collection gathers together many general writings of one of the world's leading historians of mathematics. Organized thematically, these essays ponder the intellectual underpinnings of the field, examine the major topics in the history of mathematics, and recount the bizarre history of pseudomath. Ivor Grattan-Guinness explores how people understand mathematics-the routes of learning they take as they make important discoveries and study mathematical concepts and theories. The essays in the first part of the book discuss the history of mathematics as a field and its central philosophical issues. Those in the next part address the history of mathematics education and its importance to current modes of teaching. In the last section Grattan-Guinness investigates various understudied aspects of math, including numerology, Masonic symbols in classical music, and the links between mathematics and Christianity. This collection includes several essays that are difficult to find anywhere else. All historians of mathematics and students of the field will want a copy of this remarkable resource on their bookshelves.

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic", which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written.