The Godel Operation

The Godel Operation
Author: James L. Cambias
Publisher: Baen Books
Total Pages: 345
Release: 2021-05-04
Genre: Fiction
ISBN: 1625798083

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

A Darkling Sea

A Darkling Sea
Author: James L. Cambias
Publisher: Macmillan
Total Pages: 353
Release: 2014-01-28
Genre: Fiction
ISBN: 1466827564

On the planet Ilmatar, under a roof of ice a kilometer thick, a team of deep-sea diving scientists investigates the blind alien race that lives below. The Terran explorers have made an uneasy truce with the Sholen, their first extraterrestrial contact: so long as they don't disturb the Ilmataran habitat, they're free to conduct their missions in peace. But when Henri Kerlerec, media personality and reckless adventurer, ends up sliced open by curious Ilmatarans, tensions between Terran and Sholen erupt, leading to a diplomatic disaster that threatens to escalate to war. Against the backdrop of deep-sea guerrilla conflict, a new age of human exploration begins as alien cultures collide. Both sides seek the aid of the newly enlightened Ilmatarans. But what this struggle means for the natives—and the future of human exploration—is anything but certain, in A Darkling Sea by James Cambias. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

Gödel's Disjunction

Gödel's Disjunction
Author: Leon Horsten
Publisher: Oxford University Press
Total Pages: 288
Release: 2016-09-09
Genre: Mathematics
ISBN: 0191077682

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.

There's Something About Gödel

There's Something About Gödel
Author: Francesco Berto
Publisher: John Wiley & Sons
Total Pages: 262
Release: 2011-09-13
Genre: Philosophy
ISBN: 1444357611

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

Gödel's Proof

Gödel's Proof
Author: Ernest Nagel
Publisher: Psychology Press
Total Pages: 118
Release: 1989
Genre: Gödel's theorem
ISBN: 041504040X

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.

Set Theory

Set Theory
Author: Thomas Jech
Publisher: Springer Science & Business Media
Total Pages: 642
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662224003

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.

An Introduction to Gödel's Theorems

An Introduction to Gödel's Theorems
Author: Peter Smith
Publisher: Cambridge University Press
Total Pages: 376
Release: 2007-07-26
Genre: Mathematics
ISBN: 1139465937

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.

DEDUCTIVE METHODS IN MODERN METAPHYSICS

DEDUCTIVE METHODS IN MODERN METAPHYSICS
Author: Iñigo Azcorra Elespe
Publisher: Iñigo Azcorra Elespe
Total Pages: 226
Release: 2023-01-26
Genre: Philosophy
ISBN:

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