Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Gödel, Kurt (1906-1978)
Titre(s) : Kurt Gödel [Texte imprimé] : the Princeton lectures on intuitionism / Maria Hämeen-Anttila, Jan von Plato, editors
Publication : Cham : Springer, copyright 2021
Description matérielle : 1 vol. (IX-133 p.) ; 24 cm
Collection : Sources and studies in the history of mathematics and physical sciences, ISSN 2196-8810
Lien à la collection : Sources and studies in the history of mathematics and physical sciences
Note(s) : Bibliogr. p. 128-132. Index
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of unpublished notes on how to extend the results of his lectures to the theory of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
Autre(s) auteur(s) : Hämeen-Anttila, Maria. Éditeur scientifique
Plato, Jan von (1951-....). Éditeur scientifique
Sujet(s) : Mathématiques intuitionnistes
Indice(s) Dewey :
511.3 (23e éd.) = Logique mathématique
Identifiants, prix et caractéristiques : ISBN 978-3-030-87295-3 (rel.). - ISBN 3030872955 (rel.)
EAN 9783030872953
Identifiant de la notice : ark:/12148/cb47084841v
Notice n° :
FRBNF47084841
(notice reprise d'un réservoir extérieur)
