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Beschreibung
Paris of the year 1900 left two landmarks: the Tour 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's incompleteness theorem . Gödel then went on to… attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about 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 seeming faux pas going 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 It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers.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. 117,69 €
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Technische Daten
Erscheinungsdatum
17.12.2022
Sprache
Englisch
EAN
9783030872984
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Sources and Studies in the History of Mathematics and Physical Sciences
Sonderedition
Nein
Seitenanzahl
133
Einbandart
Broschiert
Buch Untertitel
The Princeton Lectures on Intuitionism
Schlagwörter
axiomatic intuitionistic logic, properties of partial recursive functions, Heyting arithmetic, Arbeitshefte, constructive reasoning, Dialectica paper
Thema-Inhalt
PBX - Geschichte der Mathematik
QDTL - Philosophie: Logik
QDH - Philosophische Traditionen und Denkschulen
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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