Kurt Goedel - The Princeton Lectures on Intuitionism (Paperback, 1st ed. 2021)

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 Goedel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Goedel's incompleteness theorem. Goedel 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 Goedel. The second is a problem still wide open. Goedel 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, Goedel'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 It will form a basis for further investigations into Goedel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers.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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Sources and Studies in the History of Mathematics and Physical Sciences
Release date:	December 2022
First published:	2021
Editors:	Maria Hameen-Anttila • Jan von Plato
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	133
Edition:	1st ed. 2021
ISBN-13:	978-3-03-087298-4
Categories:	Books > Science & Mathematics > Mathematics > History of mathematics Books > Humanities > Philosophy > Western philosophy > General Books > Humanities > Philosophy > Topics in philosophy > Logic Books > Philosophy > Topics in philosophy > Logic Books > Philosophy > Western philosophy > General
LSN:	3-03-087298-X
Barcode:	9783030872984

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