Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries
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Incompleteness The Proof and Paradox of Kurt G del Great Discoveries
Author | : Rebecca Goldstein |
Publsiher | : W. W. Norton & Company |
Total Pages | : 299 |
Release | : 2006-02-17 |
Genre | : Biography & Autobiography |
ISBN | : 9780393327601 |
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A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.
Incompleteness
Author | : Rebecca Goldstein |
Publsiher | : Unknown |
Total Pages | : 296 |
Release | : 2005 |
Genre | : Gödel's theorem |
ISBN | : 0739457446 |
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Godel s Proof
Author | : Ernest Nagel,James R. Newman |
Publsiher | : Routledge |
Total Pages | : 109 |
Release | : 2012-11-12 |
Genre | : Philosophy |
ISBN | : 9781134953998 |
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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.
A World Without Time
Author | : Palle Yourgrau |
Publsiher | : Basic Books |
Total Pages | : 226 |
Release | : 2009-03-04 |
Genre | : Science |
ISBN | : 9780786737000 |
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It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.
An Introduction to G del s Theorems
Author | : Peter Smith |
Publsiher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 2007-07-26 |
Genre | : Mathematics |
ISBN | : 9780521857840 |
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Peter Smith examines Gödel's Theorems, how they were established and why they matter.
A short remark on G del incompleteness theorem and its self referential paradox from Neutrosophic Logic perspective
Author | : V. Christianto,F. Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 6 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic.
Principia Mathematica
Author | : Alfred North Whitehead,Bertrand Russell |
Publsiher | : Cambridge University Press |
Total Pages | : 524 |
Release | : 1927 |
Genre | : Mathematics |
ISBN | : 052106791X |
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The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Thinking about G del and Turing
Author | : Gregory J. Chaitin |
Publsiher | : World Scientific |
Total Pages | : 368 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9789812708953 |
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Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Gdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.