Overview
- Based on the recent discovery of Gödel's work on an ``own book on foundations,'' completely unknown so far
- Reconstruction of Gödel's unpublished work by one of the leading Gödel experts in the scientific community
- A milestone in Gödel research and in the related foundational debate
Part of the book series: Vienna Circle Institute Library (VCIL, volume 6)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This volume contains English translations of Gödel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics. It also comprises most of his reading notes.
This book is a testimony to Gödel's understanding of the situation of foundational research in mathematics after his great discovery, the incompleteness theorem of 1931. It is also a source for his views on his logical predecessors, from Leibniz, Frege, and Russell to his own times. Gödel's "own book on foundations," as he called it, is essential reading for logicians and philosophers interested in foundations. Furthermore, it opens a new chapter to the life and achievement of one of the icons of 20th century science and philosophy.
Reviews
in the book chapters and in the excerpts. This is a valuable edition providing a comprehensive overview on the foundational debates of the early 20th century … .” (Volker Peckhaus, Mathematical Reviews, January, 2024)
Authors and Affiliations
About the author
Viennese logician Kurt Gödel (1906-1978) became world-famous overnight with his incompleteness theorems of 1931. The first one states the impossibility to represent all of mathematics in one closed system, the second that there is no ultimate guarantee that such systems could not lead to contradictions. Soon after the publication of Gödel's sensational article, he was invited to write, together with Arend Heyting, a concise book about the status of foundational research in mathematics. With Gödel prolonging the delivery of his part, Heyting lost patience and published his part in 1934. It has been generally believed that Gödel had made little headway with his chapters. A search in the Gödel papers showed the contrary to be the case: he had meticulously listed well over a hundred works to study and had practically finished two chapters in his Gabelsberger shorthand, and outlined a third.
Jan von Plato is professor of philosophy at the University of Helsinki. His books include Saved From the Cellar (Springer, 2017), Can Mathematics Be Proved Consistent? (Springer, 2020) and Kurt Gödel: The Princeton Lectures on Intuitionism (Edited by Maria Hämeen-Anttila and Jan von Plato, Springer 2021).
Bibliographic Information
Book Title: Chapters from Gödel’s Unfinished Book on Foundational Research in Mathematics
Authors: Jan von Plato
Series Title: Vienna Circle Institute Library
DOI: https://doi.org/10.1007/978-3-030-97134-2
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-97133-5Published: 07 May 2022
Softcover ISBN: 978-3-030-97136-6Published: 08 May 2023
eBook ISBN: 978-3-030-97134-2Published: 06 May 2022
Series ISSN: 1571-3083
Edition Number: 1
Number of Pages: IX, 214
Number of Illustrations: 1 b/w illustrations
Topics: Philosophy of Mathematics, Mathematical Logic and Foundations, History of Philosophy, History, general