G del s Theorem

Author: Torkel Franzén
Publisher: A K Peters/CRC Press
ISBN: 1568812388
Release Date: 2005-06-06
Genre: Mathematics

"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

Mathematics

Author: Morris Kline
Publisher: Oxford University Press, USA
ISBN: 0195030850
Release Date: 1982
Genre: Mathematics

Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences

Inexhaustibility

Author: Torkel Franzén
Publisher: A K Peters Ltd
ISBN: 1568811748
Release Date: 2004-09-08
Genre: Mathematics

Gödel's Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough.

Incompleteness The Proof and Paradox of Kurt G del Great Discoveries

Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 9780393327601
Release Date: 2006-02-17
Genre: Biography & Autobiography

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.

Godel s Proof

Author: Ernest Nagel
Publisher: NYU Press
ISBN: 9780814758373
Release Date: 2008-01-01
Genre: Mathematics

“Come to me, all you that labor and are heavy laden, and I will give you rest.”Mathew 11:28 (AKJV) In the early 1990s, a grassroots coalition of churches in Baltimore, Maryland helped launch what would become a national movement. Joining forces with labor and low-wage worker organizations, they passed the first municipal living wage ordinance. Since then, over 144 municipalities and counties as well as numerous universities and local businesses in the United States have enacted such ordinances. Although religious persons and organizations have been important both in the origins of the living wage movement and in its continuing success, they are often ignored or under analyzed. Drawing on participant observation in multiple cities, All You That Labor analyzes and evaluates the contributions of religious activists to the movement. The book explores the ways religious organizations do this work in concert with low-wage workers, the challenges religious activists face, and how people of faith might better nurture moral agency in relation to the political economy. Ultimately, C. Melissa Snarr provides clarity on how to continue to cultivate, renew, and expand religious resources dedicated to the moral agency of low-wage workers and their allies.

Logical Dilemmas

Author: John Dawson
Publisher: A K Peters/CRC Press
ISBN: 1568812566
Release Date: 2005-06-06
Genre: Mathematics

This authoritative biography of Kurt Goedel relates the life of this most important logician of our time to the development of the field. Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.