Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Moore, Adrian William (1956-....)
Titre(s) : Gödel's theorem [Texte imprimé] : a very short introduction / A. W. Moore
Publication : Oxford : Oxford university press, copyright 2022
Description matérielle : 1 vol. (XX-128 p.) : ill.. ; 18 cm
Collection : Very short introduction ; 718
Lien à la collection : Very short introductions
Note(s) : Bibliogr. p. 123. Index
This book provides an introduction to Gödel's theorem. Gödel's theorem states that
no axiomatization can determine the whole truth and nothing but the truth concerning
arithmetic. The content of the theorem is elucidated and distinguished from that of
other claims with which it is often confused. The significance of the theorem is also
discussed. Particular emphasis is laid on the appeal of axiomatization and on attempts
that were made, in the half century preceding Gödel's proof, to provide the very thing
that the theorem precludes. This includes discussion of Hilbert's programme, part
of which was to provide a consistent foundation for mathematics and to demonstrate
its consistency by mathematical means. Two proofs of Gödel's theorem are given. The
second and more elaborate proof is also shown to yield Gödel's second theorem: that
no consistent axiomatization of arithmetic can be used to prove a statement corresponding
to a statement of its own consistency. The final two chapters of the book explore
the implications of Gödel's results: for Hilbert's programme; for the question whether
the human mind, in its capacity to think beyond any given axiomatization of arithmetic,
has powers beyond those of any possible computer; and for the nature of mathematics
Sujet(s) : Gödel, Théorème de
Genre ou forme : Manuels d'enseignement supérieur
Indice(s) Dewey :
511.3 (23e éd.) = Logique mathématique
Identifiants, prix et caractéristiques : ISBN 978-0-19-284785-0 (br.)
Identifiant de la notice : ark:/12148/cb47128600m
Notice n° :
FRBNF47128600
(notice reprise d'un réservoir extérieur)
Table des matières : Preface ; List of illustrations ; 1 What is Gödel's theorem? ; 2 Axiomatization:
its appeal and demands ; 3 Historical background ; 4 The key concepts involved in
Gödel's theorem ; 5 The diagonal proof of Gödel's theorem ; 6 A second proof of
Gödel's theorem, and a proof of Gödel's second theorem ; 7 Hilbert's programme, the
human mind, and computers ; 8 Making sense in and of mathematics ; Appendix: A sketch
of the proof of Gödel's theorem(s) ; References ; Further reading ; Index.
