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Cover: 9783030872953 | Kurt Gödel | The Princeton Lectures on Intuitionism | Plato (u. a.)
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Kurt Gödel
The Princeton Lectures on Intuitionism
Buch von Jan Von Plato (u. a.)
Sprache: Englisch

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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 It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers.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.
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.
Zusammenfassung

Offers indispensable reading for mathematicians and computer scientists

Gives insights into thework that is needed to solve scientific questions

Forms a basis for further investigations into Gödel's vast collection of unpublished notes

Inhaltsverzeichnis
Gödel's Functional Interpretation in Context.- Part I: Axiomatic Intuitionist Logic.- Part II: The Functional Interpretation.- References.- Name Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Buch
Reihe: Sources and Studies in the History of Mathematics and Physical Sciences
Inhalt: ix
133 S.
ISBN-13: 9783030872953
ISBN-10: 3030872955
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Redaktion: Plato, Jan Von
Hämeen-Anttila, Maria
Herausgeber: Maria Hämeen-Anttila/Jan von Plato
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Sources and Studies in the History of Mathematics and Physical Sciences
Maße: 241 x 160 x 14 mm
Von/Mit: Jan Von Plato (u. a.)
Erscheinungsdatum: 16.12.2021
Gewicht: 0,389 kg
Artikel-ID: 120454041
Zusammenfassung

Offers indispensable reading for mathematicians and computer scientists

Gives insights into thework that is needed to solve scientific questions

Forms a basis for further investigations into Gödel's vast collection of unpublished notes

Inhaltsverzeichnis
Gödel's Functional Interpretation in Context.- Part I: Axiomatic Intuitionist Logic.- Part II: The Functional Interpretation.- References.- Name Index.
Details
Erscheinungsjahr: 2021
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Buch
Reihe: Sources and Studies in the History of Mathematics and Physical Sciences
Inhalt: ix
133 S.
ISBN-13: 9783030872953
ISBN-10: 3030872955
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Redaktion: Plato, Jan Von
Hämeen-Anttila, Maria
Herausgeber: Maria Hämeen-Anttila/Jan von Plato
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Sources and Studies in the History of Mathematics and Physical Sciences
Maße: 241 x 160 x 14 mm
Von/Mit: Jan Von Plato (u. a.)
Erscheinungsdatum: 16.12.2021
Gewicht: 0,389 kg
Artikel-ID: 120454041
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