Download or read book The Godel Operation written by James L. Cambias and published by Baen Books. This book was released on 2021-05-04 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science fiction at its sense-of-wonder best. A wild chase through the billion worlds of the Tenth Millennium in search of a mythical weapon that could save civilization—or doom it! A DROID AND HIS BOY, ON A SEARCH FOR A LEGENDARY WEAPON Daslakh is an AI with a problem. Its favorite human, a young man named Zee, is in love with a woman who never existed—and he will scour the Solar System to find her. But in the Tenth Millennium, a billion worlds circle the Sun—everything from terraformed planets to artificial habitats, home to a quadrillion beings. Daslakh’s nicely settled life gets more complicated when Zee helps a woman named Adya escape a gang of crooks. This gets the pair caught up in the hunt for the Godel Trigger, a legendary weapon left over from an ancient war between humans and machines—which could spell the end of civilization. In their search, they face a criminal cat and her henchmen, a paranoid supermind with a giant laser, the greatest thief in history, and a woman who might actually be Zee’s lost love. It’s up to Daslakh to save civilization, keep Zee’s love life on the right track—and make sure that nobody discovers the real secret of the Godel Trigger. At the publisher's request, this title is sold without DRM (Digital Rights Management). Praise for the work of James L. Cambias: “Beautifully written, with a story that captures the imagination the way SF should.”—Booklist, starred review “An engaging nail-biter that is exciting, fun and a satisfying read.”—The Qwillery '“An impressive debut by a gifted writer.”—Publishers Weekly, starred review “An exceptionally thoughtful, searching and intriguing debut.”—Kirkus, starred review “James Cambias will be one of the century's major names in hard science fiction.”—Robert J. Sawyer, Hugo Award–winning author of Red Planet Blues “Fast-paced, pure quill hard science fiction. . . . Cambias delivers adroit plot pivots that keep the suspense coming.”—Gregory Benford, Nebula Award-winning author of Timescape

Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

Download or read book G del s Disjunction written by Leon Horsten and published by Oxford University Press. This book was released on 2016-09-09 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

Download or read book The shackles of conviction written by James R. Meyer and published by . This book was released on 2008 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to G del s Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 or read book Set Theory written by Thomas Jech and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main body of this book consists of 106 numbered theorems and a dozen of examples of models of set theory. A large number of additional results is given in the exercises, which are scattered throughout the text. Most exer cises are provided with an outline of proof in square brackets [ ], and the more difficult ones are indicated by an asterisk. I am greatly indebted to all those mathematicians, too numerous to men tion by name, who in their letters, preprints, handwritten notes, lectures, seminars, and many conversations over the past decade shared with me their insight into this exciting subject. XI CONTENTS Preface xi PART I SETS Chapter 1 AXIOMATIC SET THEORY I. Axioms of Set Theory I 2. Ordinal Numbers 12 3. Cardinal Numbers 22 4. Real Numbers 29 5. The Axiom of Choice 38 6. Cardinal Arithmetic 42 7. Filters and Ideals. Closed Unbounded Sets 52 8. Singular Cardinals 61 9. The Axiom of Regularity 70 Appendix: Bernays-Godel Axiomatic Set Theory 76 Chapter 2 TRANSITIVE MODELS OF SET THEORY 10. Models of Set Theory 78 II. Transitive Models of ZF 87 12. Constructible Sets 99 13. Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis 108 14. The In Hierarchy of Classes, Relations, and Functions 114 15. Relative Constructibility and Ordinal Definability 126 PART II MORE SETS Chapter 3 FORCING AND GENERIC MODELS 16. Generic Models 137 17. Complete Boolean Algebras 144 18.

Download or read book There s Something About G del written by Francesco Berto and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories Written in an accessible, non-technical style

Download or read book G del s Proof written by Ernest Nagel and published by Psychology Press. This book was released on 1989 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. 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.

Download or read book A Science of Operations written by Mark Priestley and published by Springer Science & Business Media. This book was released on 2011-02-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, computers fulfil a dazzling array of roles, a flexibility resulting from the great range of programs that can be run on them. A Science of Operations examines the history of what we now call programming, defined not simply as computer programming, but more broadly as the definition of the steps involved in computations and other information-processing activities. This unique perspective highlights how the history of programming is distinct from the history of the computer, despite the close relationship between the two in the 20th century. The book also discusses how the development of programming languages is related to disparate fields which attempted to give a mechanical account of language on the one hand, and a linguistic account of machines on the other. Topics and features: Covers the early development of automatic computing, including Babbage’s “mechanical calculating engines” and the applications of punched-card technology, examines the theoretical work of mathematical logicians such as Kleene, Church, Post and Turing, and the machines built by Zuse and Aiken in the 1930s and 1940s, discusses the role that logic played in the development of the stored program computer, describes the “standard model” of machine-code programming popularised by Maurice Wilkes, presents the complete table for the universal Turing machine in the Appendices, investigates the rise of the initiatives aimed at developing higher-level programming nota tions, and how these came to be thought of as ‘languages’ that could be studied independently of a machine, examines the importance of the Algol 60 language, and the framework it provided for studying the design of programming languages and the process of software development and explores the early development of object-oriented languages, with a focus on the Smalltalk project. This fascinating text offers a new viewpoint for historians of science and technology, as well as for the general reader. The historical narrative builds the story in a clear and logical fashion, roughly following chronological order.

