The Theory of Gödel

1. Auflage 2022
ISBN: 978-3-031-13416-6
Verlag: Springer International Publishing

Buch, Englisch, Band 470, 159 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 430 g

Reihe: Synthese Library

This book presents Gödel’s incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics. Results are stated in the form most relevant for use in the philosophy of mathematics. An appendix considers their implications for Hilbert’s Program for the foundations of mathematics. The text is self-contained, all notions being explained in full detail, but of course previous exposure to the very first rudiments of mathematical logic will help.

Zielgruppe

Graduate

Autoren/Hrsg.

Cellucci, Carlo

Fachgebiete

• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Inhaltsverzeichnis

First-Order Logic.- Completeness.- First-Order Theories.- Primitive Recursive Arithmetic.- Encoding.- Incompleteness.- Other Limitative Results.- Second-Order Logic.- Second-Order Arithmetic.- Appendix.

Über Autor(innen)

Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of eight books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall’Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017); The Making of Mathematics: Heuristic Philosophy of Mathematics (Springer, 2022).