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Author | : Kurt Gödel |
Publisher | : Courier Corporation |
Total Pages | : 82 |
Release | : 2012-05-24 |
Genre | : Mathematics |
ISBN | : 0486158403 |
Download On Formally Undecidable Propositions of Principia Mathematica and Related Systems Book in PDF, ePub and Kindle
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Author | : Kurt Gödel |
Publisher | : Courier Corporation |
Total Pages | : 84 |
Release | : 1992-01-01 |
Genre | : Mathematics |
ISBN | : 9780486669809 |
Download On Formally Undecidable Propositions of Principia Mathematica and Related Systems Book in PDF, ePub and Kindle
In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Author | : Ernest Nagel |
Publisher | : Routledge |
Total Pages | : 109 |
Release | : 2012-11-12 |
Genre | : Philosophy |
ISBN | : 1134953992 |
Download Godel's Proof Book in PDF, ePub and Kindle
The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Author | : Rebecca Goldstein |
Publisher | : W. W. Norton & Company |
Total Pages | : 299 |
Release | : 2006-01-31 |
Genre | : Biography & Autobiography |
ISBN | : 0393327604 |
Download Incompleteness Book in PDF, ePub and Kindle
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Author | : Alfred Tarski |
Publisher | : Dover Books on Mathematics |
Total Pages | : 0 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 9780486477039 |
Download Undecidable Theories Book in PDF, ePub and Kindle
This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Author | : Peter Smith |
Publisher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 2007-07-26 |
Genre | : Mathematics |
ISBN | : 0521857848 |
Download An Introduction to Gödel's Theorems Book in PDF, ePub and Kindle
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Author | : Martin Davis |
Publisher | : Courier Corporation |
Total Pages | : 420 |
Release | : 2004-01-01 |
Genre | : Mathematics |
ISBN | : 9780486432281 |
Download The Undecidable Book in PDF, ePub and Kindle
"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics "Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study. The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.
Author | : Ernest Nagel |
Publisher | : Lulu.com |
Total Pages | : 132 |
Release | : 2018-09-14 |
Genre | : Gödel's theorem |
ISBN | : 0359079261 |
Download Godel's Proof Book in PDF, ePub and Kindle
In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
Author | : Raymond M. Smullyan |
Publisher | : Oxford University Press |
Total Pages | : 156 |
Release | : 1992-08-20 |
Genre | : Mathematics |
ISBN | : 0195364376 |
Download Godel's Incompleteness Theorems Book in PDF, ePub and Kindle
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
Author | : Wolfgang Rautenberg |
Publisher | : Springer |
Total Pages | : 337 |
Release | : 2010-07-01 |
Genre | : Mathematics |
ISBN | : 1441912215 |
Download A Concise Introduction to Mathematical Logic Book in PDF, ePub and Kindle
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.