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Goedel S Way

Author: Gregory Chaitin
Publisher: CRC Press
ISBN: 0415690854
Size: 59.26 MB
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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Humanity In A Creative Universe

Author: Stuart A. Kauffman
Publisher: Oxford University Press
ISBN: 0199390460
Size: 76.85 MB
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In the hard sciences, which can often feel out of grasp for many lay readers, there are "great thinkers" who go far beyond the equations, formulas, and research. Minds such as Stephen Hawking philosophize about the functions and nature of the universe, the implications of our existence, and other impossibly fascinating, yet difficult questions. Stuart A. Kauffman is one of those great thinkers. He has dedicated his lifetime to researching "complex systems" at prestigious institutions and now writes his treatise on the most complex system of all: our universe. A recent Scientific American article claims that "philosophy begins where physics ends, and physics begins where philosophy ends," and perhaps no better quote sums up what Kauffman's latest book offers. Grounded in his rigorous training and research background, Kauffman is inter-disciplinary in every sense of the word, sorting through the major questions and theories in biology, physics, and philosophy. Best known for his philosophy of evolutionary biology, Kauffman coined the term "prestatability" to call into question whether science can ever accurately and precisely predict the future development of biological features in organisms. As evidenced by the title's mention of creativity, the book refreshingly argues that our preoccupation to explain all things with scientific law has deadened our creative natures. In this fascinating read, Kauffman concludes that the development of life on earth is not entirely predictable, because no theory could ever fully account for the limitless variations of evolution. Sure to cause a stir, this book will be discussed for years to come and may even set the tone for the next "great thinker."

Goedel S Way

Author: Gregory Chaitin
Publisher: CRC Press
ISBN: 9781136587634
Size: 29.70 MB
Format: PDF, Mobi
View: 7382
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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Proving Darwin

Author: Gregory J. Chaitin
Publisher: Pantheon
ISBN: 0375423141
Size: 74.58 MB
Format: PDF
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Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world.

Impossibility

Author: John D. Barrow
Publisher: Oxford University Press on Demand
ISBN: 0195130820
Size: 42.55 MB
Format: PDF, ePub
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Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

An Introduction To G Del S Theorems

Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 1107022843
Size: 26.48 MB
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A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.

Forever Undecided

Author: Raymond M. Smullyan
Publisher: Knopf
ISBN: 0307962466
Size: 20.86 MB
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Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

Godel S Proof

Author: Ernest Nagel
Publisher: NYU Press
ISBN: 0814758371
Size: 64.67 MB
Format: PDF
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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.