Download and read online G del in PDF and EPUB Tells the life story of the contemporary and intellectual peer of Einstein, and describes his work which revolutionized mathematics, philosophy, linguistics, computer science, and cosmology.
Download and read online Godel s Theorem in Focus in PDF and EPUB 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.
Download and read online Incompleteness The Proof and Paradox of Kurt G del Great Discoveries in PDF and EPUB 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.
Download and read online Kurt G del Collected Works Volume II in PDF and EPUB This second volume of a comprehensive edition of Kurt Godel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in historical context.
Download and read online Godel s Proof in PDF and EPUB '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 Proof by 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.
Download and read online A World Without Time in PDF and EPUB In 1942, the logician Kurt Godel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics, and the lost world of German science. 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 but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.
Download and read online From Frege to G del in PDF and EPUB Gathered together in this book are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's "Begriffsschrift"--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume. The texts that follow depict the emergence of set theory and foundations of mathematics, two new fields on the borders of logic, mathematics, and philosophy. Essays trace the trends that led to "Principia mathematica," the appearance of modern paradoxes, and topics including proof theory, the theory of types, axiomatic set theory, and Lowenheim's theorem. The volume concludes with papers by Herbrand and by Godel, including the latter's famous incompleteness paper."
Download and read online A Logical Journey in PDF and EPUB
Download and read online An Introduction to G del s Theorems in PDF and EPUB 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 - extensively rewritten for its second edition - 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.
Download and read online Metamathematics Machines and G del s Proof in PDF and EPUB Describes the use of computer programs to check several proofs in the foundations of mathematics.
Download and read online Kurt G del in PDF and EPUB Kurt Gödel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century. However, unlike Russel, Gödel the mathematician published very little apart from his well-known writings in logic, metamathematics and set theory. Fortunately, Gödel the philosopher, who devoted more years of his life to philosophy than to technical investigation, wrote hundreds of pages on the philosophy of mathematics, as well as on other fields of philosophy. It was only possible to learn more about his philosophical works after the opening of his literary estate at Princeton a decade ago. The goal of this book is to make available to the scholarly public solid reconstructions and editions of two of the most important essays which Gödel wrote on the philosophy of mathematics. The book is divided into two parts. The first provides the reader with an incisive historico-philosophical introduction to Gödel's technical results and philosophical ideas. Written by the Editor, this introductory apparatus is not only devoted to the manuscripts themselves but also to the philosophical context in which they were written. The second contains two of Gödel's most important and fascinating unpublished essays: 1) the Gibbs Lecture ("Some basic theorems on the foundations of mathematics and their philosophical implications", 1951); and 2) two of the six versions of the essay which Gödel wrote for the Carnap volume of the Schilpp series The Library of Living Philosophers ("Is mathematics syntax of language?", 1953-1959).
Download and read online From Trotsky to G del in PDF and EPUB This story of a highly intelligent observer of the turbulent 20th century who was intimately involved as the secretary and bodyguard to Leon Trotsky is based on extensive interviews with the subject, Jean van Heijenoort, and his family, friends, and colleagues. The author has captured the personal drama and the professional life of her protagonist--ranging from the political passion of a young intellectual to the scientific and historic work in the most abstract and yet philosophically important area of logic--in a very readable narrative.
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Download and read online Godel s Incompleteness Theorems in PDF and EPUB 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.
Download and read online On G del in PDF and EPUB This brief text assists students in understanding Godel's philosophy and thinking so that they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the "Wadsworth Philosophers Series," (which will eventually consist of approximately 100 titles, each focusing on a single "thinker" from ancient times to the present), ON G -DEL is written by a philosopher deeply versed in the philosophy of this key thinker. Like other books in the series, this concise book offers sufficient insight into the thinking of a notable philosopher better enabling students to engage in the reading and to discuss the material in class and on paper.