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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 1930's 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.

Mathematical logic --- Arithmetic --- Set theory --- Logic, Symbolic and mathematical --- Foundations --- History --- Foundations. --- 51 <091> --- Mathematics--Historische voorstelling in de strikte zin --- 51 <091> Mathematics--Historische voorstelling in de strikte zin --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Mathematics --- Algebra, Abstract --- Metamathematics --- Syllogism --- Calculators --- Numbers, Real --- Foundations of arithmetic --- Philosophy --- Arithmetic - Foundations - History - 19th century. --- Arithmetic - Foundations - History - 20th century. --- Set theory - History - 19th century. --- Set theory - History - 20th century. --- Logic, Symbolic and mathematical - History - 19th century. --- Logic, Symbolic and mathematical - History - 20th century.

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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.

Mathematics

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This book details the history of one of astronomy's many spurious objects, the satellite of Venus. First spotted in 1645, the non-existing moon was observed more than a dozen times until the late eighteenth century. Although few astronomers believed in the existence of the moon after about 1770, it continued to attract attention for at least another century. However, it has largely disappeared from the history of astronomy, and the rich historical sources have never been exploited. By telling the story of the enigmatic satellite in its proper historical context it is demonstrated that it was much more than a mere curiosity in the annals of astronomy - Frederick II of Prussia was familiar with it, and so was Bonnet, Kant and Voltaire. The satellite of Venus belongs to the same category as other fictitious celestial bodies (such as the planet Vulcan), yet it had its own life and fascinating historical trajectory. By following this trajectory, the history of planetary astronomy is addressed in a novel way.

Human sciences (algemeen) --- Cosmology --- Astrophysics --- History of physics --- astrofysica --- geschiedenis --- cultuurwetenschap --- fysica --- kosmologie