Can Mathematics Be Proved Consistent? (eBook) von Jan von Plato
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Gödel's Shorthand Notes & Lectures on Incompleteness
eBook
Sofort lieferbar | Lieferzeit: Sofort lieferbar
ISBN-13:
9783030508760
Veröffentl:
2020
Einband:
eBook
Seiten:
263
Autor:
Jan von Plato
Serie:
Sources and Studies in the History of Mathematics and Physical Sciences
eBook Format:
PDF
eBook-Typ:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Inhaltsverzeichnis
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.
Beschreibung
Kurt Gödel (19061978) 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 arent. The result is known as Gödels 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 Gödels 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 publicationOn formally undecidable propositions was composed.The book also contains the original version of Gödels 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.
Schlagwörter zu:
Can Mathematics Be Proved Consistent? von Jan von Plato - mit der ISBN: 9783030508760
German mathematicians; Gödel incompleteness theorem; Gödel lectures; Gödel notes; Open Access; Principia Mathematica; Skolem's paradox; completeness problem; incompleteness theorems; B; Mathematical Logic and Foundations; History of Mathematical Sciences; Mathematics and Statistics, Online-Buchhandlung
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