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| Author | : Harry J. Gensler |
| Publisher | : |
| Total Pages | : 94 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student and general reader and presumes no specialized knowledge of mathematics or logic.
| Author | : Rebecca Goldstein |
| Publisher | : W. W. Norton & Company |
| Total Pages | : 299 |
| Release | : 2006-01-31 |
| Genre | : Biography & Autobiography |
| ISBN | : 0393327604 |
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
| Author | : Peter Smith |
| Publisher | : Cambridge University Press |
| Total Pages | : 376 |
| Release | : 2007-07-26 |
| Genre | : Mathematics |
| ISBN | : 0521857848 |
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
| Author | : Torkel Franzén |
| Publisher | : A K Peters/CRC Press |
| Total Pages | : 182 |
| Release | : 2005-06-06 |
| Genre | : Mathematics |
| ISBN | : 9781568812380 |
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
| Author | : Ernest Nagel |
| Publisher | : Psychology Press |
| Total Pages | : 118 |
| Release | : 1989 |
| Genre | : Gödel's theorem |
| ISBN | : 041504040X |
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
| Author | : Kurt Gödel |
| Publisher | : Courier Corporation |
| Total Pages | : 82 |
| Release | : 2012-05-24 |
| Genre | : Mathematics |
| ISBN | : 0486158403 |
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 | : Raymond M. Smullyan |
| Publisher | : Oxford University Press |
| Total Pages | : 156 |
| Release | : 1992-08-20 |
| Genre | : Mathematics |
| ISBN | : 0195364376 |
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 | : Alfred North Whitehead |
| Publisher | : |
| Total Pages | : 696 |
| Release | : 1910 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
| Author | : Raymond M. Smullyan |
| Publisher | : Knopf |
| Total Pages | : 286 |
| Release | : 2012-07-04 |
| Genre | : Mathematics |
| ISBN | : 0307962466 |
Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!
| Author | : Raymond M. Smullyan |
| Publisher | : Courier Corporation |
| Total Pages | : 240 |
| Release | : 2013-08-21 |
| Genre | : Mathematics |
| ISBN | : 0486315770 |
These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.
