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


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.

Paraconsistency Logic and Applications

Author: Koji Tanaka
Publisher: Springer Science & Business Media
ISBN: 9789400744387
Release Date: 2012-07-26
Genre: Philosophy

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.


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

Reflections on Kurt G del

Author: Hao Wang
Publisher: MIT Press
ISBN: 0262730871
Release Date: 1990-03-14
Genre: Biography & Autobiography

Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific andphilosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of thegreatest 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 ideasand their connection with grand themes in the history of mathematics and philosophy.The subjects hecovers include the completeness of elementary logic, the limits of formalization, the problem ofevidence, 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, whosereflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes hisideas from those of Gödel's and on points of agreement develops Gödel's views further.The bookprovides a generous array of information on and interpretation of the two main phases of Gödel'scareer - the years between 1924 and 1939 at the University of Vienna, which were marked by intensemathematical creativity, and the period from 1940 to his death in 1978, during which he wasaffiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interestssteadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations withthe Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate andmutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel washospitalized a number of times over the course of his life.Hao Wang is Professor of Logic at TheRockefeller University and author of scores of articles and several books on logic, computers, andphilosophy, including From Mathematics to Philosophy (extensively discussed with Gödel andcontaining contributions by him) and Beyond Analytic Philosophy: Doing Justice to What We Know (MITPress Bradford Books). He is currently preparing a companion volume, Conversations with Kurt Gödelwhich will concentrate on Gödel's unpublished ideas. A Bradford Book.

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.

Simply G del

Author: Richard Tieszen
Publisher: Simply Charly via PublishDrive
ISBN: 9781943657148
Release Date: 2017-04-11
Genre: Biography & Autobiography

Kurt Gödel (1906–1978) was born in Austria-Hungary (now the Czech Republic) and grew up in an ethnic German family. As a student, he excelled in languages and mathematics, mastering university-level math while still in high school. He received his doctorate from the University of Vienna at the age of 24 and, a year later, published the pioneering theorems on which his fame rests. In 1939, with the rise of Nazism, Gödel and his wife settled in the U.S., where he continued his groundbreaking work at the Institute for Advanced Study (IAS) in Princeton and became a close friend of Albert Einstein’s. In Simply Gödel, Richard Tieszen traces Gödel’s life and career, from his early years in tumultuous, culturally rich Vienna to his many brilliant achievements as a member of IAS, as well as his repeated battles with mental illness. In discussing Gödel’s ideas, Tieszen not only provides an accessible explanation of the incompleteness theorems, but explores some of his lesser-known writings, including his thoughts on time travel and his proof of the existence of God. With clarity and sympathy, Simply Gödel brings to life Gödel’s fascinating personal and intellectual journey and conveys the lasting impact of his work on our modern world.