Gödel's Proof

Front Cover
NYU Press, 2001 - Mathematics - 129 pages
28 Reviews

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 scholar's 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 Gödel's 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.

  

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Review: Gödel's Proof

User Review  - Al Maki - Goodreads

I give the book two stars simply because I couldn't follow it. It took a semester of lectures by Marlin Rayburn for me to grasp Godel's Proof. Read full review

Review: Gödel's Proof

User Review  - Assaad - Goodreads

I bought this book on kindle and in printed format. It is the best one can have as an easy demonstration of Godel's incompleteness theorem. I got interested about the subject after reading Hofstadter ... Read full review

Contents

Introduction
1
The Problem of Consistency
7
Absolute Proofs of Consistency
25
The Systematic Codification of Formal Logic
37
An Example of a Successful Absolute Proof of Consistency
45
The Idea of Mapping and Its Use in Mathematics
57
Godels Proofs
68
B The arithmetization of metamathematics
80
C The heart of Godels argument
92
Concluding Reflections
109
Notes
114
Brief Bibliography
125
Index
127
Copyright

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About the author (2001)

Born in Czechoslovakia, Ernest Nagel emigrated to the United States and became a naturalized American citizen. In 1923 he graduated from the City College of New York, where he had studied under Morris Cohen, with whom he later collaborated to coauthor the highly successful textbook, An Introduction to Logic and Scientific Method (1934). Pursuing graduate studies at Columbia University, he received his Ph.D. in 1930. After a year of teaching at the City College of New York, he joined the faculty of Columbia University, where in 1955 he was named John Dewey Professor of Philosophy. In 1966 he joined the faculty of Rockefeller University. Nagel was one of the leaders in the movement of logical empiricism, conjoining Viennese positivism with indigenous American naturalism and pragmatism. In 1936 he published in the Journal of Philosophy the article "Impressions and Appraisals of Analytic Philosophy," one of the earliest sympathetic accounts of the works of Ludwig Wittgenstein, Moritz Schlick, and Rudolf Carnap intended for an American audience. Nagel was esteemed for his lucid exposition of the most recondite matters in logic, mathematics, and natural science, published in essays and book reviews for professional journals, scientific periodicals, and literary reviews. Two of his books, now out of print, consisted of collections of his articles, Sovereign Reason and Other Studies in the Philosophy of Science (1954) and Logic Without Metaphysics and Other Essays in the Philosophy of Science (1957). He also wrote a monograph, Principles of the Theory of Probability (1939) which appeared in the International Encyclopedia of Unified Science. In his major book-length work, The Structure of Science, Nagel directed his attention to the logic of scientific explanations.

James R. Newman was the 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.

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