Incompleteness The Proof and Paradox of Kurt G del Great Discoveries

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

Incompleteness
Author: Rebecca Goldstein
Publsiher: Unknown
Total Pages: 296
Release: 2005
Genre: Gödel's theorem
ISBN: 0739457446

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Godel s Proof

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

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

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

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

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

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 G”del 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 G”del 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.