Download or read book Systemics of Incompleteness and Quasi Systems written by Gianfranco Minati and published by Springer. This book was released on 2019-06-20 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Seventh National Conference of the Italian Systems Society. The title, Systemics of Incompleteness and Quasi-Systems, aims to underline the need for Systemics and Systems Science to deal with the concepts of incompleteness and quasiness. Classical models of Systemics are intended to represent comprehensive aspects of phenomena and processes. They consider the phenomena in their temporal and spatial completeness. In these cases, possible incompleteness in the modelling is assumed to have a provisional or practical nature, which is still under study, and because there is no theoretical reason why the modelling cannot be complete. In principle, this is a matter of non-complex phenomena, to be considered using the concepts of the First Systemics. When dealing with emergence, there are phenomena which must be modelled by systems having multiple models, depending on the aspects being taken into consideration. Here, incompleteness in the modelling is intrinsic, theoretically relating changes in properties, structures, and status of system. Rather than consider the same system parametrically changing over time, we consider sequences of systems coherently. We consider contexts and processes for which modelling is incomplete, being related to only some properties, as well as those for which such modelling is theoretically incomplete—as in the case of processes of emergence and for approaches considered by the Second Systemics. In this regard, we consider here the generic concept of quasi explicating such incompleteness. The concept of quasi is used in various disciplines including quasi-crystals, quasi-particles, quasi-electric fields, and quasi-periodicity. In general, the concept of quasiness for systems concerns their continuous structural changes which are always meta-stable, waiting for events to collapse over other configurations and possible forms of stability; whose equivalence depends on the type of phenomenon under study. Interest in the concept of quasiness is not related to its meaning of rough approximation, but because it indicates an incompleteness which is structurally sufficient to accommodate processes of emergence and sustain coherence or generate new, equivalent or non-equivalent, levels. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognised as having prospective fundamental roles for a new Quasi-Systemics. The latter should be able to deal with problems related to complexity in more general and realistic ways, when a system is not always a system and not always the same system. In this context, the inter-disciplinarity should consist, for instance, of a constructionist, incomplete, non-ideological, multiple, contradiction-tolerant, Systemics, always in progress, and in its turn, emergent.

Download or read book Proof Theory written by Gaisi Takeuti and published by Courier Corporation. This book was released on 2013-10-10 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.

Download or read book Proof Theory written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory

Download or read book Saving Truth From Paradox written by Hartry Field and published by Oxford University Press. This book was released on 2008-03-06 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke>'s, and Lukasiewicz>'s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists>' claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.

Download or read book G del 96 written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The papers in this volume cover the wide range of topics Gödel's work touched, and affirm its continuing importance.

Download or read book Intuitive Axiomatic Set Theory written by José L Garciá and published by CRC Press. This book was released on 2024-04-04 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.

Download or read book DEDUCTIVE METHODS IN MODERN METAPHYSICS written by Iñigo Azcorra Elespe and published by Iñigo Azcorra Elespe. This book was released on 2023-01-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: DEMONSTRATION OF THE EXISTENCE OF GOD THE MIRACULOUS ADJUSTMENT OF THE CONSTANTS OF THE UNIVERSE THE MIRACULOUS ORIGIN OF LIFE THE HYPOTHESIS OF AN INTELLIGENT GOD GOD HAS MARGIN OF ACTION IN THE WORLD MACHINES WILL NEVER BE ABLE TO THINK THE SEMANTIC COLLAPSE OF THE WAVE FUNCTION THE SEMANTIC AGENT ON OTHER PROPERTIES OF THE SEMANTIC OPERATOR THE PURPOSE OF CREATION GOD IS SOMEHOW ANTHROPOMORPHIC THE CREATION IS BENIGN

Download or read book The Imagineers of War written by Sharon Weinberger and published by Vintage. This book was released on 2018-02-20 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive history of the Defense Advanced Research Projects Agency, the Pentagon agency that has quietly shaped war and technology for nearly sixty years. Founded in 1958 in response to the launch of Sputnik, the agency’s original mission was to create “the unimagined weapons of the future.” Over the decades, DARPA has been responsible for countless inventions and technologies that extend well beyond military technology. Sharon Weinberger gives us a riveting account of DARPA’s successes and failures, its remarkable innovations, and its wild-eyed schemes. We see how the threat of nuclear Armageddon sparked investment in computer networking, leading to the Internet, as well as to a proposal to power a missile-destroying particle beam by draining the Great Lakes. We learn how DARPA was responsible during the Vietnam War for both Agent Orange and the development of the world’s first armed drones, and how after 9/11 the agency sparked a national controversy over surveillance with its data-mining research. And we see how DARPA’s success with self-driving cars was followed by disappointing contributions to the Afghanistan and Iraq wars. Weinberger has interviewed more than one hundred former Pentagon officials and scientists involved in DARPA’s projects—many of whom have never spoken publicly about their work with the agency—and pored over countless declassified records from archives around the country, documents obtained under the Freedom of Information Act, and exclusive materials provided by sources. The Imagineers of War is a compelling and groundbreaking history in which science, technology, and politics collide.