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| Author | : S.G. Shanker |
| Publisher | : Taylor & Francis |
| Total Pages | : 271 |
| Release | : 2012-08-21 |
| Genre | : Philosophy |
| ISBN | : 1134947984 |
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
| Author | : Stuart Shanker |
| Publisher | : London : Croom Helm |
| Total Pages | : 261 |
| Release | : 1988-01 |
| Genre | : G ODEL`S THEOREM. |
| ISBN | : 9780709933571 |
A layman's guide to the mechanics of Godel's proof together with a lucid discussion of the issues which it raises.
| Author | : S.G. Shanker |
| Publisher | : Routledge |
| Total Pages | : 272 |
| Release | : 2012-08-21 |
| Genre | : Philosophy |
| ISBN | : 1134947976 |
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
| 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 | : Torkel Franzén |
| Publisher | : CRC Press |
| Total Pages | : 182 |
| Release | : 2005-06-06 |
| Genre | : Mathematics |
| ISBN | : 1439876924 |
"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 | : Gregory Chaitin |
| Publisher | : CRC Press |
| Total Pages | : 160 |
| Release | : 2011-10-14 |
| Genre | : Mathematics |
| ISBN | : 1136587640 |
Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8
| Author | : Yannai A. Gonczarowski |
| Publisher | : Cambridge University Press |
| Total Pages | : 286 |
| Release | : 2022-07-31 |
| Genre | : Computers |
| ISBN | : 1108957692 |
Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.
| 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.
