The Godel Operation

Author : James L. Cambias
Publisher : Baen Books
Page : 345 pages
File Size : 52,9 Mb
Release : 2021-05-04
Category : Fiction
ISBN : 9781625798084

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The Godel Operation by James L. Cambias Pdf

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

Author : Leon Horsten,Philip Welch
Publisher : Oxford University Press
Page : 289 pages
File Size : 52,8 Mb
Release : 2016
Category : Mathematics
ISBN : 9780198759591

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Gödel's Disjunction by Leon Horsten,Philip Welch Pdf

The logician Kurt Godel 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 Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

Author : Gillian Russell,Delia Graff Fara
Publisher : Routledge
Page : 941 pages
File Size : 49,7 Mb
Release : 2013-05-07
Category : Language Arts & Disciplines
ISBN : 9781136594076

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Routledge Companion to Philosophy of Language by Gillian Russell,Delia Graff Fara Pdf

Philosophy of language is the branch of philosophy that examines the nature of meaning, the relationship of language to reality, and the ways in which we use, learn, and understand language. The Routledge Companion to Philosophy of Language provides a comprehensive and up-to-date survey of the field, charting its key ideas and movements, and addressing contemporary research and enduring questions in the philosophy of language. Unique to this Companion is clear coverage of research from the related disciplines of formal logic and linguistics, and discussion of the applications in metaphysics, epistemology, ethics and philosophy of mind. Organized thematically, the Companion is divided into seven sections: Core Topics; Foundations of Semantics; Parts of Speech; Methodology; Logic for Philosophers of Language; Philosophy of Language for the Rest of Philosophy; and Historical Perspectives. Comprised of 70 never-before-published essays from leading scholars--including Sally Haslanger, Jeffrey King, Sally McConnell-Ginet, Rae Langton, Kit Fine, John MacFarlane, Jeff Pelletier, Scott Soames, Jason Stanley, Stephen Stich and Zoltan Gendler Szabo--the Routledge Companion to Philosophy of Language promises to be the most comprehensive and authoritative resource for students and scholars alike.

Author : Thomas Jech
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662224007

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Set Theory by Thomas Jech Pdf

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.

Author : Torkel Franzén
Publisher : CRC Press
Page : 182 pages
File Size : 41,6 Mb
Release : 2005-06-06
Category : Mathematics
ISBN : 9781439876923

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Gödel's Theorem by Torkel Franzén Pdf

"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 : COLOMBINI,MARINO,MODICA,SPAGNOLA
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461598282

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Partial Differential Equations and the Calculus of Variations by COLOMBINI,MARINO,MODICA,SPAGNOLA Pdf

The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.

Author : David Ballard
Publisher : American Mathematical Soc.
Page : 135 pages
File Size : 45,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821802939

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Foundational Aspects of "non"standard Mathematics by David Ballard Pdf

This work proposes a major new extension of 'non' standard mathematics. Addressed to a general mathematical audience, the book is intended to be philosophically provocative. The model theory on which 'non' standard mathematics has been based is first reformulated within point set topology, which facilitates proofs and adds perspective. These topological techniques are then used to give new, uniform conservativity proofs for the various versions of 'non'standard mathematics proposed by Nelson, Hrbacek, and Kawai.The proofs allow for sharp comparison. Addressing broader issues, Ballard then argues that what is novel in these forms of 'non'standard mathematics is the introduction, however tentative, of relativity in one's mathematical environment. This hints at the possibility of a mathematical environment which is radically relativistic. The work's major and final feature is to present and prove conservative a version of 'non'standard mathematics which, for the first time, illustrates this full radical relativism. The book is entirely self-contained, with all necessary background in point set topology, model theory, 'non'standard analysis, and set theory provided in full.

Author : Janusz Czy?
Publisher : World Scientific
Page : 768 pages
File Size : 45,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9810201893

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Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas by Janusz Czy? Pdf

In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.

