Can Mathematics Be Proved Consistent? : Gödel's Shorthand Notes & Lectures on Incompleteness. 1st ed. 2020

種類:

電子ブック

責任表示:

by Jan von Plato

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• von Plato, Jan.
• SpringerLink (Online service)

シリーズ名:

Sources and Studies in the History of Mathematics and Physical Sciences ;

ISBN:

9783030508760 [3030508765]    

注記:

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.T

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