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Can Mathematics Be Proved Consistent...
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Can Mathematics Be Proved Consistent? = Gödel's Shorthand Notes & Lectures on Incompleteness /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Can Mathematics Be Proved Consistent?/ by Jan von Plato.
其他題名:
Gödel's Shorthand Notes & Lectures on Incompleteness /
作者:
von Plato, Jan.
面頁冊數:
IX, 263 p.online resource. :
Contained By:
Springer Nature eBook
標題:
Mathematical Logic and Foundations. -
電子資源:
https://doi.org/10.1007/978-3-030-50876-0
ISBN:
9783030508760
Can Mathematics Be Proved Consistent? = Gödel's Shorthand Notes & Lectures on Incompleteness /
von Plato, Jan.
Can Mathematics Be Proved Consistent?
Gödel's Shorthand Notes & Lectures on Incompleteness /[electronic resource] :by Jan von Plato. - 1st ed. 2020. - IX, 263 p.online resource. - Sources and Studies in the History of Mathematics and Physical Sciences,2196-8810. - Sources and Studies in the History of Mathematics and Physical Sciences,.
I. Gödel's Steps Toward Incompleteness -- II. The Saved Sources on Incompleteness -- III. The Shorthand Notebooks -- IV. The Typewritten Manuscripts -- V. Lectures and Seminars on Incompleteness -- Index -- References.
Kurt Gödel (1906–1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren’t. The result is known as Gödel’s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödel’s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödel’s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.
ISBN: 9783030508760
Standard No.: 10.1007/978-3-030-50876-0doiSubjects--Topical Terms:
669393
Mathematical Logic and Foundations.
LC Class. No.: QA21-27
Dewey Class. No.: 510.9
Can Mathematics Be Proved Consistent? = Gödel's Shorthand Notes & Lectures on Incompleteness /
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