Gödels Proof

Gödels Proof

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Hardcover, Pages: 129

Genres: Science, Mathematics, Philosophy, Nonfiction

Language: English

Reads: 94

Downloads: 8554

Rating: Rated: 4659 timesRate It

Gödels Proof
Enter the sum

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Book Description

In 1931 Kurt Gödel published his fundamental paper, On Formally Undecidable Propositions of Principia Mathematica and Related Systems. This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as one of the greatest contributions to the sciences in recent times.

However, few mathematicians of the time were equipped to understand the young scholars complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödels discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

Reviews
  •    Gubei Gublader
    2020
    This book is one of those rare creations in which its clarity and succinctness of presentation highlights the most important concepts. Even if one is not interested in the theory itself the first half of the book is a must read by anyone dealing with mathematics or interested in the nature of truth. It ultimately describes the 1931 paper Kurt Godel published in German entitled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems”. The “Principia Mathematica” was the 1913 monumental 3 volume work by Alfred North Whitehead and Bertrand Russell which was thought to have placed the foundations of mathematics on a firm non-intuitive foundation using a logic based axiomatic strategy. Godel showed that this strategy cannot be used to demonstrate internal consistency, that the mathematics so derived is not always without contradiction even though that may actually be the case. Consistency is just not provable by this sort of strategy.
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  •    Fecage Moaveniyan
    2020
    A fun, concise text that illustrates one of the most profound theorems of mathematics and philosophical logic. Godel's Incompleteness Theorems are some of the most mind-boggling creations of human thought that have profound implications for more human thought. "Godel's Proof" is excellent in that the author provides a relevant background to the proof and its implications, starting with a buildup on the concepts of consistency and meta-mathematics, into the arithmetization of meta-mathematics (a mouthful) in order to supplement a background for the proof by Godel. Nagel and Newman also provide a great background in logic--as someone who already has a background in logical statements, the description of logical symbols surely felt helpful as a review, and can be beneficial for those with limited logic experience. Even the appendices, which cover Peano's axioms, quantifiers, and tautology were thorough, and the author also made sure to provide relevant footnotes for any new definitions they had built themselves. While I do agree with other reviews that certain lemmas or models are a bit hand-wavey, this allows for a more concise text that is clear for any reader, and ultimately allows the text to be inclusive for a variety of audiences. It is an astounding exposition of the proof and its consequences, and I would surely recommend this text to anyone broadly interested in philosophy and mathematics and the intricate weaving of the two disciplines.
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