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Author: Dennis E. Hesseling
Publisher: Springer Science & Business Media
ISBN:
Category : Mathematics
Languages : en
Pages : 480
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Book Description
"The book includes the precursors to and the development of intuitionism, as well as the foundational debate itself. After a general overview of the debate, the analysis centers on two main issues: the question of mathematical existence and the status of logic. Finally, the cultural context of the debate is taken into account."--Jacket.
Author: Dennis E. Hesseling
Publisher: Springer Science & Business Media
ISBN:
Category : Mathematics
Languages : en
Pages : 480
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Book Description
"The book includes the precursors to and the development of intuitionism, as well as the foundational debate itself. After a general overview of the debate, the analysis centers on two main issues: the question of mathematical existence and the status of logic. Finally, the cultural context of the debate is taken into account."--Jacket.
Author: Jeremy Gray
Publisher: Princeton University Press
ISBN: 1400829046
Category : Mathematics
Languages : en
Pages : 528
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Book Description
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Author: Dennis E. Hesseling
Publisher: Birkhäuser
ISBN: 303487989X
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.
Author: Dennis Edwin Hesseling
Publisher:
ISBN: 9789039317204
Category : Mathematics
Languages : en
Pages : 407
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Book Description
Author: William Ewald
Publisher: Springer-Verlag
ISBN: 3540694447
Category : Mathematics
Languages : de
Pages : 1062
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Book Description
The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.
Author: Dennis E. Hesseling
Publisher: Birkhauser
ISBN: 9780817665364
Category : Fiction
Languages : en
Pages : 447
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Book Description
"The book includes the precursors to and the development of intuitionism, as well as the foundational debate itself. After a general overview of the debate, the analysis centers on two main issues: the question of mathematical existence and the status of logic. Finally, the cultural context of the debate is taken into account."--Jacket.
Author: Michael G. Coney
Publisher: Hachette UK
ISBN: 0575129441
Category : Fiction
Languages : en
Pages : 320
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Book Description
There was a time when the Earth had three moons, and when the seductive sorceress Avalona could alter futures and bend "happentracks" with her spells. Indeed, in this vast chaotic universe called the Greataway, with its many imaginable futures, anything is possible. Especially when Nyneve, Avalona's bewitching human disciple, conjures up the complete legend of Camelot and when the roguish gnome Fang, slayer of the dread daggertooth, stumbles into the human happentrack, causing human and gnome worlds to overlap. For then the moons begin to disappear one by one, and Fang, Nyneve, and all their comrades find themselves caught in a happentrack from which there is no escape, a happentrack in which the legend of Arthur might prove their only salvation...
Author: Albert Einstein
Publisher: Princeton University Press
ISBN: 0691216819
Category : Biography & Autobiography
Languages : de
Pages : 1126
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Book Description
A definitive scholarly edition of the correspondence and papers of Albert Einstein During the period covered by this volume, Einstein aims to discover whether one can derive the electron’s equations of motion directly from the field equations of general relativity, and he embarks on a new approach to unified field theory founded on teleparallel geometry. On these topics, he engages in exchanges with J. Grommer, C. Lanczos, and particularly with C. H. Müntz, and corresponds with mathematicians like R. Weitzenböck and É. Cartan. Einstein attends what will be considered a historic 1927 Solvay Conference where the new quantum mechanics is discussed, but in fact he makes very few remarks. In an important prelude to his eventual emigration to the United States, he is invited in September 1927 to accept a research professorship at Princeton University. Despite the sudden onset of a severe heart ailment in 1928, followed by an almost year-long period of convalescence, Einstein maintains a sustained engagement with scientific work, correspondence, and social and political issues. He publishes many articles and interviews designed for a popular audience and continues various technical preoccupations, including publishing a patent for a novel “people’s” refrigerator and being intimately involved in the design of his famous sailboat. Einstein advocates for domestic legislative reform, gay and minority rights, European rapprochement, and conscientious objection to military service. He resigns from his positions at the Hebrew University. He also tries to avoid the fanfare marking his fiftieth birthday in March 1929 yet is “buried under a paper avalanche” from the tributes. His hiring of Helen Dukas as his assistant, who accompanies Einstein to the end of his life, is of great significance for the ultimate preservation of his written legacy.
Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 1447146166
Category : Mathematics
Languages : en
Pages : 877
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Book Description
Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.
Author: Jean Louis Ernest Meissonier
Publisher:
ISBN:
Category :
Languages : en
Pages : 274
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Book Description