Author : Janusz Czyz
Publisher : World Scientific
Page : 764 pages
File Size : 46,8 Mb
Release : 1994-01-14
Category : Electronic
ISBN : 9789814506953

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Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas by Janusz Czyz Pdf

In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched. Contents:The Paradox of the SphereInaccessible Numbers and the Hierarchal Structure of Set TheoryThe Hausdorff Measures, Hausdorff Dimensions and FractalsThe Baker-Campbell-Hausdorff FormulaHausdorff MatricesAppendixReferences Readership: Mathematicians, logicians and mathematical physicists. Keywords:Banach-Tarski Paradox;Inaccessible Cardinals;Large Cardinals;Hausdorff Dimension;Fractal;Baker-Campbell-Hausdorff Formula;Lie Superalgebra;Lie Supergroup;Hausdorfd Matrix;Hausdorff Summation;Young-Hausdorff InequalityReview: “Each chapter concludes with an extensive bibliography on the subject. The book should be accessible to mathematicians, pure and applied, as well as to theoretical physicists.” Mathematics Abstracts

Author : Radim Belohlávek
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461506331

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Fuzzy Relational Systems by Radim Belohlávek Pdf

Since their inception, fuzzy sets and fuzzy logic became popular. The reason is that the very idea of fuzzy sets and fuzzy logic attacks an old tradition in science, namely bivalent (black-or-white, all-or-none) judg ment and reasoning and the thus resulting approach to formation of scientific theories and models of reality. The idea of fuzzy logic, briefly speaking, is just the opposite of this tradition: instead of full truth and falsity, our judgment and reasoning also involve intermediate truth values. Application of this idea to various fields has become known under the term fuzzy approach (or graded truth approach). Both prac tice (many successful engineering applications) and theory (interesting nontrivial contributions and broad interest of mathematicians, logicians, and engineers) have proven the usefulness of fuzzy approach. One of the most successful areas of fuzzy methods is the application of fuzzy relational modeling. Fuzzy relations represent formal means for modeling of rather nontrivial phenomena (reasoning, decision, control, knowledge extraction, systems analysis and design, etc. ) in the pres ence of a particular kind of indeterminacy called vagueness. Models and methods based on fuzzy relations are often described by logical formulas (or by natural language statements that can be translated into logical formulas). Therefore, in order to approach these models and methods in an appropriate formal way, it is desirable to have a general theory of fuzzy relational systems with basic connections to (formal) language which enables us to describe relationships in these systems.

Author : Radim Belohlávek,Vilem Vychodil
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 52,8 Mb
Release : 2005-08-26
Category : Computers
ISBN : 3540262547

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Fuzzy Equational Logic by Radim Belohlávek,Vilem Vychodil Pdf

Author : Iñigo Azcorra Elespe
Publisher : Iñigo Azcorra Elespe
Page : 226 pages
File Size : 49,5 Mb
Release : 2023-01-26
Category : Philosophy
ISBN : 8210379456XXX

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DEDUCTIVE METHODS IN MODERN METAPHYSICS by Iñigo Azcorra Elespe Pdf

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

Author : Umberto Bottazini,Amy Dahan Dalmedico
Publisher : Routledge
Page : 305 pages
File Size : 44,5 Mb
Release : 2013-06-17
Category : History
ISBN : 9781134698745

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Changing Images in Mathematics by Umberto Bottazini,Amy Dahan Dalmedico Pdf

This book focuses on some of the major developments in the history of contemporary (19th and 20th century) mathematics as seen in the broader context of the development of science and culture. Avoiding technicalities, it displays the breadth of contrasting images of mathematics favoured by different countries, schools and historical movements, showing how the conception and practice of mathematics changed over time depending on the cultural and national context. Thus it provides an original perspective for embracing the richness and variety inherent in the development of mathematics. Attention is paid to the interaction of mathematics with themes whose proper treatment have been neglected by the traditional historiography of the discipline, such as the relationship between mathematics, statistics and medicine.

Author : Kurt Gödel
Publisher : Courier Corporation
Page : 82 pages
File Size : 43,6 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486158402

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On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel Pdf

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.

Author : Anna Horská
Publisher : Springer Science & Business Media
Page : 77 pages
File Size : 47,9 Mb
Release : 2013-10-23
Category : Philosophy
ISBN : 9783319021713

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Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals by Anna Horská Pdf

This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts.​