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"Gödel's Proof" by Ernest Nagel & James R. Newman
A fine book going through the "metamathematics" made by the famous logician himself Kurt Gödel.
Kurt Gödel is a logician responsible for bringing the world his mathematical proofs of consistency. It was during the the early 20th century when philosophers, mathematicians and logicians spending hours in their office composing and theorizing the foundations of Mathematics and its underlying philosophy. After all, what makes Mathematics the way it is?
Authors Nagel and Newman did a wonderful job breaking down chunks originally written by Gödel into something more simplistic—something where the average layperson or student can understand. The book overall covers Gödel's take on natural numbers and arithmetic, and also proof in validity on Formal Logic. It does get very tongue-twisted and mind-bending when explaining the proof but it's very much a short account in interpreting Gödel's take on Mathematical Philosophy—a branch in Philosophy that was also tackled by famous philosopher Bertrand Russell.
While it is a short book, you may want to read it twice since I'm sure there are parts you might not have understood or missed. That's normal since we're dealing with philosophical math here. I would've loved to have seen more examples of the proofs, though.
Other than that, whether you're majoring/studying advanced Mathematics, Mathematical Logic, Philosophy or Computer Science, take a feel of the water with Gödel's famous Proof.
- Good overview on some of the work by Kurt Gödel.
- Covers mostly Mathematical Logic ("Metamathematics").
- Short book but packs a lot of information.
- Too rigorous for the average reader.
|Author(s)||Ernest Nagel and James R. Newman|
|Edited and with a new Foreword by||Douglas R. Hofstadter|
|Description||[INNER FRONT FLAP]
In 1931, Kurt Gödel disrupted some of the fundamental assumptions underlying mathematics and logic with the publication of his revolutionary paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Ironically, few mathematicians of the time were able to understand the young scholar's complex proof, and the full importance of this work was largely overlooked for many years. Gödel was at last recognized by his peers and presented with the first Albert Einstein Award in 1951 for achievement in the natural sciences—the highest honor of its kind in the United States. The award committee, which included Albert Einstein and J. Robert Oppenheimer, described his work as "one of the greatest contributions to the sciences in recent times."
In Gödel's Proof, Ernest Nagel and James Newman provide a readable and non-technical explanation for both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. First published in 1958 and in print continuously in ten languages, this highly popular, seminal work offers every educated person with an interest in mathematics, logic, and philosophy the opportunity to understand a previously difficult and inaccessible subject.
[INNER BACK FLAP]
In this new edition, Pulitzer prize-winning author Douglas R. Hofstadter has reviewed and updated the text of this classic work, clarifying ambiguities, making arguments clearer, and making the text more accessible than ever before. He has also added a new Foreword which reveals his own unique personal connection to this major work and the impact it has had on his own professional life, explains the essence of Gödel's proof remains revelant today. This delightful book will appeal to students, scholars, teachers, and professionals in mathematics, computer science, logic, philosophy, and general science.
In 1931 Kurt Gödel published a revolutionary paper—one that challenged certain basic assummptions underlying much traditional research in mathematics and logic. Today his exploration of terra incognita is recognized as one of the major contributions to modern scientific thought. Gödel's Proof, now revised, expanded and updated, is the first book to present a readable explanation of the main ideas and broad implications of Gödel's proof.
|Dedication||to Bertrand Russell|
|Book Dimensions||Width: 5.38″ (5 3/8″)|
|Height: 8.25″ (8 ¼″)|
|Depth: 0.75″ (¾″)|
|Contents||Foreword to the New Edition by Douglas R. Hofstadter, Acknowledgements, Introduction, The Problem of Consistency, Absolute Proofs of Consistency, The Systematic Codification of Formal Logic, An Example of a Successful Absolute Proof of Consistency, The Idea of Mapping and Its Use in Mathematics, Gödel's Proof - Gödel numbering, The arithmetization of meta-mathematics, The heart of Gödel's argument, Concluding Reflections, Appendix: Notes, Brief Bibliography, Index|
|Published||October 1, 2008|
|Publisher||New York University Press Washington Square New York, New York (https://www.nyupress.nyu.edu)|
|Copyright||© 2001 by New York University. All Rights Reserved.|
|Manufactured in||United States of America|
|Book Format||Hardcover, Paperback, eTextbook, NOOK book|
"A little masterpiece of exegesis." —Nature
"An excellent non-technical account of the substance of Gödel's celebrated paper." —Bulletin of the American Mathematical Society
|Best Seller's List||--|
|Other||The late ERNEST NAGEL was John Dewey Professor of Philosophy at Columbia University and the late JAMES R. NEWMAN was author of What Is Science.
DOUGLAS R. HOFSTADTER is College of Arts and Sciences Professor of Computer Science and Cognitive Science at Indiana University and author of the Pulitzer prize—winning Gödel, Escher, Bach: an Eternal Golden Braid.
|Library of Congress Cataloging-in-Publication Data||1. Gödel's theorem.|
|I. Newman, James Roy, 1907-1966.|
|II. Hofstadter, Douglas R., 1945—|
|LC Control Number||2001044481|
|LC Call Number||QA9..65 .N34 2002|
|DDC Call Number||511.3—dc21|
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