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Kurt Gödel = The Princeton Lectures ...
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Kurt Gödel = The Princeton Lectures on Intuitionism /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Kurt Gödel/ edited by Maria Hämeen-Anttila, Jan von Plato.
其他題名:
The Princeton Lectures on Intuitionism /
其他作者:
von Plato, Jan.
面頁冊數:
IX, 133 p.online resource. :
Contained By:
Springer Nature eBook
標題:
History of Philosophy. -
電子資源:
https://doi.org/10.1007/978-3-030-87296-0
ISBN:
9783030872960
Kurt Gödel = The Princeton Lectures on Intuitionism /
Kurt Gödel
The Princeton Lectures on Intuitionism /[electronic resource] :edited by Maria Hämeen-Anttila, Jan von Plato. - 1st ed. 2021. - IX, 133 p.online resource. - Sources and Studies in the History of Mathematics and Physical Sciences,2196-8829. - Sources and Studies in the History of Mathematics and Physical Sciences,.
Gödel's Functional Interpretation in Context -- Part I: Axiomatic Intuitionist Logic -- Part II: The Functional Interpretation -- References -- Name Index.
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 It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers.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.
ISBN: 9783030872960
Standard No.: 10.1007/978-3-030-87296-0doiSubjects--Topical Terms:
671574
History of Philosophy.
LC Class. No.: QA21-27
Dewey Class. No.: 510.9
Kurt Gödel = The Princeton Lectures on Intuitionism /
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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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