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Catalogue Information
Field name	Details
Dewey Class	510.9
Title	Can Mathematics Be Proved Consistent? ([EBook]) : Gödel's Shorthand Notes & Lectures on Incompleteness / / by Jan von Plato.
Author	von Plato, Jan
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2020.
Physical Details	IX, 263 p. : online resource.
Series	Sources and studies in the history of mathematics and physical sciences 2196-8810
ISBN	9783030508760
Summary Note	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.:
Contents note	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.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-50876-0
Links to Related Works	Subject References: History . History of Mathematical Sciences . Mathematical logic . Mathematical Logic and Foundations . Mathematics . Authors: author . von Plato, Jan . Corporate Authors: SpringerLink (Online service) . Series: Sources and studies in the history of mathematics and physical sciences . Classification: 510.9 .

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Can Mathematics Be Proved Consistent? Gödel's Shorthand Notes & Lectures on Incompleteness

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