9783030872953 - kurt gödel: the princeton lectures on intuitionism (sources and studies in the history of mathematics and physical sciences) (3 Ergebnisse)
Sprache: Englisch
Verlag: Springer, 2021
Serie: Buch 58 von 59 - Sources and Studies in the History of Mathematics and Physical Sciences
- Hardcover
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Sprache: Englisch
Verlag: Springer, 2021
Serie: Buch 58 von 59 - Sources and Studies in the History of Mathematics and Physical Sciences
- Hardcover
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Sprache: Englisch
Verlag: Springer, 2021
Serie: Buch 58 von 59 - Sources and Studies in the History of Mathematics and Physical Sciences
- Hardcover
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Paris of the year 1900 left two landmarks: theTour Eiffel,and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete… axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel'sincompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor'scontinuum problemabout the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seemingfaux pasgoing to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers.This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
