Incompleteness

Incompleteness
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.

Belief and Incompleteness

Belief and Incompleteness
Author: Kurt Konolige
Publisher:
Total Pages: 78
Release: 1984
Genre: Analysis (Philosophy)
ISBN:

Both agents are state-of-theart constructions, incorporating the latest Al research in chess playing, natural-language understanding, planning, etc. But because of the overwhelming combinatorics of' chess, neither they nor the fastest foreseeable computers would be able to search the entire game tree to find out whether White has a forced win. Why then do they come to such an odd conclusion about their own knowledge of the game? The chess scenario is an anecdotal example of the way inaccurate cognitive models can lead to behavior that is less than intelligent in artificial agents. In this case, the agents' model of belief is not correct. They make the assumption that an agent actually knows all the consequences of his beliefs. S1 knows that chess is a finite game, and thus reasons that, in principle, knowing the rules of chess is all that is required to figure out whether White has a forced ini%ial win. Mter learning that S2 does indeed know the rules of chess he comes to the erroneous conclusion that S2 also knows this particular consequence of the rules. And S2 himself, reflecting on his own knowledge in the same manner, arrives at the same conclusion, even though in actual fact he could never carry out the computations necessary to demonstrate it.

Gödel's Theorem

Gödel's Theorem
Author: Torkel Franzén
Publisher: CRC Press
Total Pages: 184
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

Reflections on Kurt Gödel

Reflections on Kurt Gödel
Author: Hao Wang
Publisher: MIT Press
Total Pages: 366
Release: 1990-03-14
Genre: Philosophy
ISBN: 9780262730877

Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel's ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel's and on points of agreement develops Gödel's views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel's career - the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life. A Bradford Book.

An Introduction to Gödel's Theorems

An Introduction to Gödel's Theorems
Author: Peter Smith
Publisher: Cambridge University Press
Total Pages: 376
Release: 2007-07-26
Genre: Mathematics
ISBN: 1139465937

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

A World Without Time

A World Without Time
Author: Palle Yourgrau
Publisher: Basic Books
Total Pages: 226
Release: 2009-03-04
Genre: Science
ISBN: 078673700X

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.

On Belief

On Belief
Author: Slavoj Zizek
Publisher: Routledge
Total Pages: 177
Release: 2003-09-02
Genre: Philosophy
ISBN: 113452272X

What is the basis of belief in an era when globalization, multiculturalism and big business are the new religion? Slavoj Zizek, renowned philosopher and irrepressible cultural critic takes on all comers in this compelling and breathless new book. From 'cyberspace reason' to the paradox that is 'Western Buddhism', On Belief gets behind the contours of the way we normally think about belief, in particular Judaism and Christianity. Holding up the so-called authenticity of religious belief to critical light, Zizek draws on psychoanalysis, film and philosophy to reveal in startling fashion that nothing could be worse for believers than their beliefs turning out to be true.

Inexhaustibility

Inexhaustibility
Author: Torkel Franzén
Publisher: Cambridge University Press
Total Pages: 318
Release: 2017-03-30
Genre: Mathematics
ISBN: 1108641636

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance

Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance
Author: Alexandre C. Ziegler
Publisher: Springer Science & Business Media
Total Pages: 205
Release: 2012-11-02
Genre: Business & Economics
ISBN: 3540247556

After a brief review of the existing incomplete information literature, the effect of incomplete information on investors' exptected utility, risky asset prices, and interest rates is described. It is demonstrated that increasing the quality of investors' information need not increase their expected utility and the prices of risky assets. The impact of other factors is discussed in detail. It is also demonstrated that financial markets in general do not aggregate information efficiently, a fact that can explain the equity premium puzzle.

Righteous Religion

Righteous Religion
Author: Kathleen Ritter
Publisher: Psychology Press
Total Pages: 242
Release: 1996
Genre: Christianity
ISBN: 9780789060167

Stories of 17 women who have struggled for human rights throughout the world during the 20th century but have been largely overlooked by the conventional literature. They are depicted confronting authoritarian governments, struggling with race and ethnicity, seeking environmental justice, upholding women's rights as human rights, and making the world safe for children. Paper edition (unseen), $18.95. Annotation copyright by Book News, Inc., Portland, OR