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Kurt Gödel

Kurt Gödel

The Princeton Lectures on Intuitionism

Maria Hämeen-Anttila, Jan Von Plato

Springer
Publication date : 2021-12-15

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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 It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers.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.

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About the book

Author

Maria Hämeen-Anttila , Jan von Plato

Imprint

Springer

Collection

n.c

Publication date

2021-12-15

Pages

133 pages

Print ISBN

9783030872953

Language

English

Ebook informations

EAN PDF

9783030872960

Price

£99.50

Copy count 1

Print count 13

File size 1096 Ko

Informations accessibility

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About author(s)

Maria Hämeen-Anttila

Jan von Plato

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