Space, Number, and Geometry from Helmholtz to Cassirer, Biagioli Francesca

Автор: Cassirer Ernst
Название: The Individual and the Cosmos in Renaissance Philosophy
ISBN: 1621385191 ISBN-13(EAN): 9781621385196
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Автор: Cassirer, Ernst
Название: Philosophy of the enlightenment
ISBN: 069114334X ISBN-13(EAN): 9780691143347
Издательство: Wiley
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Цена: 36960.00 T
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Описание: Presents an analysis of one of history`s greatest intellectual epochs: the Enlightenment. Arguing that there was a common foundation beneath the diverse strands of thought of this period, this book shows how Enlightenment philosophers drew upon the ideas of the preceding centuries even while radically transforming them to fit the modern world.

Автор: Cassirer Ernst
Название: The Individual and the Cosmos in Renaissance Philosophy
ISBN: 1621385183 ISBN-13(EAN): 9781621385189
Издательство: Неизвестно
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Автор: Biagioli
Название: Space, Number, and Geometry from Helmholtz to Cassirer
ISBN: 3319317776 ISBN-13(EAN): 9783319317779
Издательство: Springer
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Цена: 83850.00 T
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Описание: This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincar?, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.

Автор: Michio Kuga
Название: Kuga Varieties: Fiber Varieties Over a Symmetric Space Whose Fibers are Abelian Varieties
ISBN: 7040503042 ISBN-13(EAN): 9787040503043
Издательство: Mare Nostrum (Eurospan)
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Цена: 60990.00 T
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Описание: Kuga varieties are fiber varieties over symmetric spaces whose fibers are abelian varieties and have played an important role in the theory of Shimura varieties and number theory. This book is the first systematic exposition of these varieties and was written by their creators. It contains four chapters. Chapter 1 gives a detailed generalization to vector valued harmonic forms. These results are applied to construct Kuga varieties in Chapter 2 and to understand their cohomology groups. Chapter 3 studies Hecke operators, which are the most basic operators in modular forms. All the previous results are applied in Chapter 4 to prove the modularity property of certain Kuga varieties. Note that the modularity property of elliptic curves is the key ingredient of Wiles' proof of Fermat's Last Theorem. This book also contains one of Weil's letters and a paper by Satake which are relevant to the topic of the book.

Название: Interpreting cassirer
ISBN: 1108496482 ISBN-13(EAN): 9781108496483
Издательство: Cambridge Academ
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Описание: This is the first comprehensive volume in English on Cassirer`s philosophy for over seventy years. Containing eleven essays by leading Cassirer scholars, it addresses all the key aspects of Cassirer`s multi-faceted thought and situates them in the wider context of his philosophy of culture.

Автор: Skidelsky, Edward
Название: Ernst cassirer
ISBN: 0691131341 ISBN-13(EAN): 9780691131344
Издательство: Wiley
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Цена: 24150.00 T
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Описание: A biography of the German-Jewish philosopher Ernst Cassirer (1874-1945), a leading figure on the Weimar intellectual scene and one of the last and finest representatives of the liberal-idealist tradition. It traces the development of Cassirer`s thought in its historical and intellectual setting.