Name: Gödel's Incompleteness Theorems: A Guided Tour Through Kurt Gödel's Historic Proof
Brand: Springer
SKU: 9783662695494
Price: 5390.0 INR
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Gödel's Incompleteness Theorems: A Guided Tour Through Kurt Gödel's Historic Proof

by Dirk W. Hoffmann

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ISBN13: 9783662695494
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: August 31, 2024
Pages: 385
Original Price: USD 54.99
Language: English
Edition: 2024
Item Weight: 576 grams
BISAC Subject(s): Logic

About The Book

In 1931, the mysterious-sounding article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" shook the mathematical world. In this article, Kurt GÃ¶del proved two incompleteness theorems that have fundamentally changed our view of mathematics. GÃ¶del's theorems manifest that the concept of truth and the concept of provability cannot coincide.

Since their discovery, the incompleteness theorems have attracted much attention, and a flood of articles and books have been devoted to their striking consequences. For good reasons, however, hardly any work deals with GÃ¶del's article in its original form: His complex lines of thought described with meticulous precision, the many definitions and theorems, and the now largely outdated notation turn GÃ¶del's historical masterpiece into a difficult read.

This book explores GÃ¶del's original proof in detail. All individual steps are carefully explained and illustrated with numerous examples. However, this book is more than just an annotated version of the historical article, as the proper understanding of GÃ¶del's work requires a solid grasp of history. Thus, numerous excursions take the reader back to the beginning of the twentieth century. It was the time when mathematics experienced one of its greatest crises, when type theory and axiomatic set theory were taking shape, and Hilbert's formalistic logic and Brouwer's intuitionistic mathematics were openly confronting each other.

This book is the revised translation of the second edition of the author's German language book "Die GÃ¶del'schen UnvollstÃ¤ndigkeitssÃ¤tze".

About The Author

Prof. Dr. Dirk W. Hoffmann is a professor at the Department of Computer Science and Business Information Systems at the Karlsruhe University of Applied Sciences in Germany.

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