GODELS-PROOF

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Godel S Proof

Author : Ernest Nagel
ISBN : 9780814758373
Genre : Mathematics
File Size : 62.49 MB
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“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.
Category: Mathematics

G Del S Proof

Author : Ernest Nagel
ISBN : 9780415355285
Genre : Philosophy
File Size : 52.65 MB
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'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'– The Guardian In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. Kurt Godel(1906 – 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.
Category: Philosophy

Godel S Theorem In Focus

Author : S.G. Shanker
ISBN : 9781134947973
Genre : Philosophy
File Size : 24.94 MB
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A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Category: Philosophy

Metamathematics Machines And G Del S Proof

Author : N. Shankar
ISBN : 0521585333
Genre : Computers
File Size : 71.32 MB
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Describes the use of computer programs to check several proofs in the foundations of mathematics.
Category: Computers

Godel S Incompleteness Theorems

Author : Raymond M. Smullyan
ISBN : 9780195364378
Genre : Mathematics
File Size : 24.31 MB
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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
Category: Mathematics

Kurt G Del Collected Works Volume Iii

Author : Kurt Gödel
ISBN : 0195072553
Genre : Mathematics
File Size : 87.71 MB
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Kurt Gödel was the greatest logician of this century. This third volume of his collected works consists of previously unpublished material, both essays and lectures.
Category: Mathematics

Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries

Author : Rebecca Goldstein
ISBN : 9780393327601
Genre : Biography & Autobiography
File Size : 47.1 MB
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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.
Category: Biography & Autobiography

Internal Logic

Author : Y. Gauthier
ISBN : 9789401700832
Genre : Mathematics
File Size : 55.83 MB
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Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.
Category: Mathematics

Consciousness And The Brain

Author : Gordon Globus
ISBN : 9781468421965
Genre : Psychology
File Size : 66.15 MB
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The relationship of consciousness to brain, which Schopenhauer grandly referred to as the "world knot," remains an unsolved problem within both philosophy and science. The central focus in what follows is the relevance of science---from psychoanalysis to neurophysiology and quantum physics-to the mind-brain puzzle. Many would argue that we have advanced little since the age of the Greek philosophers, and that the extraordinary accumulation of neuroscientific knowledge in this century has helped not at all. Increas ingly, philosophers and scientists have tended to go their separate ways in considering the issues, since they tend to differ in the questions that they ask, the data and ideas which are provided for consideration, their methods for answering these questions, and criteria for judging the acceptability of an answer. But it is our conviction that philosophers and scientists can usefully interchange, at least to the extent that they provide co~straints upon each other's preferred strategies, and it may prove possible for more substantive progress to be made. Philosophers have said some rather naive things by ignoring the extraordinary advances in the neurosciences in the twentieth century. The skull is not filled with green cheese! On the other hand, the arrogance of many scientists toward philosophy and their faith in the scientific method is equally naive. Scientists clearly have much to learn from philosophy as an intellectual discipline.
Category: Psychology

Advanced Logic For Applications

Author : R.E. Grandy
ISBN : 9789401011914
Genre : Philosophy
File Size : 72.3 MB
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This book is intended to be a survey of the most important results in mathematical logic for philosophers. It is a survey of results which have philosophical significance and it is intended to be accessible to philosophers. I have assumed the mathematical sophistication acquired· in an introductory logic course or in reading a basic logic text. In addition to proving the most philosophically significant results in mathematical logic, I have attempted to illustrate various methods of proof. For example, the completeness of quantification theory is proved both constructively and non-constructively and relative ad vantages of each type of proof are discussed. Similarly, constructive and non-constructive versions of Godel's first incompleteness theorem are given. I hope that the reader· will develop facility with the methods of proof and also be caused by reflect on their differences. I assume familiarity with quantification theory both in under standing the notations and in finding object language proofs. Strictly speaking the presentation is self-contained, but it would be very difficult for someone without background in the subject to follow the material from the beginning. This is necessary if the notes are to be accessible to readers who have had diverse backgrounds at a more elementary level. However, to make them accessible to readers with no background would require writing yet another introductory logic text. Numerous exercises have been included and many of these are integral parts of the proofs.
Category: Philosophy